Real teaching means real learning

Presentation on Motivating students with out marks

2012-02-16T12:57:00.000-08:00

High School Focus

Intrinsic Motivation with High School Math on Prezi

Junior High Focus

Project Based Assessment in Junior High Mathematics on Prezi

Google Doc Links:

Cut the Rope in math class.

2012-02-04T11:02:00.000-08:00

I provided my students with a laptop, which had Geogabra on it, and the following picture:

I then showed, on my iPad, how the rockets travels around the point. When the rope is cut, the rocket will fly tangent to the curve.

I used this in my calculus class and asked "Determine the exact location the rocket should be when the rope is cut"

Students determined the equation of the circle, found the derivative and made it equal to the slope between any point (x,y) on the circle and the co-ordinates of the mouth of the monster (or goblin).
**WARNING, this is a hard question**

After, I was thinking this could be used in lower classes, by changing to one the questions below:

allow students to use the tangent button on geogabra, and ask for the reference angle.
Determine the amount of time which should pass before cutting the rope.
There are always two tangent lines on a circle through an exterior point, are there two times you could cut the rope in the picture?

There are more I could think of.

My students enjoyed the activity, and feel free to change and adapt as you see necessary.

Angry Birds and calculus:

2012-02-02T06:00:00.000-08:00

First provide the students with a laptop with Geogebra, and the following photo.

Introduce the meaning of Piecewise functions, and how the yellow bird, when clicked, shoots off at a tangent to the curve.

Ask the students to describe what are the two functions that create this curve (Parabola and a line).

Using prior knowledge have students graph the maximum point on the parabola, and use the dot where the yellow bird took off at a tangent (B), to create the equation of the parabola. Have students graph the parabola in geogabra, overtop the picture, to ensure all calculations have been done correctly.

Next, ask students how to determine the equation of line.

We will need either a) two points or b) a slope and a point. Both of which is impossible, without the use of the tangent button in Geogabra. I explained, we can calculate this without that button!

Have students pick another “point on” the parabola (c), and to calculate the slope between B and C. Ask how do we make this slope more accurate to the slope of the tangent…

Move C closer to B..

Have students move C closer to B, while still staying on the parabola and calculate the new slope. Eventually move C as close as possible to B. The slope should be -0.5 Below is a picture of one of the students’ work

Next using the point B and the slope you can create the equation of line.

From here your choice for extensions: I had students graph the piecewise functions on their calculator and got the following image

Lastly, here is a video on how to determine the slope at a point:

Why we really do need scantrons!

2012-01-21T11:22:00.000-08:00

Most schools buy Scantron sheets by the thousands, and the cost per year must be over $1 000 as each pack of 500 are approximately $100. I was thinking that there must be other uses of scantrons other than their traditional use for this amount of annual costs. After doing some thinking I am now a believer that Scantron sheets do have a place in schools and below is a list, divided by subjects, for which you can use scantron sheets: I do apologize they are broken up by subject not grade.

Math

· Provide each student with a scantron sheet and ask them to guess which would be the correct answer to the first question, if you were unable to see the question.. Talk about the percentage of the students in the class which would have guessed correctly. Extend this to two questions and so on. You can then talk about the math behind probability.

· Turn the scantron side ways and draw graphs. A constant graph would be were all the answers were A, an oscillating graph would go ABCDCBA…. I bet there are many different graphs which could be drawn. You could then talk about slope, absence of concavity and so on.

· Using the scantron, you could create a ratio of Surface Area to Volume, or perimeter to Surface area, and so on.

· You could talk about the costs of buying scantrons and create a Cost graph and calculate the slope and y-intercept and explain what do these values mean.

English

· Have younger students read the instructions on the scantron sheet and have them explain to a classmate what the instructions mean.

· For students learning the alphabet, have them create the different letters by connecting the dots on a scantron in different formations. (“U” might be a tricky letter!)

Other languages (French, Spanish, etc):

· Have students translate the meaning of the instructions on the scantron sheet into the desired language.

Physics

· Push a marble down the floor and ask the class to estimate the number of scantron sheets, vertically, it would take to stop the marble. Increase the speed of the marble and estimate again. Extend this to the problem “How many scantrons would stop a car going 30 km/h?” (I would like to know this answer?)

· Talk about the air resistance as you drop a scantron from a desk to the floor, and then ask “Would the same action occur if this was a vacuum?”

Chemistry

· Determine how much water one scantron can hold by weighing 20 of them dry and then soaking them in water and comparing the weight difference.

· Take one scantron and light in on fire. Talk about the combustion of paper. You can extend this by dipping the scantron in different liquids and talk about the difference in speed of ignition.

Art

· Instead of using construction paper, have students cut up Scantron sheets and art with them. They can be colored on, and easily cut!

· Have them draw a picture only by connecting the dots on the Scantron.

The best part of these activities is that you don’t need a scantron machine ($5000) to do them…oh wait..you don’t even need the scantrons!!

However, if you have other activities, I invite you to share below!

Happy Marking!

Learning can occur on a final exam

2012-01-19T08:13:00.000-08:00

Historically, I would say that the least amount of learning occurs during exam week. This year, however, I have tried to make this statement false through giving my students a new final exam. When the first group presented, not only did I see, hear and was taught about unique examples of how to use calculus, I can actually say the group still LEARNED through the assessment.

Below is a video of their PowerPoint presentation, which they used as well as supplemented with dialogue.

After the presentation they opened the floor to me by giving me 10 minutes of questioning. Most of the questions they answered swift and correctly, until I asked “Do all functions, on a closed interval, have an absolute maximum?” . Their answer was “Yes”. Of course this is incorrect.

Now here is how the learning occurred… First I will address the traditional way of assessment:

If this was a traditional final exam, I would have marked this question wrong and moved on to the next question and continued marking. These students would never have received any feedback, as in the past, I have yet to see many students come back to see WHAT they did incorrectly on a final exam. These students would have then gone on to university/college with this false knowledge.

How it has changed this year…

I didn’t let this false information continue. I then asked, “What if I told you, I could draw a function on a closed interval without an absolute maximum?” The girls looked at each other with confused eyes, and pondered the idea. After some passing minutes, one replied accusing me of a liar. I wanted to ensure they didn't continue on with this false information, so I then asked, “Is there any kind of function that continues upward on forever?”. One quickly answered, “WAIT! A function could have a vertical asymptote and therefore have no absolute maximum. I guess you weren’t lying”, the other girl smiled and agreed.

After this, I wanted to ensure they had a true understanding and therefore I asked, “Can a function, without any asymptotes, on a closed interval, not have an absolute maximum?” The enlightenment has occurred! Both girls whispered quietly, and then turned and replied “If the curve has an open point at the highest point, then it would not have an absolute maximum”.

Learning had occurred, and yet it was a final exam.

I continued with my questioning, which they answered correctly, and I am happy to say that this experience has been a success with the first group!

15 Geeks who outsmarted the system

2012-01-18T07:56:00.000-08:00

Below is a post from Bestcollegesonline.com, and specifically Tim Handorf. Cool read about math geeks!

15 Brilliant Math Geeks Who Outsmarted the System

Geeks rule the world these days, with tech geniuses and statistics-savvy entrepreneurs owning some of the biggest and highest-grossing businesses anywhere. Yet while some use their know-how to make a fortune the old-fashioned way, through hard work, others try to outsmart the system and get rich in much less legitimate or sustainable ways.

Here, we’ve compiled a list of math geeks who’ve used their computational skills to make big bucks in Vegas, playing the lottery, or on other forms of gambling. Some did nothing illegal and simply used their knowledge to their own advantage, others used their math skills to cheat and lie their way into millions, and some figured out a system just for the fun of it. While some may not have chosen the high road, these geeks will show you that your math courses really can be useful for more than getting college credit – though we caution emulating some of the methods these enterprising math nerds used.

Edward O. Thorp

Mathematics professor Edward Thorp was a pioneer in modern applications of probability theory, which he harnessed in a variety of ways for his own, legal, financial gain. As he documented in his book Beat the Dealer, Thorp was able to show that the house advantage in blackjack could be overcome by card counting, a strategy he used to win tens of thousands of dollars at casinos during the 1960′s – practice which they now guard against, as it produced many copycats. Thorp didn’t just use his gift for math to win in Vegas, however. Applying his knowledge of probability and statistics to the stock market helped him make a fortune off of pricing anomalies in the securities markets, earning an average of a 20% rate of return over the 30 years he was investing.

MIT Blackjack Team

One of the most famous stories of math geeks outsmarting casinos centers around a group of students at MIT and Harvard during the late 1970s into the late 1990s, that was made into a recent movie called 21. Using card counting techniques and other sophisticated strategies, the students were able to win large amounts of money, doubling the initial investment in the venture in the first ten weeks. Of course, with their successes came increased attention from casino management, leading to many players being barred from casinos around the nation. These bans and other career opportunities led to most of the team disbanding by 1993, though some members were to go on to form their own blackjack teams that continued to play up until 2000.

Mohan Srivastava

Unlike many of the others on this list, Srivastava has never used his statistical skills to get rich. In fact, he only set out to crack the code on lottery scratch off cards out of curiosity, not a desire to make money. But crack it he did. Srivastava discovered that there were clear patterns in the numbers on tic-tac-toe game cards that allowed him to predict which cards would be winners with a striking degree of accuracy. He also discovered that these same rules, or adaptations of them, could be applied to other lottery games. While Srivastava could have used these methods to make money, he didn’t feel it was worth the time or the trouble (scratch off cards don’t usually have big pay outs), and he even reported the problem to the lottery authorities. While the tic-tac-toe game was pulled, his warnings were largely ignored and his findings can still be applied to scratch-off tickets in a wide range of locations.

Joan Ginther

There is no proof that Joan Ginther has used her math skills to help her win her four (yes, four) million-dollar-plus jackpots from the Texas Lottery, but there is a whole lot of speculation. Ginther has a PhD in math from Stanford, leading many to believe that this former statistics professor used her math knowledge to help her crack the code for the lottery’s algorithm. Why all the speculation? The odds of someone winning four jackpots is one in eighteen septillion – possible but highly improbable. The Lottery Commission believes Ginther won fair and square, but it’s not likely to stop people from believing that she had a little help from that math degree anytime soon.

Syndicate of British professors and tutors

Winning the lottery isn’t just luck of the draw when you’re a math genius. A syndicate of professors and tutors at Bradford University and College used their knowledge of mathematics to apply probability to playing the lottery, even developing a formula that helped them to pick winning lottery numbers. Using a computer to check lottery numbers each week, an investment of $8,700, and waiting over four years, the gamble paid off and the 17 staff members won a $13 million dollar prize.

David Phillips

David Phillips is perhaps better known as "The Pudding Guy" for the loads of pudding he bought to take advantage of a promotional program offered by Healthy Choice in 1999. Phillips, a professor at the University of California, Davis, used simple math to figure out that the value of the promotion exceeded the cost of the entree which it was offered on. Phillips found that the promotion was even more valuable, as it could be used on pudding packages, which were a mere 25 cents each. Phillips bought over $3,140 worth of pudding, taking the UPCs and donating the food to the local Salvation Army. An additional bonus for the mail-ins held in May of 1999, allowed Phillips to stockpile 1,253,000 in AAdvantage miles, a number which he continues to grow today through other promotions. Phillips may never have to pay for a flight again.

Michael Larson

Michael Larson was a contestant on the 1984 game show Press Your Luck. Larson had figured out how the patterns in the board move and, using probability, could determine which squares would be more likely to contain money. While Larson started off slow on his run through the game show, by the third round he was hitting bonuses on every turn, racking up a total of $110,237 (adjusted for inflation, that’s about $233,000 in today’s dollars). Larson’s successful run would land him a jackpot, but disqualified him from participating in future shows and resulted in changes to the patterns the game show used.

Gonzalo Garcia-Pelayo

Roulette is by and large a game of chance if there ever was one, but one man managed to figure out that certain wheels have a bias for certain numbers. Working with his family, he collected data and analyzed numbers from Casinos all over Madrid, eventually realizing that the numbers on roulette wheels weren’t, in fact, perfectly random. In fact, the statistical data pointed to a distinct pattern, which Garcia-Pelayo would learn to take advantage of. Using probability, he was able to clean up at casinos around the world, winning over $1.5 million over the course of a couple of years. By betting on the numbers he had identified as "hot," he would turn a 5% house edge into a 15% player edge. Casinos weren’t a big fan of his methods, however, and sued to get their money back. The courts sided with Garcia-Pelayo, however, and said it was the casino’s responsibility to fix their wheels. Nonetheless, Garcia-Pelayo, and many members of his family, were banned from casinos.

Keith Taft

Keith Taft is a legend in the world of blackjack. Taft entered his first blackjack game on a whim in 1969 and quickly became hooked. He read numerous books on card counting, but could never really master the strategy on his own. Instead, he invented a computer to do it for him. This is a lot more impressive when you consider that in 1969, most computers were seriously huge, taking up the better part of a room, and ran on punch cards. Taft’s computer would fit on his body so that it could be concealed when he entered the casino and was operated with his toes. After two years of work, Taft would complete the cheating system (which he named George), which used mathematics and statistics to determine the house advantage for a particular hands, count cards, figure out a smart wager, and tell Taft was move to make. The computer was a failure, but it would serve as a model for later systems which would win Taft and a team of pro players $100,000. Taft’s inventions were legal at the time, but all are banned in casinos today.

The Four Horsemen of Aberdeen

The "Four Horsemen", Roger Baldwin, Wilbert Cantey, Herbert Maisel and James McDermott, were a group of Army officers who devised one of the first blackjack strategy guides when they weren’t doing mathematical work for the military. Using probability theory, the group were able to develop strategies that could help a player improve his or her odds of winning substantially, eventually releasing the findings in a book called Playing Blackjack to Win. In fact, this book held the calculations that Ed Thorp would later use to write his own blackjack guide. Using only basic calculators, the group was able to develop a card counting system that gives the player a .1% advantage, though it’s unclear whether they ever used it to their own advantage or just enjoyed playing with the numbers to pass the time.

James Grosjean

Harvard grad and gambling expert James Grojean is the author of Beyond Counting: Exploiting Casino Games from Blackjack to Video Poker, a mathematical treatment of various forms of legal advantage play gamblers can use to increase their odds of winning – and Grosjean should know. He became a professional player after becoming enamored with casino play while a graduate student in economics at the University of Chicago. Often working with partners and a number of computers that are constantly analyzing data, Grosjean has used his mathematically-based strategies to win himself a small fortune, though casinos have fought him throughout it all. Grosjean has won numerous legal battles against casinos, and in 2005 scored a nearly $600,000 judgment in his case against Imperial Palace.

Cash WinFall Group

Gerald and Marjorie Selbee, owners of a gambling company, bought over $614,000 worth of tickets for the relatively obscure game Cash WinFall in July of 2011. With a payout of just $2 million and only one winner in the game’s seven year history, one would think this was a foolhardy way to use that kind of cash, but the Selbees had a plan. For a few days every three months, provided no one wins a jackpot, payoffs for smaller prizes swell dramatically, with pretty much assures anyone who buys at least $100,000 worth of tickets a payoff. The Selbees, along with betting groups from MIT and Northwestern, purchase about half of the tickets for the games, as with a little math know-how the game isn’t really one of chance at all. As of this year, the Selbees have claimed over $1 million in prizes and their final take is likely to be much larger.

Bruce Bukiet

For most, wagering on a baseball team to win the World Series or even to end up there, with the help of stats, of course, would be a pretty big gamble. But Professor Bruce Bukiet of the New Jersey Institute of Technology may have figured out a system that takes a lot of that chance out of the picture. Bukiet has created a mathematical model that computes the probability of one team winning a game against another team, with some surprising results. He’s beaten the odds six of the eight years he’s been using the model. Of course, his system isn’t foolproof. He predicted the Phillies, Dodgers, Cardinals, and Braves would all be division winners in the National League this year. The real winners? The Phillies, Brewers, Cardinals, and the Braves. Bukiet doesn’t gamble on his predictions, however, and states he just does them to show young people that math is relevant, even to things like sports.

John Kelly, Jr.

John Kelly, Jr. used his PhD in physics from the University of Texas to get a job working at Bell Labs in the early 60s. It was there that he developed the famous Kelly criterion (though his discoveries in computer synthesized speech were also pretty amazing). The Kelly criterion is a formula used to determine the optimal size of a series of bets, whether in a casino or on the stock market. The theory was put into practice by gamblers like Thorp and Kelly’s associate Claude Shannon, though Kelly himself never used the theory to profit himself – though perhaps he never got the chance. Kelly died in 1965 at only 41 years old, leaving behind a formula that has been used to make the fortunes of big business moguls like Warren Buffet, Bill Gross, and Jim Simons as a legacy.

Steven Skiena

Think betting on sports is a random gamble? With some sports that might be true, but when it comes to the complex betting systems of jai alai, there is a system and it works, as was proved by computer science professor Steven Skiena in 2004. Skiena began predicting sports results in 1977, correctly predicting the outcome of NFL games with 65% accuracy. He’s refined his methods a bit since then, and turned an initial investment of $250 into $1851. Skiena devised a highly complex mathematical system, and using a computer he could more accurately predict which team or player to bet on. For Skiena, the project was a mathematical exercise, not a money-making scheme, however, and he donated all of the winnings to charity.

Improving the test of provincial exams!

2012-01-13T09:18:00.001-08:00

The Alberta Government is about to do something that is going to improve learning in schools.

It is about time the Frasier institute can no longer compare schools, or allow the results of schools to be public. Finally, Lukaszuk is about to show that there is more to learning than statistics, numbers, test scores, and rankings. Peter Cowley, from the Frasier institute, says “Teaching teams can directly use the PAT results to the benefit of their students”, and then follows with “It is hard to see how improving teaching effectiveness can be considered a misuse of the PAT data”. These two statements are begging the question that PATS improve learning, which they do not.

I ask you, have you ever written a test or an exam and became smarter because of it? In Alberta, I have yet to see a farmer weigh his/her animals more to increase their weight. Just as weighing an animal won’t increase its weight, testing students won’t increase learning. Our education has always been test score driven but I wonder if this belief is actually justified? Has this norm been created out of research and studies? Is this actually authenticated by pedagogical practice? Does testing create lifelong learners? Lastly, does it improve education? I believe the answer to all of these questions is NO!

I understand that many people outside education, such as Peter Cowley, believe that only a standardized provincial exam can reveal that truth about what is actually occurring in Albertan schools, and is fighting for the idea that three years of education can be reduced to a single number on a multiple choice exam. However, this idea is completely absurd. If you find yourself disagreeing, then I strongly urge you to learn more about a standardized exam.

Just for starters, before a standardized test is given there are psychometricians who know how many students will pass and how many students will fail, and this occurs before the students ever write the exam. Why would we support the sharing of grades on an exam that has a pre-determined failure rate? Next, Peter will have us believe that these tests are an effective way of measuring education in our province, but he fails to realize these tests have a pre-selected material which is unknown to the teacher. In terms of reliability, most educators resent the idea of a confined focus of testing as it measures only a portion of the domain and ultimately distorts the depth, complexity and dedication of a student’s ability.

Lastly, Peter will try to convince people that it is these tests scores that will improve education. He fails to understand that it is not the test scores which need to increase to enhance education, but instead the trust that a teacher is a professional, dedicated to providing the best education possible, and the idea that learning cannot be reduced to a mark on a single exam.

Calculus and Kobe Bryant

2011-12-16T10:45:00.000-08:00

I used this video in my calculus class to show how math can either support or disprove a movie.

I showed this movie to my students and asked if this looked possible. One jumped up and said "No way!" while others thought it could happen. What was interesting was when I asked "Do you have proof?", as the class went silent.

The math in this movie is incredible.

Where I thought the students would go was completely the opposite of what happened. My students timed how long Kobe was in the air, we measured his height in the movie and compared it to his real height to create a scale. We used integration using gravitational pull to be -9.81m/s^2, to create a velocity and distance function. The calculus was amazing.

Whether we proved or disproved the reality is a secret I keep with me as I challenge you to give this to your students and see what they do. Just watch the movie then ask "Any questions?" I bet you will get lots. The secret is then to let them "play" with the math and the movie.

Learning is road that they must travel down themselves and we should only be guiding them not pulling them along by the hand.

Awesome Education Talk in Red Deer

2011-12-15T14:28:00.000-08:00

Yong Zhao is coming to Red Deer Wednesday February 8.
Tickets are $10 and are donated to the Red Deer Women's Shelter.

Amazing speaker for parents, future and current educators and as well as anyone interested in Education.

More information, and how to buy a ticket can be found here

Students create the problem to solve

2011-12-06T06:00:00.000-08:00

Math 31 Assessment

Option 1: The head of NASA has approached you asking for your assistance plotting a course for the International Space Station. The tracking device can be found at http://spaceflight.nasa.gov/realdata/tracking/index.html . NASA needs an equation of the path, as well as the 1^st and 2^nd derivative. The director is also asking for all relevant information about the path to be explained. Create a potential problem the satellite might encounter and provide the solution to the problem.

Option 2: Ethan Hunt, an IMF point man, is securing top secret files at the bottom a cylindrical tube. He is being lowered by rope into the room at a constant speed. Unfortunately, while being lowered, another man walks, at a constant rate, towards the room. Ethan is then raised back up out of the view of the approaching man. While suspended in air, sweat is building at a constant rate until it reaches a critical value and drops onto the floor. Using the video (a clip can be found here http://www.youtube.com/watch?v=k-oVuQpjG3s) use calculus to help out Ethan and determine various velocities, critical values, and timing to assist him in securing the evidence.

Option 3: Taking what you’ve learned this semester you must create a problem to solve. It must be based on a real world example (or movie world) and must have at least one solution. Be sure to submit your proposed solution in a sealed envelope. Five bonus points will be awarded if you are able to stump your teacher.

No matter which option you choose you must create the question and problem in the given scenario

	Calculus Student	Calculus Student Teacher	Calculus Teacher	Calculus Master
Real Life Application: Is the problem worthwhile solving? What are the implications of the result of the problem? Who would benefit with the knowledge of the answer to your problem?	Only students of this course would see the relevance of this problem. The purpose is built on strictly recalling facts. The solution is only needed to complete this assignment.	Problem is created from a plausible issue with major changes. Purpose is unclear and does not go beyond the needs of the course. Students in this course would only understand the consequences of the solution to the problem.	The problem is created from a plausible issue or problem with minor changes. The purpose is clear and slightly exceeds the needs of this course. Few, outside this course, would benefit from the solution to the problem.	The problem is created from a real life issue or problem. The purpose is meaningful beyond the needs of the course. The solution to this problem adds to the experience of the students’ real world knowledge.
Explanation of math. Are you using basic math knowledge? Are you demonstrating most of the knowledge you learned in this course?	Focuses strictly on basic recall and basic knowledge of the mathematical skills.	Requires few sections to apply higher level thinking to solve the problem. Math is still largely focused on recall of knowledge.	All levels of understanding, from basic to higher level thinking are implemented throughout the problem.	Focuses on higher level comprehension, the use of the combination of multiple skills is evident throughout the entire solution.
Communication of your answer: Does your work follow sequentially throughout your solution? Are there gaps in your communication?	Minimal response is given with multiple gaps in the explanation process.	The use of similar explanation techniques is used throughout the solution. Communication is limited with various gaps in the problem solving.	Most of the project is easily understood, and organization is mostly logical.	The use of different means of demonstration is illustrated throughout the solution. The mathematics is clearly communicated as well as the meaning of the solution(s)

Discussion with a first year teacher around marks

2011-11-30T15:42:00.001-08:00

Recently, I had a discussion with a first year teacher after 4 months of teaching in her first year, here is how it went:

Her: I’m scared I not going to have enough summative assessments at the end of this year.

Me: How many is enough?

Her: I went around to other teachers and discussed and the general consensus is around 25-30 if I averaged it out. Some teachers had even given 50.

Me: Do these other teachers teach the same exact students you do?

Her: No, they teach different courses and different subject

Me: How do the students of other classes and teachers of different subjects have anything to do with your students?

Her: Then who should I be asking?

Me: your students, ask them how important is having 30 assessments, would you prefer less assessment of higher quality or more of lower quality? We must understand that the more grades we give students, the more we lower the value of everything we have graded to far.

her: Dave, don’t we give more summative assessments to allow for students to have more chances in achieving the best grade possible.

Me: So it sounds as if this strategy has nothing to do with learning. It sounds as if we are giving more assessments to allow students to get the best score in the “Game” of school.

We then engaged in a discussion around the meaning of assessment and marks. She started from a belief that there is an actual number of summative assessments which she is required to have for each student. I hope I showed how wrong this belief was! Teachers never should have a goal of the number of summative assessments to give students, and in fact we should be aspiring to have zero summative assessments throughout the course and start moving to entirely formative assessments. The only summative assessment which should occur is at the end of the course, only under the assumption that no more learning can occur.

Facts and Myths of traditional learning in schools

2011-11-25T06:00:00.000-08:00

It is little short of a miracle that modern methods of instructions have not completely strangled the holy curiosity of inquiry – Albert Einstein

From “Breaking Free from myths about teaching and learning” by Allison Zmuda, we learn about various myths and facts about learning in the traditional classroom, and my synopsis:

Myth: The rules of this classroom and subject area are determined by each teacher:

This is false as the push for meeting provincial (and state) standards increase, the autonomy of the individual teacher decreases. Collaboration is being used to enforce compliance as well as standardizing the rules of each classroom. For learning to be meaningful it must stem from personal experiences, current issues from students, as well as address the personal attributes of each student. This cannot be achieved by blanket policies which affect all.

Fact: What the teacher wants me to say is more important than what I want to say:

This is truly a sad fact about our education system. It is entirely summed up by a student who said:

It’s easy to take what the teacher says and regurgitate it without even thinking about what was said, and it’s how we’ve been taught to learn. When I set out to write a paragraph, I actually thought I should ask my teacher to spell out what he wanted me to write… If I tried to challenge my teacher, all it would take is a little bit of him pushing back to make me drop my argument and look like a deer in the headlights, even if I had a decent argument. Now that I know how passive I’ve been, I’m ready to make some changes in my learning style.

Students need to have opinions in classes, and the teachers need to be cognisant of these ideas.

Fact: The point of an assignment is to get it done so that it’s off the to-do list:

In our schools, too many students are feeling overwhelmed to get the assigned readings complete, answer the repetitive math questions, study for the Biology exam and still have time to pursue to their own interests outside of school. One student has even said

Most students just do the assignment because there is not time to really study it. We don’t really get a chance to go further into the parts of the topic we are studying that aren’t part of the curriculum because we have already moved to a whole new topic.

We, as educators, must be aware that for students to complete all their “homework” they must take shortcuts and thus truly never understand the material at a deeper level.

Myth: I feel proud of myself only if I receive a good grade:

Students are using grades to truly sort themselves among their friends and classmates. I believe all teachers have heard comments such as:

I got an F on this exam, but that is ok because I am not good at it.
I got a B like I always do, so I am doing fine.
No one is getting an A, so makes sense that I am not getting one either.

Grades and other extrinsic rewards are actually limiting the potential success of students. Students are actually seeing the grade as an indicator as to how well they are playing the game of school. As we push for improving learning we must move away from using grades to motivate students. Students are proud of the product of their education not the mark they receive on how well they have manipulated their education

Myth: Speed is synonymous with intelligence:

Too many times we are pushing students to complete tasks at a speed which is unnatural to their own learning. We are stripping education of passion and interest and replacing it with efficiency. This can be seen in math classes when we teach “math tricks” and justify it by “this is the fastest way to get to the answer”. Other educators validate this idea of rushing to complete the course due to the amount of material that is needed to be covered in a short amount of time. The pressure to prepare students for standardized exams and complete the overwhelming curriculum is making it quite difficult for teachers to accept alternate views of learning, instruction using discovery methods, and taking time to allow for each student to deeply understand a topic before moving on.

More myths and facts exist, and I encourage all to read the book…WOW!

In the teaching to which I aspire to

2011-11-22T18:07:00.000-08:00

I would truly allow each student to be an individual. To allow students to guide, not only their learning, but as well as their assessment. Students will no longer be "passengers on a fast bus down a lone highway" but instead "participants on a field trip to a field of their choosing" . Top down mandated policies focused on increasing test scores would be replaced with guidelines, created by and with teachers, to allow for deeper learning. Teacher PD will always be encouraged as the work teachers do outside of school is just as important as the work they do inside the school.

Outcomes will no longer be delivered in the hundreds, where each is extremely specific, but come in few general outcomes. This will allow for teacher autonomy in classes and allow for learning to be focused around the needs, wants, aspirations, and goals of each student instead of the goals of the system.

Technology, with unfilitered access, will be used in classrooms to create engagement around learning instead of being implemented to trick students in completing mundane tasks. The goals of each class will be around meaningful questions instead of repeptive answers.

Teaching will be around one single absolute goal; lighting fires of interest and curiosity in each student of the school.

Food Chemistry - Enhancing Learning

2011-11-17T06:00:00.000-08:00

Jeff Lerouge is a fellow colleague at my school, one damn good foods teacher, and another teacher who is challenging the idea of using worksheets to teach material. His twitter is is here @jlerouge, his blog is found here Jeff's blog.

Before, he used to teach different ideas through worksheets, and here is how he is educating students now: GOOD JOB!

Jeff start with:

What's the big idea? Why did we do this? Did you learn something today?

We've been learning about the pigments found in vegetables and how other ingredients can affect the color of vegetables. We have also been learning about how those same ingredients can have an impact on the texture of vegetables. To gain a better understanding about what we've been talking about, we decided we needed to experiment with the actual pigments and ingredients. What we've really done is do a science experiment and made some observations that helps us make conclusions.

We started with four different vegetables that represent the four colors of pigments found in fruits and vegetables:

carrots (orange)
cauliflower (white)
broccoli (green)
red cabbage (red/blue)

We then subjected each vegetable to four "treatments" against a control (boiled in plain water):

salt
baking soda (alkali)
lemon juice (acid)
sugar

After the experiment we came to some conclusions which supported what we learned in theory. It helped so see, touch, taste and smell - enhanced understanding. Here's what we learned:

the orange pigments in carrots are very stable and are not greatly affected by acid or alkali
adding sugar made our vegetables firm
adding acid made the cauliflower stay white and kept the cabbage purple - good result
adding acid turned the broccoli and unappealing olive green color - bad result
baking soda made all of the vegetables mushy - bad result
baking soda turned the red cabbage an unnatural blue green color - bad result
baking soda turned the cauliflower an unappealing yellow color

On the same day, we also learned about different kinds of rice not by reading about them, but by cooking 10 different varieties and tasting them all. We cooked a number of whole grain rices, something many students who usually eat minute rice or white rice were not used to, especially the different in texture. Students learned that this difference in texture is from the bran layer being present on the grains.

Student guiding his own learning

2011-11-16T07:43:00.000-08:00

Below is an example of how a parent allowed his child to guide the learning. Good job Mr. Hansen!!

My 3rd grade son is deep into multiplication right now and our discussion about groups of things and multiplication eventually led to factors. And while he was pondering how many numbers can be multiplied together to get 12 or 16, he asked a very good question. He asked me "How come there isn't a division table?" and he went on to say "We could make a division table and sell it!"

I explained to him that division tables do not exist because once you put the numbers down the sides, the majority of the inside is empty because most numbers are not (evenly) divisible by the other numbers. I told him that when we do division mentally we actually use the multiplication facts in reverse, as we did with addition. But I could see in his eyes that my explanation didn't phase him much and he was still dreaming of selling millions of division tables to other 3rd graders. So I said "Let's make a division table!" Big smile.

So I opened a spreadsheet and we started making our table. I said to him "let's just go up to 20 for now and we can expand it later", otherwise we would be there for hours if we went all the way to 144 on both edges. So I numbered the rows and columns from 1 to 20 and then like a game of battleship I started calling off the rows and columns and waiting on him for the quotient, or as is the case in the majority of cells, his response "it doesn't divide".

It took less time than I imagined before he saw the light as to why it is difficult to make a good division table. Maybe it was all the dead ends with him responding "it doesn't divide", but he realized that most of the cells are empty and when you are talking about "whole" division you are actually talking about knowing which combinations of numbers are divisible in the first place which is essentially the multiplication table. But something neat happened. He noticed the diagonal of 1's (you can't really miss that) but then he spotted the 2's, so we studied that for a bit and I started coloring the 1's, then the 2's and then the 3's and so forth so that he could see how they each repeat and form a line. And then I pointed out that there were some numbers with no quotients at all, except for 1 and themselves. I colored those red and pointed out that every now and then those patterns of 2's and 3's and 4's line up in such a fashion that they skip a number entirely, we call those primes. They aren't divisible by any number, except 1 and themselves.

In the end (actually there is no end to this) I told him that what we are doing is turning the multiplication table inside out and if we go in and count all of the filled in cells there will be 144 of them (assuming we did the whole table), one for every entry in the multiplication table. You will find all of the 2's and 3's and 4's and so forth but spread out in a 144x144 table, instead of a 12x12 table.

Our division table is here...

http://dl.dropbox.com/u/39455389/DivisionTable.pdf

It was a very productive evening to say the least

More on Differentiated Assessment

2011-11-15T06:00:00.000-08:00

A couple of weeks ago, I was watching a dad teach his son how to ride a bike. The son had a helmet on, elbow pads, and training wheels on the bike. As the dad put his son on the bike, he walked behind his son as the son rode the bike in circles in the parking lot.

Just recently, I witnessed the same father and son in the school’s parking lot and this time the training wheels were off. The dad continued to walk behind the son and the son completed the same circles. At one point the son fell over and the dad quickly picked him up and put him back on the bike immediately. After about 10 minutes, where the son did not fall once, the dad stopped walking behind the child and the child started to do more complex paths on his bike.

This is how assessment should be!

It would be ridiculous to mandate that all fathers must spend exactly 10 minutes of time with their child until they stop walking behind them; as each child will require a different amount of time to learn the skill.

It would be ludicrous to allow a son to write a multiple choice test where, if he scored over 50% (even though he wrote it is ok to play in traffic on a bicycle), the father would let him ride alone as the son “passed the test”, since the son doesn’t understand all the safety issues of riding a bike.

It would be unfortunate if all fathers were required to purchase the same bicycle since not every child is the same height, or has the lower body lengths.

Yet all of these ideas are allowed in schools, why is that?

I wonder what school would look like if instead of holding teachers accountable with mandated common assessment we instead allowed teachers to teach students “how to ride a bike”?

I believe, students would learn the skills at a deeper level before moving on, they could learn at their own pace, and each “test” would be different for each student.

Still not convinced? Reflect on this picture as it represents the traditional testing model of students.

Why we should not have set deadlines in school.

2011-11-12T13:34:00.001-08:00

I wonder what school would look like if we didn’t have set timelines or completion dates for the assessments of students.

This is the thought I wanted to address this year in one of my classes. Instead of having set dates for exams, and a set timeline for project dates, I created a learning environment that is conducive for the needs of every single student in my class.

Let’s first look at the problem of having a timeline for when students must demonstrate their knowledge.

Usually, a teacher makes their year plan around the goal of covering all the outcomes of the course. This teacher must make predictions on how long it will take to cover each individual outcome, which is usually based upon previous years and other students. Test dates are then inserted strategically throughout the year to determine when it is best for the class to demonstrate their knowledge. The problem….the teacher is worrying about the class not the individual students.

I have heard teachers say they teach at a pace such that the “average students” can follow, and my assessment dates are around when the “average student” should be able to demonstrate knowledge. By definition then we are actually pleasing no one! Half of the students will feel this day comes too late as they have already learned the material and could demonstrate it classes ago, while the other half believes that the pace is too quick, and they will need more classes until they are comfortable demonstrating the material. Once again, it is very unlikely that we are meeting the needs of any student by trying to meet the needs of the “average student”.

How have I changed this?

I teach on the same timeline and give students an assessment similar to this. DA with Derivatives , but instead of taking 3 days for the test (1-2 days for review then the 3^rd to administer the exam) I provide the student with 1-2 days to complete the assessment. Students who understand the material quickly are able to work on the assessment ahead of time and complete it immediately, while students who need more time can use as much time as possible. There is no set date for completion.

What if a student gets behind?

My first comment would be “Behind what?” Some teachers have this notion that the pace of the class is the pace every student should be learning at, but does this make sense? Remember these unit plans are created before even meeting our students, so how can we make a plan that addresses the individual student? Saying that, if a student is not demonstrating the material at an acceptable standard at a time which you feel is detrimental to learning other outcomes, then instead of giving a bad mark and moving on I sit down with this student at lunch, or after school, and ensure this student learns the material. Is it not our job to educate students? By giving a test, and saying “sorry you haven’t learned everything, but I am moving on anyways” is actually not completing our job.

As teachers we must remember, our class sizes may be large and diverse but this is due to the fact that many individual students are making up this group and our assessment style should not be created to meet the needs of the “average student” but the “individual student”.

One day without mandated outcomes

2011-11-09T06:00:00.000-08:00

I was recently involved in a session about creativity in the classroom. The presenter brought forth the fallacies with common and traditional assessment. After lots of discussion, case studies, videos, and examples of alternate assessment and instruction the session ended.

First off, I have to say that the staff that participated was amazing! The open minds, deep conversations and already exemplary teaching styles were quite evident. However, nothing made me more amazed than the comment the principal said at the end of the session. After the applause to the presenter, the thank yous and handshakes the principal stood up, looked at his staff and said:

“Imagine if you were driving down the highway in a brand new 2011 Mustang. The cops have all been called away from the road, the deer have been contained, and all other drivers are giving you the full road to explore and try out this new car”

“Ummm…ok” said a teacher in the crowd

The principal paused then started again

“Now let’s take this to a classroom. One day next week, let’s pretend there are no final exams, no unit tests, no marks to update, no mandated curriculum, and no one from Alberta Education to tell you what to teach. Take one day and let your students explore their own learning. Using the taught strategies in this session, open the “learning” doors for students and just let them discover something that as meaning to them”.

If hugging was socially acceptable I would have given this administrator the biggest one ever. Driving home, I thought of “What would schools look like if all administrators gave this chance to their teachers? What if every day was this special day? What if the needs of the students overpowered the needs to teach the curriculum?

I hope all his staff follow through with his directive and truly allow for authentic and autonomous learning to occur, if only for one day.

Awesome job Mr. Principal, I have found another individual who I would feel honored to call my boss!

Halloween Challenge to Educators

2011-11-03T06:00:00.000-07:00

This week, I was inspired by NBC's "The Office" to take up a challenge in the mindset around Halloween. Near the end of the episode title "Spooked", the boss makes the following comment:

Fear places an interesting role in our lives. How dare we let it motivate us? How dare we let it into our decision-making, our livelihood, into our relationships? It's funny isn't it? We take a day a year to dress up in costume to celebrate fear?

I found myself thinking about this cartoon.

Too many times, I have heard of educators thinking of an innovative way to change instruction, assessment, engagement, classroom management, and so on, but are too scared of the outcome. This idea never gets implemented and the success (or failure) of it is never experienced. Educators are left thinking, "What if....?"

I challenge you, and myself, in Novemeber to take a "new idea", that may have been sitting on the shelf collecting dust, and try it out! The outcome could be very suprising...of course you could end up with a day of failure, but then again you could experience one day of great success. Remember, as illustrated by this 4 minute video below creativity starts with a belief.

Simplifying Radicals with Go-Fish

2011-11-02T06:00:00.000-07:00

Here is how I am going to attempt to allow my students to discover why and how to rewrite radicals.

Thank you to https://pumas.gsfc.nasa.gov/files/12_03_06_1.doc for the inspiration.

Simplifying Radicals With Go-Fish

1) In groups of 3 or 4, take a deck of cards and remove all the jokers and face cards (Jacks, Queens, and Kings) from the deck. For this activity ignore the suits of the cards.

2) Deal out all the cards, one at time, to each person.

3) Fill out the chart as follows:

a. Write down the square root of the product of all your cards, as an exact number. (Aces = 1)

b. Write the decimal approximation, to 2 decimal places

4) Put your pairs together, and keep the single cards separate.

5) Fill out the chart as follows:

a. The product of each pair. (IE if you have 2 3s and 2 4s, you would multiply 3 by 4)

b. The square root of the product of the single cards, as an exact number.

6) Multiply the product of the pairs, to the square root of the remaining cards, and round to 2 decimal places.

7) Repeat for 10 hands.

8) Answer the questions on the back page.

9) Explain, why both ways are giving you the same decimal values.

Example:

Jason was dealt a four card hand which consisted of an 8, 3, 5, and another 8. He filled in the first row and shown.

Hand Number	Square root of the Product	Decimal, to 2 decimal places	Product of the pairs.	Square root of the remaining cards	Product of the pairs and root of the remaining cards
Example		30.98	8		30.98
1
2
3
4
5
6
7
8
9
10

Short Treatise on Education

2011-11-01T13:00:00.000-07:00

Here is guest post from a great collegue Kenton Biffert

Short Treatise on Education

Over this past summer I've been meditating and researching and discussing education and schooling. When we look at this new vision of Alberta Education in the Inspiring Education document, we as teachers need to be focused on developing our students to be creative, critical thinkers, communicators, ethical, leaders, and seekers. A tall order. Of course the question arises: can we do this within the curriculum we are held accountable to? Another question arises: can we do this within the current framework of schooling as we know it. I would venture a possible yes to the first question and a definite no to the second. I believe we need to begin to rethink and teach outside this square box called a school or a classroom or a desk in order to deliver the order our government and society look to us for. Before I jump into some changes that I believe, with some guts, can be made ñ I need to wax philosophical for a moment.

A couple items disturb me as a teacher when I look at the system I teach in. First is the disturbing fact that our students are not seekers. There are exceptions of course, but even within those exceptions, these exceptions remain passive consumers of the information and it is a rare gem to find an active contributor. A seeker. It is human nature to want to know. This is what separates us from the animals and what throws a beautiful wrench into the secular theory of evolution. It is a gift. An animal at night, after eating and surviving lays down to rest and sleeps. A man at night, after eating and surviving lays down to rest and wonders (Iím quoting a Canadian philosopher here, but I canít remember his name). So, how is it I ask that our students lose their desire to know. To seek. How is it that they become so such passive learners (simply tell me how to do it and Iíll do it) vs. active learners (donít tell me how to do it, Iíll figure it out and ask for help when I need it)?

This leads to my second disconcertion: is our current system of compulsory, mass schooling a type of communism? Think about this for a moment. Indulge me. Communism fails. Why? It goes against human nature. It tries to make everyone equal, diminishes differences and trumps initiative. Could we also be doing this in our compulsory schooling system? Do we not as teachers have to teach to the lowest common denominator the same curriculum to every student despite their personal interests and then demand that they take tests (standardized or not) that are essentially meaningless to them? Could it be, that in our efforts to educate our students we uneducate them ñ deseeker them?

And this leads to my third thought on education: are kids really dumber than they were 100 years ago or are we dumbing them down? Yikes. Crazy question. I read recently in John Taylor Gattoís book Weapons of Mass Instruction that 130 years ago grade 5 students were studying Shakesphere. That prior to WWI the literacy rate in the US was 98%. This was before compulsory schooling was forced (sometimes at gunpoint) on the common people. Over the next six decades the literacy rate fell to 73% (mid 70ís) and rose back up to 83% (2004) for whites and 60% for blacks. Literacy in this case was a proficient grade 4 reading level. Hmmm… one would think that with the astronomical amount of money poured into this schooling system to teach kids that weíd see an increase. Maybe the compulsory schooling, curriculum, and modes of learning kill initiative…

Lastly, my question is specific to Catholic Education. Last year I wrote an email to various members of our board and administration in regards to recent surveys stating that students graduating from public schools are not a whole different in their views on faith and morality than Catholic students. The question would be obviously, how can we send students through 13 years of Catholic education and they graduate questioning the existence of God, having little knowledge of their faith, little to no relationship with Christ, and a secular view of morality? There would seem to be little reason for Catholic education to exist if this remains the case.

Alright ñ enough with the skepticism that has kept me up at night seeking answers and driving me into a dissonance as I try to find my own place as a teacher in this system. How about some solutions. I believe in the Inspiring Education document and the vision they have our students. What can we do at St. Martin de Porres to help bring this to fruition? The following are a list of suggestions (some Iím sure will raise hairs), but all are worth some discussion.

1. Have specialists teach the subjects that they specialize in. (this assumes that with a specialization there is a passion). If we have a teacher that is brilliant at teaching math and loves math and brings math alive for the students, then why are they not teaching math to more grades than a homeroom? Passionate, inspiring teachers increase student achievement. (see Increasing Student Achievement in Writing by Kenton E. Biffert) Why are we so concerned about our grade 3-5 students having consistency with the same teacher? I think a case could be made for K-2 in having less teachers in the classroom… maybe…

2. Multigenerational classes. Having students live 13 years of their lives with other students the same age for the formative years of their lives is unnatural. It is unhealthy. Having all the grade 4ís together simply makes teaching curriculum easier on the teacher ñ but is not necessarily best for the students. (If this is too much to swallow, maybe we could look at having multigenerational classes ñ combining grades into groups for art, music and drama as an example).

3. More minutes dedicated to LA by shaving off minutes from the other subjects. We have subjects (French, drama, math, science, social, health, art, music, religion) and we have the tools of learning (LA). LA is a tool of learning for for the most part one cannot engage effectively in any of the other subjects without a proficient grasp of literacy.

4. Parental involvement at the decision making level. Compulsory schooling is pulling apart the family. Parents take their children at age 5/6 and place them in the hands of someone they barely know and with other children raised by parents they donít know and leave them there to learn a curriculum that they barely know. (hmmm… maybe this is why the family unit seems to be less and less cohesive…). One way to combat this is to find ways to bring parents back into being the primary educators of their children. They know their children better than we do and thus should be a part of the decision making process regarding decisions about their children. One could scream ëbut teachers are the experts!í I would yell back, "Bull." One does not need a B.Ed. to teach. I have learned an infinite amount from my father who is blind with a grade 5 education ñ more than I learned in my whole B.Ed. degree. We need to empower, encourage and motivate the parents to take a larger role in the education of their students.

5. Include more time for play by adding an afternoon recess. Finland has a 15 min. recess after every 45 min. class. Retention will be more. Engagement will increase. Achievement will thus increase.

6. No movies. Watching movies results in passivity. The brain ceases to fire on so many accounts that philosophers have said watching television as close one can get to losing their personhood. We are commissioned to facilitate the development of seekers ñ not pacifiers. Further, to read a novel and engage oneís imagination and then to watch a movie about the novel simply erases all that work one did with the imagination and replaces it with some directorís artistic impression of the book. A waste of great imagination. Further again, movies should not be used as entertainment or babysitting or as rewards for good behavior. We have a gym, creative minds, and Iím sure as teachers we can come up with alternatives.

- side note on technology: we need to teach students that technology is not out there to make us consumers, voyeurs or amusement addicts. This is when it gets dangerous. Technology can be a tool to help us become stronger communicators and to help make others lives better. This is our focus.

7. Reject standardized testing (gr. 3 PATís). Now I realize we canít do this formally, but our parents sure can. There is nothing to be gained by putting a grade 3 students through the rigours of PATís. They are meaningless to them. They have no bearing on their lives. They are a detriment. We can educate parents that they have the right to refuse to have their kids take the PATís. This should be done. See http://bartlebyproject.com/ for some more info. Standardized testing is done for political reasons and economic reasons. It is not done for the best of the child.

8. Guarantee our parents that our students are getting a minimum of 30 minutes of physical activity per day as organized by the school. This is our mandate. This is regardless of the weather. We would also need to sit down as a staff and look at defining DPA. Does sitting on a desk and throwing a ball back and forth constitute DPA as an example. We need to set some standards for ourselves.

9. Scheduled class time outside. Research is proving more and more that spending time in nature and learning in the context of nature increases our studentís creativity (amoung many other aspects). We need to be teaching in a real, lived, experienced, hands-on environment and less simulated digital environments. Read Last Child in the Woods by Richard Louv for a great wake up call.

10. Relook at how we teach boys. As a female dominated staff and profession we need to look at how to teach boys. Boys need competition ñ grade 5 basketball should be keeping score so that there are winners and losers. Separate the boys and girls in phys. Ed in the upper elementary. We need to as a staff do some professional reading on boy development in the early years. Dr. Leonard Saxís book Boys Adrift addresses how boys are taught in the school system and the results are lower achievement and high incidents of assigning medications.

11. Micromanage less. I know this sounds scary. When dealing with the masses it is far easier if they are all helpless. However, we need to be developing leaders, and ëself-directed learnersí (Inspiring Education). So how can we micromanage less?

- Understand that getting hurt is a part of life and not the end of the world. In fact a ton of learning comes from getting hurt. Ex: As a kid I touched a hot iron to see how hot it was. I burnt my finger. Iíve never touched one since. Allowing the boys some leeway on the playground/gym to explore their physicality is an example of this. This is how boys learn.

- Find times to have the grade 4/5ís line up in a line less. They can be self-governed at age 10 and 11 if we expect that of them. Treating them like they are in kindergarten so we can maintain unnatural level of control keeps them helpless and dependent.

- Teach in such a way that the student must discover first. Our students are trained to do the opposite so this would be a painful process. For example: Rather than teaching students how to do long division first, I could have them try to come up with a system of division first and then teach the lesson. Or even begin math class having the students read their text and figure out how to do long division via the instructions in the text. The goal would be to make the students less dependent on me to have to teach them how to do things, and more independent in their abilities to figure things out.

12. Get a hill built on our playground so the kids can play on it in both the winter and spring and fall. Hills provide tons of play and hours of fun ñ which in turn, of course, will effect their affect as they jump back into classes.

13. Plant some trees and build a rock garden and make a forested area in our playground. This could include mud and we could nurture a small ecosystem with frogs and bugs. Yes this would mean that kids would come into the school muddy. Yes, this would mean the janitors or us teachers or the students would have to do a bit more clean up. The pay off according to Richard Louv is well worth it as time in nature develops creativity, balance, agility and fitness.

14. Medicate last. See Boys Adrift for the stats on how most of the students on ADHD medication are boys. He suggests that most of the boys donít actually have ADHD. The meds would help any student with or without ADHD to focus better. We need to be more cognizant of where boys are developmentally and maybe they arenít ready to sit in a desk to learn to read and write yet.

15. Use the fine arts more more more. The more I read on integration of drama in the arts the more I understand the absolute necessity of having the arts and engaging the right brain in our classrooms. As Sir Ken Robinson suggests ñ it is the arts that develop creativity and creativity is going to be the necessary skill these students need 30 years from now.

16. Find a time to do practice meditational prayer for 12min. per day as a class or as a school. See How God Changes your Brain for details. In a nutshell, students will increase their retention levels by 10% at 12 min./day. This in addition to the relaxation effects it has on those students who come to school with high anxiety.

17. Inculturate Catholicity. Pope Benedict XVI as Cardinal wrote a book Truth or Tolerance. He discusses in here how to make the Christian message stick with this generation. We no longer live in a Catholic culture, but a highly sexualized, highly technological, highly materialistic, highly morally relativistic society. The first step in helping our students live authentic Catholic lives in this society is of course to present them with the truth as given to the Catholic Church via Sacred Scripture and Sacred Tradition. (This assumes that we as teachers are knowledgeable enough to do this). This of course is not enough. We then actualize the faith. We must make the Catholic faith applicable to their lives. Then we must inculturate the faith. We must develop a Catholic culture. Their faith must become cultural, a part of their every day lives. Habitual. Ritual. Then faith can become permanent. See the Pontifical Biblical Commissionís The Interpretation of the Bible in the Church for an entire section on actualizing and inculturating.

18. Pray. Protestant private schools get together in the morning before school and have a devotional time. Gateway is an example. Each staff takes a turn taking a passage of scripture and giving the staff a little something to meditate on. Then the staff prays together for the students in their school. Change in our students begins with prayer.

I will end here. Prayer seems like an appropriate place to finish off this short dissertation. These are some possible answers, and with much discussion we can come up with many answers to help us develop students into seekers, leaders, ethical individuals, authentic Catholics, and communicators. We can find ways to work within a system that by its nature has been making students consumers, helpless, and dummied down. Change takes work. Guts. Passion. Compassion. We can do it.

Sincerely and respectfully,

~~Jerry Maguire~~

Kenton E. Biffert MEd

Notes about effective meetings with Laura Lipton

2011-10-29T13:25:00.000-07:00

Laura Lipton - leading groups.

If meetings are used to dispense information you are wasting people's time. Meetings should be used to process and discuss information.

A skilled group leader recognizes the needs and wants of others first and puts their own needs ands wants last.

A skilled group leader is like a zoologist who recognizes the inherent characteristics of all group members and celebrates the diversity of each.

To present is to teach and transform group members by enriching and extending their knowledge, skills, and attitudes.

Successful meetings are outcome driven not activity driven.

Skilled leaders craft presentations that help group members transform information into ideas and ideas into action.

In high performing groups expertise comes ultimately from the group not the province of any one person.

Leaders should save a place at the table for themselves, but to be equal with the group and not perceived as taking a "one-up" position relative to the rest.

If you are implementing a certain strategy but can't explain why then most likely it is not an effective strategy

It is always the group's group not your group.

The goals of a grou p should not be focused on the leader but the group. The leader should be implementing strategies and conversations to create the group more effective not the leader.

Planning with punitive action (seating plans) will get you resistance instead of engagement.

If meetings are comfortable then you are probably not talking about the right stuff.

You can't have a blueprint for change when dealing with people. There are no nice right angles with people.

Leaders should be aware of any biases they have on a topic and allow the group to create their own view. By asking the right questions and you can always get the answers You want.

Before an individual can embrace new ways, unlearning, at a variety of levels is necessary.

Instead of worrying about having "measurable" outcomes or goals start focusing on looking for evidence of learning or goals..

If when you leave a meeting you don't feel challenged you have just wasted your time

If your activity is not task orientated, it is just fluff and wasting time.

We are living with a high autonomy culture but have too much mandated collaboration.

Just because we are talking about the same issue doesn't mean we are collaborating.

The work we do outside of our classroom is just as important and critical as to the work we do inside the classroom.

Too many meetings are seen as a place where minutes are taken and hours lost.

Provide the agenda for the meeting before to allow members to reflect and create thought on the topics before the meeting.

Effective groups take collective responsibility.

The process of a meeting should not be created to make everyone feel good but to challenge and be purpose orientated.

Skillful leaders focus more energy on learning and the learners, less energy on the content and on themselves as speakers.

False collaboration may build resentment or become a disguised presentation.

Listening is more than just waiting for your turn to talk.

7 premises of effective groups:
1) groups develop, and their development can be influenced.
2) human behavior has a biological and social legacy.
3) there are predictable dynamics in groups
4) work sessions should be learning sessions.
5) investing energy in design saves energy in delivery.
6) shaping the discourse determines direction.
7) you can't lead where you won't go.

Students are talking about assessment are we listening?

2011-10-27T06:00:00.000-07:00

I recently went to a grade 12 math class where multiple choice, numerical and written response exams were abolished and replaced with open ended projects. These projects were handed in and given back with written feedback only. Then students were allowed to make changes and re-hand in the project. This could occur as many times as the student needs. The teacher noticed an increase in both student achievement and, more importantly, student learning. I am a full believer that students should have a voice in how they will be assessed. Consequently, I gave these students a quick survey on their assessment in the class. Below are the questions I asked, accompanied with the students’ answers.

First off, a very scary statistic…I asked:

In your past schooling experience, how is your knowledge demonstrated in your classes?

Every single student in the class reported: “Multiple Choice, Numerical Response, Written Response Exams”

I am saddened by the truth that after 12 years of schooling, students are shown that the ONLY way to demonstrate knowledge is on a MC, NR and WR exam!

Now, if you believe that testing is a choice that STUDENTS would prefer, I strongly ask you to read the answers below.

Comparing between open ended projects and traditional exams (multiple choice, and numerical response), which do you feel as you LEARN more as you complete the assessment?

88% Answered Projects, while 12.5% Answered Exams.

Explain why you don't feel as you learn as much from projects/exams (depending on your answer from the previous question). Start your sentence with: I don't learn as much from _____ because...

I don't learn as much from traditional exams because they don't allow you, as projects do, to use your creativity (which in my opinion should be much more important in school than it is now yet always takes a backseat to logic) or to be able to apply the information you've learned in a flexible way as opposed to the cookie-cutter approach of tests. Also, I feel that test marks are based partially on luck, as some tests might just happen to have easier questions than others, or people can make lucky guesses. Projects, on the other hand, offer a more general way to demonstrate knowledge of a subject.

I dont learn as much from exams because i cram the day before to learn everything just for the test and I get anxiety because of it anyways which then leads me to stress and worry about my mark way too much. Also, if i fail the exam because i simply dont care then i accept it and just move on. These assignments dont cause this because it gives me time to actually work on it and if i get something wrong it doesnt just end there. I can fix my mistakes and actually learn from them. Also if a exam is on a specific day and i am very busy and cannot study for it then that leaves me as being screwwed where as these assignments give you time to get them done and they also work around your life.

I don't learn as much from Exams because you write them and you finish regardless of how much you actually know. With the projects you finish them like an exam but instead of just getting the mark you would have gotten on an exam the project gives you questions of things that you need to know and gives you time to learnt them and complete them. If you didn't get 100 the first time around you get extra chances to learn the concepts until you are comfortable with the course.

I don't learn as much from traditional exams because I am less inclined to look at the questions I got wrong since it doesn't benefit my mark.

I dont learn as much from traditional exams because they assess what you remember... the projects allow me to look back at my notes are relearn things that I may have forgotten and having XXXXX checking it over and giving it back allows me a second chance to fix and understand what I did wrong

i feel that i dont learn as much from exams because i only look at what i do wrong and sometimes i just leave it because i cant get that mark back. compared to open ended projects, i can redo it and earn marks.

I don't learn as much from exams because if I don't understand something I can't ask. When I do open ended projects I can ask right then and learn right then and apply my knowledge right then.

I don't learn as much from exams because I don't get a chance to askk questions or work through any questions I don't understand. I get stressed out and hate having to prepare for them.

i dont learn as much from exams because i dont take the time to go over them. i just get upset over the mark and discouraged in my ability to understand the material. with XXXX projects, he gives us in the moment feedback to iron out any kinks and make sure we fully grasp the concepts before moving on. students that fail tests normally dont go back and look over them, so they never end up understanding the concepts.

I don't learn as much from exams because it is just memorization and when doing the projects I have to actually know how to do things and the steps involved.

I dont learn as much from multiple choice tests because they dont allow us to apply our knowledge and all it basically does is make us memorize how to answer questions instead of understanding how it works.

I don't learn as much from exams because I cant ask much questions and with the projects feel like i know the content and can be more confident more in my answers. With exama I find that they are good to an extent because we are thrown random questions that we need to know the basis of the question to asnwer. I find that both of the assessments, projects and tests are a way to assess our knowledge however I find that we need a balance of tests and projects..

i don't think i learn as much from exams because it gets marked and we don't really go over it and learn from our mistake because the teacher only goes through the question that most people did wrong

exams test my ability to regurgitate information and projects force me to get creative

I dont learn as much from exams cause they test you not teach you. But they do require you put more effort to prepare for them.

i dont learn as much the standard test because i usually dont usually get the chance to go over it and fix what i know

This is just because i get stressed out for tests and study for them so i get more practice but i still prefer the projects because they relieve the stress that tests cause and it still evaluates the extent of knowledge well.

I don't learn as much from the projects because I feel like on an exam I am being tested in a variety of ways on a certain concept instead of one or two ways in a project.

I dont learn as much fromExams because i do it then i dont really get to see what mistakes and how to fix it

I don't get to see a variety of different types of questions.

Exams are just answers and questions. If I get it wrong, I sometimes don't know time and the class moves on so its hard to ask.

I don't learn as much from exams because once I get a question wrong and I get the test back, I look over the answers but dont really care about why I got it wrong. With the projects, I am "forced" to learn the content, and I get to keep trying until I get it right. I love it.

exams because when i make a mistake on a exam i just get it back and then we move onto a different concept without me understand completely the previous one

tests, I do not get the corrections I need

Possible solution to DA of Applications of Derivatives

2011-10-26T06:00:00.000-07:00

Instead of a multiple choice, numerical response and a written response exam on "Applications of Derivatives", I gave my students an open-ended assessment.

Here is one of my student's work. As you can see, students still can demonstrate knowledge and understanding without shading in "c" on a scantron sheet.

DA with Applications of Derivatives

2011-10-19T07:19:00.000-07:00

Here is how I am assessing Applications of Derivatives:

New final Exam

2011-10-18T06:00:00.000-07:00

Here is what I am giving to my students for the Final Assessment.

Math 31 Final Assessment

This assessment will be in addition to a written component. The written component and this assessment will both be worth 15% of your final grade. In this course we covered many outcomes, the outcomes which are important to success in future calculus courses are:

· Slope at a point, using first principles.

· Limits

o when do they exist and not exist

o one sided limits.

o Limits as x approaches infinity

· Derivatives using, chain, product, quotient, and implicit differentiation rules of functions which have:

o Trigonometry

o Polynomials

o Exponential

o Natural Logs

· Absolute and relative maximums and minimums.

· Related Rates.

· Curve Sketching.

· Integration rules of functions which have:

o Trigonometry

o Polynomials

o Exponential

o Natural Logs

· Determining area between two functions, both graphically and algebraically.

You must demonstrate your knowledge of all the outcomes anyway you want. Your presentation can take any form(s) you would like, a powerpoint presentation, a prezi, a video, a skit, etc. The presentation will be as long as it takes to demonstrate your understanding; however 30 minutes is the maximum the presentation should be. You will be presenting in front of a panel of judges, one of which will NOT be a math teacher. You must relate most of your knowledge to a real world application and demonstrate how calculus is used outside of the math classroom. After the presentation, 10 minutes will be allotted for questioning from the judges. Your mark will be decided by the judges and based on your presentation and your answers from the questions you are asked.

You may work in groups up to 3; however you will each receive a separate mark and will be differentiated by your individual answers of the questions from the judges.

Here is a rubric I will use to assess their knowledge.

	Superior	Adequate	Minimal	Inadequate
Content	The speaker provides a variety of types of content appropriate, such as generalizations, details, examples and various forms of evidence. The speaker adapts the content in a specific way to the listener and situation.	The speaker focuses primarily on relevant content. The speaker sticks to the topic. The speaker adapts the content in a general way to the listener and the situation.	The speaker includes some irrelevant content. The speaker wanders off the topic. The speaker uses words and concepts which are inappropriate for the knowledge and experiences of the listener (e.g., slang, jargon, technical language).	The speaker says practically nothing. The speaker focuses primarily on irrelevant content. The speaker appears to ignore the listener and the situation.
Organization	The message is overtly organized. The speaker helps the listener understand the sequence and relationships of ideas by using organizational aids such as announcing the topic, previewing the organization, using transitions, and summarizing.	The message is organized. The listener has no difficulty understanding the sequence and relationships among the ideas in the message. The ideas in the message can outlined easily.	The organization of the message is mixed up and random. The listener must make some assumptions about the sequence and relationship of ideas.	The message is so disorganized you cannot understand most of the message.
Creativity	Very original presentation of material; captures the audience’s attention.	Some originality apparent; good variety and blending of materials / media.	Little or no variation; material presented with little originality or interpretation.	Repetitive with little or no variety; insufficient use of materials / media.

Angry Birds and Calculus

2011-10-14T06:00:00.000-07:00

During my first unit, instead of assessing with a traditional exam I used an open ended project. One of my students submitted the following video to answer question 3:

As you can see, he used a timer on his phone, a ruler and the game Angry Birds. Here is his work

DA with Quadratics

2011-10-11T06:00:00.000-07:00

Before, I have assessed Quadratic functions in the traditional sense with worksheets, homework checks and quizzes. This year I wanted to assess my students' knowledge through an open-ended project and allow for differientated assessment.

Here is the task:

Quadratic Graph Project

1. Take a digital copy of a picture which has a parabolic shape in it.

2. Log on to www.prezi.com using the following log on:

***I just created a class log on and password***

3. Select blank template.

4. Select insert picture, and import your picture onto the prezi.

5. Using insert à shapes àlines, draw in two axes. Neither axis may go through the vertex of the parabola.

6. Using either the pen tool or the circle tool, create a point on the vertex of the parabola

7. Label the vertex using points which are appropriate.

a. Vertex:____________

8. Label another co-ordinate on the graph.

a. Point:_____________

9. Using your vertex and co-ordinate you created, determine the value of a, either as a fraction or a whole number, if your parabola was written in standard form . Show your work on Prezi.

10. Label another 4 points on your graph. Try to space out the co-ordinates evenly across the parabola.

a. Point 1:_______

b. Point 2:_______

c. Point 3:_______

d. Point 4:_______

e. Vertex:_______

11. We will now have the calculator create the function.

a. On your calculator, push STAT, then EDIT…

b. In the first column (L1) input all the x-values, and in the second column (L2) input all the y-values of the points.

c. Click STAT, then the right arrow (à) to the CALC menu, then scroll down to QUADREG.

d. Write down the values your calculator gives you, to the nearest hundredth if necessary.

a:__________

b:__________

c:__________

12. Inputting your values into general formyour function will be_____________________

13. Change your general form into standard form, by completing the square. Show your work in prezi.

a. Your standard form now is ________________
b. State the vertex, domain, range, direction of opening, and axis of symmetry from the function above.

14. Write a couple of sentences explaining any differences from the vertex you stated in part 7, and the vertex in part 13.

15. Using the equation from Part 9, determine the functions x and y intercepts, if the picture was extended such that it intercepts both axes. Solve this part by graphing.

a. x-intercept________

b. y-intercept________

16. Using the equation from Part 12, determine the functions x and y intercepts, if the picture was extended such that it intercepts both axes. Solve this part by the quadratic formula.

a. x-intercept________

b. y-intercept________

Here is an example of my student working up to Section 14.

Grading with O'Connor

2011-10-06T06:00:00.000-07:00

Recently I read through "How to Grade for Learning" from Ken O' Connor, who brings up some GREAT points about grading. Here is synopsis of my own learning:

First and foremost.... "Learning can (and does) happen in the absent of grades!"...This was the biggest myth I believed for quite a while when I first started teaching. I truly believed that grades were the ONLY way learning could occur...I was wrong (the first and last time I have ever been wrong :) )

Grant Wiggin even said
"Perhaps the most counterproductive aspect of schooling as we know it is the conventional system of letter grades. The problem with grades is not the use of symbols, but the absence of any DEFENSIBLE plan for coming up with the symbol… most grades reflect what is easy to count and average into a final grade.”
O' Conner brought up his 7 persepectives underlying grading:

• Grading is not essential for learning.

• Grading is complicated.

• Grading is subjective & emotional.

• Grading is inescapable.

• Grading has a limited research base.

• Grading has no single best practice.

• Grading that is faulty damages students and teachers!

I have heard many teachers express their views that grades truly motivate students into learning, however O'Conner says:

If grades are extrinsic motivators, they can destroy intrinsic motivation. Good grades may motivate, but poor grades have no motivational value.

Even further, Gusky has said:

“Low grades push students farther from our cause, they don’t motivate students. Recording a D on a student’s paper won’t light a fire under that student to buckle down and study harder. It actually distances the student further from us and the curriculum, requiring us to build an emotional bridge to bring him or her back to the same level of investment prior to receiving the grade.”

Lastly, Marzano (after researching over 8000 studies) said:

The most powerful single modification that enhances achievement is FEEDBACK. The simplest prescription for improving education must be ‘dollops of feedback’.”

And now the big finale...here are 15 "fixes" you can do TODAY to change your assessment:

#1 - Don’t include student behaviors (effort, participation, polite manners, etc.) in grades; include only achievement.

#2 - Don’t reduce marks on late work; provide support for the learner.

#3- Don’t give points for extra credit work or use bonus points; seek only evidence that more work has resulted in a higher level of achievement.

#4- Don’t punish academic dishonesty with reduced grades; apply other consequences and reassess to determine actual level of achievement.

#5 - Don’t consider attendance in grade determination; report absences separately.

#6- Don’t include group scores in grades; use only individual achievement evidence.

#7 - Don’t organize information in grading records by assessment methods or simply summarize into a single grade; organize and report evidence by standards/learning goals.

#8 - Don’t assign grades using inappropriate or unclear performance standards; provide clear descriptions of

achievement expectations.

#9 - Don’t assign grades based on student’s achievement compared to other students; compare each student’s performance to preset standards.

#10- Don’t rely on evidence gathered using assessments that fail to meet standards of quality; rely only on quality assessments.

#11 - Don’t rely only on the mean; consider other measures of central tendency and use professional

judgment.

#12- Don’t include zeros in grade determination when evidence is missing or as punishment; use alternatives, such as reassessing to determine real achievement or use “I” for Incomplete or Insufficient Evidence.

#13- Don’t use information from formative assessments and practice to determine grades; use only summative evidence.

#14 - Don’t summarize evidence accumulated over time when learning is developmental and will grow with time and repeated opportunities; in those instances, emphasize more recent achievement.

#15 - Don’t leave students out of the grading process. Involve students; they canand should- play key roles in assessment and grading that promote achievement.

Last, Reeves says

“If you wanted to make JUST ONE change that would immediately reduce student failure rates, then the most effective place to start would be challenging prevailing grading practices.”

DA with Derivatives

2011-09-27T06:00:00.000-07:00

Math 31 Derivative Assessment

Complete a newspaper, newsletter, pamphlet, or any informational item showing how Calculus can be used in real life applications.

Your product must demonstrate your knowledge of:

· Use of the product rule by taking the derivative of the product of two functions, both which have a minimum of 2 terms and are at least degree 2.

· Use of the quotient rule by taking the derivative of a quotient of two functions, both which have a minimum of 2 terms and are at least degree 2.

· Implementing the chain rule while taking the derivative.

· Taking the derivative of a function which must use the combination of two or more of the following:

o Chain Rule

o Product Rule

o Quotient Rule

· Taking the derivative of a function which requires implicit differentiation.

In addition, you must also:

· Determine the slope at a point of a function.

· Determine the equation of a tangent line of a function at a point.

· Determine the second derivative of a function.

The work, determining the derivative and other answers can be supplied separate to your final product, but the solutions MUST make sense in the story, or scenario, you have placed them in.

Examples:

Recently the police has determined the crime rate of Red Deer can be shown by the function, c(d) = d^2, where c(d) is the amount of crimes committed on a day, and d is the day of the year. This function applies to only the first 5 days of the year, then the function changes. The rate of change of crime from day to day can then be demonstrated by the function c'(d)=2d, and the exact rate of change on the 3^rd day is 6 more crimes each day.

Sylvan lake was under attack, last night, by a mob equipped with catapults. The height of one of the arms of a catapult, in meters, could be represented by the function h(t) = -t^2+9, where t is from 3 seconds before the arm reaches its maximum height to 3 seconds after it reaches it maximum height. If the catapult launches its projectile at t = -2, the slope of the projectile would be 4 m/s and an acceleration of -2 m/s^2 with an equation of 5(x+1)=y-5

What we can learn from a single donkey

2011-09-23T06:00:00.000-07:00

Whether you believe in God or not, there is something we can learn from a single donkey Jesus rode on into the town of Jerusalem. When Jesus was riding into Jerusalem, people were waiting in angst and delight to meet Him and maybe become a recipient of one of His miracles. The donkey that Jesus rode did not receive on ounce of affection, respect, or even recognition for bringing this amazing man to their town. Not one individual recognized the efforts, by the donkey, put forth to bring Jesus to this place but he still kept on.

As a teacher I sometimes forget why I am doing my job. I lose focus that I am not here for recognition, affection or even respect from my students, but to teach them something they do not know. I am not here because of the pay, the summer holidays, or even the access to free coffee every morning. This perks are great and I am thankful for them, but education should not be about me; it is about the students who enter my class daily.

How many times do you do things because it makes your life easier, or it makes sense to you? After reflecting on the donkey I have realized it is the students who should be in spotlight and not me. My assignments, due dates, exams, quizzes, etc. should not be created to meet my needs but actually the needs of the students. In the past I have forgotten this. In previous years, I have created all multiple choice exams because they are easier to mark, I have set due dates around my schedule so I would have time to mark them, I have even taught concepts in ways that make it easier and quicker for me.

Reflection sometimes hurts!

I challenge you to change just one task into allowing the students having the full spotlight and you stepping back. Whether it is allowing each student to set their own due date, each student deciding how they will be assessed, or even each student informing you how to teach, you could make a considerable about of difference in your classroom.

Always remember that our needs and wants are not always in the best interest of student learning, and that sometimes we need to be an ass. Donkey reference there ;)

What a DA clasroom looks like

2011-09-20T06:00:00.000-07:00

I have written about how I am changing the definition of test to allow for differentiated assessment in my class. Some questions arose so here are the answers.

My current class sizes are in the low 30s, some classes I have done this with in previous years were in the low 40s while others in the 20s. With the right amount of planning, I believe this could be implemented with any class which has a reasonable amount of students. As for prep time, out of 8 courses throughout the entire year I teach 7 classes.

How does it look?

First, if you walked into my classroom you would see some students working in groups, others alone, and others receiving one-on-one assistance from me. Some students would be working on a laptop, some on paper and pen, and others researching on an I-Pad. I encourage students to assist each other, collaborate on problems and research how the math we are using relates to their own life.

I give students the whole “exam” at once and don’t set a deadline, nor do I ask students to work on it alone. The directions are to work on the “exam” during class time, create your own problems and solutions, work on it in any order you would like, and to hand in the parts as you complete them.

Students are then given 1 or 2 classes (depending on the exam) to work on it. As students complete a question, not the entire exam, I can start assessing it. If I am not helping a student I will assess the question with the student explaining their reasoning and solution. This keeps my time spent on assessment low as not all students are handing in the entire exam on the exact same day. This allows me to spend more time critically analyzing each student’s work.

Now here is the key:

I don’t grade it!

I either give them verbal feedback, or if I am assessing it outside of school, I will provide them with written feedback and comments. Students then have the option of correcting their mistakes and re-handing it in. This process continues to either the question is completed at 100% or the student chooses to take the mark I would assign as a regular exam. This is how I have turned my assessments of learning to assessments of, as, and for learning. I also have redefined the idea of 100% in my class.

What if a student does not like the project?

Easy answer, a traditional exam consisting of multiple choice, numerical response and written response is always an option. However, only a rare few of students choose this option. Keep in mind this is not a threat or a way to motivate students to complete the project but just another choice a student has as to how they are assessed.

What if a student does not complete the project in the time set?

I do not give them a zero, give them late marks, or use any kind of grading consequence but require them to start coming in during lunch, or anytime outside of class to complete it. The first meeting starts with a simple question, “Why isn’t it done?”

Some reasons are heavy workloads in other courses or outside school responsibilities and then I give the student as long as it takes to complete the project, with him/her still coming in during lunch.

Another reason I often hear is that they do not understand the material. This solution has me re-teaching the material and still requiring them to complete an assessment on the outcome.

All other reasons are dealt case by case.

I realized, with a traditional test, if students do not understand the material we give them a failing grade and move on. In the past, I have tried to have students complete their mistakes, but once I have shown them their mark all motivation to learn the intended outcome has vanished. This is the reasoning behind the no grade on their product until it is complete.

Students are enjoying this way of assessment as it gives them choice, autonomy in the way they can demonstrate their learning, and allows for authentic learning to occur. If I have not answered a specific question, or you still have concerns, please let me know.

Differentiating Assessment for Different Types of Learners and Levels

2011-09-16T06:00:00.000-07:00

Amber Henrey, whose site can be found here, is implementing a strategy to combine standardized tests in conjuction with differentiated assessment.

Differentiating Assessment for Different Types of Learners and Levels:
How one school successfully uses standardized tests in conjunction with differentiated assessments.
By Amber Henrey
September 14, 2011

Every year teachers are faced with the same dilemma: giving students the (almost) end of the year State Test. It is a standardized test, meaning it is given to all students state wide during the same time frame, in the same exact way, with the same exact questions.

The problems is that not all students were taught or learn in the same manner. As a data-manager as well as teacher for my school this problem haunted my grade level and me as we tried to sleep at night. We know that out of our 90 students we have huge discrepancies in everything. Socioeconomic status gap was far and wide. English language levels were diverse. Simply the matter of sitting still for a length of time varied between students. There was no way we could effectively teach such a diverse population without addressing the diversity within our classrooms.

We decided to switch for core subject matters from heterogeneous homerooms to homogeneous core classes. Every teacher still taught all the subjects but our kids went between us at different times of the day. It used to be called tracking but I will explain why it isn’t.

To start the year off the students are grouped by a combination of CST scores and teacher recommendations to get the core classes going. 4th grade is the first year these kids are grouped homogeneously so one teacher’s advanced student may be another’s proficient. We monitor who is standing out in the group and adjust accordingly.

During the first month of school we give dreaded assessments. Its not fun but it must be done so that we can quickly diagnose learning abilities and missing skills . We try to keep it to 30 minutes once or twice a day. The assessments are diagnostic and formative in nature. This helps us monitor gains made during the year but also helps to determine our Targeted instruction. The whole grade level takes a mock CST for 4th grade standards to help us make more decisions about who to teach and what to teach them.

Once the results are in we adjust the three groups for Language Arts and Math. If we could have 5 groups it would be ideal but we only have three fourth grade teachers. The advanced to high proficient group maxes out at 35 students specifically assigned to the teacher that has GATE credentials, and is truly an expert at teaching students to utilize their higher level thinking skills. The high basic to proficient group also maxes out at 35 students. The basic to below group hovers around 20 students unless they are pulled out for resource at this time.

The groups are taught the same skills and essential standards at the same time but in different ways. You may see different levels of text and pacing however you will see that if comparing and contrasting is occurring in the advanced class it is occurring in the below basic class as well.

We give weekly assessments based on that specific skill. We do not give “story tests” because we aren’t teaching story recall. We find an alternate text for the kids to read. We select passages that match our theme or genre. We create questions using question stems for our focus and using blooms taxonomy.

Here is where the differentiation comes in. If a student’s reading level is high they take the assessment at their reading level. The questions are the same questions given in the lower levels however they tend to be more open ended. The expectation is that they will be able to answer the question without any other prompting. The middle group has a text at their level but the questions typically have a sentence starter or frame for them to fill in. The lowest level has reading at their level. Their questions are typically fill in the blank with an example or vocabulary list. If necessary we use a multiple choice format as well. We try to mix the types of questions on each test so that we can see if the kids are able to do the standard or are just good at test taking.

Here is what is key:
We focus on the skill and standard chosen as a grade level for that week. We create tests that assess the skill and standard, not if they can do everything at once: read a certain level, write, or spell. If a group can do all those things and demonstrate mastery of the skill then they are assessed in a way that has all the components.. If they cannot do all those things then they are given an assessment in the manner that they can. Regardless of how they show it; if they can demonstrate that they can accomplish the skill or standard then they are considered a success.

Back to the issue of tracking. Our kids do not stay in the same groups all year. We have flexible groupings. If a student has demonstrated mastery for 3 or more weeks they are often switched into the higher group. The reverse also happens. If a student is not able to keep up with the rigor of the class they are in than they can be moved into the lower group. There was a time where almost an entire class has changes because one teacher was really able to teach something well while another wasn’t.

We also address the fact that kids have gaps to fill or enrichment to extend. We have another block of instruction called Target Time. We have additional support staff that help us break our groups into even smaller specific groups for 40 minutes 4 days a week. These kids are grouped based on their diagnostic assessments and given time to work on their gaps and one specific standard at a time. A pre-assessment is given every three weeks for that one standard and one skill the students are working on. Then at the end of the three weeks a post assessment is given. These assessments directly relate to the groups ability. Groups are rearranged as needed.

The students know what group they are in and why. We know kids notice that they are homogenously grouped and instead of acting like it isn’t so we are up front about why they are placed where they are. “This group was created because on the assessment we gave on making predictions using context clues you scored less than 75% we are going to focus directly on that standard for the next 3 weeks and give you an opportunity to move groups again.

This is the third year working this way and so far we haven’t had any issues of insecurity or teasing. If anything it is a relief for our students to be with common peers struggling with similar issues or ready to be challenged. Our CST test scores took a grade level from 39% proficient in third grade to 64% proficient in fourth grade. We continually evolve our procedures and streamline them.

DA with first principles and limits

2011-09-15T06:00:00.000-07:00

Here is an example of how I have changed the definition of an exam. Before, when assessing first principles and limits in my calculus class, I would have each student write an exam. This year, I am giving students the option of writing an exam or completing the following to demonstrate their learning.

Unit 1 Assessment Project

1. Create a formula for the distance of an object at any time t. The formula must be at least degree 2 with a minimum of 2 terms. Using your formula you must:

· Determine average velocity of the object for the first 10 seconds.

· Determine, with an explanation, the instantaneous velocity after 10 seconds.

· Determine, with an explanation, the instantaneous velocity for any time t.

· Determine if the object is ever traveling 50 m/s.

2. Create a piecewise function over the domain of the real numbers. The function must contain at least 3 different pieces and may not be continuous and may not have a limit at at least one point. Using your function you must:

· Provide a graph of your function.

· Explain why your function is not continuous at the specific point.

· Explain why a limit does not exist at the point above. Explain how you could change your function such that there is a limit. Calculate the left and right side limits at this point.

3. Demonstrate, through a real life application, how you can calculate the instantaneous rate of change at a specific data point. You may use data from a chart, create a video, etc., but the data may not follow a specific function. The point at which you calculate the rate is entirely up to you, but must have an explanation.

4. Create three functions, one which:

· approaches infinite,

· one which approaches 0,

· and another which approaches a line which is not 0

as you extend these functions to infinite. Explain how you can determine the limit as x approaches infinite, for each of your functions.

5. Create a real life example of a convergent series, and calculate the sum of this series.

Proof that DA works

2011-09-14T06:00:00.000-07:00

As my last post with "Problems with Common Assessment" there is another side of the coin; "Differentiated Assessment"

Some are skeptical that there is a benefit in having DA in your classroom, but Bayview Glen School from Ontario shows there truly is.

Bayview Glen school is a K – 12 school that wanted to answer the question “How, as leaders, can we facilitate a successful shift towards differentiated assessment throughout all grade levels?” The focus was to encourage teachers with the knowledge to expand their assessment policies beyond traditional tasks such as tests and quizzes.

This school completed an action research plan by providing the entire staff, in June 2009, with an assessment workshop. During this workshop, each teacher was educated on various Differentiated Assessment Tasks (DAT) which they would implement in the 2009 – 2010 academic year. Then given a simple task:

create one differentiated summative assessment for their course and present this task to the staff, reporting on the assessment and providing insight into how it impacted student learning.

Immediately, the staff demonstrated a strong commitment and their assessments which were presented were creative, engaging, challenging and incorporated reflective elements of a constructivist approach to teaching and learning.

After each teacher implemented their assessment in their own classes, they were to report their experiences with the rest of the staff. What was noticed?

“The results of these assessments lead to greater student learning experiences allowing for meaningful connections to the real world. We also realized that is wasn’t just about the culminating differentiated assessment task, rather we needed to emphasize the importance of formative assessment, digging deeper into our curriculum while placing students at the center of their learning.”

Some teachers reported:

“I am definitely trying to move away from the traditional way of instructing and assessing. By being introduced to DAT, and by taking the first two terms to incorporate the ideas into my classroom, I have realized the possibilities and I am excited to continue to develop the use in my daily teaching practices”

One student even reported.

“The assignment for Glass Menagerie helped me to realize the relevance of this books’ message and how the themes applied to my own life, allowing me to provide a better analysis, while demonstrating my inquiry skills.”

In the school there was a shift towards student-centered learning, with an emphasis on making real world connections. Inquiry-based learning activities allowed for a sense of wonder and curiosity amongst learners.

Before completing this action research all teachers completed a survey (named Survey 1) and after they completed the same survey (named Survey 2). Here is how this one task changed their ideologies:

You can notice that teachers were changing the “bulk of their summative” assessment strategies after a single DAT.

Similar data is becoming more and more prevalent and should not be ignored. Peter W. Cookson Jr stated:

“We are at a threshold of a worldwide revolution in learning. Just as the Berlin Wall fell in 1989, the wall of conventional schooling is collapsing before our eyes.”

Problems with common assessment

2011-09-13T06:00:00.000-07:00

I would like to challenge the idea of common assessment. Not just common throughout a department but common even in a single classroom. From this time further I will refer to these assessments as their true name “Standardized Assessments”. The definition of a standardized assessment is:

a test that is administered and scored in a consistent, or "standard", manner. Standardized tests are designed in such a way that the questions, conditions for administering, scoring procedures, and interpretations are consistent.

I have asked why do teachers give common assessment? I will provide the two top reasons I heard, and then my counter-argument.

1) Standardized assessment allows for fair and equal assessment practices between the same courses throughout the school.

Counter: What is fair is not always equal and what is equal isn’t always fair. If we truly want equal assessment, then should we not require all students to write with the same hand, take off their glasses, set the temperature in all the rooms to be the same, and have all students write with the same type of pencil? I know this sounds absurd, but where does the fair and equal practice stop? Each and every student, in my class, has a different set of needs and abilities yet these exams will force each student to be put through the same hole. Alberta Education recently, wrote

Differentiated assessment means selecting tools and strategies to provide each student with the best opportunity to demonstrate his or her learning. As you get to know your students, and as student differences emerge, assessment naturally becomes more differentiated, because its purpose is to meet students where they are and to coach them to the next step. In this way, assessment and instruction continue to support and inform each other.

By making these decisions before ever “knowing my students” how is one to decide which would be the “best opportunity for each student to demonstrate his or her learning”? I do not see standardized assessment as a fair and equal practice at all.

2) Standardized assessment allows for fair and equal instructional practices between courses throughout the school.

Counter: This seems like the standardized assessment is more assessing the teacher than the student now. Even if two students, in two different classes, receive the same mark this does not guarantee the same instruction has been given. One teacher could be “teaching to the test” and involving daily test prep activities while the other is implementing quality instruction and critical thinking.

Now, the problems I see with common assessment:

First and foremost: It is the duty and responsibility of the classroom teacher to determine how and when to assess each student. I am confused and distraught when people, outside the class, control the assessment strategies, without even knowing the individual students they are impacting.

Alberta Education’s ideas are:

Differentiating assessment involves rethinking the standard practice of having all students do the same assessment tasks at the same time, regardless of their individual learning needs or the learning they have already demonstrated. Rather, in this new paradigm, teachers customize the selection and use of assessment information to reflect each student’s highest level of achievement.

Also, I refer to these as standardized assessments as they are designed in such a way the class average should fall in a “reasonable” zone. This zone may differ from teacher to teacher and from class to class but this underlying bell curve does exist. I have heard of meetings where discussions such as “The average was low, so the test should be made easier” or “The average was too high, so we need to increase the difficulty” have been had. This saddens me as we are requiring students to fail such that others can feel success.

Since by the definition and the manner these assessments are designed, usually, they must fall on a specific day, common to all teachers of the same course, and also consist of some mixture of the following:

·         MC 5-10 questions
·         NR 3-5 questions
·         WR 2-5 questions with bullets

Usually the test days, and requirements are decided before the first day of school

By having standardized exams, we are going against the research and knowledge of our government. Also, it should be the freedom of the teacher to decide, and indeed, the freedom of each student to decide how and when they will be assessed on their knowledge. Of course we all know that some people employed as teachers are of different quality, but by forcing everyone to assess, and ultimately, teach the same way it may not improve teachers of a lower quality but actually hobble the good ones.

Assessment from Esme

2011-09-12T09:26:00.000-07:00

I am very pleased and honoured to have Esme Comfort, whose blog can be found here, to share her ideas on Assessment with me. Below is a guest post from a Public school Trustee in Bow Valley.

"Said the Source" by Micah Lexier, Library Installation, Hamilton, ON Photo: Wendy Bush, with permission

Pleased and proud that the teacher, @d_martin 05 (as he is known on Twitter), has asked me to do a guest post on his blog. He is a highly committed educator who is always honing his skills.

The topic? “What is the best way to gauge a student’s progress in learning?” Or [drum roll] ASSESSMENT

You may as well ask, like Lewis Carroll’s Mad Hatter, “Why is a raven like a writing desk?” because there is no one definitive answer. Rather it is a complex blend of sometimes competing interests that are served by student assessment; hence the choice of the photo above.

So what could this little old lady trustee have to offer to shine some light on the subject? First a disclaimer: I have no pedagogical credentials, just the experience of having been a student and having children who were/are students. Let’s start with some definitions and descriptions, per The Wikipedia of Esmé, i.e. my own best understanding, as a layperson.

• Formative assessment is an approach to teaching and learning with feedback as its mainstay, in a supportive classroom context. Assessment is ongoing and student-centred. Differentiated instruction, the teacher as a lifelong learner and professional learning communities – and more – will factor into this process. Parents trying to wrap their heads around this idea will often exhibit these first responses: “What d’ya mean ‘no homework’? No report cards – what the...?”

• Summative assessment is a measurement, at a specific point in time, of student learning relative to curriculum or course content. This is generally done by different sorts of tests, quizzes, set assignments with tight rubrics and so on. The Provincial Aptitude Tests and Diploma Exams are full-on examples. We are all very familiar with this “old school” methodology. Numerical marks or letter grades are usually awarded.

In my ideal world, summative assessment would only be used to inform formative assessment; PAT scores would not be published or shared, except between educators to use to inform their practice and diagnose trouble spots. Teaching and learning succeeds best, IMHO, when the teacher and the student are given respect and autonomy.

However, this is tricky stuff. Public schools are accountable to the children and parents, but also to the provincial government and the taxpayer. An easy way to determine if outcomes have been met is indeed the use of hard numbers and straightforward comparators. But what are the outcomes?

Should every student move to post-secondary education immediately after graduation? Well, all of life after high school graduation is post-secondary education, isn’t it? Hold it. Every student should graduate high school, right? At the same age and stage of life? We need to think which skills and attributes will best serve our students, will best prepare them for their individual futures. I believe those are much more difficult to – ahem – sum up. And much, much more difficult to teach.

For those of us who sat quietly at our desks, soaking up the wisdom dispersed by the pedant at the front of the room, the transformation of education will be hard to comprehend. Effective formative assessment means collaboration between teacher and pupil to adjust teaching and learning while they are happening. That was not my experience of school! That is why school district administrators and governors must involve the parents closely on this journey; it’s crucial to providing the support teachers need. Parents need to try to understand the process and work with the teachers to benefit the children.

When my first parent-teacher interview rolled around, some 20 years ago, I thought long and hard about how to use that precious 10 minutes. What did I want to know? At the time my two questions were:

• How is my child doing, relative to the teacher’s perception of his capacity?

• How is my child doing, relative to the progress of the other students in the class?

Now, it seems to me, I was really asking: “How well do you know my child?” That relationship is worth more to my child’s lifelong learning curve than the ability of the teacher to stuff facts/data into his head. Formative assessment means student and teacher are learning together, and the subject matter is always: the student. It demands more commitment, more rigour from both sides than a straight “drill and kill” testing regimen ever did. Successful students and successful teachers are “curious and curiouser” as a matter of course; the thirst for learning never is slaked.

Geometric Sequences Reductions

2011-09-09T07:00:00.000-07:00

Here is an activity I created to introduce geometric sequences.

1) Watch the movie below:

2) Determine the dimensions of the last image if the original image was 210 × 297 mm.

**I had a copy of the original and final image and had students measure the original on their own, and then check their answer by measuring the final image.**

3) Extenstions: If we combined all the images, determine the total area.

If I extended this sequence to infinite, what would be the limit of the sum of the sequence?

Intro to Tangents

2011-09-08T07:00:00.000-07:00

Here is an activity I used in my Math Calculus class to introduce tangents at a point.

I gave each student a copy of the video below.

Then, in groups of 2, students had to answer the following questions (which is part of the comments in the full YouTube video)

1) Watch the video

2) Determine the average speed for the first 5 minutes.

3) Determine the average speed for the entire trip.

4) At the end of the video, the speed of the vehicle is 109 km/h, explain any discrepancies from your calculation in part 3.

5) Determine the average speed of the vehicle after 15 min of driving.

6) Determine, with the least amount of error, the speed of the vehicle after 15 min of driving.

7) Explain, if any, the difference from part 5 and part 6.

Feel free to use, change as you seem necessary.

For the parts that is hard to see:

The time at each break in the bottom right corner is the total driving time to that point.
The distances at each break are -7.6 km/16.7 km/23.3km/32.1km

I do apologize the video is quite horrible with YouTube. The original is much better. If you require a copy of the original, email me and I can get you a copy.

The product or the mark?

2011-09-06T07:00:00.000-07:00

Over the weekend I tweeted “A great exam makes a teacher proud while a good project makes a student proud” and received some unpleasant responses. Knowing this would take more than 140 characters, I wanted to elaborate on what I meant.

I am not denying that some students are proud when they receive a great mark on an exam, but I believe these students represent the minority of the group. When I look around my classroom, I have posters, Parachutes, Enlargements, graphs, and other math projects which have all been created by students. After looking through mine, and my colleagues’ classrooms, I have yet to find a unit exam posted on the wall.

Remembering back in my own schooling, I recall creating gumball machines, paper mache figures, and even a sundial I gave to my mother for Christmas, but yet I vaguely remember the 90+% mark I received on my math 30 diploma. Going through my scrapbook, I don’t have a single test or quiz among all the projects I kept. Also, for most of these projects I don’t even have a clue as to the mark I received on them.

What does this mean?

I believe that most students are more proud of the product they create than the mark they receive on something the teacher created. Last year, I had students wanting to show their parents their creations BEFORE I had even assessed it! Has a student ever asked to show their parents their exam before you give them their mark?

School should be giving each and every student a chance to feel success and accomplishment. For some, I do believe this can be in the form of an exam, but for most this will require a different form of assessment. Open-ended projects move beyond traditional assessments and, if made properly, require students to communicate their thinking in a deeper manner.

I am not saying that high marks on exams should be discredited, or don’t represent that learning has taken place, but just suggesting that open-ended projects will allow for success for other students in the class. Remember, differentiation should start with instruction but continue onto assessment.

Differentiated Assessment

2011-09-02T07:00:00.000-07:00

I have had a great enlightening summer and would like to start things off with a bang! Differentiated Instruction (DI) and Differentiated Assessment (DA).

Most teachers speak of DI as a common practice in their class and truly teach to the needs of EVERY student. However, some teachers require these same students to jump through a common hoop of assessment. This assessment can take forms of unit exam, a worksheet, a quiz, or any assignment which is the same for ALL.

If we speak of DI so commonly, where is DA?

Rick Wormelli in Fair Isn't Always Equal: Assessing and Grading in the Differentiated Classroom states that "Assessment informs practice, and we take action".

DI MUST lead to DA in a classroom! In a truly differentiated class, students can work towards learning outcomes at different paces, using different strategies, and mastering outcomes in different order. As a result, teachers will need to assess these strategies differently and accommodate the assortment of learning styles while still measuring the learning outcomes. Assessment and instruction does not have to be different but can occur simultaneously and appear different for each individual student.

Alberta Education states, "The goal is not to have an individualized assessment plan for each student, but to have a manageable class assessment plan that is flexible enough to accommodate a range of student needs."

Some say assessment OF learning has to be common (or standardized). Here are some examples of how we can have DA in assessment OF learning. (From Alberta Education)

Assessment of learning (sometimes called summative assessment) is the process of collecting and interpreting information to judge student achievement against predetermined criteria for the purposes of grading and reporting. Assessment of learning occurs at benchmark points in learning, such as the end of a unit or chunk

of learning. Consider the following examples of differentiating assessment of learning.

• Some students in a class choose to demonstrate their learning by writing a report, while others choose to create a poster, and still others choose an oral presentation.

• A teacher provides text-to-speech software and a digital version of the test to a student who has significant difficulty reading the questions in a social studies test.

• A teacher discards some marks collected early in the semester for a student

It can be done, and some our already doing it. Assessment should not be a democratic process but an individual process. Nor should assessment be done TO students, but actually WITH students. Always remember you are not teaching statistics, data points, trends, or even groups, but actually living students with heartbeats, emotions, interests, and passions.

Thanks!

2011-06-15T07:39:00.000-07:00

Well today is our last day of regular classes, the final game of the NHL and will also mark the last blog for this school year.

I want to say thanks to everyone who helped me have the most professional developmental year ever!!! This year, I feel I have engaged my students through authentic assessments, and also with true lessons of discovery.

I will start back up again August 30th.

Below is the final compilation of how my students demonstrated their learning in my calculus class.

65 year plan when a student is 14?

2011-06-14T06:00:00.000-07:00

Here is a post from Lisa, an ex student of mine about having students plan 65 years into the future.

Why I’m hatin on life right now..

For all those who are graduating or or all those who have already gradated from high school, you probably know what I’m talking about. Everyone tries to convince you that you need to have the next 65 years of your life planned out. No joke, I had to make a 65 year plan for a CALM assignment. In reality though, everyone’s wishing they could go back to the days when the world was before them and they had time to make mistakes and choose something different. So why is everyone trying to get us kids to rush into something if they’re not even sure what they wanna be when they grow up? I get that going to school, getting a job and making money are all important. But so are things like maintaining relationships and gaining life experience. Some people think I’m foolish because I haven’t got it all figured out yet. Personally, I think the most foolish people are those who pick something to do because they feel obligated to, instead of living life to the fullest while you’re still young.

Samples of work for Integration Project

2011-06-08T06:00:00.000-07:00

Below are some samples of the work completed by various students for the Integration Project

Part 1:

Part 2:

Video for Part 3:

Work

Call of Duty and Vectors

2011-06-07T06:00:00.000-07:00

I have shown how Call of Duty can be used in Calculus, and here is how it could be used in Vectors.

A student found this video and she demonstrated her knowledge of vectors:

Playing capture the flag, Johnny was camping at a bearing of [043º] and noticed an enemy 52m away running towards Johnny’s flag approx, only 27m away from the flag. What degree does Johnny have to turn to shoot the enemy when he reaches the flag and what is the magnitude of the shot?

Vector one = 52m @ [043º] Vector two = 27m @ [134º]

90-43 = [047º]

134-90 = [044º]

47+44 = 91 = 180 – 91 = [089º]

52^2+27^2-2(52)(27)Cos89 = 58.2

The magnitude of the bullet is going to be 58.2fm.

58.2/Sin 89 = 27/Sin(y)

Sin(89)*27/58.2 = [028º]

johnny is going to have to turn 28º.