Curriculum Redesign

I currently have been to many curriculum redesign talks, symposiums, and discussions and I have never been more excited in my life around educating children in Alberta.  I am truly inspired!! Now of course not all feel this way and so I bring to you "why you should be excited."

First, David Staples from the Edmonton Journal says,

It has had a profound influence, so much so that if you have a child in school after 2016, they will get a fundamentally different education than you got.

This makes me happy.  I am not claiming I received a bad education, but I do feel that I want something better for my own daughter.  Currently we have a model where tests, which are focused on the low level of bloom's taxonomy, are being used rampant throughout our culture.  If you think this should be the norm I bring you a quote from Seth Godin,

As soon as we associate reading a book with taking a test, we've missed the point of literacy

If you are still not convinced that our curriculum needs a change, here is what Jeff Johnson, Alberta's Education Minister, says,

Our [current] packed curriculum stifles creativity in the classroom. It’s too packed. There’s too much stuff to try to get through and it doesn’t allow enough flexibility to individualize learning, which is going to be really key in the future. 

How will the new curriculum work?  Again, David Staples sums it up fairly well when he says,

Teachers will do far less direct instruction so that students can increase their knowledge base. Instead, students will focus on more group and project work. Teachers are to act as guides who assist kids as they explore areas of interest.

Finally, the goal of education will be creativity and innovation and to truly inspire students to learn more.  I think back to my math classes, which I usually finished with 95-100%, was I inspired to become a mathematician, an engineer, a scientist, or even to attend the next level of math?  From some classes yes, but this was due to the excellent teacher I had in front of me, not because of the excellent curriculum. Why did this happen? Well...just to name a few

•  Gr. 3 teachers are having a hard time inspiring students while they teach their 1352 mandated outcomes
• High School Biology teachers are having a hard time bringing in creativity when their curriculum focuses on memorization of terminology.
• Grade 12 teachers are worried around the 50% diploma and finding it hard to bring in innovation to their classrooms.

Since when we can't measure what is important we start making what we measure important.  This is what happened over the last centuries, more and more low level skills became important because that is what we can measure.  Critics, of this change, will use standardized test score data to justify that this change is not excellent for the students in our classes, and my quick response is "how do multiple choice, standardized tests, like PISA show creativity, innovation, interests, and passions of the students?".  See they can't, but they do show how well students can memorize and regurgitate; which is why these critics say these skills are important. 

What does it look like?  Well I have been changing, my own classes, already to meet the needs of the future curriculum and here is a photo which sums it up. 

You can't change the input or the process of education and not expect a different output.  Since the output is different, the way we measure this "new output" must also change.  

Lastly, I ask you...."Were you inspired while you were in school because of what (not who taught) you learned?  Did you want to attend the next level of schooling because of the number of outcomes the teacher covered?  Did you feel that your creativity and innovation was welcomed and could flourish while studying for a 50% diploma?"

If you answered yes to all of these, then maybe I have it wrong and I am simply an anomaly, however if you answered no then I ask you to join me and become inspired with the new curriculum.

References 

http://www.edmontonjournal.com/Staples+Alberta+government+plans+radical+rewrite+education+system/9550676/story.html

http://en.wikipedia.org/wiki/Bloom's_taxonomy

Stop Stealing Dreams, Seth Godin

http://realteachingmeansreallearning.blogspot.ca/2011/03/dont-teach-that-it-is-not-on-test.html
www.education.gov.ab.ca

Repetition in math class

Practice makes perfect! or Perfect Practice makes Perfect!

These, and others, are comments I hear as to why we need practice in math classes.  This "practice" can be seen by worksheets, flash cards, and multiplication tables.  I, however, disagree with this notion.

The problem occurs when we look at what the students are supposedly practicing when they complete the above tasks. 

These tasks promote the idea of efficiency over understanding.  I remember back to when I used to administer "Mad Minutes" (basic questions which have to be completed in a minute or less, and their mark was based on only the ones which were answered correctly.  If a student did not answer it, or did so and was incorrect, this student would lose marks).  On multiple occasions, I saw students writing down numbers which made no sense, simply due to the pressure put on them during this timed exam. 

Of course, how can students complete deep math questions if they don't understand their basics?  Well I have a great story against this...and the main character in this story is me!  I still to this day, 30 years old with a bachelor degree in Mathematics, and 3 courses left in my Masters of Mathematics, cannot recite the multiplication tables.  I struggle deeply with my 7 and 8 times tables.  Does this make me a weak math student?  Does this imply I will not be able to answer deep questions?  I would hope not one person would answer yes to either of these questions.  However, the way I used to assess math, through repetition, would never allow myself to succeed in my own courses. 

If it was not for my own mother, who strongly refused to use flash cards at home, I would probably have grown up hating mathematics.

As a math teacher I needed to understand that the beauty of mathematics does not come from memorization of basic facts, but instead the use of basic facts to solve problems which a person may encounter on a daily basis.  Does understanding basic facts allow for students to solve problems quicker? Of course, but should we judge the quality of answer solely based on the time given?

I have given tasks to my students, some of which are upcoming blog posts, where students have chosen to complete multiple questions, of similar types, to come to a conclusion.  The difference in these tasks, however, is the word "choice".  If we allow students to decide how many problems he/she needs to solve, to demonstrate higher level thinking, then I guarantee your students will start to see the beauty of mathematics as a wonderful, sometimes chaotic, subject which is not limited to solving petty details.

DA with Applications of Derivatives

Here is how I am assessing Applications of Derivatives:

Angry Birds and Calculus

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 Derivatives

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

Samples of work for Integration Project

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

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.  

The math behind the lotto 649

In my Math 30 Applied Class, we had to cover probability.  Instead of using context questions around dice, spinners, and marbles, I allowed students to research any topic they found interesting around probability.  I would like to show you: "The math behind the Lotto 649" by Christine, one of my students.

Many people in the world play the lottery each year. You might believe in faith, chance or luck but I believe in math.  As you already may know, the chances of winning Lotto 6 49 is not very likely. So why do people play? I can’t really answer that question but for those who are sceptical I can convince you on why you shouldn’t play.

The probability of winning the Lotto 6 49 is 1 out of 13,983,816. The probability of losing the Lotto is 13,983,815 out of 13,983,816.

I’m going to make a scenario about a man named Dave who started playing 6 49 at the age of 18 until he was 80 years old. He bought a ticket twice a week. Each ticket consists of two rows, so technically he is playing four times a week. What is the probability of Dave not winning in his life?

Dave played the lotto for 62 years in his life.

There is 52 weeks in a year.

4/week x 52/year x 62 years = 12896

The total amount of times Dave played is 12896.

13983815/13983816 = 0.9999999999999…..

0.99999999999……^12896 = 99.9%

The reason why you shouldn’t play the Lotto 6 49 is that the chance of you not winning is 99.9% in your life time.

How much money would you spend on buying the tickets?

Each line is 2 dollars and you played 12896 which is 25792$.

Using Video Games as Assessment Tools

Here is an article from Jennifer Kotler, and the link to her blog here.


In January, I attended a workshop dedicated to games, assessment and learning hosted by the MacArthur and Gates Foundations and the USC Game Innovation Lab. The workshop brought together game designers, educators, and researchers to work together on designing games around various curricula topics that would be engaging, educational, and contain features to allow for the collection and feedback about how players were faring when engaged in the game. The conversation went beyond what players could learn from games: We also focused on the valuable information we can gather from patterns of game play, such as where players might make errors and the kind of errors players might be making so that either the game or another knowledgeable player can help provide the necessary support to improve game play and therefore, learning.

This kind of thinking always reminds me of math class tests where we were asked to "show our work" so that the teachers could see how we went about solving a particular problem. A wrong answer to a division problem that had more to do with a simple subtraction error is very different from getting the wrong answer because of a fundamental lack of understanding of how to approach the problem. Patterns of responses can provide much more specific information than whether children get the answer right or wrong (as many standardized assessments generally report). Game play data may indeed provide another valuable way to assess patterns of children's understanding in a less threatening way than common testing conditions.

Not only might such games be useful in formal learning situations for assessment, but they might also encourage parents to become more engaged in children's learning. As part of some recent research around Prankster Planet on The Electric Company website that Mindy Brooks wrote about in last month's blog post, we asked parents (about 40 of them) to fill out a survey. The survey included questions about parents' interest in receiving feedback about how well their children were doing on the math and literacy activities within Prankster Planet.

I assumed that perhaps only a third of parents would be interested in receiving information on how well children were doing on the game. Surprisingly, the vast majority of parents (over 70%) said would be very likely to use information about how well their children were doing on the games. Furthermore, even more said they wanted specific feedback as to how to support the activities that the children were doing in the games even more so than general suggestions how to work on math and reading skills with their children. Parents said they would be most receptive to receiving this information through an email (rather than a text message or in a password protected site). This might be a particularly interesting opportunity to engage more parents and provide very specific information about how to extend children's learning based on children's individual game play patterns.

Before we rally for more widespread use of games as assessment tools, we likely need more investigation as to whether scores, errors, and successes in games are indeed highly correlated with the very same things that success on standardized or classroom tests are supposed to predict. Clearly, this assumes that standardized measures or classroom tests are the "gold standard" for information about what children "know" and that, of course, is the topic of much debate. Still, at this point in time, children are often classified or assigned to particular learning interventions based upon standardized assessments.

Games might provide a less "frightening" testing environment. Perhaps games might indeed reduce what Dr. Claude Steele termed "stereotype vulnerability." Girls and children of minority status might do better under conditions that don't seem test-like because they have been unfortunately conditioned to believe that children like them do not do as well as others on academic tests. Games might provide a neutral playing ground as well as reduce test anxiety.

On the other hand, perhaps children take more risks in games that they would not do if they were being tested, which may in fact be what educators encourage, but might interfere with their scores. Furthermore, I have seen situations where some children may actually choose wrong answers every so often just because the wrong answer feedback was funny, or perhaps they were just interested in seeing what would happen with a wrong answer choice.

Nevertheless, games provide a very efficient and engaging way to collect valuable information about performance. To be most useful as an assessment tool, however, game designers should work with educators and experts in assessment to ensure that information is captured in meaningful ways. Using the data in ways to support further learning is critical. Providing additional opportunities to practice skills and expand learning through additional gaming or materials for parents can only help make gaming experiences richer for children.

Assessing Creativity

If you don't think you can't assess creativity, or how do you promote creativity in your classroom, here is a 4 min video to watch.

Au Revoir to old ways of testing

Here is the finale and the solution to the Call of Duty Project.

Wanted to share what occurred in my math class when I challenged the definition of a "test".

Step 1:  Give truly open ended questions:

1)       Illustrate the knowledge of graphing a trigonometric function by using the function, and its first and second derivative.  The function, the first derivative, and the second derivative, when combined, must use at least three different trigonometric functions.

2)      Illustrate the knowledge of displacement and distance covered on a closed interval, using a trigonometric equation for distance.  The function, the first derivative, and the second derivative, when combined, must use at least two different trigonometric functions.

3)      Show a real life application of an angle changing with respect to time.  The use of a video, appropriate measurements and illustrated work must be shown. You must solve for the exact change of the angle at a certain time.

Step 2:

Allow students to use any interest to demonstrate their knowledge

Step 3:

Ensure that the students truly have demonstrated their knowledge about the outcome.

Vectors In Math class

Engaging Lessons on Vectors:

1)  I have created a glog with an embedded YouTube clip illustrating the power of cross winds on planes.  We then discussed the solutions of the two problems, also embedded in the glog.

2)  Next, we talked about heading and bearings with GeoCaching.  I created a scavenger hunt around my school, using the actual blueprints of the school.  The assignment is below.  Each group received a different set of instructions.

 “Find the Apple”.

Get Notre Dame Map draw in the following (Start on the outside left door)

a.       [030^o] for 7 cm.

b.       S10^oE for 5 cm.

c.       [210^o] for 15 cm.

d.      E5^oS 10. 5 cm.

e.       Take the stairs up.

f.       [330^o] for 10 cm.

g.      N60^oE for 9 cm.

h.      [220^o] for 20 cm.

i.        E40^oN for 4 cm.

j.        Take the stairs down.

k.      [020^o] for 8 cm.

l.        [025^o] for 8.5 cm.

m.    Go find the apple with a number 1 on it.

3) My students researched and worked on a real life application of vectors, by measuring the distance across the lake of their choosing.  The project is below.

Math 30 Applied Vector Project

Objective – Students will use vectors to determine the length of an object which can be measured directly.

1.      Using maps.google.ca find a lake for which you will measure the distance across.

2.      Take a screen shot of the lake and enough surrounding area to create two connecting vectors to the opposite side of the lake.

3.      Open Paint and paste the screenshot.  Print off the picture as well as save it to your H: Drive.

4.      On the paper copy, draw two vectors for which the resultant vector will be a vector across the lake.

5.      Determine the magnitude and direction of the resultant vector.  You may not take any measurements across water.  In practicality, your survey equipment would be in one central location, therefore, you may only measure the angles where the two vectors begin; all other angles must be calculated mathematically.

6.      Create a scenario to represent the resultant vector.

7.      Using Prezi, PowerPoint, or any other multimedia tool, illustrate your work.  Show your screenshot, your vectors used, and all work associated.

Here is an example of a student’s work.  **Super cool part… I had students completing short stories in math class on step 6!!!**

Vector Project on Prezi

Twitter for Math Nerds

I took a video from Josh Sundquist, and edited out some information.  This should allow math teachers to use it in their classrooms as they see fit.  FEEL FREE TO TAKE AND USE!

Here is the video:

Here are some questions you can use:

Twitter for Math Nerds:

1.      Determine the amount of whale fails in one year.

2.      Determine:

a.       The amount of followers Lady GaGa will have in 5 years.

b.      Which year the entire world will be following Lady GAGA.

3.      As of May 19^th, 2011, here is a list of certain people and the number of followers

Celebrity	Followers
Lady Gaga	10,183,767
Eminem	4,306,504
Johnny Depp	79,232
Rihanna	5,145,555
Justin Bieber	9,755,964

Determine the mean and standard deviation of people following the celebrities.

4.      Determine:

a.       The standard deviation of the normal curve in the video

b.      Determine the z-score of a tweet reply which is “creepy”.

c.       Determine the probability of a person replying longer than 19 hours.

d.      Mr. Martin, on average, sends out 300 tweets a month.  Determine the number of tweets he would receive a reply to in under 6 hours.

e.       Determine the 95% confidence interval for the twitter curve.

Also, here is a link to the real video

Glogging in Math Class

The results are in and my students absolutely LOVED my new idea around testing.  I have received amazing videos, and my students worked much harder on these three questions, than I have witnessed students work on 30 multiple choice questions.

To further illustrate, beyond the Call of Duty video, below are two other students’ work, and how they chose to demonstrate their learning of derivatives involving trigonometry.  First, here was the “test” question:

Show a real life application of an angle changing with respect to time.  The use of a video, appropriate measurements and illustrated work must be shown. You must solve for the exact change of the angle at a certain time.

Creating not Telling

Many people have shown interest in the "non-traditional" math instruction, here is how I changed how I introduce a concept.
In the past, I taught math by:

1) Put the steps on the board, for which the students will need to know to solve a problem

2) Complete questions of increasing difficulty.

3) Complete a word problem.

4) assign the odds on page XX; next year it would be the evens (my attempt at differentiated assessment)

I found it very strange that I would actually give steps before I have shown the students WHY they would require the steps, or even given them a chance to CREATE the steps themselves.

Here is how I have changed.

These are the steps I took to teach "How to graph a function from an equation"
1) To start, my class and I had a discussion about the importance of seeing a graph of a function. 

2)  While my students sat in groups of 4, I gave them the following question, “If I gave you a function, what would you need to graph the function?”

3)  I gave them 5 minutes to brainstorm all the information needed.

4) We then compiled all the information on the board, and determined whether we would use the function, the 1^st derivative, or the 2^nd derivative for each information.

5) In each group, students then graphed functions that we created as a class.

6) Finally, in groups of 2, each student had to illustrate they understood the steps required to graph a function.

Here is an example of one of the “illustrations”.

Justin Franco & Cory Coupal on Prezi

I truly believe my students can call this learning their own, as they were the ones who CREATED the learning in their mind, as opposed to sitting there and being TOLD what to do.

2 movies about math

Here are two YouTube movies which, through edititng, could become an engaging math problem.

If you would like to use either and can't edit them to fit your needs, please let me know and I can edit or "beep" out certain parts of the movie.


If you do use them, please let me know how so I can share with others.