Wednesday, September 12, 2012

Permutations and Combinations Lesson 7

Review:

Have students work on:

1) If you are arranging 3 different Math texbooks, 4 different Science textbooks, and 5 different English textbooks, how many different ways can you organize them if:
a) the books of the same subject must be together?
b) The shelf must start and end with an English book?
c) How many different ways can you pick 2 books from each subject?

2) Explain why 5C2=5C3?


3) Solve: n+1Cn-1=15

4) How much different monetary amounts can you make from 1 penny, 1 dime, 1 quarter, and 1 dollar?

4) Explain everything you know about the expansion of (x+y)^n.

Body:

1) If you know one row of the Pascal's Triangle is
18285670562881
Determine  the next row.

2) Determine the last term of the expansion (x-2y)^8.

3) Determine the third term of (a/b-2)^9

4) One term in the expansion of (x+a)^8 is 448x^6, determine the value of a.

5) Determine the constant term in the expansion of  (2x-1/x^2)^15

Permuatations and Combinations Lesson 6

Review:

1)Provide students with a pathways problem:
2) Create a word where the number of different arrangements is 8!/(3!5!)
3) If you invited 5 people to your party but forgot to ask them to RSVP, how many different arrangements are possible?

This last question is the key to linking past knowledge to new knowledge.

Next show the video:



Then create a plinko board on the board and ask the students to determine the number of ways for the plinko to fall.  Assuming:
1) The Plinko does not come back up
2) It either falls left or right.
(They should create the first couple of rows of Pascal's triangle)

Create enough rows to row 6 (the answer to the last question in the review).  Rewrite the last row in Combination notation instead of numeral notation.

Next, ask them to expand
(x+y)^0, (x+y)^1..., (x+y)^3.  (They should be getting irritated at this point).

Now, ask if they notice a pattern here...linking the co-efficients to the Pascal's Triangle.
Observations:
(x+y)^n has n+1 terms, uses the n+1 row of the triangle, and will have co-efficients of nC0, nC1,...,nCn

Depending on time you can create the binomial theorem with them or just state it:
tk+1=nCk(x)^(n-k)y^k

Now give them some questions:
Determine the ___ term of the expansion (__+___)^___ , where the blanks can be various numbers and variables.

Monday, September 10, 2012

Perms and Combs Lesson 5

Intro:  **I will now start to mix Perms and Combs together**



The options at Harvey's are:
Tomatoes, lettuce, pickels, hot peppers, onions, ketchup and mustard.  Determine how many different burgers are possible.

In University, some professors allow for choices on their exams.  One specific professor gave 5 questions in Part A, and 4 questions in Part B.  She required the class to complete 2 questions from each part.  Determine the number of arrangements possible. 

On the secon exam, the professor allowed for bonus marks and gave 3 questions in each part, and asked the students to do a minimum of 2 questions in each part.  Determine the number of arrangements.

In the class there were 28 people, 15 men and 13 women.  If the professor wanted to choose a president and vice president from both the men and women, determine the number of arrangements possible. 

Lastly, out of the whole class, up to 3 had to be selected to be on the Dean's survey group.  Determine the number of possible arrangements.

Body:  Algebra with Combinations:

1) Solve for n:
a)2(nC2)=n+1C3


b) 720(nC5)=n+1P5

2) Explain why 8C3 = 8C5.





Friday, September 7, 2012

Permutations and Combinations Lesson 4

Review:  Provide students with the following images, and explain the following:


Oreos have evolved largely over the last years, and now have many different types of cookies.  The pictures show only some of the option available to consumers these days. 
The pictures show:
  • Chocolate or Vanilla flavoured cookies
  • Strawberry, Chocolate, or Vanilla fillings
  • A single layer, a double layer, or double layer with an additional cookie in between.
Since I cannot find any Oreo's with a different kind of cookie throughout, we shall assume all the cookies used have to be the same.  Determine the total number of different Oreo's which could be created.
 
Body:
 
Provide students each with the following diagram
Ask them to determine the number of paths from various corners to other corners. **This might take some struggling...but let them struggle!**. Start with points close then further and further away. Leading them towards solving it by which ever method you prefer to teach.
Provide them with different paths and restrictions such as must start at XX go through XX and end up at XX.
 
Now introduce Combinations.  In the recent Olympics, 8 men ran the 100m in the Final medal Race.  First place recieved Gold, Second place recieved Silver, Third placed recieved Bronze.  Determine the number of different ways the men could have placed.
 
Before the Finals there were heats were only the top 3 times in each heat would advance to the next level.  If in the first heat, there were 8 men running, determine the number of different combination of men who could advance to the next round.
 
After the race, the men shake hands to congratulate each other.  Determine the total number of handshakes for the 8 men. 
 
Give students time to work together and lead them towards the idea, and then eventually explain, that when order DOES not make a difference, the number of combinations are
n!/(n-r)!r!
 
Permutations - order makes a difference - n!/(n-r)!
Combinations - order does not make a difference - n!/(n-r)!r!
 
How many different sums of money can you make with $5, $10, a penny, and a dime?

Thursday, September 6, 2012

Permutations and Combinations Lesson 3

Intro:  I would play this movie to catch the attention:



Review of previously learned material consists of the following problems:  ***You will have to decide how many people are lining up and how many are men/women together as a class**

1)  In the video how many different ways can the people line up with
a) no restrictions
b) The men behind the women.
c) the women standing together
d) the women aren't standing together

2) Later, 3 cab drivers pull up simultaneously.  Determine the number of distinct permutations you could have if each person travels alone.

3) The next day, 2 cabs pull up and there are 30 different ways they can drive the number of people present with one person in each cab.  Determine the number of people waiting in line.

4) How many different possible values of r could there be if we were calculating 8Pr?

Go through the questions, after giving some time for the students to work on them cooperatively.

Body:
 
A thief was trying to break into a keypad and he sprayed it with Luminol.  A chemical which brightens when it comes into contact with the oils left by a finger.  He noticed that there were a fingerprint on the number 2 and 7, and two fingerprints on the number 4.  How many different possibilities are there for the code to the safe?

Let students work and struggle through, and lead them towards the identity of:

Organizing a objects where there are n repetitions of one object, there are a!/n! distinct permutations.
 
Questions:
1) Hertz Rental Cars has 3 identical SUVs, 5 identical cars, and 6 identical trucks.  Determine the number of arrangements Hertz can have using all their vehicles.
2) How many PIN numbers can you create if they must be 5 digits long where 3 digits must be the same?
3) Create a scenario where you would calculate 8!/(3!2!) to arrive at the solution.
 
 
 
 


Wednesday, September 5, 2012

Science and Religion

2

I used to believe there was a dichotomy between science and religion. It seemed in the past, that when science could not explain why something was true, we turned to religion and simply attributed to God. There have also been arguments against the existence of a God,

from The problem of Evil to Michael Martins proof, A Disproof of Gods Existence. Even after growing up in a Catholic home, I believed that one person was either religious or logical and scientific, but not both; a Venn-diagram with no overlap. 8 years ago, this all changed when I started teaching at Notre Dame; a Catholic high school. When I make references to Church and Religion, I will be referring to the Catholic Church.

Once I started working at Notre Dame, I met many Catholic Science teachers and was shown that you can be a Catholic logical thinker. My eyes were opened to the reality that this Venn-Diagram does have an overlap. I believe, like others in the past, I did not understand the implications that Religion has on Science and also how Science impacts Religion. I will show, through my own stories how Science and Religion can, and do, coexist.

When I first started teaching Science, I was worried I would go against the teachings of the Church when I started to address the age of our Planet. Before, I took the literal sense of the Word in the book of Genesis which stated that the Earth was formed in six days, some 6000 years ago. Science has shown that the Universe is around 15 Billion years old. An obvious contradiction! After some research, on how I will address this in my Science Class, I read Frank Sheed (1982) say

"one shouldnt be forced to choose between evolution and creation."

and he continues on to say that
"Creation answers the question why does everything exist, why there isnt nothing? While evolution, is a theory, as to how come the Universe did develop once it existed." (Pg. 58)

As well, when Genesis was written, humanity did not fully understand the workings of the universe and these six days just corresponded with the Babylonian creation myth Enuma Elish, and does not really mean God created the Earth in six day at all. Religion now fully accepts the fact the Earth is not 6000 years old and that uses science to determine when God created the Universe
One discussion which arose in my class was around the idea of evolution for Apes versus the creation of humans by God. Again, before looking deeper I believed these were two contradictory ideas, but instead they are not. The Church has said it is not against the idea of evolution, and in fact evolution exists in our current era (Some people will not grow molars), and that the evolution of the body is an almost certain fact. However, religion teaches us that the soul, in which is inside our body, was not the result of any certain evolution but instead infused by God Himself; again not contradictory, but two theories from the same thread of truth.

Due to the limit of words I will not go further into detail, but science and religion also agree on when life starts, how pre maritial sex will lead to increased divorce rates, and many other theories. Science and religion are both logical, deal with science and fact, and truthfully it is
because of Science that my faith is strong.

Permutations and Combinations Lesson 2

Students will learn how to apply the Fundamental Counting Princple with restrictions and Permutations.

Intro: Show the following video:

Since there is an abundant amount of different ways these books are arranged, simply ask
"How would we determine the total number of ways the book shelf could be arranged?"

Next ask

"What would we need to know?"

After some discussion, show the picture of the top left shelf as seen below:

Then I would ask the following questions:
 
1) How many different ways can these books be arranged, if the spine of the book must be facing out, and:
a)  The shelf will only have 4 books and a pink book must be on each end?
b) The shelf will only have 8 books the pink books must be next to each other?
c) All books are on the shelf with no restrictions?
 
The last question is there to assist with introducing factorial notation.
 
Explain that: "!" is the symbol for factorial notation and can be used on any non-negative integer n.  The formal defintion is:
n!=n(n-1)(n-2)(n-3)...(3)(2)(1)
As well as how to get use it on the calculator.
 
I would then go through operations on factorials showing that (n!)(x!) does not equal (nx)! nor does it hold for any other operation.  As well that 0! = 1
 
Next ask for the previous picture:
2) How many different ways can you arrange the books on the shelf if you only want:
a) 4 books on the shelf?
b) 7 books on the shelf?
c) 13 books on the shelf?
 
Using the process, you can introduce nPr, and how the previous answers can be solved with n!/(n-r)!, with guiding the students towards this answer.
 
The formal definition being:
When permutating n objects picking r at a time we would write nPr = n!/(n-r)!
 
 
Ask the students how many diffeerent ways to arrange the letter FILE, then FILL, then FLLL, then LLLL.
 
Let students work and struggle through, and lead them towards the identity of:
 
Organizing a objects where there are n repetitions of one object, there are a!/n! distinct permutations. 
 
From here I have yet to find real life scenarios and would give various questions and words to rearrange such as MISSISSIPPI. (Would love ideas here if you have any...)
 
 
 
 

Tuesday, September 4, 2012

Permutations and Combinations Lesson 1

Here is my lesson plan for my first lesson in Math 30-1 on Permutations and Combinations. Which covers the outcome: Apply the fundamental counting principle to solve problems.

(My students sit in groups of 4 and 5)

First show the following funny video,


Next, show this video:


After which, ask the question "How many different possible pin numbers could there be?"

Give the students about 2-3 minutes to discuss and then re-ask the last question
"Is there any more information you need?"

This is where you can go in any direction you please.  In my lesson, the gentleman in the movie has either a 4 or 5 digit PIN number (we don't know).

Now allow students to work for approximately 10 minutes.

After this is done, ask the class:

How did you arrive at your number?  Here I would actually have students come up and solve on the board

What assumptions did you make?

Is there a way we could arrive at the answer more efficiently?

Take this time to discuss that you should multiply the different possibilities of having a 5 digit pin, and the possibilities of having a 4 digit pin, and then you should ADD these answers together.

Next show the students the following picture of a hand knit mitten, and explain the following:

Jennifer makes this mitten out of four different parts, the fabric of the entire mitten, the middle "tree or leaf" part, the bead, and the strings which tie them together, and has multiple different colours for each part.

Then ask: How many different mittens can Jennifer make?

I would let students talk as long as they needed until they realized they are missing a lot of vital information.  Ask for any questions or information they might need (just like the previous question) and provide them with the following: (You can change as you see fit)

5 different colours of yarn for the mitten
3 different tree/leaf colours
2 different beads
5 different colours for the string.

Give time to solve and then ask


How did you arrive at your number?  Here I would actually have students come up and solve on the board

What assumptions did you make?

Is there a way we could arrive at the answer more efficiently?

Next, you can go the link https://order.bostonpizza.com/EN#content=/Menu/ViewMenu/&CategoryItemsContainer=/Menu/CategoryGroup/dfa5509b-935b-4776-b157-bfefef2ab654

Which shows that Boston Pizza currently has 4 different types of wings with 21 different flavours of each type of wing.

The problem:  Red Deer Rebels (or whichever local hockey team you want) is having dinner and orders 8 different double orders of chicken wings, how many different combinations could there be?

Again, using the same process students will need to know if you can have more than 1 flavour, and you can have up to 2 flavours PER double order, or they could be the same flavour as well.

After, ask the three crucial questions again, with some leading if needed.

If you have more time I would ask the following question:

Should Alberta, currently, be concerned with the number of phone numbers in the province and truly needed to add the 3rd area code (587)?

Following the same procedure of asking if they require more information and then the three crucial questions of debrief.







Friday, August 31, 2012

What kind of Learner are you?

Here is a wicked visual about "What type of learner are you" from OnlineCollege.org

What Type of Learner Are You?
Compiled By: OnlineCollege.org

Thursday, August 30, 2012

How my Dog taught me about Math


Over the summer, my wife and I adopted a puppy found in a local dumpster.  After reading about 3 or 4 books I decided I was going to teach my dog how to sit, stay, roll over, bark and……mathematics.  

How do you teach a dog math?

Very easy, but first you have to teach your dog how to bark.  Once this is done, I have trained my dog to bark twice every time I say "One plus one".  She barks three times when I say "Two plus one".  Lastly, I have trained her to remain silent when I say "Four times zero".

She understands math correct?

Before an argument is started, I do not believe she truly understand math, but only has memorized mathematical commands.  I wonder how many students go through math class with the knowledge similar to my dog; memorized facts, but has very little understanding.  

Years ago, my class was set up in a way that I was training dogs, not teaching students.  I would give students questions out of context, assign redundant homework, and lastly reward speed and repetition with marks.  My dog has taught me a more valuable lesson than I could ever provide to her; there is a large difference between memorization and knowledge.

Wednesday, July 11, 2012

Cartesian Co-Ordinate System


When teaching about the Cartesian Co-ordinate system I fear that most teachers focus on the how and not enough on the why. The how is taught, traditionally, by the teacher showing the students two number lines, perpendicular to each other, labeling the intersection of the lines (0,0) and then labeling the positive and negative x and y axes. After, the students are then given many different points to label, of varying difficulty, and then given a word problem. The lesson ends with the students working on page XX and completing either the odds or the evens.

This method, I believe, does not allow the students to understand why the Cartesian Co-ordinate system is extremely valuable. Here is how I introduce this concept:

Breaking the class up into groups of 4, each group then picks a wall in my classroom, or in the hallway. Each group of 4 is then divided up into two pairs of 2, and one pair remains at the wall, while the other pair leaves the wall for 5 minutes. I then walk to each wall and point to a particular section on the wall and leave an erasable mark on it. The following task is then given to the pair of students who are waiting at the wall:

You must create a set of instructions, which you leave at your wall, for the other 2 students to read. These instructions can include whatever you would like but the goal of the instructions is to assist your other group members in finding the point. Once you complete your instructions you are to take a picture of the wall, with the mark showing, and then erase the mark.


I supply my students with flipcams, ipods, and iPads to take the picture.

Once this part is complete, the other 2 students are to return, read the instructions and make a mark of their own. Their mark and the picture is then compared. Afterward we do some debriefing as a class. I ask for groups read their instructions, and share on why their instructions worked or didn't work. Every single time I have done this with my class I always get the same remark:

We need some sort of similar explanation which we all understand before hand


It is only then that I introduce the Cartesian co-oridinate system and tell this story:

Some mathematics historians claim it may be that Descartes's inspiration for the coordinate system was due to his lifelong habit of staying late in bed. According to some accounts, one morning Descartes noticed a fly walking across the ceiling of his bedroom. As he watched the fly, Descartes began to think of how the fly's path could be described without actually tracing its path. His further reflections about describing a path by means of mathematics led to La GĂ©ometrie and Descartes's invention of coordinate geometry.


Thursday, June 28, 2012

Criteria for Implementing Flipped Instruction

This is from Ivan Hannel and can be found through ivan@k12workshops.com

 
Today's learners are in a unique and enviable position. Their universe of available knowledge is nearly unconstrained. The Internet gives them access to an immeasurable amount of information, instantly received at a very low cost or free. The educator in each of us sees the potential here to vastly accelerate student learning. Developing some criteria that may help to guide this transformation in terms of classroom instruction is a good starting point.


The "flipped classroom" is the moniker given to a construct for making better use of students' new and remarkable access to information. In the flipped classroom, direct instruction is the gambit of the home, while the classroom is the time for what we might call coached instruction or guided practice.


The basic idea is that the traditional stream of direct instruction-often a lecture--is reassigned to students as homework to be viewed via video or guided animation or podcast on the student's own time. The teacher then uses the next day's in-class time to coach students individually, ask and answer questions, conduct experiments, deepen the learning or otherwise do everything but lecture.


Until recently, high quality online lectures covering the grounds of K-12 education were hard to find. But websites like Kahn Academy and many others have tackled that ambitious task. You can find impressive videos on almost any strand of instruction you can think of.


As schools consider the flipped instruction model, what criteria might be used to determine what should be required of the direction instruction and the coaching component? Put another way, how do we know that the video is going to work for our students and what are we going to do after that? 


Because there is no definitive framework for the flipped classroom, feel free to amend or enhance these suggested criteria with ones of your own.


Direct Instruction
Below, I refer mostly to "video" as the format used in the direct instruction. But I do so just for the sake of convenience and recognize that the direct instruction may have many different formats. When thinking of the direction instruction, we should ask does the video?
__ Cover the content
The video must of course address the material described in the curriculum and do so in a way that is comprehensive and accurate.


__ Describe and organize the learning
Even if the information in the direct instruction is comprehensive, many videos don't frame the learning for the learner at the start. The author may assume the student "knows where they are." Does the author put things in context and tell the student what they are going to learn in the video and/or what is prerequisite?
__ Scaffold the concepts or skills to be learned
A video that covers the information in terms of the content but does not scaffold the actual learning during the video may not help the learner to actually learn. The content, concepts and underlying skills must be organized so that the learning builds up. This is essentially a question about ordering.

__ Allow for discussion amongst other learners
Learners often can help each other through forums. Is there a way for learners to ask and answer each other's questions on the same site where they receive the video?

__ Frame the learning in different ways
Does the author represent the information in different ways or perspectives? If there are multiple approaches to the content, does the author explain or address those alternatives?

__ Help the learner to self-assess
Some authors provide both the direct instruction and quizzes to help the learner know whether s/he has mastered the content at relevant times. Can the learner do a self-check for understanding?

__ Engage the learner
Ultimately, our hope is that the very best of direct instruction is what the student receives-the most interesting teacher teaching in the most interesting way. Will this author's video interest the student?

The Coaching instruction

The coaching instruction is the art of teaching. This is when the teacher actually works with students one-on-one to reinforce or hopefully enhance what was learned in the direct instruction. Because there are so many ways of doing this, from asking questions to creating experiments to dramatizing events to revising essays, there isn't a set of criteria to address every form of coaching. But there is one thing that should remain true of all coaching instruction: The teacher should strive to construct mediated learning experiences (MLE) with students during the coaching component.


The term MLE is attributed to Dr. Reuven Feuerstein of Israel, a psychologist, educator, and student of Jean Piaget. During an MLE, the role of the teacher is to stand between the learner and the underlying content and continually filter, frame, focus and guide the cognitive acts of the learner until he or she has reached understanding.
The teacher should:
___ Present himself or herself as exploring the content with rather than to the learner
___ Intend to teach not just the content but the underlying cognitive skills that underlie its acquisition
___ Help the learner evaluate his or her own learning
___ Bridge what was learned to other uses.

MLEs place a premium on the idea of engagement between teacher and learner rather than placing a primacy on the delivery of content itself. The opportunities for MLEs with the individual student are far fewer during a lecture, when the primary objective is often simply to present the content to all.

The flipped classroom thus places a premium on the capacity of teachers to create MLE's more so than being master-presenters of the underlying content. 


Creating MLEs is the part of teaching most congruent with our hope for individualized student learning. It allows lecture and other direct instruction to be outsourced to the proverbial Einstein's of lecture, while giving the classroom teacher time to bring his or her teaching skill to meet the immediate needs of the individual student.


The concept of the flipped classroom will be fleshed out over time. It will be most interesting to see how the incredible breadth of the Internet may be combined with the particular skills of teachers to enhance our students' educational futures.

Wednesday, June 27, 2012

Nine Dangerous Things You Were Taught In School

Originally from http://finance.yahoo.com/news/nine-dangerous-things-you-were-taught-in-school.html

Dangerous things you were taught in school:

1. The people in charge have all the answers.

That’s why they are so wealthy and happy and healthy and powerful—ask any teacher.

 

2. Learning ends when you leave the classroom.
Your fort building, trail forging, frog catching, friend making, game playing, and drawing won’t earn you any extra credit. Just watch TV.




[More from Forbes.com: The Six Enemies of Greatness (and Happiness)]



3. The best and brightest follow the rules.
You will be rewarded for your subordination, just not as much as your superiors, who, of course, have their own rules.




 

4. What the books say is always true.
Now go read your creationism chapter. There will be a test.




5. There is a very clear, single path to success.
It’s called college. Everyone can join the top 1% if they do well enough in school and ignore the basic math problem inherent in that idea.




[More from Forbes.com: Why Weird is Wonderful (and Bankable)]



6. Behaving yourself is as important as getting good marks.
Whistle-blowing, questioning the status quo, and thinking your own thoughts are no-nos. Be quiet and get back on the assembly line.




7. Standardized tests measure your value.
By value, I’m talking about future earning potential, not anything else that might have other kinds of value.




8. Days off are always more fun than sitting in the classroom.
You are trained from a young age to base your life around dribbles of allocated vacation. Be grateful for them.




[Related: Is Going to College Worth It?]

9. The purpose of your education is your future career.
And so you will be taught to be a good worker. You have to teach yourself how to be something more.




Wednesday, June 6, 2012

Integration and Geogebra

I gave the following as my integration unit exam.  I have to thank Bowman Dickson @bowmanimal, his blog is http://bowmandickson.com/, for giving me the instructions and project with the geogebra.  Below is the assignment as well as some of the pictures I recieved.

Integration Project

1.      Create an equation for the velocity of a particle at any time t, stating the initial position, which cannot equal 0.  The equation must include all of:

·         A polynomial function

·         Rational function –Chain rule must be applied

·         Trigonometric function

a.       Determine, using appropriate sums of rectangles, an over and under estimation of the displacement of the particle in the first 10 seconds.

                                                              i.      Explain how this estimation could be made more exact.

b.      Determine the exact displacement of the particle for the first 10 seconds, and then determine the exact location of the particle after 10 seconds.

c.       Determine the average acceleration of the particle from 0.  Illustrate how your answer could have been determined by the graphs.



2.      Complete a picture using geogebra with at least 5 areas calculated by hand.
Examples of the pictures



 And here is what one looks like after the lines are removed.

Instructions for Geogebra:


Friday, May 4, 2012

Calculus Speed trap


Catching speeders from our math class

Instead of using a worksheet, or pseudo-context question from a textbook you can show how related rates can be used to estimate the speed of a car from our classroom window.

1)      I used the Distmeasure app to determine the distance my classroom window is from the road.


2)      A student extended his arm and followed a car with arm until it hit a 45 degree angle.  Different students timed how long it took and we averaged the times.  [This will allow us to calculate the average rate of change of his arm in radians/second] in our class this took 4.6 seconds, as the following:


3)      Perform the calculations below
Since we know that student stopped at 45 degrees we can use the special triangle of 45/45/90 to substitute into the above formula.

We can then deduce that car is speeding through the school zone.


4)      Talk about the limitations of this activity, and how accurate this is.

Wednesday, May 2, 2012

Changing Assessment Presentation

I am putting on a session called "Globablization of Assessment" Below is my presentation and talking points:


My Talking points:

Math teachers indicated that they rely on a textbook for more than 80% of their teaching and most math teachers (at least 60%) reported that their instruction is quite similar to textbook tests. – Center for the study of testing, evaluation, and education policy.

Mayor of New Jersey strongly backed the pedagogical approach of using “constant drill and repetition” and even said “It is not that hard to give answers if someone just told you what to say.  They memorize back and know and get used to a lot of A’s on quizzes”  But when asked if he would send his own children to this type of school, he answered “no, those schools are best only for certain children”.

Imagine the difference between your child running home and saying “I had a great day because I got an A, got the highest mark in the class, won the math challenge” or saying “I know understand how to reduce fractions, multiply two digit numbers, or argue critically”.  One is saying learning is a means while the other is regarding learning as an end.

Research has shown that an overemphasis on achievement:

1)      Undermines students interest in learning

2)      Makes failure overwhelming

3)      Leads students to avoid challenging themselves

4)      Reduces the quality of learning

5)      Invites students to think about how smart they are instead of how hard they tried.

When we get carried away with results, we wind up, paradoxically, with results that are less than ideal.  Evidence has shown that our ideal long term goals for our children and students are less likely to become reality when the education system and its stakeholders become preoccupied with standards and achievement.

If the point of school is to achieve and demonstrate success instead of stretch your thinking and be challenged, then it is completely logical that a child will always take the easiest route; sometimes the unethical easier route.

501 mothers were questioned and more preferred their children to complete projects that would involve less struggling but result in success than those where their children would learn a lot more, struggle through it, and could potentially make a lot of mistakes.  Is this right?

Candle project – rewards slowed down the thinking.

The probability of getting a reward has the same brain action as someone who is addicted to drugs.  Rewards promote just as much bad behaviour as good ones.

People of different abilities tend to learn more effectively on a range of tasks when they’re able to cooperate with one another than when they are trying to defeat one another.

Grades divert attention from education itself and otherwise prove counterproductive.  They also do not provide accurate and reliable information.

Interesting studies:

When teachers use hands-on interactive learning activities, students who were not graded at all did just as well on a proficiency exam as those who were.  Students who attended elementary schools where no grades were used matched a sample of students who had received traditional report cards for 6 years.  5th graders who were told they would be graded on how well they remembered the social studies curriculum had more trouble understanding the main point of the text than did those who were told no grades will be used.  Even on strict recall the graded group remembered less.

Studies have shown over and over the more creative the task the worse of the performance of students when grades are used.  Only when comments are given, instead of numerical scores, will the learning increase.  Ruth Butler’s experiment
Tests and grades may make students learn today but will they may not want to tomorrow

Monday, April 30, 2012

Session: Globalization of Assessment

On Wednesday, May 2nd, I am speaking, in Spruce Grove Alberta, on the needed change of assessment, below is the title and some information.

Globalization of Assessment

The economy has drastically changed and now the education system needs to change how it is preparing students for the world outside the walls of the classroom. Traditional assessment and instructional techniques are preparing students for the traditional world not the current one. Education cannot keep doing what it has always been doing and expect a different outcome.
Presented by David Martin

Dave has been teaching High School Mathematics for 5 years. He is currently teaching Calculus, but has taught both Junior High and High School Math. Recently, Dave was nominated for Alberta Teacher of Excellence in the field of technology innovation. At one point in time, Dave used worksheets, tests and homework to motivate students to learn math, however, currently he has outlawed all three in his classroom.

Dave is currently teaching at Notre Dame High School in Red Deer, Alberta. Dave graduated from the University of Lethbridge with a degree in both Mathematics and Education, and is currently taking his Masters of Mathematics Education through the University of Waterloo. He has spoken at events throughout Alberta, sharing his message of how he is moving away from traditional assessments and towards an approach where he instructs through his assessments and how learning is always the focus.

At the Horizon Stage in Spruce Grove

Wednesday May 2, 2012 7-8:15pm
Doors open at 6:45
No ticket required

Wednesday, April 25, 2012

Math and Super Mario Brothers

Usually I would hand out a worksheet on calculating when a function is closest to a point and have students complete 10-12 questions.  This year, I took the a different approach by bringing Super Mario Brothers in my class.

Using this picture,
I informed my class about Mario Brothers; when you jump, with Yoshi, you can jump again.  I then posed the question, "When would be the best time to jump off Yoshi if you want to get to the top level?"

Using Calculus, and geogebra you can calculate the path of Yoshi and the co-ordinate of the top level to get:

From here we calculated the equation of the parabola, and a distance function based on any point (x, f(x)) on the function.  Ultimately, we calculated the closest distance Yoshi comes to the point, and when to double jump to get the coin.
Students enjoyed this more than completing the 10 questions on the worksheet.  Feel free to use and fix as you see fit.

Monday, April 23, 2012

Why do teachers bargain?

Teachers are not fighting for higher pay, we are fighting for creating the conditions for best professional practice. These include:
  • Class size and composition
  • Hours of instruction and other assigned duties
  • Inclusion requirements
  • Pay
  • Benefits
  • Leaves
  • Professional Development
  • Hiring and Tenure
Our fighting is not about working less but instead we are asking for more control around our hours of work.  When teachers come to the table asking for anything, we are simply asking for the best conditions that will ensure the best quality of practice, that will ultimately allow for teachers to use their skills to the best of their ability to the children in the seats in front of them. 

The simple truth is the working conditions of the teachers is the exact same as the learning conditions of the students.

Saturday, April 21, 2012

7 Reasons why not to use Grades in School

1) Truly extinguishes intrinsic motivation.

2) Actually diminishes performance.

3) Crushes creativity

4) Overcrowds good behaviour

5) Encourages cheating and other unethical behaviour

6) Will cause addictive behaviour

7) Fosters short term thinking.

Enough said.

Friday, April 20, 2012

10 Reasons why not to Vote for Wild Rose

In Red Deer, I have heard multiple speeches from the Wild Rose and I have now compiled my TOP 10 WHY NOT TO VOTE FOR Wild Rose.
1)      Using “Danny Dollars”, they will drive the economy of Alberta back in time instead of forwards.

2)      The leader, Danielle Smith, has very little elected political experience, aside from being on the Calgary school Board in her 20s, before all of its members were fired by the education minister.

3)      In Education, they have the mentallity that to prepare students for the tests of life, they should write many many tests in schools.  This will take time away from real learning.

4)      One candidate, Ron Leech, believes, due to being Caucasian, can be speak to all of the community.

5)      In their platform, Wild Rose has a “wait time guarantee”, but this potentially will just open the door to more private health care, which the leader supports greatly,

6)       The leader, Danielle Smith, cancels interviews and is becoming increasingly inaccessible to media.

7)       Wild Rose wants K-12 standardized testing, that will ultimately put real deep learning on the list in schools.

8)      Wild Rose is supporter of Merit Pay in education, and here is the problem with that.

9)       Wild Rose wants to advance private-property rights, which is a hallmark of the Fraser institute thinking.  This would allow Smith to freeze private land for public purposes.

10)    Still not convinced; just wait a day and you will have another reason based on a blog or a comment from one of the Wild Rose Canidates.