Sound of music day

I was truly inspired yesterday.  Last night, I went to our school’s play “The Sound of Music”.  My inspiration started with the curtains being drawn back displaying the perfected and detailed set created by Rick Knievel and students.  The inspiration continued with the flawless sounds coming from the pit, conducted by Glen Traquair.  Continuing to motivate me was the seamless direction from Jennifer Warder.

The highlight, however, were the faces of the students showing true satisfaction and fulfillment at the end of the play, while they were showered with applause.  The students’ performance was outstanding and mind-blowing.

Why was this the highlight?

The students were not part of the play for a grade, nor did it help them to improve their performance for an exam.  The set designers did not have to complete hours of redundant homework, but instead spent quality time completing one single project.  The musicians in the pit, who could barely be seen from the audience, had zero extrinsic rewards, but instead the internal satisfaction of a marvelous job done.  Finally, the actors and actresses understood the importance of each word in the play, and the reason behind the execution of each scene.

I ask one simple question, “Why does this only happen in fine art classes?”

Simply put, the students are part of the play because of true intrinsic motivation.  Each student is allowed to work on the part of the play he/she chooses.  This teaching practice should be demonstrated in all classes of school.

 Some have called it a “Fed Ex day”, or an “Artlassian day”, and now I will call it a “Sound of music” day.  I am making an oath to my students:

Before the semester ends, I will give them one “Sound of Music” day, where I will provide them with multiple resources so they can work on WHATEVER they deem necessary.  There will be no limitations, no suggestions, no constraints, but one challenge: Learn something that you have always wanted to know! 

Of course, there will be one requirement of this class; you must be ready to demonstrate the learning that has occurred.  I will not test my students after this day, nor will I require more homework to be done.  This day, will not improve their test scores, it will not improve their mark in my class, nor will it cover a mandated outcome.  “Sound of Music” day will demonstrate what can be accomplished when you put the reins in the students’ hands, and say “Show me where you want to go!”

Math motivation through creative assignments

How do you motivate students to show their best without the use of marks?  The answer to this is very simple; Allow them to complete an assignment in a way such that their creativity, passion, and interests can shine.  Instead of marking this assignment, let them show it off.

Back in elementary school I had “show and tell”.  When it was my day I was allowed to stand in front of the class and show off who I was and tell my class who is the real David Martin (to this day I am still unsure though who I really am ;) ).  My teacher never graded me on this, and I was allowed to bring in anything from home.  How can this activity and true intrinsic motivation be mimicked in other grades?

I wanted to see if “show and tell” could be used in a gr. 12 classroom.  In my calculus class, we were studying functions and how to graph them.  Instead of asking my students to graph a function that had no meaning to them, I asked them to create a drawing (using multiple and piecewise functions) that represented who they truly were.  I was amazed by what I got, and here are some of the pictures:

Before I hear criticism and the stereotype that only calculus students are high achievers, I also gave an assignment about the Alberta winter games to my math 30 applied class.  In the assignment, students were allowed to represent the math in a creative way.   A student used an actual hockey jersey to represent their work.

Why did this work?

Students were asked to create something they can truly call their own and then to present their work to the class.  They were told to inform the class on WHY they drew or created the project they did.  Not only did we learn about math throughout this assignment, but the class also learned a little more about each other.  Students want to be treated as individuals and our assignments should allow this individualization to shine. 

Video compiling ideas about motivation

Here is the video I started my intrinsic motivation presentation with. 

Talk on Intrinsic Motivation

I created and used the following Prezi, http://prezi.com/e2t9cslyzhm6/intrinsic-motivation-with-high-school-math/

Each ** represents advancing to the next part. 

Here is my presentation on Intrinsic Motivation:

**

I have stopped assigning daily required homework to my students.  Over the last 4 years of my teaching career, I assigned daily homework, and at the start of each class I would "check", or assess, the completion of their work.  Every day I would either send home a worksheet, a page out of the textbook, or a task to be completed for next class.

*

Was this excellent practice or malpractice?  When I started to think about it, what I was doing could be considered malpractice.  The students would open their work booklets to the assigned page and I would walk up and down the rows and either give a grade of 100% or 0%.  It is ludicrous to call this true assessment.  I was grading their work ethic more than their actual knowledge of math.  Almost every students' mark was being either inflated or deflated due to their work ethic.

**

Why did I give homework? At first, I had believed that daily homework teaches good work habits and/or develops positive character traits. 

**

After reading the research I have yet to find one piece of evidence that supports this claim. 

**

After reading this I still believed in homework as it gave students more time to master a topic or skill.  I have read reports from researcher Richard C. Anderson that claims "the actual learning that is occurring depends strictly on time spent learning the concept". 

**

However, when Anderson completed further research he found that this claim also turns out to be false. The majority of people that I have encountered that are supporters of daily required homework fail to look at the tasks from the students’ point of view. 

**

Most “drill and practice” assignments actually do the contrary to students’ learning, and actually “drill and kill” any interest to the subject area.   Also, when students are struggling with a concept, asking them to complete questions on this concept will become frustrating and still no actual learning will occur.  I have realized that I need to stop treating my students with the notion that “if I give them more to do, then they will know more”.

**

In my classes, I challenge students in meaningful contexts and provide them with questions that are similar to the ones in class.  I do not require my students to complete these questions, I do not grade these questions, and I do not force my students to do work which is not important to them.  The meaning of the math is what I put as a priority in my class, and homework as second. How can we change this?

**

Here is a worksheet I used to use during class.  The students would follow along and write the answers in.  Students became disengaged.  I was constantly asking students to “pay attention”.  What I failed to realize that these students did not find any value or merit in the assigned task.  Now, at the beginning of class I have created structured review questions for the students work on in collaboration with their group members.  Once completed, I move onto the lesson for which we complete until the end of class.  The next day we start again.

**

Difference; the questions that are given are no longer pseudo-context but actual real life application.  Here is an example of a question I currently use.  First I ask my students about their knowledge of the JFK assassination.  Some talk about conspiracies they may have heard.  Next, the task;

1)      Determine the distance all three bullets travelled before hitting an object

2)      Determine the closest distance the car came to the shooter.

These are two specific outcomes in my Math 20 Pure course.  Before I would give my students the equation of the line and the point from which they had to calculate the distance.  Now, my students must CREATE the line of the car, the co-ordinate system, and label which points are important.  Depending on where you set the origin for your Cartesian Co-Ordinate system the points and equations of the line may differ. 

THIS IS OK! Students need to realize that there isn’t always ONE way to complete a question.  Contrary to popular belief, in math there are multiple paths to an answer.  For this question, there is a “right” answer, and for other questions there may be multiple “right” answers.  This needs to be taught.

DISCUSSION about homework and meaningful tasks

** 

This is what are students are telling us.  They leave their homes and lives, where entertainment and engagement exist readily and enter our schools where we are asking them to “calm down.”  Instead we should be awakening them by challenging their minds.  We can no longer motivate students by carrots and sticks, or grades and consequences.   Asking a student to complete something with the reasons, “I told you so”, or “It will be important later” is no longer motivating students. Students need to have motivation within.

**

To illustrate this let’s take two teachers, who both work in middle class Red Deer:

Ivan – a teacher who is motivated by true intrinsic motivation.  Ivan loves to teach solely to inspire young minds.

Edward – a teacher who is motivated by only extrinsic motivation.  Edward loves to teach for the 2 months off at summer, the pay check, and the honour of calling himself a teacher.

Scenario 1: They are paid $100 000 a year for teaching; a pay which allows them to both live comfortably.  Their administration then offers a 10% (or $10 000) increase in pay if they were to take on extra teaching duties.  Due to their motivations Ivan would say “Yes”, while Edward would decline.

Ivan is agreeing as he is seeing an opportunity to stimulate more young minds.  Edward declines since he does not need the increase in pay to sustain his lifestyle.

Scenario 2: They are paid $30 000 a year; a pay which will NOT allow them to both live comfortably.  Their administration offers the same deal, 10% (or $3 000) increase to take on extra teaching duties.  This time, however, they both accept the deal.

Even though the increase is less this time than in scenario 1, Edward needs the increase to maintain and continue living his lifestyle. 

Teachers need to understand that extrinsic rewards, or carrots, only motivate students to a point.  For some, this point is a 50%, and others it may be a 90%, but there is a mark XX% for every child.

**

I used to believe that this mark was where students would jump from.  They came into my class wanting to achieve AT LEAST that mark, and from there try their hardest.  After watching how students reacted to their marks closely, I found the complete opposite.

**

 Once a student achieves his/her XX%, the learning curve will drop drastically.  To further illustrate this, an actual comment from a student:

“My parents require me to be on the honour roll, which is to have an average of 80% or higher.  Since my mark in this class is an 85%, I can stop trying.”   Students are using their wanted mark as a ceiling for their performance not a floor! This is occurring more often than we realize!  When we start creating classrooms based on learning, and not marks, the paradigm shift will be amazing.  Students will start holding themselves accountable for their learning, and there will no longer be an XX% for which students will maximize their performance at.  We need to start answering the question of “Is this for marks?” with “NO! It is for learning!”

What does guide motivation?

**

Autonomy: students want to be self-directed, and to have control over their own learning.  If you only want compliance from students, then you cannot allow them to be self-directed.  However, self-direction will allow for true engagement to flourish in a classroom.

**

Proof: A software company called Atlassian, out of Australia, does something very unique.  Once, every quarter, they allow their employees to work on whatever they, with whomever they want, and however they want.  They are provided with beer, cake, etc. so as to create a fun environment.  The only catch: whatever you create, fix, or solve, you must show your results.  The company has seen, just in these 24 hours alone, a large array of fixes for existing software, new software, and so on.  “Pure un-diluted autonomy truly works!”

**

Mastery and purpose: Students truly want to get better at tasks they are required to complete.  No one enjoys not knowing, or not being good, at something.   Also, students need to know the WHY part just as much as the HOW.

**

Proof: “People will do things for free, spend time doing it for the fun of it and never expect any reward from it” Most people will shake their head at this statement.  If you are one of those people, look at the site “Wikipedia”.  Here is a site that is created solely on people doing research, spending time reading, and then providing their knowledge FOR FREE.  Look at how many educational blogs there are; people sharing their ideas, thoughts and answers with the world, for no gain at all.  What drives them? “Mastery and contribution”.

**

What does this look like in a high school math class room?  Here is an assignment I once used.  Before giving it, I knew the students were not going to be engaged, so I put some humour “textie bookie”.  Of course this made them laugh a bit, but entertainment does not necessarily mean engagement.  After some thought I realized there is no autonomy here.  I am giving students the price of their house, the mortgage rate and even the years they will amortize the mortgage over.  Since when does this happen?  In life we have choices but in school we are told what to think.  This year, I changed the assignment to this.

**

Start giving questions that don’t just have one right answer.  Instead of giving students information why not just provide them the context but ask them to research the information?  I allowed students to collaborate with others or work alone.  The world was their boundaries.  This time I heard comments such as “WOW! I can’t afford that” or “Geez, never thought it would be that expensive”.  Also, some students informed me of great conversation they had with their parents because of this assignment.  They had autonomy and understood the purpose.

**

Another example from Math 30 Applied; here is a page from our work booklet.  BORING!  I have been to very few places with perfect square blocks, but this is what I gave my students in previous years.  This has now been changed to this:

**

Using the city plan of NY, NY, students were asked to create different paths from an actual location to another actual location on the map.  No longer is this out of context, nor did I say “In case you ever encounter a perfect set of city blocks this how to solve”.  We actually came up with the REAL solution from different points in the city of New York.  Students even challenged other groups from different points.  Again autonomy and purpose!

**

Once we realize that our job should focus around students, and the outcomes, reasons, and justifications surround the student, we will then be promoting learning in schools and not just ranking students.  Students will become intrinsically motivated to complete tasks, not because of marks, but actually due to the fact that they understand the purpose, want to master the task and have autonomy about how to solve it. 

Prime and composite numbers

The Transformation of a math teacher from one who “drilled and killed” to one who engages

Many teachers have commented that I talk a lot about theory but not enough about practicality.  I decided I will start focusing on how I changed my teaching style, through specific lessons, to allow for true engagement with my students.

Prime and composite numbers: The "old" way:
1) I would write the following definitions on the board:

Prime number – a number which has only two factors, 1 and itself

Composite number – a number which has more than 2 factors

2) I would then ask students to classify the following numbers as prime or composite 2, 4, 13….

3) I would then assign questions out of the textbook.

This is how I used to teach the difference between prime and composite.  Students found zero meaning and therefore never reached true engagement during this exercise.  Also, I had to assume that the students understood what a factor was, which usually took more time to redefine that term.   In all my years of teaching and studying mathematics I have never actually used the definitions of prime and composite, but instead required to apply what prime and composite numbers are.  If I, the master of the classroom, have never used the definition, why am I requiring my students to learn it?

This year I scrapped the definition of these two words and taught application and use; here is how:

I gave my students the following problem:

You are planning a wedding and you and your spouse are very particular about seating arrangements.  You can arrange the tables in any way as long as there is the same amount of people at each table.  You have a total of 100 people coming to your wedding, how can you arrange the tables?

(Usually I would start with a small number and increase the difficulty, but this year I have all my students sitting in groups where collaboration is promoted and therefore started with a larger number.)

My students started talking, “25 tables of 4 each, or 4 tables of 25 each, …..”, all groups even generated “1 group of 100 and 100 groups of 1”.  We then discussed reasonable sitting and why 1 group of 100 is unpractical (This discussion needs to occur to fully understand the application of prime and composite).  I then added the following sentence:

Your spouse forgot to invite her favourite uncle, now bringing the total 101.  Describe any problems and solutions.

At first students were confused.  They couldn’t find a number for which 101 could be broken up into.  After some thought, groups were starting to write “101 groups of 1 or 1 group of 101”.  Groups were commenting “I wouldn’t have 101 people; we would need to invite 3 more people so the total is 104 and have 13 tables of 8 each”.  I smiled!

Students understood the difference between these weird numbers that could not be broken up and the other ones where actual application could be used.  I concluded the lesson with the formal terms of prime and composite.

Application should be the focus of math class not formal definitions.  Math has beauty all throughout it, and the more we show off this beauty the more students will become engaged to learn math.

More on intrinsic motivation before extrinsic

An argument to my blog about motivation is “Would you work if you weren’t paid?”  Society needs to understand that extrinsic motivation will only induce and encourage people to a certain point, while intrinsic motivation will provoke and inspire behaviour beyond that point.

To illustrate this let’s take two teachers, who both work in middle class Red Deer:

Ivan – a teacher who is motivated by true intrinsic motivation.  Ivan loves to teach solely to inspire young minds.

Edward – a teacher who is motivated by only extrinsic motivation.  Edward loves to teach for the 2 months off at summer, the pay check, and the honour of calling himself a teacher.

Scenario 1: They are paid $100 000 a year for teaching; a pay which allows them to both live comfortably.  Their administration then offers a 10% (or $10 000) increase in pay if they were to take on extra teaching duties.  Due to their motivations Ivan would say “Yes”, while Edward would decline.

Ivan is agreeing as he is seeing an opportunity to stimulate more young minds.  Edward declines since he does not need the increase in pay to sustain his lifestyle.

Scenario 2: They are paid $30 000 a year; a pay which will NOT allow them to both live comfortably.  Their administration offers the same deal, 10% (or $3 000) increase to take on extra teaching duties.  This time, however, they both accept the deal.

Even though the increase is less this time than in scenario 1, Edward needs the increase to maintain and continue living his lifestyle. 

Teachers need to understand that extrinsic rewards, or carrots, only motivate students to a point.  For some, this point is a 50%, and others it may be a 90%, but there is a mark XX% for every child.  Once a student achieves his/her XX%, the learning curve will drop drastically.  To further illustrate this, an actual comment from a student:

“My parents require me to be on the honour roll, which is to have an average of 80% or higher.  Since my mark in this class is an 85%, I can stop trying”

This is occurring more often than we realize!  When we start creating classrooms based on learning, and not marks, the paradigm shift will be amazing.  Students will start holding themselves accountable for their learning, and there will no longer be an XX% for which students will maximize their performance at.  We need to start answering the question of “Is this for marks?” with “NO! It is for learning!”

Autonomy, mastery and purpose first, carrots and sticks second

“People are not as endlessly manipulable and predictable as you would think”  Most people believe that the more you reward a certain behaviour you will get more of it, while by creating a set of punishments will make you get less of certain behaviour.  This is actually not true!

A study was done with MIT, University of Chicago and Carnegie Mellon, on a large group of people.  The people were given various different tasks from memorizing strings of numbers to physical tasks as shooting a basketball.  Three different sets of monetary rewards were given. 

Level 1 – People who performed pretty well were given a small monetary award.

Level 2 – People who performed medium well were given a medium monetary award.

Level 3 – People who performed at the top were given a large monetary award. (Top prize of $50)

This is truly the system for people who work for commissions, or other monetary incentive systems. 

What was found out?

For the skills that used only mechanical skills, what most would expect was seen, the larger the pay the better the performance.  However, with skills that required even the basic cognitive ability, the larger the pay the WORSE the performance. 

Some could argue that $50 is not enough incentive for a MIT student to perform their best on a task.  To defeat this argument the group then went to Madurai India (Rural India), where the top prize IS actually a significant amount of money.  The prizes now became:

Level 1 – 2 weeks salary

Level 2 – 1 month salary

Level 3 – 2 month salary

Again what was witnessed was, “Higher incentives lead to worse performance”.

Moral of the story:

For simple incentive tasks, rewards work great, but for more complicated and in depth tasks, rewards actually demoralize the ability to complete the task.   If you want a student to have the smallest basis of understanding for a concept, then rewards (or carrots) will work wonders.  When you ask the student to be creative, think critically, or show some cognitive understanding you will not need marks.

This then asks the questions what are the factors for motivation, which the video explains as:

1) Autonomy: students want to be self-directed, and to have control over their own learning.  If you only want compliance from students, then you cannot allow them to be self-directed.  However, self-direction will allow for true engagement to flourish in a classroom.

Proof: A software company called Atlassian, out of Australia, does something very unique.  Once, every quarter, they allow their employees to work on whatever they, with whomever they want, and however they want.  They are provided with beer, cake, etc. so as to create a fun environment.  The only catch: whatever you create, fix, or solve, you must show your results.  The company has seen, just in these 24 hours alone, a large array of fixes for existing software, new software, and so on.  “Pure un-diluted autonomy truly works!”

2) Mastery and purpose: Students truly want to get better at tasks they are required to complete.  No one enjoys not knowing, or not being good, at something. 

Proof: “People will do things for free, spend time doing it for the fun of it and never expect any reward from it” Most people will shake their head at this statement.  If you are one of those people, look at the site “Wikipedia”.  Here is a site that is created solely on people doing research, spending time reading, and then providing their knowledge FOR FREE.  Look at how many educational blogs there are; people sharing their ideas, thoughts and answers with the world, for no gain at all.  What drives them? “Mastery and contribution”.

Educators need to start realizing we are teaching kids and that “carrots” and “sticks” are no longer driving motivation.  Instead, we need to give students autonomy, mastery and purpose.

Intrinsic motivation first, extrinsic second (or even never)

When students are learning due to intrinsic motivation over extrinsic motivation, the learning is far more substantial.   Sadly, most classes are providing students with extrinsic motivators.

Intrinsic motivation is when a student is motivated by internal factors.  Students who are demonstrating intrinsic motivation will be driven to do things “just for the fun of it”, or because they truly believe it is worthwhile to do.

Extrinsic motivation is when a student is motivated by external factors.  Students who are demonstrating this type will be driven to do things because of rewards in a class, such as grades. 

When a student is completing a task because of intrinsic motivation, he/she does not need an explanation to complete it, due to the simple fact that he/she already understands the meaning behind it.  Extrinsic motivation forces the students to complete the task for a reward, and most students will become more interested in the reward than the actual task itself. 

Which is better? Here is some research:

Lepper, Greene and Nisbett (1973) asked two groups of children to do some drawings. One group was promised a 'good player medal' for their work and the other was promised nothing. On a return visit, the groups were given paper and crayons and what they did was observed. The group who had been given the medal for drawing previously spent significantly less this time drawing as compared with the no-reward group.

Most classes are offering external motivators such as rewards (I would even call this bribery) or even threats.  Extrinsic is the “easy way out” to trick a student into learning.  When a class is run this way, the moment you stop giving the reward the learning also stops.   Again some research:

Greene, Sternberg and Lepper (1976) played mathematical games with schoolchildren, which the children seemed to enjoy. After a while, they started giving rewards for success. When they took away the rewards, the children quickly gave up playing the games. 

The explanation was that the children had decided that they were playing for the reward, not for the fun.

Many times I have heard, “If I don’t mark it, they won’t do it!”  My reply; “If they won’t do it, maybe it is not worthwhile for them to do it”.  In education, we need to start relying on true intrinsic motivators and stop providing students with extrinsic motivation.