Dave Martin on how to teach math

Take 7 minutes and listen to my friend and colleague Dave Martin talk about math:

Dave backs up this interview with tons of examples from his class room on his blog.

Should Albertans panic about math?

This was written by Dave Martin who is high school math teacher in Red Deer. He blogs here and tweets here. This post was originally found here.

by Dave Martin

Edmonton Journal's David Staples has been writing about

Grade inflation and flex time harm education, high school teacher warns

and

Alberta schools are no longer the best

and most recently,

Students ‘cheated’ by way math is taught, say educators and parents

If you read all these articles, you will notice one important commonality...Staples refuses to write about the "other side" of the story. Thus I offer a view from another David.

I invite you to read his articles to see one side, and then read below to see the other.

First, Staples wrote:

It’s common for students to get much higher marks in their classroom than they get on their diploma exams...the number of EPSB students who have been graded as “excellent” or “acceptable” on province wide diploma exams has dropped by 1.9 per cent. In the classroom, however, the number who have been graded “excellent” or “acceptable” has gone up by seven per cent.

He creates an idea that this should not be the norm and the teacher mark should be the same on the diploma. This is great in theory, but before you nod your head I ask you to remember some minor details:

• The teacher spends almost 5 months with your child, while the diploma spends 3 hours. 
• The teacher has met, talked, and learned about the interests of your child, while the diploma was made in an office by people who have, most likely, never met your child. 
• Your child is allowed to use real word devices, such as Dictionaries, Apps, Blogs, Web Articles, etc, in the classroom, while the diploma creates a false sense that knowledge is only valuable if you can memorize it, not apply it.
• Lastly, because Staples writes about the Math diploma, the teacher gives various types of questions, in various formats, in various ways to your child, while the diploma only asks Multiple Choice and Numerical Response.

Now I ask, which mark should have more merit? I pose a different problem... Why is the diploma mark lower than the mark given by the teacher? Isn't it time we change our standardized assessment strategies?

Next, Staples writes:

Alberta students used to be ranked at the top of the world academically, but they are sliding...In 2000, Alberta ranked top worldwide in reading, third overall in science and math. Our teachers and curriculum were top notch and our accountability, through provincial exams, was state-of-the-art....Since then, however, Alberta has steadily dropped. This week when the 2012 PISA results came out, we ranked 11th in math, fifth in reading and fourth in science... 

First, I don't believe we can put our faith in a two-hour exam, as my arguments from above still stand, however lets go beyond that.

Staples will have you believe that this drop is due to the fact that the math curriculum has changed, and even that we need better teachers in the classrooms to be educating your child. When I read this, I remember back to my Science class when we learned about constant, dependent, and independent variables.

Before we go witch hunting on the teachers, lets remember that these teachers are the same ones who were instructing in 2000. Unless I am unaware, the graduation requirements to become a teacher in 2000 are the same as they are now. Thus, teachers would be the constant variable in this. Now that we can't blame teachers, we can ask what changed?

Sure the math curriculum changed, but was there more? Class sizes over the last year have also increased, funding of AISI projects have been reduced to 0. I don't understand how if more than one thing has changed (independent variables), how can we point our finger to one of them and ignore the rest?

My last debate comes from the fact that Staples will have you believe that because we don't teach memorization of math facts students won't understand math.

The reality is that being told number facts, and forced to regurgitate these facts, will not create an environment which is conducive to deeper learning. The best way a student can understand, not just recite, mathematics is through discovering the facts on their own. For some, this discovery process can take seconds, while for others it may take an entire class. The role the teacher plays in this is by acting as a tour guide. By keeping the students on the “path” towards the discovery, it will ensure that all students create their own individual, and innovative, techniques in learning mathematics.

I often ask myself, which skills do I want for my own children? Do I want them to be taught the skills to memorize, and ultimately be able to complete algorithmic tasks, or the ability to create and design which will lead them down a road towards a career with heuristic tasks?

The reality is that the age old saying that “Practice makes perfect”, does not apply to deep learning in mathematics. Traditionally, students have been given worksheets which have multiplication facts on them and are given a strict time limit to complete these (named Mad Minutes), but in actuality the mark given on these “Mad” sheets really does not indicate to anyone as to knowledge of the student writing them.

The weak students truly suffer the most from this model of proficiency-driven, because they find these tasks dull, repetitive, and entirely unusable in the world outside the walls of the classroom. I would agree that sometimes, knowing facts as the days of the week are important, but these facts should be a by-product of use and application not out of necessity.

Another fact is, by spending time forcing these facts to be memorized is truly interfering with a child’s innovative and creative ability. Most of these worksheets require low level thinking and usually can lock the thought process of a student into understanding simple algorithms. Eleanor Duckworth summed it up the best,

“Knowing the right answer requires no decisions, carries no risk, and makes no demands. It is automatic. It is thoughtless.” 

Is this the environment in which math students should be learning?

The new math curriculum believes, among many things, that:

• Students learn by attaching meaning to what they do, and they need to construct their own meaning of mathematics.

• Students need to explore problem-solving situations in order to develop personal strategies and become mathematically literate. They must realize that it is acceptable to solve problems in a variety of ways and that a variety of solutions may be acceptable.

• Curiosity about mathematics is fostered when children are engaged in, and talking about, such activities as comparing quantities, searching for patterns, sorting objects, ordering objects, creating designs and building with blocks

I end with a link to a petition asking the Edmonton Journal to stop writing one sided, bias, articles, and until they do so you agree to stop reading their paper.

STOP WRITING BIAS EDUCATIONAL REPORTS

Not every child can learn

This was written by my friend and colleague Dave Martin. He is a high school math teacher who blogs here and tweets here. This post was originally found here.

by Dave Martin

Lets face the truth now. It is about time we stop saying  "every child can learn".

After 8 years of teaching, I have realized that it is true that not every child can learn....by Friday.

Not every child can learn....by me standing at the front talking.

Not every child can learn....by working alone.

Not every child can learn....by reading the textbook.

Not every child can learn....by worksheets.

Not every child can learn....by passively taking notes.

So if we aren't going to talk about "every child can learn", we can then start talking about "what do we do when they don't".

Grading Moratorium: Dave Martin

Dave Martin has joined the Grading Moratorium. Want to join? Here's how.

Dave Martin

Red Deer, Alberta, Canada

High School Math

teacher.davidmartin@gmail.com

@d_martin05

I started teaching highschool Calculus at my school a couple of years ago. When I started teaching the course, I used a traditional assessment strategy. I would assign homework daily, end the week with a quiz, and then end the unit with a multiple choice/written exam.

My classes would start around 30 students, and by the end of the semester the class size would be 20. What I did was "weed out the weak". One day I realized that I wasn't weeding out the weak mathematicians, but instead weeding out the weak test writers.

This year, after many talks with first year University and College professors, administrators, teachers, students, and parents, I am proud to say that I have abolished grading. We are currently in the middle of our semester and I have not graded a single item of student work.

Before you continue, I want to remind you that this does not mean I have not assessed, but not one student in my Calculus classes has received a grade at this point. (Other than the report card mark which I must give).

How does it work?

First, I went through my outcomes, given to me by the government, and identified what the "Rocks" are. These rocks are the outcomes which I expect the students to master above all other outcomes. I chose these certain outcomes after my discussions with others and as well as what will be helpful for students to succeed in the future.

Next, these outcomes were rewritten in student friendly language and then provided to the students on the first day of class.

My teaching schedule did not change, nor did the speed on which I have taught the course, but what has changed is the speed at which the students can learn at. Once I had taught 2 or 3 outcomes at a level where I felt that the class has mastered the outcome, I administered a summative assessment. For this assessment, each child wrote it as a traditional exam, but it looked drastically different than a traditional exam. Each assessment was entirely written, broken up by outcomes, and tested only the basics of the outcomes. There were no "trick questions", just simple questions that would assess "Can the child demonstrate this outcome, on their own, as a basic level of understanding?"

When I assessed these assessments, I would write comments only on them, and either a "Outcome demonstrated" or "Need to learn" for each outcome assessed (Not on the overall assessment). It is very important to understand that "Outcome demonstrated" is not a 100%, as a student could make a minor mistake and still achieve this, as I am assessing understanding the outcome, not perfection.

Next, if the child received a "Need to learn" he/she must do the following:
1) Demonstrate the understanding of the questions given at a later date. This usually occurs after a lunch session, a quick conversation, or multiple conversations with the child.
2) A conversation explaining how he/she made the mistake earlier and how their understanding has changed now
3) Write another assessment on the outcomes.

If after completing these 3 steps, he/she can demonstrate the outcomes then I would I count this as "Outcome demonstrated" just as if the child had done it the first time. I do not deduct marks based on the number of tries needed.

If the child still does not demonstrate, (which is extremely unlikely as I have seen) then he/she must repeat the same 3 steps.

After 5-7 outcomes have been taught, then each child is assigned an open ended project. This project consists of each student creating a problem around the math in the 5-7 outcomes and solving it. The expectation is the problem is one which is deep, relevant, and for a purpose. This part is not always easy!

An example: A student to demonstrate his understanding created a Call of Duty video and determined the rate of change of a ballistic knife falling in the video.

These projects usually range from 3-5 pages and must be handed in individually, but can be worked on with assistance from others and/or textbooks.

To assess these projects, I follow the same pedagogy from above. I use comments only, and give guidance towards any errors I see. The projects are then handed back to each student, who can go back, make corrections, and rehand it in. This process is repeated until the child receives perfection on the project.

I have even abolished the traditional final exam. The expectation is the students must give me a 30-45 minute presentation around the rocks of the course, and demonstrate their understanding of all rocks.

How do I get a final mark percentage?

I simply take the number of outcomes and projects completed (at the end of the course) and divide by the total number of outcomes and projects. This is not the best strategy, but it seems to work for me at this moment. I do weigh projects twice as much. (I have 20 outcomes, and 5 projects, so the total is (20+5x2=30)

Let me know if your thoughts

Dave Martin on changing assessment

Here is my friend Dave Martin talking about changing assessment.



Dave Martin teaches high school math in Red Deer, Alberta. You can find his blog here and follow him on Twitter here.

Why do teachers bargain?

David Martin teaches high school math in Red Deer, Alberta. You can find David's blog here and follow him on Twitter here. This post was originally found here.

by David Martin

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.

Scantrons for Science

Dave Martin's witty post on Why we really do need scantrons finished by inviting others to share creative ways scantrons could be used to support real learning. Craig left this brilliant comment:

Drop a scantron off the school and time how long it takes to drift down to the ground. Next, poke all the holes out of the scantron sheet and re-time. Do you the holes make it fall faster? Slower?

Why we really do need scantrons!

David Martin teaches high school math in Red Deer, Alberta. You can find David's blog here and follow him on Twitter here. This post was originally found here.

by David Martin

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

Math

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

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

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

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

English

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

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

Other languages (French, Spanish, etc):

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

Physics

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

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

Chemistry

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

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

Art

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

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


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

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

Happy Marking!

Common Assessment = Undifferentiated Assessment

Here is a guest post by Dave Martin. He tweets here and blogs a lot about math here.

by Dave Martin

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

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

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

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

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

Usually the test days, and requirements are decided before the first day of schoolI have asked why do teachers give common assessment? I will provide the two top reasons I heard, and then my counter-argument.

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

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

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

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

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

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

Now, the problems I see with common assessment:

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

Alberta Education’s ideas are:

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

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

Dave Martin on Professional Development

My friend Dave Martin is running for Professional Development Chair in his local. Here is a quick glance at his philosophy around teacher professional development. You can follow Dave on Twitter and check out his blog here.

by Dave Martin

I, David Martin, am currently running for the Red Deer Catholic Local’s PD chair. On the day
the elections opened up, I put my name forward and since then, have been asked questions about
my philosophy around PD, my goals of PD, and other various questions. Here is a simple FAQ
about my ideas around PD.


1) What is your philosophy around PD?


I believe we should be focusing on teacher learning and not about teacher professional
development. Some teachers may only associate PD days with the term professional
development, and therefore actually believe PD is an event, a workshop, or a program, rather
than an ongoing daily part of a job. How then do we make deeper daily learning a reality for
teachers? Replacing the concept of professional development with professional learning is a
good start; understanding that professional learning “in context” is the only learning that changes
classroom instruction is a second step. Also, recent research shows that traditional methods of
presenting classroom innovations to teachers in workshops does not generally result in either
changed classroom practice or improved student learning.


2) How do you plan to implement PD in the local?


The planners of PD need to avoid the “one size fits all” approach and remember different
educators have different expectations. Mandated PD in top-down programs sometimes does
not recognize the differences required by the teachers it is mandated to and thus can destroy the
teachers “will to learn”. Andy Hargreaves said, “Most teacher development initiatives, even the
most innovative ones, neglect the emotion of teaching.” We need to understand that classroom
practices will improve, assessment will change, and more learning will occur if we motivate
instead of mandate.


3) What does PD look like?


I believe that true professional learning could range from formal credentialed post-graduate
courses to simply having a conversation with a colleague over a beverage. Teachers, myself
included, have learned many innovated educational ideas solely from “googling”. Recently, I
read: “Guest speakers with PowerPoint presentations are the norm and informal learning time
is viewed with suspicion. Administrators with board or school improvement plans to implement
may insist that PD opportunities meet the latest “edu-babble” criteria;”


My response: If professional learning is truly personal then it cannot be mandated to anyone by
anyone. I will encourage that PD stays in the hands of the teachers.


Vote Dave Martin for PD chair!

Why do we give exams (part 3)

David Martin teaches high school math in Red Deer, Alberta. You can find David's blog here and follow him on Twitter here.

by David Martin

Why do we give exams Part 3?

After asking many teachers the top three answers that have been given are:

1)      “To assess, and find out actually what the students know” Rebuttal to this

2)      “If we don’t test it, the students won’t want to learn it” Rebuttal to this

3)      “Hold teachers accountable for their teaching"

Rebuttal to 3:

This reason does not even make sense to me.  If I want to make sure my doctor is being professional, would I book more appointments with him?  Should men and women see the doctor more than once a year to ensure the doctor is keeping informed with medicinal breakthroughs?

We need to start trusting our teachers as professionals, and not as people who don’t care about their career.  Are there teachers who aren’t professional? Absolutely, just as there are doctors who are not professional, or managers, or gas attendants, or dentists, etc.  In any job, career, or field of study, there are people who “fly under the radar”, but I guarantee it is not an overwhelming percentage.

One solution; “Raise the bar” by administering common exams or create benchmarks that are common for the same course throughout a school.  Your high to middle performing teachers will rise to this new level; however the same teachers who weren’t at the level before, will still remain not functioning at the expected level.  

I have heard many teachers say “Fire those lazy teachers!”.  This also is not the solution!

From Washington post: and this blog:

Talking about the systematic firings, he notes, “In the long run, it would probably be superior…to develop systems that upgrade the overall effectiveness of teachers.” He points out, however, that these efforts have not been successful in the past. But have we really tried?

Instead of trying to fire our way to the high performance of Finland or anywhere else, why not try to emulate the policies that these nations actually employ? It seems very strange to shoot for the achievement levels of these nations by doing the exact opposite of what they do.

We are playing with students’ marks and confidence levels by worrying about whether or not a teacher is doing his/her job.  This needs to stop.  Trust the professionals, and you will see teachers starting to create new and innovative ways of assessment. 

I truly believe we will then witness ground-breaking and truly inventive ways of differentiated assessment.  We need to stop the idea of “Every student can learn differently, but all have to demonstrate their learning the same and on the same day”.

I have addressed the top three reasons of why teachers give an exam, but I ask this, if you are administering exams in your school, why do YOU give exams?

Why do we give exams (part 2)

David Martin teaches high school math in Red Deer, Alberta. You can find David's blog here and follow him on Twitter here.

by David Martin

Why do we give exams?

After asking many teachers the top three answers that have been given are:

1.      “To assess, and find out actually what the students know” Rebuttal to this

2.      “If we don’t test it, the students won’t want to learn it”

3.      “Hold teachers accountable for their teaching`

Rebuttal to 2:

First, we need to understand that there is difference between learning and achievement.  For more click here.  

Second, if a student asks you, “Why do I have to learn this?” and your first or only response is “for the test”, then you are actually destroying any possible engagement.  People need to understand that learners don’t ask for the application to challenge the teacher, but actually want to understand the meaning behind the concept.  

If there truly is NO real life application then I would first advise you to contact those in charge of your mandated outcomes and ask them why you need to teach the specific outcome.  In the defense of the government, if they don’t know there is a problem, how can we expect them to find a solution?

Assuming that the outcome does have real life application, we should be focusing on the relevance and not the mindless repetition of the outcome.  Contrary to some popular belief, students do crave knowledge, but they need to be shown the “why” just as often as the “how”.  

For some outcomes this is an easy task, while for others I understand this can be quite difficult.  I, however, do believe that no matter how challenging it might be to show the “why”, the learning that will occur because of it, will make the journey worth taking.  

An exam should not be the reason anything is taught in a class.  “Teaching to the test” should be the equivalent of swearing in a classroom; something that should NEVER be done or even entertained. I read the following, and became sick to my stomach!

Everything that has to do with the test has been given such a high priority, that there is no priority any more but that … The bottom line question comes down to, "Well, what’s going to help them do better on the test?" And if it’s not going to help them do better on the test, well, we don’t have time for that right now (Wright, 2002, p.10).

I would hope, that most agree, that the above statement is not one that teachers should be making.  If you believe, however, that a test is the only way students will learn, you are on your way to making the statement above.  I strongly encourage educators to allow students to find significance in given tasks, and you will start to see that your test no longer becomes the reason students want to learn.

Why do we give exams?

David Martin teaches high school math in Red Deer, Alberta. He enjoys long walks on the beach and is a Capricorn... he's also a damn good educator. I'm pretty excited to him guest post here on my blog. You can find David's blog here and follow him on Twitter here.

by David Martin

Why do we give exams?

After asking many teachers the top three answers that have been given are:

1. “To assess, and find out actually what the students know”

2. “If we don’t test it, the students won’t want to learn it”

3. “Hold teachers accountable for their teaching”

After many hours of thought, I have decided to post my rebuttal to these three reasons, over the next three blogs:

1) To argue this I would like to start by quoting Einstein “Not everything that counts can be counted, and not everything that can be counted counts”. I believe that discrete statistical data, derived from tests, actually devalue the professional judgement of a teacher. Teachers should be able to rely on the personal interaction with their students that they have on a day-to-day basis and not the mark received on an exam.

To further illustrate this, before a student even writes an exam, he/she could explain to the teacher what his/her mark will be on the evaluation. Furthermore, I would even go as far saying that most teachers know what mark the student will receive on the exam as well. If both the teacher and the student know what mark is going to be achieved, why waste valuable class time giving an examination?

Tests are also discouraging to any student achieving a mark that is not sufficient. A student, in this category, will walk into your class KNOWING they will not achieve an adequate mark, and then write the exam. When you hand back the exam, marked, their knowledge will be confirmed with the poor mark. We are beating their confidence down with their own knowledge.

Alfie Kohn, would say:

Most assessment systems are based on an out-dated behaviourist model that assumes nearly everything can -- and should -- be quantified. But the more educators allow themselves to be turned into accountants, the more trivial their teaching becomes and the more their assessments miss.

Some would then argue; give more exams. The more chances a student has to demonstrate their learning, the better the picture the teacher has of what the student knows. Psychologists Martin Maehr and Carol Midgly would say “an overemphasis on assessment can actually undermine the pursuit of excellence”.

It has been shown, many times, that the more a student is told to focus on their marks, the less engaged they become about the learning. Classrooms should have less of an emphasis on achievement and marks, and more emphasis on autonomy, mastery, and purpose.

Flaw of Averages: pay per week

It is my pleasure to have Dave Martin guest blog today. He is a high school math teacher.

By Dave Martin

John was interviewed for a job at a factory where the management consisted of Dave, his brother, and 6 relatives.  The workforce consisted of 5 foremen, and 10 workers.  Dave informed John that the pay was well here, with an average salary of $600 per week.

After one week of work, John was upset as he only was paid $200.  John stormed into Dave's office, and accused Dave of lying.  Dave, the magical mathematician, explained, "Every week I get $4800, my brother gets $2000, my six relatives make $500, each foreman gets $400, and the ten workers get $200.  Averaging to a salary of $600 per week."

Unless, we talk about mean, median, and mode, the AVERAGE, can be meaningless.

If you use averaging to calculate student grades, how does this story affect your assessment practices?