Monday, March 16, 2015

Math Midterm

Here is a copy of my Math 31 Midterm.  I am trying to get students to self-assess their own learning and ultimately grade themselves.

Students will receive the grade they chose, provided their explanation is supported with evidence.


Math 31 Midterm

This is due _________.  You are to do this individually, but feel free to converse, discuss and collaborate on this assignment.

You are to create a “Google Slides” presentation, and self-assess your own learning. 
Next, you are to assess your knowledge of the following outcomes

  • Determining f(x)>0
  • Limits
  •  Left and Right Limits
  • Continuous vs Discontinuous
  •  1st Principles
  •  Simple Derivatives
  •  Derivative Rules

Each outcome should take between 1-3 slides, and complete the following:
  • Describe your knowledge of this outcome.  (“I have mastered this outcome fully” or “I understand most of this but I struggle when it comes to…”)
  • Give a short description to demonstrate your understanding of the outcome “When you are doing this you…”)
  •  Give an example of you demonstrating this outcome (Here is a question and my solution).  May be something you created before, just can’t be a class example.

On your last slide you are to give yourself a percentage mark based on your understanding of the course so far.

When finished…


Click the blue “SHARE”,  then click “Shareable Link”, then click the drop down menu and change it to “ON- Anyone with this link”, then click “SAVE”.  Lastly, click “COPY LINK”.  Fill in the form below.

Friday, March 13, 2015

What students are saying around less grades

 People have their doubts around the removal of grades.  Over the last 6 years, I have graded less and less and have been challenged many times.  Instead of me defending this movement, I have compiled a set of responses around what I do from my students.  These are not edited in any way, or were these students "prepped" into their responses around me removing grades.

First, a most recent student of mine, Michael says:



Addressing the commenters who attack Mr. Martin's approach as "coddling", "unaccountable" or "unrealistic". I am a former student of Mr. Martin's class who has received over $115,000 in academic scholarships from some of the top universities in Canada. Anyone who knows Mr. Martin can testify that he is tremendously hardworking and invested in the big picture success of his pupils. As a current high school student, I would like to share some insights into Mr. Martin's philosophy that make what he does so valuable to us. There will always be a bell curve of students in the high school system, with a minority of extremely self motivated students who will succeed in whatever environment they are placed in, and a minority of disadvantaged students who struggle because they lack the support to succeed. Neither of these groups of students should be used as an indicator of effectiveness for any teaching method. However what makes Mr. Martin's teaching philosophy so effective, is that he is able to positively motivate and support the majority of students who fall in the middle, students who are seeking a good education but may find achieving a standard of excellence extremely difficult in a conventional classroom setting. He challenges his students to strive for true understanding of the concepts taught, and does not punish them for their individual learning styles. He provides the tools and the learning environment that allow for total understanding of both basic and advanced concepts, if the student is willing to put in the necessary effort. What is so encouraging about this approach is that the majority (I would venture to say all) of his students develop a desire to excel and work hard in this classroom, regardless of their previous experiences or attitude towards math. Finally, there is nothing ambiguous about his marking system. For students to succeed on the tested outcomes, final exams and projects, they must demonstrate a complete understanding of the concepts taught. Throughout the course, they are evaluated for their understanding on a concept by concept basis, so both students and parents have a real time indication of their success in the class. Your grades are completely "quantifiable" and "real", for lack of a better expression.

Next is Karl,



Thank you Mr. Martin for teaching me to love calculus, you are the reason I chose a math major. I am in my 3rd year at Macewan with a 3.87 GPA in a program I was told as a child I could not learn. The article is good but there is so much more to say about why your students are so successful, your applicable and interesting math examples and love of the subjects and knowing the interests of each of your students are also why your classes are full.

Here is Logan,

Hi, I'm a former student of Mr. Martin's, and now a current Electrical Engineering student at the University of Calgary. Mr. Martin's teaching methods are innovative and greatly helpful, and I have yet to get as much understanding and knowledge out of a course since taking his AP calculus course, despite going into a field that should by all rights have "better" education systems in place than any high school. His reinventing of the "cognitive and empirical wheel regarding math instruction" is a great help to many of his students, despite or more accurately because of his different method of evaluating students. Because of his classes, myself and others in my situation were much more well prepared for the "REAL WORLD" of dealing with higher mathematics than many others who were taught under standard systems, as many of them were pushed through the highschool level without gaining real comprehension of what they were doing, completely contrarily to the education style of Mr. Martin. Obviously one (or even a few) data point(s) do not point to causation, but just about everyone that I have seen take Mr. Martin's classes have greatly benefited from them, much more than people taking courses with very similar learning outcomes from any teacher who follows the standard method of teaching high school math. Clearly he's doing a lot of things that are very right for those he's doing them for.

 Lastly, what Ray says around exams



Exams are “said” to represent one’s knowledge of course material, this statement is both true and false.
Exams do test what we know but misses the main idea of why the answer is so. In most of today’s classes a student can pay attention in class, do their homework and study hard and they should obtain a decent mark but does this mark really display what they know? Exams force us students to memorize what material will be on that exam and to ignore the concepts that won’t be on it. Throughout my schooling there have been countless times when I have asked a teacher “Do we need to know this for the exam? “And they have replied with “No” so my fellow classmates and I don’t worry about it. 
I have noticed that the kids who take interest in the subject want to know WHY and it’s these students that seem to obtain the most success and useful knowledge from that class.  Most courses you can memorize all the material and know what it is but not understand why it is so and how you can use it in your life. Exams limit one’s potential and quite frankly not to many students like them. 
For example the dreaded diploma examinations that are worth 50% of our mark. We put in many hours into each subject in school over 6 hours a week and then 50% of our mark is based on a 3 hour exam? This time limit puts even more stress and pressure on us students, then we are told to manage our time for this exam we have never seen and aren’t sure what to expect. Personally when going in to write my math 30 diploma I was told I’d have lots of time so I took my time on each question. The pressure got to me, as I would second guess myself on each question. Before I knew it I was way behind, panicking as I knew I was in trouble.  I ended up having to guess on 7 questions as I had run out of time, me a kid who is quite familiar with managing time. 
What I’m getting at is that the exam couldn’t accurately represent my knowledge as it had a set of rules with it and could only cover so many concepts.  I was successful all year understanding each concept feeling confident with my learning then ONE exam dictates half of my mark. It dropped my mark a sizable amount and I felt ripped off. This exam did not represent my knowledge but more so the mark I got after some unfortunate questions that got the best of me. 
Exams limit our potential. In the real world we will have access to technology, others input and potentially more time which can help us great amounts. We will have real life situations where the “why” will be more important because the “how” can easily and quickly be taught to us due to the fact we understand the concepts present. 
Value of feedback assessments? 
Contrary to exam focused classes, assessments provide us with the “why”, “how” and even gives us experience and ways to use it in our life. To create our own examples we need to know why something occurs and then how this works or occurs. When we go out and create our projects we make our own examples that relate to us and stuff we are interested in which is another aspect missed by exam focused courses. The importance of feedback in school to me seems quite important and valuable.  
We learn from our mistakes and that’s the honest truth. We shouldn’t be punished for mistakes rather taught and encouraged how to not make them again. In exam situations we sometimes get to go over the questions and see how to do it correctly, with the diplomas and final exams no such luxury is granted. You do what you can and you get a mark, no feedback or an idea of what questions and concepts you struggled with, no learning!

“If a child can't learn the way we teach, maybe we should teach the way they learn.” -Ignacio Estrada

Wednesday, March 11, 2015

No percentages in Math

Recently, the Edmonton Journal did an article around my no percentage grades

EDMONTON - High school math teach­er Dave Martin has stopped grad­ing his stu­dents’ as­sign­ments with percentage marks.
In­stead, the Red Deer teach­er writes com­ments on homework and unit exams, then urges stu­dents to fix mis­takes and dem­on­strate their know­ledge again.
For one of his mid-terms, Martin asked his stu­dents what mark they want­ed and why, “and as long as they could jus­tify it, I gave it to them,” said Martin, who made a pres­en­ta­tion about his teach­ing meth­ods just over a week ago at the Great­er Edmonton Teachers Conference.
“It was real­ly in­ter­est­ing because people didn’t take ad­van­tage of this ... My class aver­age, when I did that, was lower than what it usu­al­ly is.”
Math edu­ca­tion has been a lightning rod for de­bate in Alberta and across the coun­try re­cent­ly, sparking pro­tests and a back-to-basics cam­paign that prompted for­mer edu­ca­tion min­is­ter Jeff Johnson to make ad­just­ments to Alberta’s K-9 math cur­ricu­lum.
Grad­ing and stu­dent as­sess­ment have also come under scru­tiny.
For­mer phys­ics teach­er Lynden Dor­val made na­tion­al head­lines in the spring of 2012 when he re­fused to fol­low a new pol­icy at Ross Sheppard High School that re­quired teach­ers to stop grad­ing with ze­ros and use be­hav­iour codes.
And a year ago, the Bat­tle River School Division in Camrose de­cid­ed high school stu­dents would again be graded with per­cent­age marks after par­ents and stu­dents fought a con­tro­ver­sial sys­tem that marked stu­dents with one of four achieve­ment lev­els.
It’s not until the end of Martin’s math cours­es that he as­signs each stu­dent a per­cent­age grade, which is re­quired by Alberta Education. To cal­cu­late that grade, Martin looks at the cur­ricu­lum out­comes for the course and fig­ures out what per­cent­age of those out­comes each stu­dent has learn­ed.
“So if a kid gets a 60 per cent (of the out­comes), then I can ac­tual­ly say, here is the 40 per cent he or she doesn’t under­stand, as op­posed to get­ting 60 on every test,” Martin said. “Think about the kid who gets 70 per cent all year. You know what that means? He never ac­tual­ly mas­tered any­thing.”
Martin said he wants stu­dents to learn the course ma­teri­al by the end of the year, so he has stopped pun­ish­ing stu­dents with re­duced marks when they learn the ma­teri­al more slow­ly. That means a stu­dent who makes mis­takes on as­sign­ments but final­ly grasps a con­cept at the end of the course can score the same mark as a stu­dent who aces it from the be­gin­ning, said Martin.
“I’ve been do­ing this for about five years now,” said Martin.
“Why do Eng­lish teach­ers get rough drafts but math teach­ers never al­low stu­dents to have rough drafts? So that’s kind of what I do. I al­low kids to dem­on­strate their learn­ing mul­tiple times ... I don’t be­lieve every kid can learn cal­cu­lus by, say, Fri­day, but I do be­lieve every kid can learn calculus.”
Martin started off teach­ing math the way he was taught math but the vast ma­jor­ity of his stu­dents hated it, he said. About 44 per cent of his cal­cu­lus stu­dents failed or dropped out. The rate was sim­i­lar when he com­pared it with other schools. Last se­mes­ter, his drop­out and fail­ure rate was zero.
Students are more in­clined to take on high­er-level math, even math out­side the cur­ricu­lum, if they know they’re not go­ing to be pun­ished for mak­ing a mis­take, he said.
It’s a far less stress­ful way to learn math, but the work isn’t easy, said Grade 12 cal­cu­lus stu­dent Hec­tor Jordan.
“You’ve got to under­stand it fully,” Jordan said. “You end up lik­ing math ... Ac­tual­ly, all his class­es are packed.”
Math teach­er Patricia Shoe­maker de­cid­ed to try Martin’s meth­ods with some of her Grade 10 stu­dents a year ago. Now that she grades with com­ments, at­tend­ance has sky­rock­eted at her mini-les­son study ses­sions. Shoe­maker said her stu­dents did as well or bet­ter on a com­mon final math test than other Grade 10 class­es at the school.
“I’m not grad­ing them on if their as­sign­ments are late anymore. I’m not grad­ing them on if they’re mis­sing an as­sign­ment. What I’m grad­ing them on is what they ac­tual­ly under­stand and what the out­comes are.”
asands@edmontonjournal.comTwitter.com/Ansands

I wanted to share two comments from my own students....these were written on their own without any request from myself.


Friday, November 28, 2014

Teachers; more than "teach"ers

Julie changes one student every day as he is mentally unable to change himself.  She has to wipe, clean, undress and dress this student every single day.

Jason, after school, coaches 15 boys basketball.  He has to plan drills, prepare his students both mentally and physically for the next game, book hotels and busses, and ensure each player is caught up in all classes.

Lindsey listened in silence as her student confessed that one night she drank too much and danced naked in front of other students.  After calling a counselor and organizing a third party psychologist to come in, Lindsey watched for days as this student dealt with turmoil, bullying, and public ridicule.  Through various supports, which Lindsey organized, this student over came this incidence and regained her mental health.

Chris wakes up every morning at 5 am to ensure he is at school to drive the cross-country running team on the bus.  Being one of the few teachers who have a bus license, he is called to drive the team to and from the track every morning.  While they train, Chris sits, enjoys a book, listens, and waits for the coach, whom is another teacher, to finish the daily training so he can drive the students back.

Brenda spent her Saturday on the phone with local RCMP discussing the mental health of a suicidal student.  She then drove to the hospital to sit with the student, as his family abandoned him and Brenda was the closest person he had left.  Only knowing the student for 3 months, she had very little information to give to the RCMP however the time she spent with him on Saturday may be the only reason he is alive today.

Carol has students who arrive to school starving.  Knowing that it is hard to focus when your stomach is louder than the people around you, she cooks a simple breakfast in her classroom every morning.  Usually coming out of her own pocket, she shops once a week to buy bagels, bread, eggs, fruit, and other simple breakfast items. 


The root word of teacher may be “teach” however this word represents only a part of the day of a teacher.   Teachers do teach, as well as act as parents, friends, shoulders, counselors, emergency contacts, cooks, bus drivers, coaches, and most importantly non-judgmental people.

Wednesday, November 5, 2014

TV around a corner

What is the largest TV that could fit around a corner in your house?

This was the question we answered in my calculus class.

First I showed this applet and had students play with it




Next I asked what do we need to know?

Students asked for the width of the hallways which are 0.8 m and 0.9 m wide.

Next we realized that actually to determine the largest TV we actually need to MINIMIZE the length of the line.  As the smallest line will be the line that can fit around the entire corner.

Calling the, angle between the TV and the 0.8 m wall, theta you get the equation of the TV length at any angle to be



Next taking the derivative, and solving for when it equals 0, gives us


Substituting this back into the equation gives us a TV (or any rigid object) with a length of 2.4 m or 94.45 in across.  

We then did have a discussion around what assumptions are we making?  Some are...
  • The TV has no depth at all
  • The TV will scrap across the wall
  • The TV is out of the box


Wednesday, October 22, 2014

Bowling and Math

Recently, I joined a weekly bingo league and realized that simple addition and daily physical activity could be integrated together.  First, give each student a bingo sheet which has all the numbers 0-99 (inclusive) on it.  In Red Deer, Heritage Lanes has these already made up.  An example of one box might look like



Essentially, you have a total of 4 boxes, each with 25 squares and therefore all numbers will appear once.

How to play:

Take the last two digits of your TOTAL score on each frame of bowling and cross off the respective number on your bingo sheet.  First to a line, X, blackout, etc..wins!  Students would play at least 3 games with the same sheet for all games.

Where is the math?

Students, most likely, would play the first game not caring what score they receive and simply crossing off the scores.  Starting the second game, students will probably start becoming strategic towards the scores they want.  This is where the math will come out, and you will want to do some teaching on how bowling scores work.

Crucial knowledge includes:

  • Pins are worth 2,3,5,3,2 from left to right
  • Strikes are worth 15 points plus the score of the next two balls thrown. (Frame ends)
  • Spares are worth 15 points plus the score of the next ball thrown. (Frame ends)
  • The 10th (final) frame, you throw 3 balls no matter what you knock down on each ball.

Here is what recently happened on my team:
One of the bowlers needed a score of 68 to complete a line and was currently at a score of 17.  He threw a strike and therefore the machine doesn't update your score until his next 2 balls are scored and I saw him doing some math on the back of his bingo sheet.

He realized that essentially he has 32, and the next two balls are worth double points, as they count towards the next frame as well as the previous strike.  Quickly, him and I talked about how he needed 36 points.

There are many options to get this, but one essential question he asked is "Can I get another strike, or will this put me over?"  The answer to this will determine how he throws the first ball in the next frame.

If he throws another strike then, the first strike is now worth 30 points plus the next ball thrown, and the second strike will be worth 15 points plus the next 2 balls thrown, and therefore he essentially would have a score of 62 and the next ball would be worth triple points.  Which means if he throws another strike, then a 2 pin and gutters the 2 balls after this (to complete the third frame) he would be at 68.

What I realized is that the 3 adults on my team (all over age 25) had to think about this problem and it wasn't easily solved.  I wonder if this could help students learn simple addition and multiplication in a context and for a purpose.

If you teach younger grades and want to embed movement into your math classes, I suggest a field trip to a local bowling place. If you are in Red Deer, then I advise you to go to Heritage Lanes, as these sheets are already made.