Saturday, October 17, 2015

My First Blog Post

Its the THINKING stuped!

I tell this story often to anyone that will listen about my experience teaching math since the curriculum revisions in Ontario that occured in 1999. So my apologies to my colleagues who have heard me drone on about this before.

But first a look back...lets go back to a time long ago in a classroom that may look suspiciously like the ones we see now. Pre-1999, the curriculum in Ontario was an anomaly in North America...well specifically at the high school level. Students completed a five year program with the university bound students taking OAC (Ontario Academic Credit) in their final year. College bound students could choose from technical math credits or business math credits in their final year. Students needed 30 credits to earn their Ontario Secondary School Diploma (OSSD) and two of those had to be math credits.

The assessment and evaluation experience was also significantly different. A typical course outline might include the following in the determination of a student's mark:

Tests ____%
Quizzes ____%
Homework _____%
Participation ______%
Attendance ______%
Final Exam _____%

I taught in a Catholic school when I first got into teaching and can recall including a student's adherence to the uniform policy being included in some final evaluations.

How did things change when the new curriculum was introduced and the 5th year of high school was phased out?

The curriculum changed! What was taught in Gr. 9  through 12 changed to reflect the reduction from 5 to 4 years. The names of the courses were intended to now reflect the pathways that students were intending to pursue once they left high school (Academic -- University, Applied -- College, Locally Developed -- Workplace). The OAC courses that university bound students had taken in the past were replaced with Grade 12 University level courses that reflected a similar content to those in the OAC courses.

But the changes went a lot deeper than just labels. The spirit of the curriculum emphasized exploration and investigation over the rote memorization of skills. A value was placed on reasoning and justification that was not as evident in the past. But math was still math. Students still needed to solve equations, factor, derive and all of the things they were asked to in the past.

One of the most significant changes occurred in the assessment and evaluation practices that were outlined in the curriculum and supporting documents. Most of the items that had been included in the past such as participation or homework were no longer to be included in a student's final mark. They were now commented on as learning skills that were the same from Grade 1 to 12 (responsibility, organization, independent work, collaboration, initiative and self-regulation). Student marks we now to be determined by their performance in four achievement categories: Knowledge & Understanding, Thinking, Communication and Application (p28-29 of the Grade 11-12 curriculum documents).

What is fascinating in looking back at the changes is how the community of math educators reacted to these changes especially around assessment and evaluation. Speaking from my own experience at the time, what most of us did in the classroom was take our old tests and started placing Ks, As, Cs and Ts next to questions as we started the exercise of categorizing the questions we were asking. Easy peasy. New curriculum and new assessment and evaluation practices - no problem. If you were dropped into a math classroom in 1995 and then in 2005 I would challenge you to try to tell the difference. In fact, I would challenge you to tell the difference in 2015 for some math classrooms.

You can probably guess at what types of questions were labeled with each category label. And so we boldly stepped into a new day of curriculum with the assessments we had always used in the past. What were the consequences of this approach? It didn't take long for the alarm bells to go off. We could now see the areas where students struggled. It was like lifting up the rug after sweeping a lot of dirt under it for years or not realizing there was dirt there all along. Which category gaped like a black hole showing us what we had neglected for so long? THINKING! Students struggled in solving what were designated as thinking questions. The questions they were asked were those that we usually didn't assign from the homework - those questions from section C in each textbook lesson.

The focus of this post isn't the questions themselves - another time another post for that discussion but rather the reaction many of us in the math community had once we saw the results. The majority of schools that I encountered just DECREASED the amount that thinking factored into the determination of a student's mark. I know that's what we did at the school I was in at the time. Reflecting on this and recognizing what is taught it still boggles my mind that the achievement chart category that emphasizes planning, executing and reflecting on solving a problem is worth the least in a mathematics category.

My challenge as a department head and my challenge maybe to you is think of strategies as to how you can improve student performance in this category. It isn't solely for the benefit of seeing a bump in marks but for what it can indirectly provide. It can provide you the opportunity to dig deeper into the curriculum and assessment documents (e.g. Growing Success) but more importantly in my mind is the opportunity to value what we should value in teaching and doing mathematics --- SOLVING PROBLEMS!  We didn't get into teaching math to do 30 factoring questions. Another byproduct could be the fostering of persistence in problem solving that doesn't come from 30 factoring questions. The answers to the problems that our students will be solving will not be found in the back of the book. We need to provide them with opportunities for solving rich problems that demonstrate WHY we teach the skills we teach. Just like a carpenter isn't regularly tested on how to use a hammer but rather on how well they can put together a sturdy enough house. Let's value what our subject is about....its the thinking.


  1. Thoughtful comments, Paul. As we shift our assessment practices in mathematics (and other subject areas) to focus more on thinking, I suggest we need to shift our assessment practices more to assessment for learning, as opposed to assessment of learning. Turning our attention and our students' attention away from the grade, and to the learning will help them understand that thinking and learning is the primary focus. A grade will come along no matter what happens. Congratulations on your first blog post!

  2. Thanks Kristen. An even bigger battle is making them (students, parents and all other stakeholders) understanding that thinking AND learning should be the focus rather than grades.

  3. 30 factor questions is the repetitive stuff needed to grasp abstract. Just as an athlete will stay in the gym and take 100 foul shots after practice (DUKE!!!) to master this skill which is part of the complete package for that athlete, a student should master the essentials. However I fully agree with problem solving being the heart of the issue. Students without the flexibility to see things multiple ways struggle to extend to higher level math. They get stuck in memorizing a rule rather than seeing connections between concepts (expanding and factoring are like multiplying and dividing)
    Great blog - as expected!

    1. Thanks Duke fan!!! I agree that practicing the foul shots is important but we don't keep the player from playing the game and just make them practice foul shots. They eventually play the game. Same thing with someone learning isn't scales ad nauseam without trying to string the notes together to make music. The focus on skills at the expense of doing math is my point. Too many classroom experiences are that the skills are the math.

  4. Hockey Canada supports fewer games more drills. Sometimes the beauty of pure math needs to be enough. I don't think waiting 3-4 days to use the skills in context is too much. I love learning through problem solving but I've always thought the pressure to put everything in context doesn't teach an appreciation for what math is....flexibility with numbers and thinking intertwined.

  5. I agree that the beauty of math is the sum of geometric shapes on the legs of a right triangle equal the similar shape on the hypotenuse. Or all the patterns we can find in Pascal's Triangle That's cool!!! But I don't think that 30 factoring questions is where I find the beauty of pure math. I am not asking for context for everything. I am asking for a purpose.