My Comfort Quote

I'm pretty sure I'm not alone in that I have a quote that I come back to once in a while that helps keep me going and reminds me of why I am doing what I am doing in my classroom.

My quote came from an article written by Ann Kajander in the September 2005 OAME Gazette. Ann is an associate professor in the department of undergraduate studies in education and the recipient of 2014 Margaret Sinclair Memorial Award. I highly recommend her regular feature in the Gazette: Mb4T: Mathematics by and for Teachers.

The article was entitled "Supports for the Effective Implementation of The Revised Grade 9/10 Curriculum: The Role of Manipulatives in Making Algebra Meaningful".

September 2005 OAME Gazette

The sentences that hit me squarely between the eyes were:

"Put bluntly, learning based purely on procedural methods has little meaning or long term retention for most students, and does not facilitate the depth of understanding needed to use math for any worthwhile endeavor outside (or inside) of school. Even more bluntly, its boring, demeaning, and encourages the all-too-prevalent perception that mathematics is difficult, useless and unintelligible."

Sometimes it isn't a quote itself that makes the impact although it plays a big part. Sometimes you have to be ready for the message. I guess the quote hit me at the right time and the right place. I had been struggling for a while in my teaching and recall relating to a colleague that was teaching Grade 10 Applied math with me that I was bored out of my mind. And if I was bored out of my mind I couldn't imagine how the students felt! That feeling coupled with what I read in the article was the catalyst that changed everything for me in my teaching. We redesigned the course with the idea that a good task was key to bringing the math out and would lead to that deep understanding. 

I can clearly remember playing the game of frogs to introduce quadratic relations and having the vice-principal walk in while students were jumping around the room. Or building tetrahedral pyramids that outgrew what our classroom could contain. All of the work we did to redesign the grade 10 course made us want to share the learning and so we presented at OAME in 2006. Our workshop title was Grade 10 Applied: The New Frontier. And on the last slide of our slide deck was what all good workshops should end with...a quote. Guess which one appeared on our last slide?

I would love to hear what quotes have inspired you in your own teaching. Feel free to leave them in the comments section. Thanks!

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.