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Teacher working with elementary student at table

Math Outside the Textbook

Vera C. Teschow

Get out much? of the math textbook, I mean. I know that until recently, I didn’t! Even after leaving the classroom for a few years to do a stint as a program resource consultant, and preaching  the  message of  problem-based  learning  and three-part lesson planning while I was teaching preservice at the university, when I got back into a classroom, it didn’t take long for me to revert to the textbook as my primary and almost exclusive source for math programming.

It wasn’t that I didn’t believe in a constructivist approach to teaching and learning math. But with all the pizza money to collect, report cards to write, monthly newsletters and curriculum updates to send home, guided reading groups to plan, baseline data to enter into the board-mandated school success computer program, and … Well, you get the idea. The textbook was just so tempting. It offered a lesson-by- lesson approach that was relatively simple to follow, especially for a busy generalist teacher with a touch of math phobia! I quickly gave in to temptation.

It wasn’t until last year, when my colleague Dale Trinder and I applied for and were granted a ministry-funded Teacher Leadership and Learning Program  (TLLP) project that I once again attempted – this time with considerably more success – to venture beyond the textbook in my mathematical programming.

Our project revolved around endeavouring to use an Interactive White Board (IWB) to teach math, through the use of bansho.“Bansho” is a technical term developed by Japanese teachers, and means “board writing.” It is an artifact that visually documents a problem-based math lesson. It consumes a large amount of board space, so that students can visually refer back to various parts of the lesson as it progresses. (As an aside, we documented our learning, and posted numerous lessons at

Because we were receiving upwards of $20,000 in funding, and were expected to submit a final report at the end of our year-long exploration, the pressure was on to get to work. This stress was further intensified by the self-imposed removal of the class set of math textbooks from our classroom, and the arrival and installation of two big, shiny Smart Boards only days before the start of the school year!

Thankfully, the vast majority of our funding had been allocated to teacher release time, and my colleague and I had approximately one day every 10 to visit other schools, to read and research, to get a little informal training on the Smart Board, and to develop non-textbook math lessons.

Once forced to examine the actual curriculum and develop math lessons that addressed specific curriculum expectations and catered to the unique needs of our  specific group of students, we soon discovered that not everything in the textbook is in the curriculum. Nor is everything that the students in any given class need in the textbook! For example, while “mode” is referred to in the Grade 3 Math curriculum, it is not included in the textbook. Furthermore, I had students in my class whose numeracy skills were considerably  below  grade  level,  and  in  many cases the multi-digit addition and subtraction problems presented in the textbook were decidedly out of reach. Creating our own lesson plans that allowed students to consolidate skills from previous curriculum years helped them begin to meet the expectations of their grade level in a more realistic manner.

As we worked together to look at students’ work, and use ongoing assessment to develop lesson and unit plans for each new topic in the math curriculum, my colleague and I began to build up a much stronger mathematical and pedagogical understanding.

Departing from the textbook meant that we could modify lessons on the fly more easily, or create entirely new lessons in order to respond to what we were seeing in the classroom. For instance, when we developed an oral  geometry  assessment/mini-conference to complete with each individual student, we were able to use the one-on-one time to confirm what each student knew, and do some intensive,  on-the-spot  teaching  with  those who needed a little extra support. I remember the light bulb going on for one little girl as I gently probed her understanding  of  clock- wise and counter clockwise turns of varying degrees; the comfort she had developed as a mathematical risk taker allowed her to make connections to what she already knew, and to celebrate her evolving understanding of this geometric concept.

One of the things I liked about developing our own lessons was that we could choose the context, and often, we changed names or scenarios to reflect the cultural reality in our classrooms. Apples became  samosas, while Halloween parties  became  Eid  or  Chinese New Year’s celebrations as we modified problems from other sources. The students were excited to explore math  concepts  found in their own worlds, and it was clear from their increased engagement that they were able to relate in a way that was different from previous classes I had taught.

Towards the end of the year, we started to venture into more specifically social justice related problems, using picture books and other rich mentor texts as context. My  students very much enjoyed the “rich mentor text wall” we created together as we engaged in conversations about a variety of “big” topics from racism to literacy to poverty, inspired by books like Eve Bunting’s The Wednesday Surprise or  Evelyn  Coleman’s  White Socks Only. I could see the connections they made in their writing and in the comments they made during our  conversations later in the year as they thought about the world and their ability to effect change in it.

Integrating the mathematics of these big ideas is something I’d like to do with more intentionality in the future. (Currently,  my students and I are exploring the math behind the cartoneros (waste pickers) who work the streets of Buenos Aires, where I am teaching this year. And my colleague Dale Trinder has started planting a garden with his class this year; the math generated by this project is rich indeed, and I am looking forward to following the related mathematical developments in his classroom.)

Ditching the textbook forces us to think more holistically not just about the math, but also about opportunities for  teaching through the lens of social justice. Without the constraints of a pre-planned program that someone else has  developed, we have more opportunity for context-specific instructional creativity.

When I say we got “out” of the textbook, I don’t mean to imply that we threw the proverbial baby out with the bathwater. Current math texts in Ontario offer a number of rich problems, and we often used them as grounding for the lessons we developed. But we also used many additional resources, for example, Marion Small’s Good Questions book, as well as her more recent Eyes on Math, a visual approach to teaching various  concepts, co-authored with Amy Lin. We also heavily consulted Van de Walle’s compendiums for K-2 as well as 3-5, and of course, used several of the suggested problems right in the curriculum itself.

Despite the abundance of release time, I confess that we taught some units directly out of the textbook, because we still found that we simply didn’t have the time to develop non-textbook plans for every single concept in all strands of math!

While teaching “freestyle” did not solve all the problems in my math program, being more directly engaged with math as the teacher and personal developer of each math unit, I definitely had a better idea of what the problems were and how I could intervene to help students with next steps. As a whole, the students also seemed to enjoy the math program much more than classes I had had in previous, more textbook-reliant years.

For teachers thinking about  stretching their mathematical instruction beyond the textbook, I offer the  following considerations:

  • Begin by choosing  ONE  unit  to plan entirely “from  scratch.”
  • Set the textbook  aside for this unit, and gather  together  a few alternate resources  (including the curriculum!). Your teacher-librarian or a board program  resource  consultant, or even  a colleague down  the hall  who’s  already been  experimenting can help  direct  you to a few good resources.
  • Consider which  curriculum expectations need  to be addressed  for this unit  and think  about  how  students  will get there (begin with  the end in mind); for ELLs and students  with  LDs,  develop  a list of necessary  vocabulary to pre-teach.
  • Develop a set of five  or six lesson plans  for the  unit,  including some  that can serve as formative assessment  checkpoints along  the  way.
  • Develop your lessons  in a three-part framework: Minds On  (a warm-up or thinking question), Action  (the  “big” problem for students  to work  on),  and Consolidate/Debrief (taking up the problem as a class, sharing  various students’  solutions, assigning a similar  problem so that students  can apply their  new  math  skills).
  • Tell your students  what  you’re  up to: It’s good for them  to see you as a life-long learner, and they will become  your biggest champions as you slog through  the failures  and successes  of your little experiment!
  • Take some  time  at the end of your unit to celebrate  the things  that went  well, and reflect  on why  some  things  may not have gone so well  (and  what  you might  do differently next time). Consider asking  your students  which  method of learning math  they prefer  and why; this can provide  clues for improving future  instruction.
  • Share your work  with  others,  and ask them  to share  their  work  with  you. Although we found  that a lot of our own  learning came  from  developing the lessons  and units  ourselves,  we were constantly aware  of the time  crunch  many teachers – including ourselves  – face,  and were  always  grateful  to get a great idea from  somewhere else that we could  easily  incorporate into our classrooms.