Building a Culture of Mathematics – Creating a Mathematical Environment in the Intermediate Classroom

As the end of summer approaches, teachers begin to feel that tinge of panic and excitement as they begin to think about their new class in September.  As teachers, we have many questions that come to mind when developing our math program.  Questions like,

How will I cover all the expectations?  How will I engage my students in math?  How can I encourage them to take risks?  How do I get them to write/explain in math?

But most of all…  How do I get my students to be interested and like math?

As teachers examine their programs with their school teams, much of the focus is on how to divide strands for each reporting term.   But does the planning include ways to help students become better risk takers, ways to teach how to articulate their thinking through oral and written explanations, and ways to enjoy and appreciate mathematics?  At the end of the school year, what do we want our students to learn from our class?

If we don’t think about developing risk takers then how will we really know what they know or don’t know?  When students say, “I know it but can’t explain it.”  then what part did they understand?  Do we want mathematics to be a subject they just had to take at school or do we want them to say, “Wow, I remember in math when we did…”.  This is the type of impact we want to have on our students.

Mathematics has been viewed as a subject that is unrelated to students’ interests.  We need to do a better job at having students (and parents) view mathematics as a real, tangible subject.  Something they can be passionate about, can argue about, relate to and see as a beautiful subject.  We need to create a culture that lets our students understand what math is really about.

It is quite common to hear people say, “I’m not good at math.” and responses like “Yeah, neither am I.”.  But how often do we hear people say, “I’m not good at reading?”  Why does our society so readily accept this attitude about math?  I remember sitting in conference and hearing Dr. Ed Barbeau, mathematics professor at the University of Toronto, say that intermediate math should be about recreational math.  I was fascinated by this statement and understood it to mean that students should have more opportunity to problem solve, collaborate with one another, debate and justify their solutions and learn to develop strategies to problem solve. The idea of incorporating more time to just explore problems really had an impact on how I taught math.  Perhaps the reason many feel they are not good at math is that they never really had an opportunity to explore mathematics and develop  higher level skills to make math a habit of mind rather than a list of skills to be learned.

So how do we program and create an environment so students are more involved in the math they do?  According to child development experts [2, 6], adolescent students thrive on arguments and discussions.  They are introspective and often critical of their own thoughts. They need to feel relevant and are concerned with justice and fairness. They are very self-aware and worry about what others think of them.    We should take advantage of adolescent motivations and concerns, and use them to help us teach students mathematics.

Anthony and Walshaw [1] have developed the following set of principles of effective pedagogy of mathematics.


We can use this guide to create a diverse program that makes mathematics a habit of mind. The principles address content as well as ways to think about and approach math.  We need to think about what a classroom environment supporting these principles looks like.

Below are some suggested ways to help you create a culture of mathematics in your classroom for September.

Representing Mathematics in the Classroom

  • Post a variety of puzzles on the walls in class or in the hallways.  Students might as well be intrigued by puzzles on the walls while waiting to come into class.
  • ThinkFunHave games that require persistence, thinking and problem solving available during breaks and for weekend loans. Games like Rush Hour or other Thinkfun games are perfect to develop these types of skills.  Be sure to incorporate this into your program.
  • Provide print materials like puzzle magazines or math story books available for students to read.  Why not read math related materials during independent reading time?
  • Ask students to describe their culture’s number system.  Post these on the walls for future reference.
  • Include a word wall for mathematics to be used during discussions and debates.
  • Post question prompts like “This solution is similar/different from this solution because…” or “I agree/disagree with your solution because…” or “I like how you represented your solution by…”.  Intermediate students like to debate and discuss, so let’s take advantage of this trait!
  • Post newspaper clippings, advertisements, photographs, art or anything related to a mathematics inquiry.  Encourage students to examine fairness and question the use of statistics in the media. Draw connections between math, patterns, art and architecture.
  • Have a variety of tools available in the classroom for students to represent their thinking.  Manipulatives and technology provides hands-on experiences to help bridge concrete representations to abstract models.

Developing Risk Takers and Questioning Skills


I noticed that my grade 8 students left many questions blank on the first test I gave them.  At first I thought they just didn’t understand the math. I later realized that understanding was only part of the problem. They were afraid to take the risks needed to investigate and solve problems. Students gave up when a solution was not immediately apparent.  I decided to use the game Mind Trap at the beginning of each class to encourage students to take risks and ask questions.  This game consists of questions that are set in a crime context. Students become more comfortable struggling with a problem, learned to ask better questions and identified specific properties of the problem to help them solve the crime.  It’s a great resource for intermediate students.

Life Size Mathematics

North Option OISE/UT students dramatizing Frogs

North Option OISE/UT students dramatizing Frogs

Take mathematics off the textbook page and bring it into the real world.  Students are engaged when they are part of the mathematics.  Frogs is an excellent way to dramatize mathematics and demonstrate problem solving.  In this task, students wear Hawaiian leis to represent green and yellow frogs.  Teachers act as facilitators to help identify patterns for when students get stuck.  Towers of Hanoi is another great puzzle to do using cardboard boxes of varied sizes.  These are great ways to build collaboration and introduce them to reasoning at the beginning of the year.

Problems for Pairs or Triads

Students need more opportunities to regularly explore math problems.  Working in pairs or triads creates a safe community where they can struggle with a problem, contribute their own thoughts, build on one another’s ideas and debate in a more controlled setting.   When students are given opportunities daily to discuss and work together on problems, they eventually feel more confident and are able to take more risks.    Puzzles like Shikaku [5} or Paint by Numbers (also known as Pic-A-Pics) are great logic puzzles for students to develop their reasoning.

MoreGoodQuestionsGoodQuestionsQuestions from More Good Questions [4] and Good Questions for Math Teaching [3] are great questions to further develop their problem solving and connect to the curriculum they are learning.

Talk Time

Adolescents love to talk so let’s give them this opportunity!  Not only do we want them to talk in their math pairs or triads, but as a whole group as well.  Provide many opportunities to debate, justify and ask questions to one another.  If they don’t understand another group’s solution, have them challenge them and ask questions to clarify their thinking.  Use question prompts that are posted on the walls as reminders to help them focus their questions. It’s such an amazing thing when you hear a heated debate about mathematics in your intermediate classroom!

In conclusion, if we want our students to value reasoning, be active participants, and to enjoy mathematics, we need to build a culture of mathematics by providing an environment to help them see and be part of the math.  As teachers, we need to model problem solving and work out problems together with the class.  If teachers are more excited and engaged about math then students will be as well.   Doing this at the beginning of the year will set a positive attitude and immerse students in a place that develops those habits of mind for mathematics.  When you hear your students say, “I remember in math when we did…” then you know they’ve got you excited about math too.


  1. Anthony, G. and M. Walshaw, “Characteristics of Effective Teaching of Mathematics:  A View from the West”, Journal of Mathematics Education,      Vol 2, No. 2, (Dec 2009), pp 147-164.
  2. Health Canada, “Growing Healthy Canadians – Transition to Adolescents”,
  3. Schuster, L. and Anderson, N., “Good Questions for math Teaching:  Why Ask Them and What to Ask, Grades 5-8”, Toronto:  Pearson Education, 2005.
  4. Small, M. & A. Lin, “More Good Questions:  Great Ways to Differentiate Secondary Mathematics Instruction”, Toronto:  Nelson Education Ltd, 2010.
  5. Wanko, J., “Deductive Puzzling”, Mathematics Teaching in the Middle School,  Vol 15, No. 9, (May 2010), pp 524 – 531.
  6. Washington State Online Foster Parent Class. “Child Development Guide”,

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