Focus on Math

Helping children become mathematicians!

A Small Change but a Big Result May 13, 2011

Yesterday a teacher in our district, Kevin, shared with me a wonderful story about math in his classroom. Kevin and I go back a ways — I was the Faculty Associate when he completed his Professional Development Program (student teaching) through SFU, and he had also taken the “how to teach math” course from me. He was hired in my district, and he has spent most of his career teaching at a rural K-12 school where for the past number of years he has taught the gr 8-12 math courses.

Kevin told me of his frustration, as well as his students’ frustration, in the math classes over the last years. He would present a lesson, have the students begin working on the problem set in the text book, and then have the students do the remainder of the assigned problems for homework. However, invariably the students had difficulty with the homework problems and would become increasingly frustrated with trying to solve those problems. The next day Kevin often felt he needed to get on with the new lesson, but clearly time was needed with these homework questions which, being later in the practice group, were often the more difficult problems in the set.

Kevin remembered the emphasis I had put in the “how-to-teach-math class” on the power of students solving problems, and he decided to change up the class time with his students to see if he could incorporate more problem solving in his class.  So, instead of this:

  • teach a concept
  • do the first, easier problems in the practice set in class, students working together
  • send home the later, harder problems in the practice set, students working alone,

Kevin changed his time with students to look like this:

  • do the later, harder problems from yesterday’s lesson in class, students working together
  • teach a new concept
  • send home the first, easier problems as homework, students working alone.

Kevin found this to make a profound difference for his students. Where many of them had felt unsuccessful in math, never being able to complete the homework on their own, they were now able to do so. This began to build their confidence. When they worked on  the harder problems together in school, most students found the knew most of what to do. Sometimes they were forgetting only a small step. Kevin realized when the students had tried the problems at home, if they could not arrive at the answer at the back of the text, most would erase all of their work, believing they were completely off track. Working together in class students had the opportunity to make connections to previous lessons, to communicate their thinking, to reason about the logic of what they were doing, to justify their answers. By engaging in these processes day after day, the students began to build a set of problems solving skills and strategies than empowered their mathematics thinking.

The three “chunks” of the lesson really did not change, but in changing the order in which they happened (which in turn changed which problems were addressed through the mathematical processes**) Kevin facilitated a change in student understanding and success. Way to go, Kevin!

I hope you will look at how math is going in your classroom and see if you need to turn it “upside down”!
Mathematically yours,

P.S. The NCTM lists the process standards as these: connections, communication, problem solving, reasoning and proof, and representation. More information about these can be found at this link:
In BC, and for the members of the WNCP in Canada, the mathematical processes are defined as these: communication, connections, mental math and estimation, problem solving, reasoning, technology, and visualization. More information about these can be found in the “front matter” of the BC IRP curricular documents found at this link:


One Response to “A Small Change but a Big Result”

  1. Hyun Says:

    This is a great idea! Yes, we can do upside-down and it can make a huge difference! Thanks for your tips!

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