Category Archives: problem solving

OAME 2011

Here i am working hard on Problem Solving for Enrichment in grades 5-8, just one of the many great workshops at OAME 2011. The package of problems i’m working on will be made available to the Numeracy Committee at our June meeting. For information on next year’s conference, SO YOU CAN PUT IT ON YOUR LEARNING PLAN, please click here.

What effective math teachers have in common

Here is an article that Mrs. Brant passed on to me. It is about using an inquiry based model in your math class.

12 Days of Problem Solving

Whilst visiting ECG teachers yesterday, the Amazing Alice Anderson shared a lesson with me that she and Mrs. Bomberry did with their grade ones and twos. It is everything a model problem solving lesson should be: open to student exploration, various methods for solving, engaging and connected to other classroom content, etc.

Mrs. Anderson sang the 12 Days of Christmas with the students. i believe they also read a book about the traditional Christmas song. The students were then asked to figure out, just how many gifts does the person receive in the song, exactly?
Students were left to their own devices, chart paper and markers, to figure out how they were going to solve this question. Mrs. Anderson shared some of the attempts with me, which ranged from writing a number sentence, to creating a graphic or pictorial image of the songs’ gifts, to the construction of a list, table or graph. Others were drawing and grouping pictures of the gifts from the song.
These types of activities allow the students to use mathematical processes to solve a problem. It does not dictate exactly which method they need to use. By doing this, the students reveal plenty of interesting data concerning their abilities to understand and apply the knowledge they currently possess in math. It gives the teacher an opportunity to see what their students truly know about certain concepts and mathematical application or skills.
Bravo, Alice and Beth for tying in music, language and the holiday with a mathematical problem solving situation!! One quote from Mrs. Anderson that resonates with me is when she said, “There wasn’t a single kid saying, ‘I don’t want to do this,’ or ‘I don’t know how to do this.’ They were all trying their best to figure out the answer.
Afterwards, the groups can share their process and enlighten the rest of the class with the various ways one can approach a problem using mathematical processes.
Consider this a gift from Mrs. Anderson and Mrs. Bomberry. Try it out this last week before Christmas Break. It can be easily adapted to suit older grades (have them come up with an algebraic formula perhaps?) or other examples of compounded/growing patterns. It also lends itself to various strands.

Why Use Problem Solving?

Have you noticed a diatribe in my posting? Here’s the latest “gem” from an OCT colleague:

While not really a theory, for me one of the most influential ‘models’ in shaping my approach to teaching is of doing so through problem solving. “By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding” (Ontario Mathematics Curriculum, p 11). I find it surprising that many colleagues still struggle with this model, uncertain as to implementation and misunderstanding the “time factor” (“that would take waaaaay too much work to do – I don’t have time for that”).

As I learned to follow a problem solving approach to teaching and learning, what was impactful for me was the realization that, by teaching students mathematical concepts through problem solving, I can incorporate many critical skills while also providing opportunities for students to learn, connect, and apply concepts in meaningful and purposeful ways. “Students who engage in problem solving build a repertoire of reasoning skills and strategies…Students who work together to solve problems learn from one another as they demonstrate and communicate their mathematical understanding.“ (Guide to Effective Instruction K-6, Volume 1, p 27) Teaching through problem solving also provides a means to incorporate different strands of the curriculum as well as to integrate math into other curriculum areas. Too, it offers me a flexible framework in which to consider students’ needs, strengths, prior knowledge, and learning styles when planning, allowing me to differentiate based on their individual/common needs.

A problem solving approach also establishes a learning environment that values students’ thinking, communication, and participation, making students feel important, respected, and appreciated as a group member. It supports students in feeling accepted and valued for their different strategies, methods, and perspectives in solving problems, fostering confidence in themselves and their abilities to be successful in math.