Why do it?

So, why should we teach math through problem solving?

One does not have to look very far to find evidence that math should be taught through a problem based approach. The mathematics curriculum guide itself, the very document that outlines what we have to teach in math states in a very straightforward way that math should be taught in a problem solving mode. Mathematics Grade 6 (2005) suggests that “our mathematics curriculum has been guided by the principals of NCTM – National Council of Teachers of Mathematics, which establishes problem solving as one of the four central elements of the curriculum. These unifying ideas, or the central elements, have been incorporated into our key stage outcomes that serve to link the content to methodology” (p.5). It goes on to state that “they (the unifying ideas) make it clear that mathematics is to be taught in a problem-solving mode, that classroom activities and student assignments must be structured so as to provide opportunities for students to communicate mathematically, that via teacher encouragement and questioning, students must explain and clarify their mathematical reasoning and that the mathematics with which students are involved on any given day must be connected to other mathematics, other disciplines and/or the world around them” (p.5). The Mathematics Grade 6 (2005) curriculum guide does not simply suggest that students engage in problem solving once and a while, but state that “students will be expected to address routine and/or non-routine mathematical problems on a daily basis” (p.5).

Upon thinking about how to teach students mathematics we should reflect upon the following questions: What is the purpose of teaching mathematics? Is it to have children memorize how to do something? Or is it to teach math so students can understand the concepts well enough to be able to apply them to other situations? Hopefully, it is the latter. Teaching math means we help students to understand the math they are learning, if there is no understanding going on, are they really learning? If a child can recite their multiplication facts, what does this tell us? Nothing, only they have a good memory. We need to teach for understanding and not merely for knowing how to do something. To teach for understanding, we need to create classrooms that promote this type of learning. Borgioli (2008) state that “in classrooms that promote teaching and learning mathematics with understanding (instead of memorizing abstract algorithms and mimicking teachers’ solution paths), students collaboratively engage in making sense of mathematical tasks in their own ways and communicate their thinking with one another” (p.186). She then goes on to say that one of the three critical pieces to create this type of classroom is in the actual tasks that teachers pose or give to students. Borgiolo (2008) suggest that “the tasks be complex and problematic for the learner and involve meaningful problem solving as opposed to simple drill and practice exercises” (p.186). We really need to begin listening to this research, as many of our classrooms today still use drill and practice as the only means to teaching and learning math. I would then have to argue whether or not students are actually learning.