Resources and Tools for Elementary Math Specialists and Teachers

More time for Problem Solving

This discussion is part of a collection:Learning Math Through Problem Solving

There is no doubt that problem solving skills are necessary, or that both NCTM and CCSS standards encourage them, but often our schools are not equiped with enough time to get through the content skills and therefore, omit teaching, or allowing students to experience problem solving. During a time when more and more school districts are mandating every moment of instruction, how do you make time to step outside of the box and have students creatively problem solve?

Replies

I think that an emphasis on problem solving over skills work is an efficient way to achieve thinking and cooperation skills, as well as content skills, but the teacher in question needs to be comfortable with students taking the lead in ideas, with handling their false starts and frustrations, and with valuing divergence in the work. This mind set can be achieved when ed. leaders instill confidence and empowerment in the teacher force.

One way to start is to make more offerings in pd that develop teachers as mathematicians, people who appreciate the depth and beauty of the subject and who appreciate the individual achievements in its historical development. As one ps example, the problem “What 4-digit number, when multiplied by 4, results in a product the has the same digits in reverse order?” is one that involves some good reasoning, estimating, and a good bit of mental and manual calculating, but the question, “Are there other examples?” leads to much, much more skills work, a deeper understanding of place value, some pre-algebraic and formal thinking, surprising generalizations, and new avenues to explore. When students and teachers routinely ask Qs like that we are making progress.

We definitely need stronger faith in our educators as mathematicians and increases in PD will definitely provide that. In my experience PD is usually focused on an increase in reading strategies since they touch on all subject areas, but I think that content specific PD is necessary as well. Early in my teaching career I had the privilage of working with a math specialist who insisted that we start most of our lessons with a word problem or problem solving situation and then come back to a similar problem at the end of the lesson to show students that throughout the lesson they had learned to solve this problem.