Posted on November 7th, 2011
Idorenyin (Ido) Jamar is a Mathematics Professional Development Specialist with the Teachers Development Group. In this video she discusses why it is important to let students work on a mathematics task without first showing them how to solve it.
[Video Transcript] Why is it important to let students work on a math task without first showing them how to solve it? We know that parents and students often expect the teacher to teach them, to tell them, to show them how to solve a problem, or to teach a concept. However, skilled math teachers often won't do this. They will often hand out a task, making sure that students understand what it is that you want them to do, but then giving students a chance to figure out as much of it as they can on their own, without instruction.
Why do they do this? Why is this important? Why not just teach them? First of all, mathematics is highly, highly connected. New knowledge builds upon old knowledge. New knowledge connects with old knowledge. By giving students a chance to approach a new topic in this way, the students themselves have to draw upon what they already know. The students then make connections for themselves. They're also more likely to remember this new knowledge, and then when they see novel problems or new topics, they're more likely to be able to see how the old knowledge applies to the new, because that's been part of the learning process.
Next, students' errors and misconceptions emerge when you let them go on their own. Now this is—it's productive, although we might think it's not. It's very productive for their learning because new knowledge, developing new knowledge, really does require you to address your old misconceptions, those things that were incomplete. This of course can only be done if the misconceptions are allowed to surface.
Also in the process, students learn that mistakes are just a normal part of the learning process.
Finally, problem solving is a very important part of mathematics, but not just problems in books or on tests, but problems in the real world and problems in the workplace. Solving problems requires you to first analyze the problem and then go back into your tools and select the concepts and skills and procedures that you know already, that you can bring to bear on solving that problem. So when you let students explore rich tasks in the classroom in this way, they're more likely to see this importance of problem solving in mathematics, and also they're able to develop mathematical practices, such as making sense of problems and persevering and solving them.
Of course, after students have had a chance to explore a task on their own, the teacher must bring the class together for a discussion, and then the teacher can build on what, the ideas that have emerged in the students' work, and move the class towards the key mathematical goals of the lesson. But by first having had a chance to work on the task on their own, students are able to come to this discussion and bring their thinking to the process. They have an entry point into the discussion, and they're much better able to understand the ideas as they emerge.
Idorenyin (Ido) Jamar is a Mathematics Professional Development Specialist. She provides school-based coaching and professional learning experiences for mathematics teachers, coaches, and school administrators. Ido was formerly a Fellow at the Institute for Learning. As a member of the Institute for Learning's Disciplinary Literacy mathematics team she designed and facilitated professional development sessions for teachers, coaches and administrators in urban districts around the country. She has also been involved in the revision and development of secondary mathematics instructional materials. Prior to working for the Institute for Learning, Jamar taught secondary mathematics in urban schools and was an Assistant Professor of Mathematics Education at the University of Pittsburgh and Bayero University (Kano, Nigeria).