How can I help students develop a deeper understanding of Mathematics?

The Formative Assessment Lessons are of two types; those that focus on the development of conceptual understanding and those that focus on problem solving. Concept Development lessons are intended to assess and develop students’ understanding of fundamental concepts through activities that engage them in classifying and defining, representing concepts in multiple ways, testing and challenging common misconceptions and exploring structure. Problem Solving FALs are intended to assess and develop students’ capacity to select and deploy their mathematical knowledge in non-routine contexts and typically involve students in comparing and critiquing alternative approaches to solving a problem.

In this PD module, we focus on Concept Development lessomss. Research has shown that individual, routine practice on standard problems does little to help students deepen their understanding of mathematical concepts. Teaching becomes more effective when existing interpretations (and misinterpretations) of concepts are shared and systematically explored within the classroom. The FALs described here typically begin with a formative assessment task that exposes students’ existing ways of thinking. The teacher is then offered specific suggestions on how these may be challenged and developed on through collaborative activities. New ideas are constructed through reflective discussion. This process places considerable pedagogic demands on teachers, and it these demands that this module is intended to explore.

About the MAP PD Modules

These modules have been developed by the Shell Center team at the Center for Research in Mathematics Education, University of Nottingham. They draw on successful materials developed by the team for Bowland Maths and Improving Learning in Mathematics.

Getting started

Download the print materials (links on the left) and read the main Module Guide.

Use the tabs at the top of the screen to browse the video which accompanies this module.