## 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. (Requires Adobe Flash Player).