## Do I stand back and watch, or intervene and tell them what to do?

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 *Problem Solving* lessons. In
most Mathematics classrooms, students are provided with structured tasks
and are told precisely which techniques to use: students learn by
following instructions. Even tasks described as ‘problem solving’ often
amount to mathematical exercises rephrased in ‘plain English’, with a
well-defined ‘correct’ solution method. Problems and situations that
arise in the world , however, are rarely exercises in the use of a
particular skill or concept. Such problems require students to make
simplifications, model situations, choose appropriate knowledge and
processes from their ‘toolkit’, and test whether their solution is ‘good
enough’ for the purpose in hand. If students are to learn to use their
skills autonomously in their future lives, they will need opportunities
to work on less structured problems in their classrooms.

### 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).