The Bowland Maths Assessment Materials
The role of assessment is to see how far a pupil's responses match performance goals in mathematics. There is an international recognition that performance goals in maths should go well beyond the mastery of procedures, as exemplified in a statement from the recent USA ‘Common Core State Standards’:
"Proficient students of all ages expect mathematics to make sense. They take an active stance in solving mathematical problems. When faced with a non-routine problem, they have the courage to plunge in and try something, and they have the procedural and conceptual tools to carry through. They are experimenters and inventors, and can adapt known strategies to new problems. They think strategically."
(from the recent USA Common Core State Standards)
Most forms of assessment common in the UK only address one aspect of mathematical mastery - assessing whether students "have the procedural and conceptual tools". Bowland Maths provides materials that can develop pupil capacity in understanding and applying maths skills in real and diverse contexts. For instance, the Bowland Case Studies engage pupils' interest in mathematics, and help them develop the ability to apply their mathematical knowledge to rich and diverse problems. The teaching materials are ideal not only for developing pupils’ understanding about why mathematics matters in life, but also helping them to become proficient in problem solving. But how can such proficiency be assessed?
But how can this proficiency be assessed?
Bowland self-contained assessment tasks
Bowland Maths includes 35 assessment tasks designed to help teachers to assess their pupils' achievements and progression. To help with this assessment, each task comes with sample pupils' work and a "progression table", showing how pupils' work on this task can provide evidence of progress. These self-contained tasks take between twenty minutes and an hour.
These materials are also ideal for formative assessment which provides the types of rich feedback that have been proved to help pupils improve their reasoning.
Assessing the Case Studies
For seven of the most popular Case Studies, Bowland has developed comprehensive guides to help teachers to assess pupils' achievement and progression as they work on the activities. As teachers gain familiarity with these assessment techniques, they should be able to apply them to the other Case Studies.
The Case Studies with Assessment Guides are:
Assessment in Bowland Professional Development Modules
Two of professional development modules are specifically designed to help teachers understand assessment in problem solving. These are:
Applying Mathematical Processes (AMP) materials – Nuffield Foundation
The Nuffield Foundation has developed some related resources, consisting of 20 Applying Mathematical Processes (AMP) activities that support the teaching and assessment of key processes. Bowland and Nuffield worked together to ensure that the two sets of resources had a coordinated approach. Similar advice and guidance for teachers as in the Bowland assessment tasks is given for each Nuffield AMP activity.
The AMP activities are updated versions of some investigations and practical problems from the Graded Assessment in Mathematics (GAIM) resources, originally developed in the 1980s.
These materials can be found on the Nuffield website at www.nuffieldcurriculumcentre.org