### Overview

A first phase of collaboration between our project teams at Wits and Rhodes Universities, the Department of Basic Education, international experts and a range of provincial professional, research and NGO bodies focused on developing diagnostic assessments for supporting number sense teaching and learning in Foundation Phase Grade 3.

This collaboration, begun in 2016, drew from consensus on the absence of attention to mental strategies and strategic awareness based on using number relations and structure in ways that promote the effectiveness and efficiencies involved in basic number sense in existing assessments. There was also agreement that assessment influences practice. This absence pointed to the need for assessments that address this gap. Policy level interest in diagnostic assessment formats that could be administered with an orientation grounded in feedback loops into teaching and learning was noted.

Following a study of the CAPS Curriculum, and the literature base on developing effective, efficient and flexible early number working, three types of early number items were identified as important to assess:

• Rapid recall items - noted in the CAPS curriculum for mental mathematics: e.g. multiplying by 2, adding and subtracting 1, 2, 3, 4, 5 and 10 to any number; place value decompositions of number, and key fact triples between 1 and 20.
• Strategic calculating items - include items such as 99 + 99 which are laborious to do in a ‘procedural’ calculation orientation – but very easy to do if the problem is recognised as one that is amenable to either rounding to 100, doubling 100 and then compensating (i.e. 2 x 100 – 2 = 198) or by using a number line – written or mental – to ‘bridge through 100’ (i.e. 99 + 1 + 98 = 198).
• Strategic thinking items - focused on understanding number structure, properties and relationships, and the behaviour of operations. Items focus on how using number and relationships can limit the extent of calculation needed: e.g. Given 43 + 138 = 181 then what is 181 – 43 = __ ?

These strands needed to work across key early number strategy skills specified in CAPS and backed by the literature:

• Bridging through 10
• Jump strategies
• Re-ordering
• Relationship between + and –
• Compensation
• Doubling and Halving

Promising outcomes of initial trials in Gauteng and the Eastern Cape focused on the ‘bridging-through-10’  strand. There is currently a proposal for starting extended trails on this strand.

### Teaching and learning resources

#### ** Bridging through ten strand

Assessment Testlets

Teaching Support Materials: includes teaching sequence and learner takehome worksheets