Hamsa Venkat, Mellony Graven & Broader Team Research, Development, Collaboration for Number Sense – Strengthening Caps implementation by foregrounding reasoning and strategies in diagnostic assessments and PD programs Collabrative project between the two SA Numeracy Chairs in SA Mandate to use the research to develop interventions with potential to work at scale to improve outcomes in Maths at primary level Share details of a collaboration between Chairs, national and provincial DoEs, AMESA, SAARMSTE and NGO communities, and ongoing work on exploring scale-ability Hamsa Venkat, Mellony Graven & Broader Team

Concerns with primary learners’ number skills Limited evidence of work with mental recall of a bank of basic facts, and of development and application of this recall in problem-solving Limited evidence of work with mental recall of a bank of basic facts

Current FP curriculum & assessment FP curriculum specification does include attention to key clusters of fluent recall skills, and problems that can be efficiently and flexibly solved with good number sense BUT ANAs and Common Assessment largely did/do not assess for these kinds of number skills in marking for the correct answer only

KEY NUMBER SKILL CLUSTERS IN CAPS FP - Bridging through 10 (16 + 7) - Jump strategies (102 – 27) - Re-ordering (3 + 78; 19 + 27 + 21) - Relationship between + and – (13 + __ = 81) - Compensation (54 – 9) - Doubling and Halving (26 + 26 ; 76 divided by 2) All of these strategies rest on known or rapidly recalled facts, mostly set in the 1-20 number range Currently, assessment does not test for either rapid recall or for strategic, rather than procedural, calculation

STRATEGIC CALCULATING ITEM CATEGORIES RAPID RECALL STRATEGIC CALCULATING STRATEGIC THINKING Basic doubles Items such as 99+99, that are laborious to do in a procedural calculation orientation, but easy to compute mentally if recognized in relation to 100 +100 Items focused on number structure, properties and relationships, and the behaviour of operations, rather than on ‘operating’: e.g. Given that 43+138=181 What is 181-43? Add/subtract 1, 2, 3, 4, 5 and 10 to any number Place value decompositions of number Fact triples in 1-20 range

Diagnostic Assessment format 2-3 week testlet format focused on a particular cluster (e.g. Bridging though 10), including Rapid Recall, Strategic Calculating and Strategic Thinking items. Test-teach-test model: time-limited test Teacher marking followed by guidance for interim ‘reasoning chain’ activities related to cluster for mental maths lesson section Re-test provides feedback on learning, and hence, success of teaching 3-4 clusters/term

Rapid recall items Variations and connections as key design principles

Strategic calculating

Strategic thinking

Reasoning Chain booklet

2017: Initial feasibility trials in Gauteng & EC G3 Eastern Cape

Broader trial plans with DBE Work with three provinces: Assessment & FP leadership in these provinces and 10 FP Subject Advisers Chair teams to run training session for SAs on supporting teacher working with testlets and reasoning chain materials SAs to run testlets; Assessment leaders to observe teaching of an interim lesson, and collate testlet data If results are promising, testlets and teaching materials to be developed for remaining four clusters