1. 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

3. 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

4. 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

5. KEY NUMBER SKILL CLUSTERS IN CAPS FP
- Bridging through 10 (16 + 7)
- Jump strategies (102 – 27)
- Re-ordering (3 + 78; )
- Relationship between + and – (13 + __ = 81)
- Compensation (54 – 9)
- Doubling and Halving ( ; 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

6. 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
Items focused on number structure, properties and relationships, and the behaviour of operations, rather than on ‘operating’: e.g.
Given that =181
What is ?
Add/subtract 1, 2, 3, 4, 5 and 10 to any number
Place value decompositions of number
Fact triples in 1-20 range

7. 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

8. Rapid recall items
Variations and connections as key design principles

9. Strategic calculating

10. Strategic thinking

11. Reasoning Chain booklet

12. 2017: Initial feasibility trials in Gauteng & EC G3
Eastern Cape

13. 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