1. Numeracy Chairs assessment working group
Assessing fluencies and strategies in national diagnostic assessment: Panelists: Mellony Graven & Hamsa Venkat; Mark Chetty; Busi Goba
Numeracy Chairs assessment working group
Mellony Graven And Hamsa Venkat
INTERNATIONAL EXPERTS: Mike Askew & Bob Wright
DBE: Mark Chetty
EC DoE: Nolunthu Baart & Zanele Mofu
AMESA: Busi Goba
SAARMSTE: Lyn Webb
NGO SECTOR: Lynn Bowie
Wits MATHS CONNECT: Corin Mathews, Samantha Morrison, Thulelah Takane, Herman Tshesane & Marie Weitz
SANC: Debbie Stott & Lise Westaway

2. SA Numeracy Chairs: Rhodes & Wits
Dual foci on research & development
Making a difference in the schools, teachers, learners and communities that we work with
Researching ways forward to the many challenges we face in numeracy education: investigate challenges BUT focus on what is possible within context of challenge – i.e. do something!
Range of projects –focus on our collaboration in relation to assessment

3. SA assessment & performance context
ANA – part of FFL campaign; aimed to support teaching and learning
Since 2015 teacher resistance to ANAs

4. Earlier research across Chairs
In 2012 & 2013 we researched teacher experiences of ANAs across the two Chair projects
Resulted in publications directed to:
researchers (AJRMSTE)
teachers (LTM)
a discussion document (sent to DBE stakeholders)

5. Key findings
Teachers bought into the aims but critical of process, memoranda and time issues (learner pace); average 4 weeks taken out of teaching
One teacher wrote:
“It took nearly +-4 weeks. The first week was spent photostatting. One exemplar was 26 pages! One paper took nearly 2 weeks to go through. I neglected my other assessment tasks.”
While intention was for ANA to feed diagnostically into teaching, experience was of ANA disrupting teaching and learning

6. Lack of ANA attention to strategic sophistication
Improving profile of FP performance on ANA, but not feeding through sufficiently into IP and SP
ANAs overlook assessment of mental strategies & sophistication of strategies. This absence in the ANAs leads to lack of teaching for mental strategies, even whilst emphasized within the CAPS documents for FP & IP (Graven, Venkat, Westaway & Tshsane, 2014)
Learner weaknesses clear in continued concrete or ‘steps gone wrong’ working e.g tally lines or column method answer of 910 in IP

7. Widespread unit tally use in Gr 4 & beyond
G4 CAPS item:
234 x 68

8. ‘James’: 66.7% ANA vs 18.2% Wright
MR assessment (Wright et al, 2006)
Able to identify most numbers in range
Unable to state the number word after a given number beyond 1-10 range, without reverting to counting from 1
Able to answer early addition/subtraction and missing number problems with counters.
ANA
Marking for answers, without attention to sophistication of strategies is probably not helpful in the early years. Unhelpful feedback loop into teaching
Weitz & Venkat, 2013

9. Space for change
Because assessment feedback loops back into teaching and learning –assessments should be carefully developed to address mental maths fluency & strategy, underpinned by number sense
DBE interest in diagnostic assessments is an opportunity. Focus on assessments that can support improved mental fluency and strategic thinking
Establishment of working group with range of participants looking at developing diagnostic assessment items to promote development of strategic thinking and numeracy fluency

10. MENTAL MATHS STRANDS IN CAPS FP
Using research base to identify fluencies and strategies, we looked into FP CAPS.
Strategic calculation categories
- 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)
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

11. STRATEGIC CALCULATING
ITEM CATEGORIES
RAPID RECALL ITEMS
STRATEGIC CALCULATING
STRATEGIC THINKING
In CAPS mental maths strand
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 ?
Basic doubles
Add/subtract 1, 2, 3, 4, 5, 10 and 100 to any number
Place value compositions and decompositions
Fact triples in 1-20 range
Strategic sophistication & efficiency built on number relationships and the behaviour of operations, rather than focusing on individual, separate calculations

12. Diagnostic assessment G3
‘Test-let’, focused on a particular strategy (e.g. doubling and halving), with rapid recall, strategic calculating & strategic thinking items; time-restricted format
2-week block begins and ends with a 15 minute test-let
Teacher marking of test-let, followed with 6-8 ’reasoning chain’ activities for the interim lessons’ mental maths sections, aimed at developing fluencies and strategies;
Marking of re-test provides feedback on learning & hence, successes of teaching
3-4 strategies in focus each term

13. RAPID RECALL ITEMS Doubling and halving
Inclusion of ‘variations’ and ‘connections’ as key principles

14. Strategic calculating Strategic thinking

15. From diagnosis to 'reasoning chains’
Basic doubles of numbers in the 1-10 range with associated images, followed by reasoning chains linked to adjusted images:
6 + 6
6 + 7
6 + 7 =
‘Doubles means I have two rows the same length.’
‘6 and 7 is one block more than 6 and 6’

16. 2017 and beyond Prepare time limited testlets for each strategy
Prepare activities and teacher guidelines for reasoning chains
Small scale piloting across contexts: SAARMSTE community involvement welcome
Collation of findings
Revisions for larger scale national piloting in 2018 with DBE
2019 input with framework and exemplars for broadening into national policy