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

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

SA assessment & performance context ANA 2012-2014 – part of FFL campaign; aimed to support teaching and learning Since 2015 teacher resistance to ANAs

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)

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

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. 98+2 tally lines or column method answer of 910 in IP

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

‘James’: 66.7% ANA vs 18.2% Wright MR assessment (Wright et al, 2006) Able to identify most numbers in 1-100 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

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

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; 19 + 27 + 21) - Relationship between + and – (13 + __ = 81) - Compensation (54 – 9) - Doubling and Halving (26 + 26 ; 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

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 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? 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

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

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

Strategic calculating Strategic thinking

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 = 6 + 6 + 1 ‘Doubles means I have two rows the same length.’ ‘6 and 7 is one block more than 6 and 6’

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