Page 123 Graven, M., & Venkatakrishnan, H. PROMOTING TEACHING AND LEARNING OF STRATEGIC CALCULATION AND THINKING THROUGH DIAGNOSTIC ASSESSMENTS Professor Mellony Graven Rhodes University, South Africa and University of Queensland, Australia m.graven@ru.ac.za Professor Hamsa Venkatakrishnan University of Witwatersrand, South Africa Hamsa.Venkatakrishnan@wits.ac.za ABSTRACT This paper shares the results of the first of a series of diagnostic assessments focused on promoting the teaching and learning of calculation strategies for Grade 3 learners in South Africa. The series of assessments address calculation strategies such as bridging through ten, jump strategies and doubling and halving. They are accompanied by reasoning chains for teacher use in eight ten-minute mental mathematics sessions designed to develop learner fluency in related skills and the focal strategy. The assessments are then used as a post-test to gauge the improvement in student learning. Initial trials were conducted for the ‘bridging through ten’ strategy in six classes across two provinces in South Africa. Results show positive learner outcomes. The format of these assessments and the accompanying reasoning chains are informing the national landscape where summative end year assessments have been abandoned in favor of assessments that can inform teaching throughout the year. Keywords: Diagnostic assessment; reasoning chains; strategic thinking INTRODUCTION AND CONTEXT Mathematics education in South Africa is argued to be ‘in crisis’ (Fleisch, 2008) with learners performing below expectations on national, regional and international studies. Furthermore, performance is highly polarised indicating among the greatest performance gaps internationally in mathematics between rich and poor (Reddy, 2006). Spaull and Kotze (2015) argue that by Grade 4 a majority of learners are already two grades behind expectations. A factor widely identified as contributing to poor performance and weak progression is a lack of number sense and a dominance of concrete methods of calculation. Schollar’s (2008) study for example found that 79.5% of the Grade 5 test scripts from 154 schools across all 9 provinces relied on simple unit counting to solve problems. Our own research across the multiple schools concurs with this and we have widespread evidence of learners using drawn tallies for simple calculations such as 10+10+10 (e.g., Weitz & Venkat, 2013). The implementation of the Annual National Assessments (ANAs) by the Department of Basic Education in 2011 for Grades 1-6 and 9 did little to address poor performance and weak number sense. As Diamond (2007, p. 306) argues while high-stakes assessments ‘may get teachers’ attention, they provide few resources for addressing issues of inequality in schools.’ The ANAs were criticised by teachers and teacher unions and ended with refusal by some schools to write them. They were abandoned in 2016. Among the criticisms was that they did little to encourage the teaching of number sense and the focus on correct answers fed Citation: Graven, M., & Venkatakrishnan, H. (2018). Promoting teaching and learning of strategic calculation and thinking through diagnostic assessments. Integrated Education for the Real World 5th International STEM in Education Conference (pp. 123-129). Brisbane: Queensland University of Technology.