Mohan Chinnappan’s research while affiliated with University of South Australia and other places

Understanding children’s attitudes towards mathematics provides insights into their lived mathematical experience and engagement. Despite the considerable amount of research into students’ attitudes toward mathematics, limited research has been conducted into young children’s attitudes toward mathematics (YCATM). Within this limited research, investigating YCATM has certain challenges. From a methodological perspective, limitations exist regarding the type of research techniques that can be employed to study the nuances of the issue. The foci of this paper are to present and evaluate a methodological approach that used children’s drawings (N = 106) and interview responses as the primary sources of data. Findings indicate that the strategy of “Draw yourself doing mathematics”, when used with other research methods, generated rich attitudinal data in the form of personal stories about YCATM.

A deep understanding of fraction concepts and operations is necessary if pre-service teachers (PSTs) are to present the concepts in multiple forms to learners. Such an understanding needs to be grounded in rich conceptual knowledge. In the present study, we explore the development of this understanding by supporting a cohort of 103 PSTs, who had previously demonstrated poor conceptual understanding of fraction concepts and operations, with a Representational Reasoning in Teaching and Learning (RRTL) approach aimed at strengthening their conceptual knowledge. A comparison of pre- and post-test results indicated that participants showed a significant improvement in shifting the balance of their fraction knowledge to the conceptual end of the procedural-conceptual spectrum. Insights into how this approach assisted in developing PSTs’ conceptual understanding were explored through interviews with four participants and an analysis of their pre- and post-test responses. We suggest that the use of teaching strategies such as RRTL are necessary in order to assist PSTs develop strong conceptual knowledge of fractions.

This chapter seeks to take a modest and yet formative approach in proposing computer-based test (CBT) as the inevitable next wave in digital assessment. The major section reports on the practical design of developing and administering CBT in a mathematics competition by HOTS educational innovation development (HEID) in a mathematics competition. This chapter describes the CBT developmental process undertaken by HEID, which focuses on constructing multiple-choice test items, administering CBT, and scoring the test. While CBT offers the possibility of improving assessment, the process of preparing items and conducting online competition have nevertheless encountered several challenges such as getting quality test items, school and teacher readiness, seat time in front of computer, computer compatibility, and internet speed. As with many other educational reforms at infancy, more research in the area of implementing CBT to facilitate international competitions is needed in landscaping the assessment platform of Education 4.0.

The benefit of homework (HW) has been the subject of ongoing debate among various stakeholders. Within this debate, and in relation to teacher development, prospective teachers’ views of HW have received limited attention. In this study, we survey primary pre-service teachers’ (‘PSTs’) views of HW use (n = 45 teaching grades 2–5; n = 39 teaching grades 6 and 7) in a single discipline (mathematics) at one large Australian university. The literature suggests students in upper primary and secondary grades will benefit from the use of mathematics HW. Results of the study, in contrast, suggest our PSTs teaching early primary grades planned to give proportionally (but not significantly) more mathematics HW than those teaching later grades. Reasons for this disparity are discussed. We argue there is a need in teacher development to equip PSTs with a better understanding of how classroom and home-based learning work together in the development of mathematical understanding.

The use of fully online instruction has been proliferating in higher education. In undergraduate mathematics, arguments about the effectiveness of fully online instruction have been met with contrasting claims about its potential. Some assert that fully online instruction can promote a deeper and richer conceptual understanding of mathematical ideas while others claim it is difficult to teach mathematics effectively in a fully online context. The aim of this study is to examine these claims by documenting relevant empirical evidence, the findings of which we hope will inform current efforts, by both faculty and administrators, to improve fully online mathematics instruction. 50 free e-prints may be found here: https://www.tandfonline.com/eprint/FRTEBCVWYEKBIHU84M87/full?target=10.1080/10511970.2018.1472685

Teacher knowledge that supports effective mathematics teaching has come under scrutiny alongside associated theoretical developments in the education field. Amongst these developments, the Mathematics Knowledge for Teaching (MKT) framework by Ball et al. (J Teacher Educ 59(5):389–407, 2008) has been one of the most influential. While MKT has been useful in helping us identify the knowledge strands teachers need for effective practice, the interplay among MKT’s knowledge strands during the course of teaching has received less attention. In this study, we address this issue by exploring interaction between Subject Matter Knowledge (SMK) and Pedagogical Content Knowledge (PCK) in the domain of secondary geometry. We provide results of a preliminary study of SMK and PCK in the context of a teacher teaching students how to construct and bisect an acute angle with the aid of compass and ruler only. Our analysis suggests future research needs to consider (a) the particular characteristics of the discipline of geometry and (b) the developmental knowledge trajectories of teachers of geometry in order to better understand how teachers’ SMK influences and influenced by PCK.

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, although it is unclear whether this is because regular users are generally weaker mathematics students or because RLV use is somehow depressing student learning. Through the lens of cognitive engagement, a quasi-experimental pre- and post-test design study was conducted to investigate the latter possibility. Cognitive engagement was operationalized using the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F), which measures learning approaches on two major scales: surface and deep. In two mathematics courses at two universities, in Australia and the UK, participants were administered the questionnaire near the course start and finish. Overall findings were similar in both contexts: a reduction in live lecture attendance coupled with a dependence on RLVs was associated with an increase in surface approaches to learning. This study has important implications for future pedagogical development and adds to the sense of urgency regarding research into best practices using RLVs in mathematics.

Two key variables emerged from the literature review is that Specific Matter Knowledge [SMK] and Pedagogical Content Knowledge [PCK] can influence the mathematics teachers’ Professional Development [PD] needs. However, the key variables of SMK and PCK that were being investigated were not defined clearly. Empirical evidence that support relationship between SMK and PD and PCK and PD were not verified. In addition, how does PCK mediate SMK and PD is not clear and somewhat lacking. Therefore, the purpose of this paper was to examine the relationship between primary mathematics teacher’s SMK, PCK and PD needs. Results of path analysis with SmartPLS indicated that the direct effect of SMK on PD was mediated via PCK. This data provide support for the claim that PD programs for future teachers of primary mathematics should be driven by a more nuanced understanding of the link between SMK and PCK.

The Malaysian Ministry of Education had advocated for the integration of Higher Order Thinking Skills [HOTS] in mathematics and science. The result of TIMSS has placed greater emphasis on the need to teach HOTS effectively. Our argument is that in order for HOTS to have a significant impact on students' engagement with and improvement on mathematical problem solving, researchers ought to undertake a fine-grained analysis of student performances in relation to particular tasks and use this information to help teachers understand and integrate HOTS in their teaching. In this paper, we present a critical analysis of selected mathematical problem tasks and demonstrate how to better support students in the use of HOTS in making progress with such tasks. In so doing we present a methodology that can be utilised by teachers better understand the role of HOTS in empowering students move from lower to higher levels of cognitive funtioning in the context of demanding tasks. Our methodology provides an important starting point for the design of future professional development programs for Malaysian mathematics teachers in articulating HOTS and implementing them in regular mathematical problem solving teaching and learning.

Proceedings of the 39th annual conference of the Mathematics Education Research Group of Australasia, in Adelaide, South Australia. Available at https://www.merga.net.au/node/38?year=2016