International comparisons of mathematics classrooms and curricula: the validity-comparability compromise

The pursuit of commensurability in international comparative research by imposing general classificatory frameworks can misrepresent valued performances, school knowledge and classroom practice as these are actually conceived by each community and sacrifice validity in the interest of comparability. The “validity-comparability compromise” is proposed as a theoretical concern with significant implications for international cross-cultural research. We draw on current international research to illustrate a variety of aspects of the issue and its consequences for the manner in which international research is conducted and its results interpreted. The effects extend to data generation and analysis and constitute essential contingencies on the interpretation and application of international comparative research.

The presence of mathematics anxiety in future primary school teachers and factors affecting abatement

This study reflects on the implementation of various teaching initiatives for reducing anxiety toward mathematics in students studying to become primary school teachers. We highlight similarities between these practices and those promoted by the 'Whole Teacher' approach - in particular, the aim to develop attitudes along with knowledge and skills. Here, the negative past associations with mathematics and anxiety toward mathematics that students bring with them have been a key consideration when designing the subject content and delivery. Given the important role these students will have in shaping mathematics education in the future, we suggest frameworks such as that of the 'Whole Teacher' could be extended to the university setting. We investigate four years of student feedback pertaining to a first year undergraduate mathematics unit, contending that the teaching initiatives introduced over time have helped students develop a positive attitude toward mathematics. We note, however, that the student-teacher relationship was still the most prominent factor directly identified by students who previously had a fear or negative attitude toward mathematics.

Use and perceptions of worked example videos for first-year students studying mathematics in a primary education degree

Worked example videos have great potential to be useful for students when learning mathematics as they can work through the questions at their own pace, pausing as needed, but still learn from the way the demonstrator thinks and solves problems. We created worked example videos each week for a mathematics subject taught in the first year of a primary education degree and investigated student perceptions and their usage patterns. An additional aspect of this undertaking was the inclusion of subtitles to make the videos accessible to hearing impaired and ESL students. This report will reflect on the process of creating these videos, as well as some initial findings on their success.

Once upon a time: children's literature and mathematics

What was your favourite book as a child? Remember the joy of reading it over and over again until the pages were worn and the corners curled. Have you thought about introducing your favourite book into a mathematics classroom? Utilising books in mathematics can engage and benefit every child in your class. Building on children’s wonder of literature can enhance their experience in mathematics. Building on children’s wonder of mathematics can enhance their experience of literature. In this paper we present the joy and value of employing children’s literature in the middle to upper primary mathematics classroom supported with engaging tasks that will have your students noticing maths in every story they read.

Multi-dimensional assessment of student capabilities in mathematics and science

This study investigated relationships between students’ understanding, performance, and disposition in mathematics and science. The results indicated that assessments should be used to promote all aspects of student capability. Separate frameworks of student capability in mathematics and science need to be created to capture the individual nuances within each subject.

Distinguishing between mathematics classrooms in Australia, China, Japan, Korea and the USA through the lens of the distribution of responsibility for knowledge generation : public oral interactivity and mathematical orality

The research reported in this paper examined spoken mathematics in particular well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA from the perspective of the distribution of responsibility for knowledge generation in order to identify similarities and differences in classroom practice and the implicit pedagogical principles that underlie those practices. The methodology of the Learner’s Perspective Study (LPS) documented the voicing of mathematical ideas in public discussion and in teacher-student conversations and the relative priority accorded by different teachers to student oral contributions to classroom activity. Significant differences were identified among the classrooms studied, challenging simplistic characterisations of ‘the Asian classroom’ as enacting a single pedagogy, and suggesting that, irrespective of cultural similarities, local pedagogies reflect very different assumptions about learning and instruction. We have employed spoken mathematical terms as a form of surrogate variable, possibly indicative of the location of the agency for knowledge generation in the various classrooms studied (but also of interest in itself). The analysis distinguished one classroom from another on the basis of “public oral interactivity” (the number of utterances in whole class and teacher-student interactions in each lesson) and “mathematical orality” (the frequency of occurrence of key mathematical terms in each lesson). Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. In particular, the results suggest that one characteristic that might be identified with a national norm of practice could be the level of mathematical orality: relatively high mathematical orality characterising the mathematics classes in Shanghai with some consistency, while lessons in Seoul and Hong Kong consistently involved much less frequent spoken mathematical terms. The relative contributions of teacher and students to this spoken mathematics provided an indication of how the responsibility for knowledge generation was shared between teacher and student in those classrooms. Specific analysis of the patterns of interaction by which key mathematical terms were introduced or solicited revealed significant differences. It is suggested that the empirical investigation of mathematical orality and its likely connection to the distribution of the responsibility for knowledge generation are central to the development of any theory of mathematics instruction.

Using the Internet in high school mathematics

Whilst the technological, pedagogical and content knowledge (TPACK) model has been increasingly adopted for understanding teachers’ use of technology, there have been many calls for greater discussion about the constituent constructs, their relationship with one another and the central TPACK. This paper analyses qualitatively the TPACK demonstrated by the teacher of a Year 11class who used web-based simulated contexts and interactive web objects in a Mathematics Studies course. The findings indicate aspects of TPK relating to academiclearning time and the transformational mode of the technology were not fully realised in this case study. The implications these has for teacher professional development are discussed.