Spoken mathematics as an instructional strategy: the public discourse of mathematics classrooms in different countries

This chapter examines the use of spoken mathematics in the public discourse of eighth-grade mathematics classrooms internationally. By “spoken mathematics” we mean the recognizably mathematical terms used in spoken interaction in the classroom. Our principal focus was the relatively sophisticated terms by which each lesson’s central concepts or procedures were named. In our analysis we addressed the question(s): “What is the occurrence of publicly spoken mathematics in the different classrooms studied and what efforts do the teachers appear to make to promote students’ use of technical mathematical terms in their public classroom talk?” A companion chapter examines the question of students’ private spoken mathematics in the classroom and the possible learning that might result.

A comparative study of content settings of mathematics curriculum standards from China, Australia, and Finland

The study investigated the mathematics curricula standards set by the governments in China, Australia(Victoria) and Finland in the aspects of the amount of content statements, the structure of content areas, level of details, level of requirement, the distribution of content, and the changes of content areas. The results show that China's mathematics standard has the biggest amount of and the most detailed content statements; that of Australia is in the second place; and Finnish standard has the least amount of content statements that are very general. The standards in all three countries emphasize numbers and operation and geometry.However,China's standards present a dynamic change, with different focus for different grades; Australian standards have similar proportion of each part of content for different grades and the amount of each part increases with grade; there is no fixed setting and proportion of content in Finnish standard, which is not confined by any mode.

Student speech as an instructional priority: mathematics classrooms in seven culturally-differentiated cities

Student spoken use of mathematical terminology in public and private classroom discourse distinguishes one mathematics classroom from another. While student-student spoken interactions were frequent in the classrooms studied in Berlin, Melbourne, and San Diego, and non-existent in Shanghai and Seoul, student use of mathematical terminology varied significantly. The variation between the practices of the mathematics classrooms studied in Seoul, Shanghai, Hong Kong and Tokyo problematizes any simplistic characterization of “the Asian classroom.” Our results demonstrate that student spoken facility with the technical language of mathematics requires deliberate scaffolding and, interestingly, this can be achieved through either public or private discourse.

Spoken mathematics as a distinguishing characteristics of mathematics classrooms in different countries

This paper reports research into the occurrence of spoken mathematics in some well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA. 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). Our concern in this analysis was to document the opportunity provided to students for the oral articulation of the relatively sophisticated mathematical terms that formed the conceptual content of the lesson. Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. The contribution of student-student conversations also varied significantly. Of particular interest are the different learning theories implicit in the role accorded to spoken mathematics in each classroom.

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.

Utilisation of general practitioner services and achievement of guideline targets by people with diabetes who joined a peer-support program in Victoria, Australia

This paper describes the use of general practitioner (GP) services and achievement of guideline targets by 285 adults with type 2 diabetes in urban and regional areas of Victoria, Australia. Anthropometric and biomedical measures and responses to a self-administered questionnaire were collected. Findings indicate that almost all participants had visited a GP and had had their hypoglycated haemoglobin (HbA1c) measured in the past 6 months; less than one-third had visited a practice nurse. Fifty per cent achieved a HbA1c target of ≤7.0%; 40%, a total cholesterol ≤4.00 mmol/L; 39%, BP Systolic ≤130 mmHg; 51%, BP Diastolic ≤80 mmHg; 15%, body mass index ≤25 kg/m2; and 34% reported a moderately intense level of physical activity, that is, ≥30 min, 5 days a week. However, 39% of individuals achieved at least two targets and 18% achieved at least three of these guideline targets. Regional participants were more likely to report having a management plan and having visited a practice nurse, but they were less likely to have visited other health professionals. Therefore, a more sustained effort that also includes collaborative care approaches is required to improve the management of diabetes in Australia.

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.