Mathematical thinking: a screening profile for 'operations'

This paper comments on and adapts the screening profile developed from 'ACER Mathematics Profile Series (MAPS): Operations' (1977). A sample screening profile worksheet for 'Operations' is provided. This adaptation of the ACER MAPS Operations test may help teachers identify students who are able to use more advanced levels of mathematical thinking. Survey results may help form ability groups, deliver special needs curriculum materials, and guide students tackling the algebra curriculum.

The development of young children's mathematical understanding

Early childhood mathematics education research is burgeoning in Australasia. This chapter highlights and critiques key research in the area that has been published between 2004 and 2007. In particular, it considers specific mathematical topics such as number and numeracy, space and measurement, and structure and patterning; contextual matters such as links among home, school, pri or·to·sch 001 settings and community, indigenous learners and mathematics learning as children start school; assessment of mathematics learning in early childhood settings and the professional development of early childhood teachers of mathematics. It concludes with some suggestions for fruitful areas of future research.

Communities of mathematical inquiry : a primary pedagogy in peril

This paper outlines some examples from an Australian education system, and its classrooms, that provide evidence of practices that are considered as antithetical to establishing and maintaining Communities of Mathematical Inquiry (CoMI). Although some possible solutions are posed, implementation is left open for readers to consider, as contexts vary widely from jurisdiction to jurisdiction.

Mathematical power of special-needs pupils : an ICT-based dynamic assessment format to reveal weak pupils' learning potential

This paper reports a study aimed at revealing special-educational-needs pupils' learning potential by means of an ICT-based assessment including a dynamic visual tool that might help pupils when solving mathematics problems. The study focused on subtraction problems up to 100, which require 'borrowing'. These problems, in which the value of the ones-digit of the subtrahend is larger than the ones-digit of the minuend, are known as a serious difficulty for weak pupils in mathematics. Seven of such problems from a standardised test were placed in the ICT environment. Data were collected from two test conditions: the standardised written test format and the ICT version of the test items including the tool that provided pupils with a set of virtual manipulatives. The 37 pupils involved in the study were 8–12 years old and from two special-education schools in the Netherlands. Comparison of the performance scores in the two formats showed that an ICT-based assessment format, including a dynamic visual tool, can reveal weak pupils' learning potential and strategy use. The study also pointed out that 'partial-tool use', ie, not carrying out the complete subtraction operation with the tool, can provide sufficient support to find the correct answer.

Critical perspectives on communities of mathematical inquiry

While the notion of Communities of Inquiry (CoI) has its origins in philosophy, there has been widespread interest in mathematics classrooms as Communities of Mathematical Inquiry (CoMI). This paper outlines the structure and content of Research Forum 2: Critical Perspectives on Communities of Mathematical Inquiry, gives a brief review of research in the area, and highlights some key issues.

Spatial thinking processes employed by primary school students engaged in mathematical problem solving

This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

Effect of social background on the development of probabilistic concepts

This research explores how the social backgrounds of a group of students contributed to their intuitive knowledge in probabilistic reasoning, and influenced their processing of the associated mathematics. A group of Year 11 students who came from families for whom the phenomenon of track gambling formed an important part of their cultural background was identified. Another group consisting of students in the same mathematics course (Year 11 Maths in Society) but from families for whom the phenomenon of gambling in any form was totally absent from their social backgrounds was identified. Twenty students were selected from each group. The research employed a qualitative methodology in which a phenomenographic approach was used to investigate the qualitatively different ways in which individuals within the two groups thought about concepts involving probabilistic reasoning, and processed the related mathematical skills and concepts. The cognitive processes involved in the applications of probabilistic and related mathematical concepts in a variety of both gambling and non-gambling situations were studied in order to determine whether this culturally based knowledge could be viewed as a type of ‘ethnomathematics.’ Data were obtained through individual structured interviews which enabled patterns of reasoning to be compared and contrasted. Analyses of these data enabled intuitive mathematical understandings possessed by the gamblers not only to be identified, but also to be linked with their social backgrounds. Also differences between how individuals in the two groups processed probabilistic and associated mathematical knowledge were determined. This research complements and extends existing knowledge and theories related to culturally-based mathematical knowledge. Implications for further research, for classroom teaching, and for curriculum development in the study of probability in senior secondary mathematics classes are discussed.