Using spreadsheets in chemical education to avoid symbolic mathematics.

Traditionally, quantum theory has traditionally relied heavily on the use of  mathematics. However, there is a significant cohort of students who are  weak in mathematics, for example, students who are majoring in   biochemistry, biological sciences, etc. This paper reports on the use of  spreadsheets to generate approximate numerical solutions and visual  (graphical) descriptions as a method of avoiding or minimizing symbolic  manipulations, mathematical derivations and numerical computation. A  specific example from quantum theory is provided. Some aspects of  educational pedagogy of spreadsheet usage are discussed.

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.

Assessment of mathematical development in early childhood : some views of preschool practitioners in regional and rural Australia

As part of the project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice directors, teachers, and assistants in prior-to-school settings from regional and rural eastern Australia were interviewed to ascertain their beliefs and practices concerning early childhood mathematics. This paper reports the responses to  uestions about their assessment of children’s mathematical activity and development. The practitioners provided examples of both incidental and planned assessment activities, the different forms these took, methods of recording, and how the results were used.

How early childhood practitioners view young children's mathematical thinking

Interviews were held with 64 professionals in childcare centres. This paper reports on their responses to 3 questions seeking their perceptions of mathematical thinking in very young children. Generally, the interviewees were found to have a good sense of mathematical concepts relevant to babies and toddlers, and they cited evidence of young children’s mathematical development. It is concluded that this practical knowledge would provide a strong foundation for further professional development.

A primer on mathematical modelling in economics

The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics (Krueger, 1991; Colander, 1998, 2005). This paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists. In the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of Arrow's impossibility theorem. Common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students, teachers and researchers specializing in different sub-fields of economics.

The mathematical and science skills of students who are deaf or hard of hearing educated in inclusive settings

This study examined the science and mathematics achievements of 16 Year 9 students with hearing loss in an inclusive high-school setting in Western Australia. Results from the Monitoring Standards in Education (MSE) compulsory state tests were compared with state and class averages for students with normal hearing. Data were collected from three cohorts of Year 9 students across a 3-year period (2005‐2007). Results from mathematics MSE9 and the MSE9 science assessments showed that the majority of students with hearing loss performed below the state average (88%). Findings in this study suggest that students with hearing loss demonstrated more mathematical strength in the areas of space and measurement, which use visuo-spatial skills. Results for students with hearing loss in the five sections of the science assessment suggest more consistency across the different areas tested in the MSE. Comparisons with the MSE9 English paper for the 2005 cohort of students with hearing loss suggest a strong relationship between reading and writing skills and performance on mathematics and science assessment. In particular, questions with high language content created difficulty. On the science assessment, questions requiring a written explanation appeared to be particularly challenging. These findings have implications for teaching and learning in these crucial areas for students with hearing loss in inclusive secondary school settings. Greater attention to the interpretation of the language of mathematics and to writing about science concepts may help to improve outcomes for students with hearing loss on statewide assessments

Deepening the mathematical knowledge of secondary mathematics teachers who lack tertiary mathematics qualifications

A professional learning program for unqualified practising secondary mathematics teachers regarding senior secondary mathematics teaching is described in this paper. The VCE (Victorian Certificate of Education) mathematics professional learning program for senior secondary mathematics was designed for practising secondary teachers of mathematics who had no experience of teaching advanced senior secondary mathematics and who had not completed the recommended qualifications. Professional learning episodes, artefacts and reflections of three teachers who participated in the program are analysed to identify the development of these teachers' mathematical and pedagogical content knowledge (PCK). The PCK framework developed by Chick et al. was used to analyse teachers' knowledge, and the cases of teachers' knowledge presented in the paper illustrate the entwining of knowledge of mathematics and knowledge of teaching and learning The findings indicate that a program designed for senior secondary mathematics can enable practising teachers to deepen and broaden their understanding of junior secondary mathematical pedagogy.

Narrative structure analysis with education and training videos for e-learning

This paper deals with the problem ofstructuralizing education and training videos for high-level semantics extraction and nonlinear media presentation in e-learning applications. Drawing guidance from production knowledge in instructional media, we propose six main narrative structures employed in education and training videos for both motivation and demonstration during learning and practical training. We devise a powerful audiovisual feature set, accompanied by a hierarchical decision tree-based classification system to determine and discriminate between these structures. Based on a two-liered hierarchical model, we demonstrate that we can achieve an accuracy of 84.7% on a comprehensive set of education and training video data.