Mathematical Problem Posing as a Measure of Curricular Effect on Students\u27 Learning

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students\u27 learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students\u27 responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed

Curricular orientations to real-world contexts in mathematics

A common claim about mathematics education is that it should equip students to use mathematics in the ‘real world’. In this paper, we examine how relationships between mathematics education and the real world are materialised in the curriculum across a sample of eleven jurisdictions. In particular, we address the orientation of the curriculum towards application of mathematics, the ways that real-world contexts are positioned within the curriculum content, the ways in which different groups of students are expected to engage with real-world contexts, and the extent to which high-stakes assessments include real-world problem solving. The analysis reveals variation across jurisdictions and some lack of coherence between official orientations towards use of mathematics in the real world and the ways that this is materialised in the organisation of the content for students

Developing Mathematics Enrichment Workshops for Middle School Students: Philosophy and Sample Workshops

This paper describes our approach to organizing enrichment activities using advanced mathematics topics for diverse audiences of middle school students. We discuss our philosophy and approaches for the structure of these workshops, and then provide sample schedules and resource materials. The workshops cover activities on the following topics: Graphing Calculators; The Chaos Game; Statistical Sampling; CT Scans–the reconstruction problem; The Platonic and Archimedean solids; The Shape of Space; Symmetry; The Binary Number System and the game of NIM; Graph Theory: Proof by Counterexample