The purpose of this study was to investigate the effect of instruction in alternative solutions on Taiwanese eighth-grade students' mathematical problem solving performance. This study was exploratory rather than experimental. Alternative-Solution Worksheet (ASW) was developed to encourage students' engagement with alternative solutions to…

This study investigates the similarities and differences of mathematics-related teaching competencies between the future secondary school teachers of Taiwan and Singapore by using data from the international Teacher Education and Development Study in Mathematics (TEDS-M), organized by the International Association for the Evaluation of Educational…

In this paper we demonstrate that "lesson study" may be adapted from its primary use as a professional development strategy for use as a research strategy, especially to identify principles of good lesson design. We report on a project undertaken in two Australian secondary schools where lesson study research was used to investigate the…

Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy. Even students who are able to "create" bar graphs may struggle to correctly "interpret" them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information…

The purpose of this study was to explore the effect of providing preservice teachers the opportunity to collect real data in a science methods inquiry investigation and using the data, design data displays in their mathematics methods course. The research questions focused on how preservice teachers' understandings of data displays, research…

This paper reports on study that investigated the tacit-explicit dimension of the learning of mathematics. The study was carried out in a secondary school and consisted of an episode analysis related to a class discussion about the difference between plane figures and spatial figures. The data analysis was based on integration between some aspects…

In this article, the author shows some simple examples of ways in which "Autograph" can enhance learning in the KS3 curriculum. He began using version 2 with A-level students to help them visualise concepts in pure mathematics. He has "Autograph" projected to the front board to keep learners focused on mathematical activity…

Project questions are real-world problems with multiple solutions, no obvious solution sequence, requiring hands-on data collection, and investigation of topics within and outside mathematics. Discusses evaluation of solution processes, describes a detailed example involving the trajectory of a baseball, and suggests 19 other project questions.…

Statistical data can be represented in a number of qualitatively different ways, the choice depending on the following three conditions: the concepts to be investigated; the nature of the data; and the purpose for which they were collected. This paper begins by setting out frameworks that describe the nature of statistical thinking in schools, and…

Describes a mathematical investigation centered on collecting and analyzing data in a scientific setting. The first experiment teaches the basics of data collection--students should be able to identify variables that might have affected experimental results. The second activity includes designing an experiment to control for these variables. The…