The non-normative application of proportional strategies in non-proportional covariance situations is widespread and documented in studies conducted in many countries and with participants across a wide range of ages. In the present study, we found that preservice middle-grades teachers have many of the same problems with proportional reasoning as…

Students' development of an understanding of covariation was the focus of a research project that investigated the way in which 12 Year 5/6 students engaged with the learning environment afforded by the graphing software, "TinkerPlots." Using data generated from individual interviews, the results demonstrate that upper primary students…

The value of a consideration of large numbers and exponentiation in primary and early secondary school should not be underrated. In Indian history of mathematics, consistent naming of, and working with large numbers, including powers of ten, appears to have provided the impetus for the development of a place value system. While today's students do…

The research reported here was motivated by curiosity about ways of suggesting tasks and activities to teachers that assist them in their planning and which allow them to see the purpose of the suggested tasks. A group of junior secondary teachers involved in a larger project worked through a set of tasks that sought to address the content they…

This study investigates how 217 students in Years 5, 6 and 7 from three schools in Nanjing, China, link number and algebra (called relational thinking in this study). It categorizes their performances in terms of five levels, and uses these levels to create profiles of algebraic thinking across Years 5, 6, and 7. The study examines the…

Large numbers of students in California's 112 community colleges are struggling to pass college-level math classes, including courses they need to complete a degree or transfer to a four-year institution. Community college students' success in rigorous math is crucial to their futures and to any effort to improve college completion rates in…

This paper discusses the results of a pilot study that explored how prospective secondary school teachers are shaped by learning experiences during their undergraduate mathematics education. The collaborative study, which was conducted by a mathematician and a mathematics educator, drew from the experiences of prospective teachers in a…

This article adds to the growing body of research surrounding the use of virtual manipulatives for mathematics learning. The study reported herein used five different virtual manipulatives from four different websites, all within a sixth grade unit on proportional thinking. While many studies have reported on student achievement when using virtual…

This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school…

This article presents findings from a study in which the author served as an expert coach and provided ongoing support to four elementary school teachers related to employing standards-based pedagogies in their mathematics classrooms. In addition to assisting teachers, the author examined which supports they sought and the impact of them on…

Proportional reasoning is an important aspect of formal thinking that is acquired during the developmental years that approximate the middle years of schooling. Students who fail to acquire sound proportional reasoning often experience difficulties in subjects that require quantitative thinking, such as science, technology, engineering, and…

The aim of the study was to investigate the teaching of fractions by Ordinary level mathematics teachers at Radcliff high school in Zimbabwe. The main objective of the study was to establish how teachers teach the concept of fraction and to find out why they teach in the manner they do. A case study research design was used and purposive sampling…

In this article we contribute a perspective on mathematical embodied cognition consistent with a phenomenological understanding of perception and body motion. It is based on the analysis of 4 selected episodes in 1 session of an undergraduate mathematics class. The theme of this particular class session was the geometric interpretation of the…

This article outlines how a Brisbane independent school, Clayfield College, improved the ability of its Year 3 students to solve addition and subtraction word problems by utilising a schematic approach. It was observed that while students could read the words in the text of a written problem, many had difficulty identifying the core information…

Three-dimensional dynamic geometry software has the power to enhance students' learning of spatial geometry. The purpose of this research is to clarify what potential using three-dimensional dynamic geometry software can offer us in terms of how to develop the spatial geometry curriculum in lower secondary schools. By focusing on the impacts the…