This paper discusses the relevance of using physical situations to introduce the concept of angles at elementary school. We compare the effectiveness of two geometry teaching sequences. In the first one (physical sequence), the pupils learned the angle concept by experimenting on the playground (i.e. mesospace) and then modelling the situation. In…

In this paper, we report on the outcomes of a survey of students across 12 higher education institutions in Ireland and the UK. Participants were asked to give their views on what tutors should do and not do when they are providing Mathematics Learning Support to students. We present the categories that emerged from an analysis of student…

This study focused on improving students' learning mathematical of proofs and proving by using combinations of proof strategies that span different levels of understanding of proof structure; we refer to these as 'level-spanning proof-production strategies'. We analysed the level-specific proof-production strategies evident in the lessons and…

A research project on using comics for teaching mathematics was initiated in one Singapore primary school. One class of Grade 5 (students of age 11-12) students was exposed to comics for mathematics instruction. This paper reports a case study of seven students' perception of the features of the comics instructional package and how these features…

The aim of this study is to determine the effect of computer-supported collaborative learning (CSCL) using GeoGebra software on 11th grade students' achievement in exponential and logarithmic functions. This study was carried out with quasi-experimental design consisting of a pre-test and a post-test with the experimental group and the control…

This study is a case study within a three-year-long design research study. The purposes of this study are twofold. The first purpose includes investigating whether there is a significant difference in seventh-grade students' proportional reasoning skills before and after a teaching experiment conducted in line with the perspectives of Hypothetical…

Summative assessment data are rarely adapted into instructional decision making. In this project, teachers and researchers work together to identify how teachers use diagnostic data (students' development of common core standards). We analysed students' responses to trimester tests that teachers and researchers modified together using cognitive…

This study evaluates the implementation of a collaborative/game-based learning strategy on final year B.Sc. students focused on reinforcing the Taylor theorem (a mathematical concept previously learned, usually forgotten over time and widely used in chemical engineering) and analyses its effect on their academic performance. To this end, the…

The purpose of this paper is to follow the reasoning of high school students when asked to explain the standard trigonometric limit lim/[theta][right arrow] sin[theta]/[theta]. An observational study was conducted in four different phases in order to investigate if visualization, by means of an interactive technology environment (Geogebra), can…

This paper reports on an intervention as part of which direction fields were introduced to students learning ordinary differential equations (ODEs). The intervention was designed and implemented to address issues with students' conceptions of the solutions of ODEs. These were identified by a diagnostic survey and through a review of the…

This study investigated how Turkish mathematics teachers evaluate the effectiveness of classroom teaching in terms of improving students' mathematical proficiency. To this purpose, teachers were asked to evaluate a mathematics lesson as presented them in a vignette. By means of cluster analysis, the participants' evaluations of the lesson were…

This study aimed to explore the effects of an instructional intervention in which GeoGebra and the think-pair-share method were used to teach the relationship between the graph of a parametric curve and the derivatives of its component functions. The participants in the study were 19 prospective mathematics teachers. To assess the understanding of…

The purpose of this work was to explore how elementary pre-service teachers responded to a novel strategy for justifying the triangle area formula. We conducted interviews with 24 pre-service teachers, asking them to evaluate and respond to a hypothetical student strategy for the triangle area. Findings highlighted several interesting struggles…

The aim of this research was to examine the effect of Augmented Reality (AR) supported geometry teaching on students' 3D thinking skills. This research consisted of 3 steps: (1) developing a 3D thinking ability scale, (ii) design and development of an AR Geometry Tutorial System (ARGTS) and (iii) implementation and assessment of geometry teaching…

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…