In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…

This paper examines the learning by students who were participating in a project designed to promote persistence while working on mathematical tasks. We examined their learning of mathematics concepts and learning about the processes of engaging in mathematical tasks. There were substantial increases in students' knowledge of angles and also…

Research that has explored students' interpretations of graphical representations has not extended to include how students apply understanding of particular statistical concepts related to one graphical representation to interpret different representations. This paper reports on the way in which students' understanding of covariation, evidenced…

Studies have shown that people can learn valuable skills by playing games, and more teachers are using digital games in classrooms. While researchers understand the difficulties of using digital games, further inquiries are needed to see how teachers effectively use games to improve students' learning. This paper begins to address these issues by…

This article reports on a study that investigated the extent to which 57 Grade 6 students at a particular school have misconceptions regarding equality, with the equal sign as focus. It also investigated this school's three Grade 5 and 6 teachers' mathematical knowledge for teaching regarding equality, again focusing on the equal sign. The…

The main objective of this research is to determine the feasibility of using a multi touch tabletop system for applied mathematics learning in primary education with students with special needs (SEN). The instructional content designed on the tabletop focuses on understanding and managing money, coins, and banknotes. The study also analyzes the…

The relationship between enactment of Common Core State Standards-Mathematics (CCSSM), student misconceptions, student achievement and teacher variables was investigated. After providing professional development on CCSSM enactment, observations were conducted to determine the degree of enactment of CCSSM content and Standards for Mathematical…

The aim of this qualitative study is to embed ICT in the teaching and learning of A-level vectors. Initially, students' learning difficulties and misconceptions in A-level vectors were diagnosed. Then, based on the difficulties identified, concepts in vectors together with interactive tools were developed and integrated in a webpage to enhance the…

The brief explains how exposing young children to early math concepts supports their development of reasoning and problem solving skills and later success in and out of school. It describes the unique ways each of five family engagement programs funded by the Heising-Simons Foundation developed, tested, and integrated early math learning into…

We analysed multivariable calculus students' meanings for domain and range and their generalisation of that meaning as they reasoned about the domain and range of multivariable functions. We found that students' thinking about domain and range fell into three broad categories: input/output, independence/dependence, and/or as attached to specific…

Many people are discussing the issues surrounding mathematics at all levels of education. Politicians, parents, students, universities, education departments all have a view about what the problem is and all have ideas about what should happen. This article represents a synthesis of the issues and implications of one of the problems evident in…

Recent research on annual growth measured using curriculum-based measurement (CBM) indicates that growth may not be linear across the year and instead varies across semesters. Numerous studies in reading have confirmed this phenomenon with only one study of math computation yielding a similar finding. This study further investigated the presence…

This article describes the Lissajous generalized figure and the original instrument for its investigation. Two specially prepared electrodynamic loudspeakers--a horizontal and a vertical--cause oscillations in two mirrors. It is possible to precisely control the motion of the mirrors, achieve a high frequency of oscillation and investigate…

In this article, associate professor Chrystal Dean describes how teachers can challenge their upper elementary students' understanding of area beyond a memorized formula. Herein she describes an activity that will show students the "why" behind using A = l × w to solve rectangular area problems. The activity will help deepen…

I am a volunteer reader at the Princeton unit of "Learning Ally" (formerly "Recording for the Blind & Dyslexic") and I recently discovered that high school students are introduced to the concept of quantization well before they take chemistry and physics. For the past few months I have been reading onto computer files a…