Recognizing identity not only as an important educational outcome but also as being inter-related to students' knowledge and practice, this paper explores an affordance of proof scripts; exploring students' identities. Specifically, drawing on data from teaching experiments and the construct of perceptual ambiguity, this paper presents an analysis…

A central issue in the mathematics curriculum is that we want students to make connections. This issue has been analysed in a series of curricula and instruction design and analysis studies. Moving towards mathematics connections--and away from treating mathematics as a body of isolated concepts and procedures--is an important goal of mathematics…

Whole Number Arithmetic (WNA) appears as the very first topic in school mathematics and establishes the foundation for later mathematical content. Without solid mastery of WNA, students may experience difficulties in learning fractions, ratio and proportion, and algebra. The challenge of students' learning and mastery of fractions, decimals, ratio…

Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-ten place-value system (i.e., grouping, place value, base). Understanding these features is crucial to…

Research has documented that mathematics teachers rarely use communicative activities; activities that allow for the sharing of ideas and clarification of understandings (NCTM, 2000). Teacher metacognitive awareness provides a possible framework for understanding the difficulties secondary mathematics teachers face when attempting to incorporate…

This paper shares how fourth grade students solved a unique type of number line task. Instead of giving students the unit and asking them to locate a fraction on the number line, students were given two points on the number line and asked to either find 1, or another number on the number line. This type of task is called "reconstructing the…

The right types of technology can create new opportunities for students to demonstrate mathematical understandings and can strengthen existing formative assessment practices. The authors write that they frequently use the Math Learning Center apps--covering the range of manipulatives and models--to empower students to explain their thinking. The…

In this brief article, the author illustrates the flaws of FOIL (multiply the First, Outer, Inner, and Last terms of two binomials) and introduces the box method. Much like FOIL, the box method can become easy to use. Unlike FOIL, however, the box method is a more direct and visible link to using the distributive property to determine area, a…

Research on students' attitudes toward statistics has attracted many statistics instructors and statistics education researchers. In this study, we use confirmatory factor analysis to analyze data collected from an introductory statistics course using the Survey of Attitudes toward Statistics. The results suggest that the items and six factors are…

The aim of this study is to investigate the anxiety levels of high school students towards mathematics lesson according to gender variable. A total of 89 ninth grade students (29 females and 60 males) from various high schools were enrolled in Van province center in the 2017-2018 academic year. In the study, the data were collected by using the…

Open Educational Resources (OER) have the potential to replace commercial learning materials in education. An empirical examination of this potential was conducted, comparing the end-of-year mathematics test results of 12,110 elementary school students clustered within 95 schools from five school districts in the state of Washington in the United…

One of the research objectives was formulated to improve the quality of education, namely by understanding the problems of students and teachers. There were three main groups of quality characteristics of education highlighted in scientific and academic literature in Russia, namely the quality of educational objectives, the quality of the…

The study reported here investigates the role, experiences and aspirations of a community of mathematics postgraduates as they learn to tutor in a mathematics support centre in a research-intensive university. This is achieved through in-depth interviews with nine postgraduate tutors all of whom had experience working in the centre. The data is…

Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called…

This study examined third-grade students' reasoning and discussions on multiplication when they initially encounter it in the classroom. The aim of the study was to analyse the data from teaching and learning multiplication in 24 classrooms and, thus make a contribution to the research and conceptualisations about students' reasoning and strategy…