In this paper, we analyse a large, opportunistic dataset of responses (N = 219,826) to online, diagnostic multiple-choice mathematics questions, provided by 6-16-year-old UK school mathematics students (N = 7302). For each response, students were invited to indicate on a 5-point Likert-type scale how confident they were that their response was…

Historic achievement gaps in mathematics favoring male students have recently started to narrow, close, or even shift in favor of female students. Still, in many countries, male students continue to outperform their female counterparts in international mathematics assessments. Chile has one of the highest mathematics achievement gaps in the world,…

Research focusing on algebra from primary to early secondary school level has made several major advances over the past decades. Students' difficulties have been identified and supportive teaching and learning environments have been set up (Cai & Knuth, 2011; Kieran, 2007; Radford, 2008, "Mathematics Education Research Journal," 26,…

This study explored progression of students' level of reasoning and generalization in numerical and figural reasoning approaches across grades and in different pattern generalization types. An instrument that included four figural patterns was administered to a sample of 1232 students from grades 4 to 11 from five private schools. The findings…

The researchers in this study investigated the impact of mathematics-focused parental involvement on Kindergarten to Grade 8 children and parents as well as factors prompting that impact. Qualitative analysis consisting of parent, child, and teacher interviews and 3-year quantitative testing showed significant improvements in students' mathematics…

The natural number bias is known to explain many difficulties learners have with understanding rational numbers. The research field distinguishes three aspects where natural number properties are sometimes inappropriately applied in rational number tasks: density, size, and operations. The overall goal of this study was to characterize the…

This study describes the types of explanations one student, Sharon, gives and prefers at different ages. Sharon is interviewed in the second grade regarding multiplication of one-digit numbers, in the fifth grade regarding even and odd numbers, and in the sixth grade regarding equivalent fractions. In the tenth grade, she revisits each of these…

There is broad acceptance that mathematics teachers' beliefs about the nature of mathematics influence the ways in which they teach the subject. It is also recognised that mathematics as practised in typical school classrooms is different from the mathematical activity of mathematicians. This paper presents case studies of two secondary…

"From Another Perspective" is a year-long course for teachers of mathematics that is designed to enhance teachers' awareness of the way that their students think when they are experiencing difficulties in geometry. It also aims at equipping teachers with tools needed to analyze and cope with Problematic Learning Situations in geometry (Gal &…

Working with Navajo Indian informants in Arizona, USA we became aware of the capabilities of children and adults to find their way in vast and clearly "chaotic" canyons. One thing we did was describe what people actually did and said about their ways to find the way back home in such contexts. A second one was to use these data in order…

This article presents a description of a South African mathematics teacher's struggles to mediate a new national assessment tool called the Common Tasks for Assessment with her grade 9 learners, who are unprepared for the assessment. The purpose of the study is to describe and to identify the constraints on the teacher's mediation attempts. The…

The notion of equivalence relation is arguably one of the most fundamental ideas of mathematics. Accordingly, it plays an important role in teaching mathematics at all levels, whether explicitly or implicitly. Our success in introducing this notion for its own sake or as a means to teach other mathematical concepts, however, depends largely on our…

How do teachers conceptualize and deal with context of mathematics word problems in their teaching? This question is discussed based on a study of 14 experienced teachers at the elementary, junior high and senior high school levels. Bruner's notions of paradigmatic and narrative modes of knowing formed the basis of analysis of data from sources…

We find that students in the big mathematics service courses at the Johns Hopkins University who were encouraged to use calculators in K-12 have somewhat lower grades than those who weren't.

A series of 13 survey questions based on a 50-50 spinner is used to explore school students' understanding of statistical variation in a chance setting. Five questions set the context by assessing the understanding of theoretical expectation and representation of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to…