This position paper examines the phenomenon of the McNamara Fallacy to analyse flawed conceptions of "success" in mathematics learning, normalised assessment structures and their implications for mathematics education. The established presence of the McNamara Fallacy and the ramifications of this statistical fallacy provide a foundation…

Preferences for solution methods have an important implication teaching and learning mathematics and students' mathematical performances. In the domain of learning mathematics, there are two modes of processing mathematical information: verbal logical and visual-pictorial. Learners who process mathematical information using verbal logical and…

This paper quantifies the learning gain that accrues to 15-year-old students over one year of schooling in 18 countries and economies, where the cohort eligible to sit the OECD Programme for International Student Assessment (PISA)ISA test overlaps with two distinct school cohorts. School-entry regulations are used as an exogenous source of…

For the first time, this volume provides a definitive collection of Gloria Ladson-Billings's groundbreaking concept of Culturally Relevant Pedagogy (CRP). After repeatedly confronting deficit perspectives that asked, "What's wrong with 'those kids?,'" Ladson-Billings decided to ask a different question, one that fundamentally shifted the…

Inquiry is promoted as a way to engage students so that they learn more deeply; inquiry is also an end in itself, introducing students to the research process and the behaviors of a mathematician. This article reflects on an individual exploratory project used in a sophomore-level number theory course, examining how it supported student inquiry…

The paper applies Goffman's frame analysis and ethnomethodology to student performance on mathematical word problems. In educational research, frame analysis has usually been limited to primary frames. Instead, in this paper I focus on the kind of secondary frame that Goffman calls 'utilitarian make-believe'. The data consist of a fragment of…

This article addresses the conceptual question "what is lesson study?" as an issue that arises in the context of the globalisation of lesson study as a method for improving teaching and learning beyond its presumed origins in the Japanese education system. To what extent can adaptations of the method in different national settings be…

Individual differences in inhibitory control have been shown to relate to general mathematics achievement, but whether this relation varies for specific areas within mathematics is a question that remains open. Here, we evaluate if inhibitory processes play a specific role in the particular case of fraction comparison, where learners must ignore…

Taking lower-secondary schooling within the English educational system as an example, this paper illustrates the contribution of two bodies of international scholarship to the scoping of research-based pedagogical development aimed at improving student attitude and achievement in science and mathematics. After sketching the English context of…

Metacognition is one of the promising contemporary research fields in psychology and education. The concept has been introduced to describe and explain how people gain control over their learning and thinking, particularly in the case of cognitive failures and difficulties they meet when dealing with information processing and problem solving…

The results from tests set as part of a large mathematics teaching development project are explored using both quantitative and qualitative methods to seek differences in performance between boys and girls. The outcome appears to confirm the theory developed from earlier research into gender differences that there might be a tendency for girls to…

This mixed-methods study investigates the effects of student attitudes and behaviours on the outcomes of learning mathematics with computer tools. A computer tool was used to help students develop the mathematical concept of function. In the whole sample (N = 521), student attitudes could account for a 3.4 point difference in test scores between…

In this study, we examined the development of maths skills in 269 Estonian primary school children (119 boys and 150 girls; 20 classes). Testing was carried out over a three-year period (Grade 1-Grade 3). Before the last testing session, children's verbal skills and motivational orientations were also tested. In addition, teachers evaluated…

Developing a software environment to enhance 3D geometric proficiency demands the consideration of theoretical views of the learning process. Simultaneously, this effort requires taking into account the range of tools that technology offers, as well as their limitations. In this paper, we report on the design of Virtual Spaces 1.0 software, a…

For students to compete in the 21st-century global economy, knowledge of and proficiency in mathematics are critical. Whether headed to college or to the workforce, today's high school graduates need solid mathematics skill. The National Mathematics Advisory Panel was created in 2006 and charged with reviewing the best available scientific…