This article builds upon a systematic review of 53 articles in international research journals and makes three main contributions. First, it develops a method for identifying motives, values, and assumptions in research by analysing segments of text in journal articles. Second, it represents a reflective account of research within the field of…

This article argues the importance of teaching students about the philosophical and mathematical underpinnings of Australia's superannuation system as an example of a real-world problem context. It also provides a rationale for teaching financial modelling and decision-making in ways that respect the diverse financial realities represented in…

Ciphers based on rotor machines were the state-of-the-art in the mid-1900s, with arguably the most famous being the German Enigma. We have found that students have great interest in the Enigma and its cryptanalysis, so we created our own rotor cipher that is simulated with shifting tables and can be cryptanalyzed. Ours and the historic rotor…

The Enforcement Decree of the Elementary and Secondary School Act (2015) mandates that from 2016 all middle schools in Korea must administer one semester as a free semester (FS), called an exam-free semester or, alternatively, a free learning semester. Consequently, some Korean parents and students have expressed a feeling of anxiety about having…

A typical mathematics assignment consists of a block of problems devoted to the same topic, yet several classroom-based randomized controlled trials have found that students obtain higher test scores when most practice problems are mixed with different kinds of problems--a format known as interleaved practice. Interleaving prevents students from…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear…

Justifying and generalizing are essential forms of mathematical reasoning, yet, teachers struggle both to produce and identify justifications and generalizations. In comparing elementary school teachers' self-reported levels of noticing justifying and generalizing in their own classrooms and the levels researchers observed in two consecutive…

This paper aims at contributing to the debate in Mathematics Education about the understanding of the dynamics of students' group interactions by proposing an interpretative lens, which defines four modes of participating in a group on the basis of different kinds of utterances, gestures, postures, and glances that each student makes. We apply…

In this paper, I explore how mathematics education research is always already entangled with and in ontological, epistemological, and ethical considerations--that is, philosophical considerations--of the researcher (or research team) from beginning to end. The danger in too much of the existing mathematics education research, however, is limited…

The present study is part of a hermeneutic inquiry that re-conceptualizes mathematics curriculum as recursive through the lens of complexity thinking. In recognizing the pervasiveness of the phenomenon of a learner encountering something she has previously encountered before and the lack of attention in orientating such reencountering towards…

A typical mathematics assignment consists of a block of problems devoted to the same topic, yet several classroom-based randomized controlled trials have found that students obtain higher test scores when most practice problems are mixed with different kinds of problems -- a format known as interleaved practice. Interleaving prevents students from…

This case study investigates, at three Swedish schools, primary school students' knowledge of the equal sign. The schools were chosen as representatives of schools whose students have different socioeconomic backgrounds. The data consist of Grade 3 and 6 students' responses to an assessment form based on Matthews et al. ("JRME,"…

Mathematic connection is one of the basic abilities someone must have in order to learn mathematic successfully. Mathematic connection helps someone to understand the function of mathematics, improving mathematic concept, determining the correlation among mathematic concepts, and identifying the application of mathematic in the surrounding…

We conducted a comprehensive synthesis of computer-assisted instruction (CAI) research that aimed to facilitate the learning of mathematical word problem solving involving elementary and secondary school students with learning disabilities or difficulties in mathematics. We examined a total of 13 studies under the four instructional categories:…