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:…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Many studies in the past decades have focused on low and typical mathematics achievers, yet little is known about children with high mathematics achievement, particularly at a young age. The current study aimed to fill this gap and started from the early work of Krutetskii (1976) as a theoretical lens to study the characteristics of high…

Developmental or remedial education is a strategy that assists underprepared or unprepared students. Though prominent in the higher education remedial education landscape, low course and degree completion rates plague developmental mathematics courses. Research is replete with studies addressing students' underpreparedness for college-level…

In the context of Programme for International Student Assessment (PISA), paradoxical findings concerning the relationship between questionnaire scales and student achievement are often documented. These questionnaire scales are found to correlate positively with student achievement within countries at the individual level, but negatively at the…