The National Council of Teachers of Mathematics (NCTM) and the Australian National Curriculum encourage the integration of literacy and numeracy, and "Teaching Children Mathematics" ("TCM") regularly includes articles on incorporating picture books into the mathematics program. Marston has developed a new framework (2010) to assist teachers in…

The psychology supporting the use of quantifier words (e.g., "some," "most," "more") is of interest to both scientists studying quantity representation (e.g., number, area) and to scientists and linguists studying the syntax and semantics of these terms. Understanding quantifiers requires both a mastery of the…

Most teachers agree that if a student understands a particular mathematical topic well, he/she will probably be able to do problems correctly. The converse, however, frequently fails: students who do problems correctly sometimes do not actually have robust understandings of the topic in question. In this paper we explore this phenomenon in the…

In this article I use Sfard's theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus) task required students to examine a function at an undefined point…

In this study, ways in which problem posing activities aid our understanding of children's learning of addition of unlike fractions and product of proper fractions was examined. In particular, how a simple problem posing activity helps teachers take a second, deeper look at children's understanding of fraction concepts will be discussed. The…

Teacher educators need to identify those aspects of preservice teacher (PST) mathematical content knowledge (MCK) that need developing. A methodology that unpacks the MCK that PSTs use in their teaching is presented in this paper. MCK in the teaching acts themselves and in the PST reflections on those acts is categorised and evaluated. The process…

Argumentation in mathematics teaching has potential to move students beyond tacit understanding of mathematical concepts and procedures towards articulation and justification of their ideas; a practice in which evidence is central. Design-based research was used to examine the nature of evidence used by a class of primary students through levels…

A single-case multiple baseline design was used to evaluate the effects of supplemental mathematics instruction with Numicon on the number sense skills of kindergarteners with varying degrees of math difficulty. Nine students participated in the study. Intervention consisted of 20 minutes of supplemental mathematics instruction using the…

This paper describes a task-based dynamic geometry platform that is able to record student responses in a collective fashion to pre-designed dragging tasks. The platform provides a new type of data and opens up a quantitative dimension to interpret students' geometrical perception in dynamic geometry environments. The platform is capable of…

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures…

About 80 middle and secondary school teachers participated in the professional development sequence as a part of a larger professional development project. Sessions provided participants with half-day experiences in an inquiry-oriented classroom taught by a master teacher, in which they experienced examples of inquiry lessons as both student and…

What better way to engage young students in physical science concepts than to have them engineer flying toy rockets? The integration of engineering into science classrooms is advocated by the "Next Generation Science Standards" (NGSS) and researchers alike (Brophy et al. 2008), as engineering provides: (1) A "real-world…

If you want to get the attention of a group of eighth grade math students, tell them they are going to build a life-size cardboard boat. To increase interest, follow up this statement by telling them that two to four of them will actually be rowing this boat across a small pond. Eighth grade math students at Oasis Charter Middle School in…

Several studies on learning mathematics for rural area's student indicate that students have difficulty in understanding the concept of division operation. Students are more likely to be introduced by the use of the formula without involving the concept itself and learning division separate the concrete situation of learning process. This…