In this paper, we frame mathematics classrooms as heterogeneous spaces wherein students draw on multiple storylines based on different notions of schooling and school mathematics to both communicate mathematical ideas and position themselves and one another. We focus on a fourth grade (age range 9.4-10.8 years) mathematics classroom discussion in…

Helping students generalise mathematical ideas is an essential component of teaching and learning of mathematics (Lannin, Ellis, Elliott & Zbiek, 2011). However, it can be challenging for primary teachers to assess and promote generalisation. Because generalisation is an essential part of mathematics instruction, the authors highlight the…

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…

This study investigated analogical transfer of conceptual structure from a prior-knowledge domain to support learning in a new domain of mathematics: division by fractions. Before a procedural lesson on division by fractions, fifth and sixth graders practiced with a surface analogue (other operations on fractions) or a structural analogue (whole…

Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

Although it is evident that advanced aspects of numeracy are dependent on the successful acquisition of early skills, this developmental process does not occur in isolation from other academic factors. Early literacy skills are intertwined with the acquisition of early numeracy skills, particularly at the informal numeracy and numeral knowledge…

In this article, we share a model of flipped instruction that allowed us to gain a window into our students' mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be…

In many mathematics classrooms, the teacher provides "worked examples" to demonstrate how students should perform certain algorithms or processes. Some students find it difficult to generalize from the examples that teachers provide and cannot apply what they have learned in new situations (Watson and Mason 2002). Instead, teachers might…

This paper used narrative to present the author's understanding process of "concept study" in teachers' professional learning. The understanding process was advanced by several questions emerging from the preparation of doing "concept study". Thus, the several questions and their solutions became the threads of the narrative.…

As a link between Mathematics and children's literature, the e-book emerges from the need to enrich the teaching and learning of mathematics through the use of content which illustrations are made by children from stories included in children's literature. In this paper we describe some educational experiments with some connection of these two…

The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…

Skilled instructors observe consistent errors that young children may make in particular situations and seek ways to help children reform their thinking through conceptual understanding. Such teacher observations as those presented at the beginning of this article, combined with similar observations by teachers in other preschool and kindergarten…

The process of the mathematization of physical situations through differential calculus requires an understanding of the justification for and the meaning of the differential in the context of physics. In this work, four different conceptions about the differential in physics are identified and assessed according to their utility for the…

In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…