There is a long-standing and ongoing debate about the relations between conceptual and procedural knowledge (i.e., knowledge of concepts and procedures). Although there is broad consensus that conceptual knowledge supports procedural knowledge, there is controversy over whether procedural knowledge supports conceptual knowledge and how instruction…

This article draws on extensive experience working with secondary and tertiary teachers and educators using an applet to display rational polynomials (up to degree 7 in numerator and denominator), as support for the challenge to deduce as much as possible about the graph from the graphs of the numerator and the denominator. Pedagogical and design…

The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. The authors conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical…

The Common Core State Standards for Mathematics expect students to build on their knowledge of the number system, expressions and equations, and functions throughout school mathematics. For example, students learn that they can add something to both sides of an equation and that doing so will not affect the equivalency; however, squaring both…

When measurement is taught without a context, students may struggle to make sense of the numbers and units involved. To master measurement, elementary school students need opportunities to discuss how they measured and applied their developing skills and reasoning in context. Measurement is an essential life skill, required to do everything from…

This study investigates students' ways of attending to linear sequential data in two tasks, and conjectures possible relationships between those ways and elements of the task design. Drawing on the substantial literature about such situations, we focus for this paper on linear rate of change, and on covariation and correspondence approaches to…

Several researchers have documented prospective teachers' (PTs') conceptions of various mathematical topics. However, less is known about how PTs' conceptions develop. To address this gap, I designed two tasks with the goals of addressing the PTs' initial conceptions of multidigit whole numbers and helping them develop more sophisticated ones. I…

Teaching statistics meaningfully at school level requires that mathematics teachers conduct classroom discussions in ways that give statistical meaning to mathematical concepts and enable learners to develop integrated statistical thinking. Key to statistical discourse are narratives about variation within and between distributions of measurements…

In accordance with the general principles of the present inclusion in advanced education systems, which are based on the support of children with special educational needs and their inclusion in regular teaching process along with their peers, inclusive values are gradually becoming a reality in the Montenegrin educational process. The paper aims…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

In this article I explore some of the underlying mathematics of Poke´mon battles and describe ways that teachers at the secondary level could explore concepts of mathematical game theory in this context. I discuss various ways of representing and analyzing a Poke´mon battle using game theory and conclude with an example of applying concepts of…

This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term "knowledge of curriculum embedded mathematics" (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and…

This article examines the use of the computer algebra system SAGE for undergraduate student research projects. After reading this article, the reader should understand the benefits of using SAGE as a source of research projects and how to commence working with SAGE. The author proposes a tiered working group model to allow maximum benefit to the…

Even though many educators are becoming increasingly aware of the importance of STEM (science, technology, engineering, and math), science often does not receive the attention in elementary school that it should. One way to ensure that elementary school children have the science experiences they need and deserve is to use it as a context to teach…

Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of…