In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning…

Paying attention to the planning of lessons represents a crucial teaching task. This paper analyses teachers' framing of lesson objectives and their descriptions of how they would introduce particular mathematics topics. Connections between the objectives and the instructional strategies employed, were also studied. The study involved 75 South…

Do your students need more opportunities do develop number sense and reasoning? Are you looking to get your students energized and talking about mathematics? Have you wondered how practical, replicable, and engaging activities would complement your mathematics instruction? This guide answers the question "What could I do differently?" by…

The purpose of this action research was to evaluate the implementation of technology integration with multiplication concepts (i.e., repeated, arrays, and decomposing numbers) for struggling third grade mathematics students. This study incorporated the use of virtual manipulatives and student think-aloud recordings to measure students' conceptual…

An important decision that professional development (PD) facilitators must make when preparing for activities with teachers is to select an appropriate tool for the intended learning goals of the PD (Sztajn, Borko, & Smith, 2017). One important and prevalent tool is artifacts of student thinking (e.g. Jacobs & Philipp, 2004). In this paper…

In this article, we review approaches to modeling a connection between spatial and mathematical thinking across development. We critically evaluate the strengths and weaknesses of factor analyses, meta-analyses, and experimental literatures. We examine those studies that set out to describe the nature and number of spatial and mathematical skills…

This paper describes innovative ways of bringing mathematical learning into community venues in rural settings. We selected highly engaging mathematical activities, adapted them for middle school youth and their families, and brought them to the "locavore" contexts of Farmers Markets and community agricultural fairs. "STEM…

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

Mathematics instruction in the United States has historically focused on procedures, facts, and algorithms. Because of that focus, mathematics instruction, in essence, becomes lessons in arithmetic and efficiency. While there are promising changes occurring in mathematics instruction, we still need to help both teachers and students develop a more…

In this paper I present a case study to illustrate conflicts between different 'realizations' of the concept of 'continuous function' held by a university first year student. Sfard's commognitve framework is used in the analysis of a student's work on continuity. I point out how these conflicting realizations have arisen from the inconsistent…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

This qualitative research reports the results of a short learning intervention programme conducted by South African National Roads Agency Limited (SANRAL) Chair in Science and Mathematics Education to enhance the mathematical knowledge of teachers in some South African schools. The short learning programme comprised the fostering of teachers'…

This paper reports the performance of 30 rising seventh-grade girls on a task in which they were asked to order four fractions from least to greatest. Less than three-fifths attained correct answers. The performance gap was widest between students who attended Title I schools and those who did not, the latter being much more likely to attain…