This study examines how sampled Chinese and U.S. third and fourth grade students (N[subscript China] = 167, N[subscript US] = 97) understand the commutative, associative, and distributive properties. These students took both pre- and post-tests conducted at the beginning and end of a school year. Comparisons between students' pre- and post-tests…

This study explored prospective middle school mathematics teachers' developing understanding of geometric transformations through designing and implementing an instructional unit in a technology supported classroom environment. The instructional unit including seven activities was developed by considering past research on learners' pre-existing…

The study aimed to expose how pre-service teachers perceived the value of an inquiry-based geometrical task with dynamic geometry software for increasing and deepening their understanding of the task itself, and for heightening their mathematical, pedagogical, and technological knowledge in the case of reflection and transformation. Twenty-seven…

Research has shown that a profound place value understanding is crucial for success in learning mathematics. At the same time, a substantial number of students struggles with developing a sustainable place value understanding. In this regard, two aspects of the place value system appear especially relevant: First, the knowledge of the decimal…

This paper advances the conceptualization of STEM teacher professional knowledge reflecting the specialized knowledge needed to support English learner (EL) language development during science and mathematics instruction. What distinguishes this model is the integration of conceptual understanding, a key feature of subject matter knowledge, with…

Background: Educational video games are increasingly used in classrooms because they can offer meaningful contexts for problem solving. However, educational video games bring together two historically disparate activities: school mathematics and video games. How these two activities complement, compromise, or contradict each other influences how…

In this paper I explore the question of what counts as successful implementation of a mathematics professional development (PD) project at scale. Two kinds of upscale are presented and differentiated from one another: upscale of settings and upscale of values, and the link between this differentiation and how success may be defined is discussed.…

This study examines the construct of distance -- the degree of difficulty of interacting with something -- as part of activity involving children using touchscreen digital games to learn mathematics. Ten fifth-grade children engaged in video-recorded semi-structured task-based interviews in which they used two touchscreen digital mathematics games…

The construction of the National Common Curricular Base (NCCB) for the area of Mathematics and its High School Technologies in Brazil and the last update of the Mathematics Program for High School in Paraguay are prescribed curriculum documents in force for the teaching of Mathematics in these countries. The construction of each one of them…

The modelling approach to teaching and learning mathematics emphasizes the usefulness of mathematics in the real-world. The aim of the current study is to examine whether engagement in modelling activities provides learners an opportunity to expand their knowledge of a specific concept -- the "average" concept. Our data include…

Fractions are perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity are fractions having five interrelated constructs (part-whole, ratio, operator, quotient and measure) and teachers' pedagogical approaches to address these constructs. The present…

Modified schema-based instruction (MSBI) is a strategy to teach mathematical word problem solving to students with moderate and severe disabilities (MSD). In this comprehensive review, we explore the current state of research on MSBI to determine whether MSBI is an evidence-based practice (EBP) for students with MSD. We reviewed 12 studies, of…

Limited research exists to target algebra instruction for students with intellectual and developmental disabilities (IDD). In this study, researchers compared the use of concrete -- with scaffolds added by researchers -- and virtual algebra tiles -- with inherent scaffolds -- to support the acquisition, fluency, and generalization of linear…

There is a growing interest in the value of teachers guiding students to generate their own representations to support conceptual learning in science and across complementary subjects such as mathematics. However, this approach to an interdisciplinary focus poses challenges for programme design and learning assessment. In this paper, we report on…

Scholars use "position" to refer to the social expectations and range of available things a person can say and do in any given interaction (Harré and van Langenhove 1999; van Langenhove 2011). In the classroom, there are different social expectations for teachers and students. Teachers are often expected to give directions, present…