In classroom learning, students need mathematical cognitive flexibility to be able to solve mathematical problems with the various ideas they express. To solve the problems, they must be able to grasp the problem, see it from various points of view, and should not be rigid thinking with one solving method. In fact, the students still lack the…

Statistical literacy and statistical reasoning are important learning goals that instructors aim to develop in statistics students. However, there is a lack of clarity regarding the relationship among these learning goals and to what extent they overlap. The REasoning and Literacy Instrument (REALI) was designed to concurrently measure statistical…

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…

Many preservice teacher (PST) programs throughout the world are preparing students to implement the Core Standards, which require deeper conceptual understandings of mathematics and an informed approach for teaching. In this qualitative multi-case study, researchers explored the teaching methods for two university instructors and changes in PSTs…

In this paper, we discuss the process of identifying and validating students' abilities to think proportionally. More specifically, we describe the methodology we used to identify these proportional reasoning attributes, beginning with the selection and review of relevant literature on proportional reasoning. We then continue with the…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

The purpose of this study is to examine a mathematics student teacher's lessons by using example types named "teaching concepts and procedures" and "the provision of exercises." The participant's two lessons regarding the probability concept were observed and the semi-structured interviews were realized. The participant…

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these…

This paper describes the implications of constructivism both for what to teach and for how to teach. The first part discusses three approaches on what to teach: (1) relating mathematical knowledge to other knowledge; (2) checking for self-consistency; and (3) putting thinking before facts. The second part is on how to teach based on…

Research is only beginning to show the benefits of the effective use of manipulatives with students who have disabilities. This article highlights how teachers can incorporate three manipulative instructional strategies to help students with high-incidence disabilities.