The balance model is often used for teaching linear equation solving. Little research has investigated the influence of various representations of this model on students' learning outcomes. In this quasi-experimental study, we examined the effects of two learning environments with balance models on primary school students' reasoning related to…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning…

We describe results of a long-term design experiment focused on promoting mathematics learning among multilingual ninth graders classified as English Learners. The intervention at a linguistically diverse public high school in the US focused on a unit introducing concepts related to linear rates of change. We analyze results from a…

Algebra is the foundational mathematics course that students take as they begin their high school career and is often difficult for the average learner. In order for students with disabilities and those with mathematics difficulties to meet the high expectations of future mathematical courses, providing quality instruction by implementing…

Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals.…

After being introduced to the distributive law in meaningful contexts, students need to extend its scope of application to unfamiliar expressions. In this article, a process model for the development of structure sense is developed. Building on this model, this article reports on a design research project in which exercise tasks support students…

Despite the proliferation of video-based instruction and its benefits--such as promoting student autonomy and self-paced learning--the complexities of online teaching remain a challenge. To be effective, educators require extensive training in digital teaching methodologies. As such, there's a pressing need to examine and comprehend the…

Previously, we had reported on the relationship between AP physics experience and exam scores, and student scores on the Force and Motion Conceptual Evaluation and in an introductory calculus-based mechanics course [E. W. Burkholder and C. E. Wieman, Phys. Rev. Phys. Educ. Res. 15, 020117 (2019)]. Two limitations to our previous work were that we…

The aim of this study is to develop a valid and reliable measurement tool that measures mathematical visualization perceptions for mathematics teacher candidates. Therefore, the type of study is a survey research. Research was carried out with 462 (336 Female, 125 Male) mathematics teacher candidates from a university located in the Eastern…

This study explores how online mathematics games contribute to Grade 8 learners' understanding of basic principles and more sophisticated aspects of algebra. This project documents the trajectory of a purposive sample of 30 Grade 8 learners doing mathematics and one mathematics educator. The study is premised on the argument that learners with the…

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…

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…

A study was conducted to explore the beliefs and practices of 49 New South Wales (NSW) primary school teachers regarding their beliefs and practices concerning the use of concrete materials in the learning and teaching of Number and Algebra. This paper reports on elements of the study regarding why and how teachers use concrete materials. Not only…

In Intelligent Tutoring Systems (ITS), methods to choose the next exercise for a student are inspired from generic recommender systems, used, for instance, in online shopping or multimedia recommendation. As such, collaborative filtering, especially matrix factorization, is often included as a part of recommendation algorithms in ITS. One notable…