The number line has been proposed as a central construct used by students to solve a range of mathematics problems. Given the capacity of number lines to represent all real numbers and to be used in a variety of contexts, there have been calls to increase the use of number lines in mathematics instruction. However, due to the recency of these…

There is growing evidence that the ability to perceive structure is essential for students' mathematical development. Looking at students' structure sense in basic numerical and patterning tasks seems promising for understanding how these tasks set the foundation for the development of later mathematical skills. Previous studies have shown how…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with…

Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements--imagined as well as real ones…

We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

In the area of early literacy, the children learned new vocabulary to describe the attributes of triangles and shapes. Through math talk and class discussions, the children also learned about listening to others, turn taking, and voicing their ideas. Although the children described in this article were generally competent in the English language…

Despite the standardization of calculus education as a Calculus and Analytic Geometry course after the 1950s, curriculum updates have been slow to penetrate the undergraduate mathematics classroom practice, taking decades to manifest. Common struggles with the teaching and learning of calculus, such as relying on a procedural understanding of…

Mathematically gifted students have a potential for understanding and connecting mathematics concept. Pattern generalization as a part of functional thinking becomes one of the benchmarks for gifted students in mathematics. The mathematics curriculum in Indonesia that has not accommodated the functional thinking ability of elementary school…

Learning mathematics is difficult for many students, especially students with mathematics learning disabilities MLD. To improve the academic achievement for students with MLD, educational legislations (IDEA 2004; ESSA 2015) mandate that schools must use evidence-base core curricula. Textbooks conveys the intended values and principles for…

In this paper we present the results of a survey of research studies on the learning of multivariable calculus in a wide geographic spectrum. The goal of this study is to describe what research results tell us about students' learning of calculus of two-variable functions, and how they inform its teaching. In spite of the diversity of cultures and…

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified…

Mathematical learning is to produce a high competence individual with multiple skills in line with the needs of the 21st century. However, mathematical education is still plagued with problem of mastery of mathematical concepts. In addressing this problem, various initiatives and interventions need to be implemented to ensure that mathematical…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…