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…

In this article we review the research on the flexible or adaptive use of solution strategies in school mathematics, with a focus on the most recent work in the field. After a short introduction, we provide an overview of the various ways in which strategy flexibility has been conceptualized and investigated in the research literature. Then we…

This single-case study assessed the effectiveness of a mnemonic pegword strategy designed to enhance the multiplication fact fluency of three 6th-grade students who demonstrated persistent learning difficulties in mathematics. A nonconcurrent multiple baseline across subjects design was utilized, incorporating 3-5 baseline sessions followed by…

Various independent variables affect or have a relationship with students' mathematics academic achievement theoretically, practically, and statistically. These variables include the learning needs of students, use of general teaching principles, and learning strategies. This study aims to examine the predictive level of learning needs, learning…

Problem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non-routine tasks and propose the explicit teaching of domain-specific problem-solving tactics…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

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…

In this article, the authors share one approach to Number Talks that may help more students participate, increase access to and learning of mathematics, and provide some variation in routines. Number Talks are commonplace in the elementary mathematics classroom, thanks to Parker and Humphreys (e.g., 2018) and Parrish (e.g., 2011). They are a…

In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed…

Many instructional videos in mathematics education target knowledge of procedures and algorithms. To design instructional videos that support students in a non-algorithmic domain, such as mathematical modeling, we developed a framework based on research on heuristic worked examples and instructional videos. Because students' perceptions play an…

Education has always been and will continue to be the key that unlocks doors of opportunity and success for all. Our national test scores, over the last several decades, reveal that a majority of America's students are failing to meet academic benchmarks and standards, thus limiting the possibilities for opportunity. Mathematics, in particular,…

While in traditional mathematics teaching methods, it is possible to prove concepts while teaching geometry and to reach generalizations that require more complex definitions by using concept findings, while in today's geometry teaching, learning that activates the student's discovery process gains importance. In this context, the aim of this…

The authors wondered if there was a way to support their reluctant Grades 4, 5, and 6 students in contributing their starting points and strategies and advancing their collective knowledge. They wanted to ensure that the students had the space to develop and take ownership of the strategies they produced through a visual representation of ideas…

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

Considering the content of history of mathematics textbooks, it's evident that their emphasis is primarily on the illustrative aspects of recurring numerical sequences, with a particular focus on the Fibonacci sequence. Unfortunately, this limited approach results in the neglect of other sequences akin to the Fibonacci numbers, thus rendering the…