Background: Educational technologies typically provide teachers with analytics regarding student proficiency, but few digital tools provide teachers with process-based information about students' variable problem-solving strategies as they solve problems. Utilising design thinking and co-designing with teachers can provide insight to researchers…

The problem solving performed by students in solving mathematical literacy problems shows that at the developmental stage of proportional reasoning students have different strategies, especially at the developmental stage of functional and scalar relationships. The purpose of this study is to identify and explore the developmental stages of…

Eddie Woo discusses the importance of problem solving in mathematics education. He points to the need for teachers to carefully consider the approaches they use to best support the growth of problem-solving abilities in students.

The basic notions of combinatorics, including systematic listing and permutations, are important topics of mathematics that are recommended to be learned eventually from elementary schools. However, there is little research in mathematics education regarding elementary students' combinatorial strategies. The purpose of this research is to…

Successful adoption of proven effective practice strategies such as distributed practice may contribute to much-needed improvement in mathematics performance. However, it is not yet fully understood if distributed practice is beneficial for long-term retention of complex procedural knowledge and, if so, for which initial practice performance level…

Struggling with mathematics is important for several reasons. According to learning theorists and empirical studies, the act of struggling can help students learn mathematics. Also, several important mathematics education documents advocate that students should engage in struggle as part of the problem-solving process. In addition, being able to…

Due to the sudden and unexpected move to remote learning in 2020 influenced by COVID-19, both mathematics teacher educators (MTEs) and prospective elementary teachers (PTs) faced a new challenge in creating a productive remote teaching and learning environment. In this study, we used Parrish's (2014) addition strategies and Thanheiser's (2009)…

The National Council of Teachers of Mathematics (2000) emphasizes the importance of communication in mathematics and mathematics education. Effective mathematical communication is essential in mathematics instruction, as it is a collaborative and social activity between teachers and students (Moschkovich, 2002; Khairunnisa et al., 2020). This…

In preparing to study teacher-student interactions in mathematics classrooms in Iran, this paper as a literature review considers relevant mathematics education literature. I explore which aspects of classroom environments orient researchers to judge patterns of classroom interactions as productive. I examine patterns of classroom interactions…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) emphasizes eight teaching practices for effective mathematics teaching, one of which is to "use and connect multiple representations" (NCTM 2014, p. 24). An action that describes how teachers might promote this practice is to "allocate substantial…

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.

Mathematics teachers often resist generic literacy strategies because they do not seem relevant to math learning. Discipline-specific literacy practices that emerge directly from the math content and processes under study are more likely to be embraced by math teachers. Furthermore, national and state-level mathematics standards as well as Common…

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Classroom instructional quality is seen as crucial to student learning. Of particular interest is the interpretation and enactment of the intended mathematics curriculum in Singapore schools by experienced mathematics teachers towards quality learning outcomes. This paper discusses the findings from the study which investigate the instructional…

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…