Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural…

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

This purpose of this quasi-experimental, ex-post facto study was to examine the effect of SpringMath as a classwide intervention for students in grades kindergarten through second grade within one elementary school. In order to research the effects of SpringMath on the whole-number computational fluency of kindergarten through second grade…

School reform efforts are situated within social and political contexts and, as such, are susceptible to the commonsense discourses circulating through, and shaping, society. Two discourses prevalent in US education reform are those perpetuating the ideologies of neoliberalism and neoconservatism. These ideologies are inherently…

The purpose of this correlational study was to investigate the relationship of number sense comprehension and mathematics attitudes on mathematics achievement and intention to pursue a mathematics-related career for final-year high school students in Kenya. The sample for the study comprised of final-year high school students from three schools,…

Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like the square root…

In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with…

Educated adults and children engage a network of frontal and parietal brain regions for numerical thinking. Recent studies document some prominent changes as this network emerges over development, including a unilateral right to bilateral shift in number-selective parietal brain activity, a strengthening of intra- and interhemispheric parietal…

This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

Whole-number arithmetic is a core content area of primary mathematics, which lays the foundation for children's later conceptual development. This paper focuses on teaching whole-number multiplication (WNM) to build a stepping stone for children's proportional reasoning. Our intention in writing this paper is to obtain a practice-based perspective…

Numerous variants of Kahneman and Tversky's (1972) hospital problem have been used to investigate intuitions about the Empirical Law of Large Numbers (eLLN). A largely separate line of research has focused on interactions between context knowledge and statistical reasoning. The present study merges these two lines of research by analyzing tertiary…

This study aims to evaluate ChatGPT's capabilities in certain numerical analysis problem: solving ordinary differential equations. The methodology which is developed in order to conduct this research takes into account the following mathematical abilities (defined according to National Centre for Education Statistics): Conceptual Understanding,…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

Conceptual body movement in education is an external representation mode that research suggests can support children's learning about mathematical phenomena. Children's learning and understanding of mathematical concepts and processes, such as number structure and relationships, number sequencing, position, or geometric properties, may be…