Over the last years, there is a growing interest in studying students' difficulties with rational numbers from a cognitive/developmental perspective, focusing on the role of prior knowledge in students' understanding of rational numbers. The present study tests the effect of the "whole" or "natural number bias" (i.e., the…

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This…

Background: Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered. Aims: To examine the extent to which…

Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

Background: Although research on mathematics learning programs has taken off in recent years, little is known about how different person characteristics are related to practice behaviour with such programs. When implementing a mathematics learning program in the classroom, it might be important to know whether students with specific…

Background: In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations. Aim: In order to address this question, our goal was to determine the…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction "x/y," children are often taught to use "partitioning": break the whole into "y" parts, and shade in "x" parts. Past research has shown that partitioning on number lines supports children's fraction…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…

Students' previous knowledge at a superficial level is reviewed when they solve mathematical problems. This action is imperative to strengthen their knowledge and provide the right information needed to solve the problems. Furthermore, Pirie and Kieren's theory stated that the act of returning to a previous level of understanding is called folding…

Teacher knowledge is particularly important in middle school mathematics to enhance the meaningful transition from arithmetic to algebra. Developing a solid understanding of algebra requires teachers to unpack the meaning underlying the basic concepts, make clear and explicit distinctions among concepts, and facilitate students to connect these…

Children and adults often have difficulties comparing decimal magnitudes. Although individuals attempt to reconcile decimals with prior whole-number and fraction knowledge, conceptual and procedural differences between decimals and prior knowledge of whole numbers and fractions can lead to incorrect strategies. The dynamic strategy choice account…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

Existing frameworks of teachers' knowledge required to teach mathematics do not adequately capture the dynamic aspects of knowledge manifested in teaching practice. In this paper, we examine the knowledge demands that arise in situ, in the course of a teacher listening and responding to students' thinking, while teaching the topic of decimal…

How does the visual system recognize images of a novel object after a single observation despite possible variations in the viewpoint of that object relative to the observer? One possibility is comparing the image with a prototype for invariance over a relevant transformation set (e.g., translations and dilations). However, invariance over…

While Educational Data Mining research has traditionally emphasized the practical aspects of learner modeling, such as predictive modeling, estimating students knowledge, and informing adaptive instruction, in the current study, we argue that Educational Data Mining can also be used to test and improve our fundamental theories of human learning.…