The challenge in serious games is to improve the effectiveness of learning by stimulating relevant cognitive processes. In this paper, we investigate the potential of surprise in two experiments with prevocational students in the domain of proportional reasoning. Surprise involves an emotional reaction, but it also serves a cognitive goal as it…

Introductory statistical concepts are some of the most challenging to convey in quantitative literacy courses. Analogies supplemented by visual illustrations can be highly effective teaching tools. This literature review shows that to exploit the power of analogies, teachers must select analogies familiar to the audience, explicitly link the…

Over half of 4th grade students did not meet proficiency standards in mathematics on the National Assessment of Educational Performance in 2019 and this problem has persisted over time. This underachievement coupled with the numerous barriers to implementing evidence-based practices in schools reveals a need to provide a menu of effective…

In this article, the author asserts that asking and responding to diagnostic questions is the single most important part of teaching secondary school mathematics. He notes the importance of formative assessment and recommends a formative assessment strategy that requires students to be public about their answers to questions, displaying their…

In our exploration of the order of operations we focus on the following claim: "In the conventional order of operations, division should be performed before multiplication." This initially surprising claim is based on the acronym BEDMAS, a popular mnemonic used in Canada to assist students in remembering the order of operations. The…

This paper explores an innovative assessment framework for measuring children's formal and informal mathematical knowledge. Many existing standardized measures, such as the Early Grade Mathematics Assessment, measure children's performance in early primary grade skills that have been identified by researchers and policy makers as foundational and…

This study evaluated a classroom implementation of augmented reality (AR) for improving subitizing skills of preschool students. Children explored the mathematical concept of subitizing by using an AR enhanced board game, called "Creature Counting." The AR markers, which were friendly creatures, triggered the augmented reality functions.…

This study explores kindergarten students' early notions of mathematical equivalence in the United States. In particular, it uses qualitative methods to examine the understandings children hold about the equal sign prior to formal instruction and how these understandings shift throughout an 8-week classroom teaching experiment designed to develop…

This article is about the systematization and representation young children spontaneously use when they are working on a combinatorial task. In this article, documentations from 123 children working on the same task are analysed. The question asked is if there are any connections between the systematizations and representations used in the…

Three-in-a-Row Lucky Numbers is an engaging, enjoyable, mathematically meaningful, game-based activity involving dice and a hundred chart, which can be used to introduce students to multiplication. The game provides a mechanism for students to explore the structure of multiplication, experiment with the distributive property, and begin to…

This paper synthesizes research from three separate studies, analysing how different representations of a mathematical concept may affect young children's engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of…

Research has highlighted that inquiry-based learning (IBL) instruction leads to many positive student outcomes in undergraduate mathematics. Although this research points to the value of IBL instruction, the practices of IBL instructors are not well-understood. Here, we offer a characterization of a particular form of IBL instruction:…

Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. In this article, the work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between…

This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of…

The purpose of this research study was to understand how mathematics majors make sense of similar matrices, a linear algebra topic that is rich in internal and external connections, in a series of in-depth qualitative interviews in a technology-assisted (MATLAB) learning environment. The study was also an attempt to develop a cognitive theory in…