This chapter describes instances of play within a teaching episode on integer addition and subtraction. Specifically, this chapter makes the theoretical distinction between integer play and playing with integers. Describing instances of integer play and playing with integers is important for facilitating this type of intellectual play in the…

An instructional approach is presented for teaching the mole concept to high school introductory-level chemistry classes. Extensions to the strategy are presented for more advanced classes. The strength of the approach is based upon discovery. Students discover the Avogadro number and the mole concept. The discovery is based upon calculations that…

Place value concept that learns especially in primary school ages is also the basis of many issues students will encounter throughout their learning lives. This research aims to developmentally determine understanding of the place value concept in early childhood. The model of research is a case study from qualitative research methods. The study…

We offer this synthesized framework as a tool to reveal mathematical activity in a non-formal makerspace. In particular, we connect research at different grain sizes to illustrate and explain how mathematics plays a crucial, if often implicit, role in this activity. We begin with describing the Approximate Number System and the Ratio-Processing…

This study aims to explore seventh-grade students' understanding of negative integers as they engaged in mathematics history integrated model-eliciting activities in small groups. For this educational case study, we designed model-eliciting activities based on six design principles of the models-and-modeling perspective that incorporated history…

The purpose of this qualitative, single-case study was to examine teachers' perceptions of using guided notes to improve the proficiency rate of middle-grade students in mathematics number systems. This study was conducted in one school system in North Carolina where students were failing to meet the state standards for mathematics achievement at…

This article describes Ulrich Kortenkamp's Place Value Chart app and the accompanying teacher guide developed by the members of an international research team led by regular contributor Kevin Larkin.

The empirical law of large numbers is an important content in secondary school mathematics. Tasks used to analyze students' understanding of this law are often based on the hospital problem, but vary in various features, leading to mixed and conflicting empirical results. To identify task features that support students when approaching this type…

A striking characteristic of human thought is that we form representations about abstract kinds (Giraffes have purple tongues), despite experiencing only particular individuals (This giraffe has a purple tongue). These generic generalizations have been hypothesized to be a cognitive default, that is, more basic and automatic than other forms of…

Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often-reported gender differences in later mathematics and STEM-related abilities. Using a…

Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial-numeric mappings from other numeric abilities, such as counting or…

The book synergizes research on number across two disciplines--mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children's activity, including mental and physical actions. Subsequent chapters are organized into sections that…

Few research studies within the field of mathematics education have focused on the ability to recognize quantities quickly and accurately without counting (i.e. subitizing). The aim of this research was to empirically explore the role of conceptual subitizing activities for enhancing preschool class children's learning of the part-part- whole…

In this study, we share our broad and deep search for what is known from blind-peer-reviewed research publications about the efficacy of the instructional practice of Number Talks. We describe our process for literature review and the subsequent analysis that revealed a shallow depth of articles for which one can discern the factors of quality of…

This study aims to explore the students' mathematical understanding in integers division operation through the context of archipelago traditional cakes in class VII. This research is related to the Indonesian Realistic Mathematics Approach (PMRI) as a learning approach used. The methodology used in this study is Design Research consisting of three…