To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

In this paper, differences in the implementation of a number activity called the snake game are studied. Nine Swedish preschool teachers worked in collaboration with a research team, enacting the same activity with their groups of 5-year-old children over a 3-month period. Variation theory forms the basis for the analysis of 67 videorecorded…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

This article describes some of the essential mathematics that underpins the use of algorithms through a series of learning pathways. To begin, a graphic depicting the mathematical ideas and concepts that underpin the learning of algorithms for multiplication and division is provided. The understanding and use of algorithms is informed by two…

A strong foundation in early number concepts is crucial for students' future success in statistics. Despite its importance in statistics, many first-year students struggle to comprehend the normal distribution due to a lack of basic number sense. Students get confused about the order and magnitude of negative z-scores on a standard normal curve or…

This practical book draws on Ronit Bird's teaching experience to create detailed strategies and teaching plans for students aged 9-16 who have difficulties with number. Activities and games are used to teach numeracy skills in these key areas: number components, bridging, multiplication, division and reasoning strategies. New to this edition: (1)…

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

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…

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.

Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…

Recent studies show that English learning students are a growing population within the United States school system. Language barriers have been shown to negatively influence reading scores as well as math scores, and math scores are a predictor of future academic success in many subject areas. This qualitative action research study demonstrates…

Numeration units (ones, tens, hundreds, etc.) are an epistemological foundation for place value. Here, we assume that they are a didactic support in countries where spoken numbers are incongruent with written numbers. In France, teaching practices neglect the relations between units, and numeration units are typically used only to designate the…

Through the historical analysis of Dienes' works and through the suggestions of activities, the objective of this text is to understand the movement of systematization of knowledge for teaching and to teach classification, ranking, and ordination through the use of logical blocks during the Modern Mathematics Movement (1960-1980), a time of…

The aim of this research is to propose indicators of epistemic and mediational suitability to assess tasks designed in a mobile learning context, using theoretical and methodological elements of the onto-semiotic approach (OSA) and the SAMR model (substitution, augmentation, modification, and redefinition). With these indicators, 110 tasks…

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)…