The role of a teacher is different from that in traditional mathematics instruction when the implementation of a lesson is based on students' ideas. The author's experience teaching the same lesson (of the latter format) to two different classes of pre-service teachers in an elementary mathematics methods course is described. Since whole-class…

Predictions of the Identical Elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) about transfer between arithmetic facts were tested in primary school children. The aim of the study was to test whether the IE model, constructed to explain adult performance, also applies to children. The IE model…

Many sets of state and national mathematics standards have come and gone in the past two decades. The Common Core State Mathematics Standards (CCSMS), which were released in June of 2010, have been adopted by almost all states and will be phased in across the nation in 2014. The main difference between these standards and most of the others is…

The purpose of this study was to determine whether there are different growth trajectories of arithmetic strategies and whether these trajectories result in different achievement outcomes. Longitudinal data were collected on 240 students who began the study as 2nd graders. In the 1st year of the study, the 2nd-grade students were assessed on…

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental…

Teaching students how to multiply fractions is challenging, not so much from a computational point of view but from a conceptual one. The algorithm for multiplying fractions is much easier to learn than many other algorithms, such as subtraction with regrouping, long division, and certainly addition of fractions with unlike denominators. However,…

Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years 1 and 2 on the…

Some years ago, Hatano differentiated between routine and adaptive expertise and made a strong plea for the development and implementation of learning environments that aim at the latter type of expertise and not just the former. In this contribution we reflect on one aspect of adaptivity, namely the adaptive use of solution strategies in…

Processing information in working memory requires selective access to a subset of working-memory contents by a focus of attention. Complex cognition often requires joint access to 2 items in working memory. How does the focus select 2 items? Two experiments with an arithmetic task and 1 with a spatial task investigate time demands for successive…

Results from 2 relational-priming experiments suggest the existence of an automatic analogical coordination between semantic and arithmetic relations. Word pairs denoting object sets served as primes in a task that elicits "obligatory" activation of addition facts (5 + 3 activates 8; J. LeFevre, J. Bisanz, & L. Mrkonjic, 1988). Semantic relations…

Three studies addressed children's arithmetic. First, 50 3- to 5-year-olds judged physical demonstrations of addition, subtraction and inversion, with and without number words. Second, 20 3- to 4-year-olds made equivalence judgments of additions and subtractions. Third, 60 4- to 6-year-olds solved addition, subtraction and inversion problems that…

This paper discusses the impact of action research methodology used in the teaching and learning process and professional teacher development. In this study are including 58 students of three second grade classes, 3 teachers of those classes and a university professor. Aiming at using a different approach in their teaching of multiplication and…

The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

This article reports on an ethnographic study of a 10-year-old's pursuit of school-based mathematics across school and home to suggest that participating in school-based mathematics is a cross-setting phenomenon in at least 2 ways. First, I illustrate how accomplishing school-based mathematics literally extends into the home and how individuals…

The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it. According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a particular concept are better equipped to…