For more than one hundred years teachers have paddled beside the great ocean of mathematical adventure. Between them they have taught millions of young people. A few have dived in and kept swimming, some have lingered on the shore playing in pools, but most have dipped their toes in and run like heck in the other direction never to return. There…

In recent years, a strong functional relationship between finger counting and number processing has been suggested. Developmental studies have shown specific effects of the structure of the individual finger counting system on arithmetic abilities. Moreover, the orientation of the mental quantity representation ("number line") seems to be…

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…

There is evidence for both semantic and asemantic routes for naming Arabic digits, but neuropsychological dissociations suggest that number-fact retrieval (2x3=6) can inhibit the semantic route for digit naming. Here, we tested the hypothesis that such inhibition should slow digit naming, based on the principle that reduced access to multiple…

Number sense has been recognised as central to young children's development of mathematics for a number of decades. A student with a "good" sense of number normally has a thorough understanding of relationships among numbers and operations--being able flexibly to partition and combine numbers in convenient ways to allow appropriate…

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…

Verguts and Van Opstal [Verguts, T., & Van Opstal, F. (2008). A colorful walk, but is it on the mental number line? Reply to Cohen Kadosh, Tzelgov, and Henik, Cognition, 106, 558-563] cleverly explained the results of Cohen Kadosh, Tzelgov, and Henik [Cohen Kadosh, R., Tzelgov, J., & Henik, A. (2008). A synesthetic walk on the mental number line:…

Letter identities and number identities are usually thought to imply different cortical mechanisms. Specifically, the left fusiform gyrus responds more to letters than to digits (T. A. Polk et al., 2002). However, a widely circulated statement on the internet illustrates that it is possible to use numbers (leet digits) as parts of words, 4ND TH3…

This study is an exploratory study of the relationship between collaboration and mathematics and game outcomes in a video game aimed at teaching concepts related to rational numbers. The sample included 243 middle school students who played the video game either with one partner or individually for 40 minutes. Results suggest that participants…

Due to their motivational nature, there has been growing interest in the potential of games to help teach academic content and skills. This report examines how different levels of detail about a game's scoring rules affect math learning and performance. Data were collected from 164 students in the fourth to sixth grades at five after-school…

This is the second and final report of the Middle School Mathematics Professional Development Impact Study, which examines the impact of providing a professional development (PD) program in rational number topics to seventh-grade mathematics teachers. An interim report (Garet et al. 2010) described the findings after one year of PD. The current…

Early measures of mathematics skill and development have focused on early numeracy skills like counting, number identification, and sequencing of numbers. This study attempted to expand early mathematics assessment. Six new measures of early mathematics skill competence were developed and evaluated. Four existing measures also were examined.…

This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…

We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.