Decipipes are a representational model that can be used to help students develop conceptual understanding of decimal place value. They provide a non-standard tool for representing length, which in turn can be represented using conventional decimal notation. They are conceptually identical to Linear Arithmetic Blocks. This article reviews theory…

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations.…

Previous investigations on the subjective scale of numerical representations assumed that the scale type can be inferred directly from stimulus-response mapping. This is not a valid assumption, as mapping from the subjective scale into behavior may be nonlinear and/or distorted by response bias. Here we present a method for differentiating between…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

Research Findings: There is growing evidence that home learning stimulation that includes informal numeracy experiences can promote math-related learning in school. Furthermore, national studies suggest that children who start kindergarten with stronger math skills are more likely to succeed in high school. This study used a large sample of…

This article illustrates how activities or tasks can be designed that are based on the Necessity Principle. Two sections illustrate how tasks can be formulated to provoke the need to use two mathematical ideas--prime factorization and least common multiple. In each section, the author presents two examples to illustrate how some mathematical tasks…

Research about geologic time conceptions generally focuses on the placement of events on the geologic timescale, with few studies dealing with the duration of geologic processes or events. Those studies indicate that students often have very poor conceptions about temporal durations of geologic processes, but the reasons for that are relatively…

This issue of Clubbers' Guide contains an article written by Liz Carter, Senior Science Technician at the Warwick School, Redhill, Surrey (UK), describing some of the wide variety of science, technology, engineering and mathematics (STEM) based activities that her school puts on during an eight-day summer school in the holidays for prospective…

Although students' invented strategies typically prove to be effective in the improvement of students' mathematical understanding, little is known about how preservice teachers interpret and respond to student-invented strategies on whole number multiplication. This study investigated the nature of 25 preservice teachers' interpretations of and…

What would the curriculum look like if it were developed from the perspective of measuring? Without formal tools, the Yup'ik Eskimos of Alaska used their body as a measuring device and employed ratios extensively in their daily practices. "Math in a Cultural Context" is developing curriculum materials based on Yup'ik Elders use of…

The theme of the 39th proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) conference was "Synergy at the Crossroads: Future Directions for Theory, Research, and Practice." The metaphor of crossroads was inspired by the conference venue--the historic Indianapolis Union…

Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery…

This paper describes the development and intended uses of the Early Grades Mathematics Assessment (EGMA), which measures essential early mathematical knowledge and skills that are foundational to more sophisticated mathematical abilities, predictive of later achievement, and teachable. Administering the EGMA can provide policy makers,…

The purpose of the present study was to reveal the developmental pathway from third grade cognitive competencies to sixth grade conceptual and procedural fraction knowledge through the intervening whole numerical skills at fifth grade. The study used empirical data that come from 536 students in nine schools across two Delaware public school…

This compendium organizes information on the math and science projects sponsored by NCER and NCSER into two main sections: Mathematics and Science. Within each section, projects are sorted into chapters based on content area, grade level, and intended outcome. In determining the chapters, we considered the emerging college- and career-readiness…