This article confronts the issue of why secondary and post-secondary students resist accepting the equality of 0.999... and 1, even after they have seen and understood logical arguments for the equality. In some sense, we might say that the equality holds by definition of 0.999..., but this definition depends upon accepting properties of the real…

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…

Although number sense is difficult to define, it involves having a good intuition about numbers and their relationships, including the ability to have a "feel" for the relative size of numbers and to make reasonable estimations. Students with good number sense typically recognise the relative magnitude of numbers, appreciate the effect…

Many students have trouble grasping algebra. In this book, bestselling authors Judith, Gary, and Erin Muschla offer help for math teachers who must instruct their students (even those who are struggling) about the complexities of algebra. In simple terms, the authors outline 150 classroom-tested lessons, focused on those concepts often most…

This paper examines Roy Harris' discussion of number and the language of science in his book "History, Science and the Limits of Language" in light of recent work in cognitive linguistics. While many of his points are valid, linguistic theory has since addressed some of these concerns by formulating usage-based, cognitive frameworks to explore and…

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…

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…

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…