This paper reports part of an ongoing investigation into the understanding of irrational numbers by prospective secondary school teachers. It focuses on the representation of irrational numbers as points on a number line. In a written questionnaire, followed by a clinical interview, participants were asked to indicate the exact location of the…

Many students find proofs frustrating, and teachers struggle with how to help students write proofs. In fact, it is well documented that most students who have studied proofs in high school geometry courses do not master them and do not understand their function. And yet, according to NCTM's "Principles and Standards for School Mathematics"…

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltesz et al., 2007) here our objective was to identify and compare…

Recent work on the acquisition of number words has emphasized the importance of integrating linguistic and developmental perspectives [Musolino, J. (2004). The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. "Cognition 93", 1-41; Papafragou, A., Musolino, J. (2003). Scalar implicatures: Scalar…

A conceptual knowledge of numbers, especially fractions, is an important link to a conceptual understanding of variables. This article suggests activities that explicitly show the connections between numbers and variables using the number line as the connecting device. (Contains 7 figures and a bibliography.)

North Korea is one of the most closed nations in the world. It is difficult to access information about their education system. North Korea's economic system was reorganized on July 1, 2002, as well as the education system. This change has impacted North Korea's mathematics education. With limited information on North Korean mathematics textbooks,…

Few researches have been concerned about relation between children's spatial thinking and number sense. Narrowing for this small research, we focused on one component of spatial thinking, that is structuring objects, and one component of number senses, that is cardinality by determining quantities. This study focused on a design research that was…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research,…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Sandards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research,…

A tight correspondence has been postulated between the representations of number and space. The spatial numerical association of response codes (SNARC) effect, which reflects the observation that people respond faster with the left-hand side to small numbers and with the right-hand side to large numbers, is regarded as strong evidence for this…

This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…

This paper examines three historical geometric constructions for handcrafting stringed instruments. Using elementary geometry--in particular, triangles--these methods can provide quite good rational approximations to the irrationals that arise from tuning instruments in equal temperament. Interestingly, continued fractions help explain the…

Four experiments were conducted in order to examine effects of notation--Arabic and verbal numbers--on relevant and irrelevant numerical processing. In Experiment 1, notation interacted with the numerical distance effect, and irrelevant physical size affected numerical processing (i.e., size congruity effect) for both notations but to a lesser…