In this study, 244 children (average age: 61 months) and their parents from the Dallas and Fort Worth metroplex area in Texas were surveyed to investigate children's proficiency in mathematics content on numbering, sizes, comparisons, and shapes. The researchers investigated children's proficiency in mathematics associated with children's gender,…

This study evaluated the effects of simulation training to teach functional community skills to four students with developmental disabilities in middle school. A multiple probe across participants and multiple probe across behaviors allowed for an evaluation of a functional relation between simulation and skill acquisition. Students learned how to…

In this article, I discuss a case of pre-primary and primary school teacher education concerning place value in number representation. In primary school (in Italy, in grades 1 and 2), the topic is usually introduced by means of manipulatives (for instance, abaci and base ten blocks). But it is well known that no artefact is transparent for…

The Educational Policy Improvement Center (EPIC) conducted an investigation of the Intersegmental Committee for the Academic Senates (ICAS) Statements of Competencies for Mathematics and Academic Literacy. The purpose of this work is to understand how the ICAS competencies relate to college and career readiness, as represented by the augmented…

This paper describes a synthesis conducted to determine what research says regarding preservice teachers' understanding of fractions and identify the gaps in their existing knowledge basis. Specifically, this paper will address a smaller portion of the synthesis and report the findings from fraction multiplication and division topics. Results…

Supporting a productive discourse is an important element of reform teaching, as it gives students opportunities to understand mathematical reasoning. In this study, the practices of an expert seventh-grade mathematics teacher are described to illustrate how she created and sustained a genuine mathematical discourse environment during the teaching…

In synesthesia, stimulation of one sensory modality leads to a percept in another nonstimulated modality, for example, graphemes trigger an additional color percept in grapheme-color synesthesia, which encompasses the variants letter-color and digit-color synesthesia. Until recently, it was assumed that synesthesia occurs strictly unidirectional:…

Several new and sharp inequalities involving the constant e and the sequence (1 + 1/n)[superscript n] are proved.

R. Sekuler, P. Tynan, and E. Levinson (1973) found that when 2 characters are presented side-by-side with a short onset asynchrony, subjectively they often appear in a "first-left, then-right" order. The authors of this article conducted 6 experiments in which observers judged the temporal order (TOJs) in which 2 digits were presented. They found…

Previous research has shown that time to name single-digit Arabic numbers is about 15 ms slower when naming trials are interleaved with simple multiplication (e.g., state product of 2 x 3) than when naming digits is interleaved with magnitude comparison (e.g., state larger; 2 [arrow up] 3). To explain this phenomenon, J. I. D. Campbell and A. W.…

While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated…

It is known that the ratios of consecutive terms of Fibonacci and Tribonacci sequences converge to the fixed ratio. In this article, we consider the generalized form of Tribonacci numbers and derive the "golden proportion" for the whole family of this generalized sequence. (Contains 2 tables.)

Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…

This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of "r" natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers.

The SNARC (spatial-numerical association of response codes) effect refers to the finding that small numbers facilitate left responses, whereas larger numbers facilitate right responses. The development of this spatial association was studied in 7-, 8-, and 9-year-olds, as well as in adults, using a task where number magnitude was essential to…