This study tested whether 10- and 12-year-olds who can correctly compare the magnitudes of fractions with common components access the magnitudes of the whole fractions rather than only compare the magnitudes of their components. Time for comparing two fractions was predicted by the numerical distance between the whole fractions, suggesting an…

In this sequence 1/1, 7/5, 41/29, 239/169 and so on, Thomas notes that the sequence converges to square root of 2. By observation, the sequence of numbers in the numerator of the above sequence, have a pattern of generation which is the same as that in the denominator. That is, the next term is found by multiplying the previous term by six and…

In collaboration with two other research organizations, the authors integrate principles of the BEAR Assessment System with Universal Design for Learning principles to develop and validate learning progressions and an aligned, universally designed formative and summative classroom assessment system for promoting conceptual understanding of number…

The widely adopted Common Core State Standards for Mathematics (CCSSM) are designed to deepen instruction of number sense and will demand that elementary school teachers have a strong understanding of number. These changes arrive at a time when it is still understood that teachers and the curriculum in the United States have not been fundamentally…

This article argues for the necessity of phonetic analysis in signed language linguistics and presents a case study of one analytical system being used in a preliminary attempt to identify natural classes and investigate variation in ASL handshapes. Robbin Battison (1978) first described what is now a widely accepted list of basic handshapes,…

In this article, we directly question the common practice in growth mixture model (GMM) applications that exclusively rely on the fitting model without covariates for GMM class enumeration. We provide theoretical and simulation evidence to demonstrate that exclusion of covariates from GMM class enumeration could be problematic in many cases. Based…

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…

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…

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…