Numbers are thought to be represented in space along a mental left-right oriented number line. Number magnitude has also been associated with the size of grip aperture, which might suggest a connection between number magnitude and intensity. The present experiment aimed to confirm this possibility more directly by using force as a response…

We analyzed the effects of verbal mediating responses on the acquisition and generalization of say-do correspondence and noncorrespondence. Participants were assigned to groups in which either reinforcers (feedback and tokens) were arranged for say-do correspondence and noncorrespondence, or no reinforcers were programmed. Participants in these…

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…

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…

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…