Research Findings: A total of 72 Head Start children (M age = 53.26 months, SD = 5.07) were randomly assigned to 4 conditions. Some were taught the oddity principle (choosing the object that differs from others in a group) and seriation (ordering objects on a dimension and inserting new objects into such orders), which are forms of thinking that…

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

Given the vital importance of using a scientific approach for curriculum development, the authors employed a design experiment methodology (Brown, 1992; Shavelson et al., 2003) to develop and evaluate, FUSION, a first grade mathematics intervention intended for students with or at-risk for mathematics disabilities. FUSION, funded through IES…

To investigate the functional connection between numerical cognition and action planning, the authors required participants to perform different grasping responses depending on the parity status of Arabic digits. The results show that precision grip actions were initiated faster in response to small numbers, whereas power grips were initiated…

Numbers--of publications, grant money, PhD students, and invited talks, for example--play too large a role in assessments of faculty. The author's thirty-five years of experience in higher education have convinced him that overreliance on such numbers is a big problem, especially, but not exclusively, in the sciences. Every scientist recognizes…

In 1225 Fibonacci visited the court of the Holy Roman Emperor, Frederick II. Because Frederick was an important patron of learning, this visit was important to Fibonacci. During the audience, Frederick's court mathematician posed three problems to test Fibonacci. The third was to find the real solution to the equation: x[superscript 3] +…

This note presents another elementary method to evaluate the Fresnel integrals. It is interesting to see that this technique is also strong enough to capture a number of pairs of parameter integrals. The main ingredients of the method are the consideration of some related derivatives and linear differential equations.

This paper discusses some common iterations of complex functions. The presentation is such that similar processes can easily be implemented and understood by undergraduate students. The aim is to illustrate some of the beauty of complex dynamics in an informal setting, while providing a couple of results that are not otherwise readily available in…

The relation between short-term and long-term change (also known as learning and development) has been of great interest throughout the history of developmental psychology. Werner and Vygotsky believed that the two involved basically similar progressions of qualitatively distinct knowledge states; behaviorists such as Kendler and Kendler believed…

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory…

An annotated list of children's books published within the last 15 years and related to Louisiana culture, environment, and economics are linked to the Louisiana Content Standards. Readability levels of selected books are included, providing guidance as to whether a book is appropriate for independent student use. The thirty-three books listed are…

Lexical variation abounds in New Zealand Sign Language (NZSL) and is commonly associated with the introduction of the Australasian Signed English lexicon into Deaf education in 1979, before NZSL was acknowledged as a language. Evidence from dictionaries of NZSL collated between 1986 and 1997 reveal many coexisting variants for the numbers from one…

The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants' content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group…

Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental…