A number derivative is a numerical mapping that satisfies the product rule. In this paper, we determine all number derivatives on the set of integers modulo n. We also give a list of undergraduate research projects to pursue using these maps as a starting point.

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…

This second edition of the bestselling book "The Young Child and Mathematics" reflects recent developments in math education in a wealth of vignettes from classrooms, activity ideas, and strategies for teaching young children about math processes and concepts. Using standards and guidelines from the National Council of Teachers of Mathematics…

Previous studies have shown that as a group 6-month-old infants successfully discriminate numerical changes when the values differ by at least a 1:2 ratio but fail at a 2:3 ratio (e.g. 8 vs. 16 but not 8 vs. 12). However, no studies have yet examined individual differences in number discrimination in infancy. Using a novel numerical change…

How can teachers encourage their geography students to make sense of big numbers? The key math skills geography students need to apply are ones they learned long ago in fifth grade: estimation and place value. However, in order to recognize the size of a city, or strength of a country's per capita income, or value of a birth rate, they need…

The aim of this article is to characterize the 2 x 2 matrices "X" satisfying X[superscript 2] = X + I and obtain some new identities concerning with Fibonacci and Lucas numbers. The recommendations regarding the teaching of the identities given in this article can be presented in two cases. The first is related to the pedagogical aspect. The…

This study investigated the effects of two generative learning activities on students' academic achievement of the part-whole meaning of rational numbers while using virtual manipulatives. Third-grade students were divided randomly in two groups to evaluate the effects of two generative learning activities: answering-questions and…

Proportional reasoning is perhaps one of the most important types of mathematical thinking for elementary school students to develop. It includes aspects of rational numbers, spans the entire mathematics curriculum, and is a significant foundation for mathematical proficiency. Understanding students' use of proportional reasoning is a basis on…

The current study investigated the neural activity patterns associated with numerical sensitivity in adults. Event-related potentials (ERPs) were recorded while adults observed sequentially presented display arrays (S1 and S2) of non-symbolic numerical stimuli (dots) and made same/different judgments of these stimuli by pressing a button only when…

Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4-8 (aged 9-14). In this paper, we assert that students' development of algebraic…

Researchers (Ball, 2003; Ma, 1999; Schulman, 1986) have long investigated how a teacher's subject matter and pedagogical content knowledge impact on students' learning of mathematics. In an attempt to account for the relationship between teacher knowledge and student learning, this study examined four Romanian first grade teachers' knowledge about…

The present study examined predictive power of behavioral self-regulation, family and child characteristics on children's number sense. The participants consisted of 101 kindergarten children. A subsample of 30 children was randomly chosen for the reliability procedures of Assessing Number Sense and Head, Toes, Knees and Shoulders instruments.…

This study investigated the effects of computer-based practice on the acquisition and maintenance of basic academic skills for two children with moderate to intensive disabilities. The special education teacher created individualized computer games that enabled the participants to independently practice academic skills that corresponded with their…

This article describes the affordances of using clinical interviews with struggling mathematics learners to inform intervention and instruction. A case study of a fourth grade student, Danny, is presented to give an illustrative example of the complexity of the student's mathematical understandings in terms of place value. From the clinical…

Small numbers are spontaneously associated with left space and larger numbers with right space (the SNARC effect), for example when classifying numbers by parity. This effect is often attributed to reading habits but a causal link has so far never been documented. We report that bilingual Russian-Hebrew readers show a SNARC effect after reading…