In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields…

This manual is collection of examinations. The first part contains 150 examination papers, the questions for which have been selected mainly from the English, French, and German collections of problems. These papers may be divided into three groups. The first 50 papers are confined to the simple rules, fractions, and weights and measures; the next…

This book is about playing with mathematics, teaching: (1) How to multiply and divide large numbers mentally; (2) Making addition and subtraction easy; (3) Tricks for understanding fractions and decimals; and (4) How to quickly check answers for each calculation. Described as a foolproof way to do multiplication, division, factoring estimating,…

This book contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors…

This article explores how conceptualization of absolute value can start long before it is introduced. The manner in which absolute value is introduced to students in middle school has far-reaching consequences for their future mathematical understanding. It begins to lay the foundation for students' understanding of algebra, which can change…

Current neurocognitive theories of number processing [Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. "Cognitive Neuropsychology," 20, 487-506] state that mathematical performance is made possible by two functionally and anatomically distinct subsystems of number processing: a verbal system…

This article summarizes research on how students who are bilingual or learning English use two languages and examines how this research is relevant to mathematics classrooms. It is easy to notice that bilingual students sometimes use two languages. It is more difficult to know whether this practice might be significant to learning mathematics.…

This study examines the communication between pre-service teachers and sixth grade students in a project in which email was used for communication as students learned about fractions and were supported by the pre-service teachers. Specifically, the study investigated how the pre-service teachers applied their mathematical knowledge to understand…

Two developments have contributed to the convergence of views about the benefits of real-life and inquiry-based pedagogies in mathematics learning. First, the mathematics teaching community is increasingly focused on the learning of mathematics that involves the transfer of prior knowledge to novel problem-solving situations, a key element in…

Previous research suggests that infants can calculate simple arithmetic (Wynn, 1992). This study sought to replicate this finding and examine how familiarization may influence response. Experiment 1 confirmed that 3- to 5-month-old infants looked longer at an incorrect outcome (1 + 1 = 1) when no familiarization trials were presented. Experiment 2…

This paper describes six tricks on different mathematical concepts for mathematics classrooms. The mathematical concepts emphasized in these activities include arithmetic, modular arithmetic, limit cycles, graph theory, pairings, combinatorics, cyclic groups, induction, and sequences. (ASK)

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…

Background: There is increasing interest in applying neuroscience findings to topics in education. Purpose: This application requires a proper conceptualization of the relation between cognition and brain function. This paper considers two such conceptualizations. The area focus understands each cognitive competency as the product of one (and only…

This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…