Discusses the use and construction of "fact fans," fun and easy-to-make manipulatives that provide elementary school students with the opportunity to explore mathematics operations being studied in the classroom and to practice addition, subtraction, multiplication, and division facts. (BB)

Presents student comments as they explain their mathematical reasoning and thinking about place value in addition and subtraction. (ASK)

A five-year follow-up of arithmetic calculation abilities of 10 low-income fourth graders with specific language impairment (SLI) involved comparisons with typically developing same age peers and with typically developing younger subjects. Results support evidence that children with SLI have difficulty with rote memory and document the…

Analyzes the interpretations of equality and the equal symbol of third grade children who participated in a year-long, whole-class socio-constructivist teaching experiment. Concludes that children expanded their conceptualizations of equality due to an active role in class discussions and the arithmetical tasks that took into account children's…

This study evaluated the effectiveness of teaching multiplication facts and related word problems using the concrete-representational-abstract teaching sequence and strategy instruction to three middle school students with mental retardation. Evaluation of the 21 scripted lessons given each student found only four occurrences (out of 63 lessons)…

Investigates the relative contribution of two main components often used in the instruction of arithmetic and word-problem solving to first-grade children and children with learning problems: external representation with manipulatives and formal mathematical representation with number sequences. Four computer-aided treatments were developed along…

This study explored first graders' fraction learning when the teacher elicited and built on children's informal knowledge of fractions during discussions of equal-sharing tasks; the study focused on key classroom interactions resulting in cognitive change. Findings suggest that thinking about fractions is influenced by the structure of the child's…

There has been little research in the UK into how students learning English as an additional language (EAL) learn mathematics. This article reports results from a three-year study of the participation of learners of EAL in Year 5 in an arithmetic word problem task. The research, drawing on ideas from discursive psychology, used discourse analysis…

Number sense, an integral part of the curriculum in primary school mathematics, has always been thought of as playing a major role in pupils' understanding and use of numbers in calculation. Research in number sense has been carried out in the West, as well as in Malaysia. That a study of such a nature be done to reflect on the abilities of…

This is the second of two papers that propose an expanded and enriched view of arithmetic problem solving by stressing the need to provide learning activities that include problems of varying structures. The first paper included a framework for the enhancement of text-based problems. This second paper proposes a scheme for the development of…

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a "divide-and-conquer" approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the…

Estimation is an important skill for everyday living. Good estimators usually have a sound knowledge of basic facts, understand place value and use a variety of strategies to make their estimates. This paper describes an activity which is designed to provide students with opportunities to practice their rounding strategies with addition and…

This paper considers the unique and successful combination of using Direct Instruction programs with special education populations. The introduction establishes the need for valid, scientifically based materials. Next is a description of studies using Direct Instruction with students who have high-incidence disabilities. Thirty-seven studies were…

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

NCTM Past President Cathy L. Seeley shares her messages on today's most relevant topics and issues in education. Based on Cathy L. Seeley's award-winning NCTM President's Messages, and including dozens of new messages, this must-have K-12 resource offers straight talk and common sense about some of today's most important, thought-provoking issues…