Presents a first-semester course in mathematics for 6-year-old children by formulating certain general requirements for the curriculum and the instructional methods with the aim of leading children to form their initial mathematical concepts. (ASK)

Dicusses teachers' beliefs and perceptions of children's knowledge and learning about place value, addition, subtraction, multiplication, and division and how to teach those subjects. (ASK)

Matrix organization can be used to construct math word problems for children with mild disabilities. Matrix organization specifies the characteristics of problems, such as problem theme or setting, operations, level of computation complexity, reading vocabulary level, and need for classification. A sample scope and sequence and 16 sample word…

Notes strong and widespread pressures for middle school teachers to teach fractions. Discusses experimental and empirical evidence that traditional fractions instruction is highly vulnerable to criticism from a number of angles. (SR)

Comparison of pre- and posttest scores in mathematics computation of 2 classes of (n=91) ninth-grade students, 1 class emphasizing drill and practice and the other focusing on learning concepts, found the mean grade equivalent score for computation of the concept class increased more than 2 years and these students attempted to answer more…

Provides an overview of research on transfer, highlighting its main tenets. Looks at interviews of two grade 5 students learning about mathematical concepts regarding operations on positive and negative quantities. Focuses on how their learning is influenced by prior knowledge and experience. (Author/MM)

Describes a classroom-based model for professional development that allows teachers to gain further insight into matching learning experiences with a child's potential. (ASK)

The unpacking of the mathematical knowledge necessary for teaching division is examined. A core task for surfacing and unpacking one's division knowledge is presented and the understandings that might comprise a package of teacher knowledge for division is discussed.

This article focuses on a form of instructional design that is deemed fitting for reform mathematics education. Reform mathematics education requires instruction that helps students in developing their current ways of reasoning into more sophisticated ways of mathematical reasoning. This implies that there has to be ample room for teachers to…

"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…

This study investigated ability-related differences in strategy use and development in the domain of simple arithmetic, in terms of the model of strategic change, using the choice/no-choice method and the chronological-age/ability-level-match design. Twenty-six second-graders with strong mathematical abilities (MA), 25 second-graders with weak MA,…

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

During the twentieth century, major changes occurred in conception of arithmetic as a school subject. These changes resulted from both the study of arithmetic itself and from influences from movements and developments outside the subject matter; and they have affected both the content of arithmetic and the methodology of presenting that content to…

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

This investigation involves first assessing and then designing instruction to resolve student difficulties with addition facts. The ultimate goal was improving students' computational fluency.