Presented are the results of two pilot studies about multidigit addition and subtraction. The results are discussed in relation to possible alternative sequences in the teaching of addition and subtraction and the relationship between basic fact mastery and numeration concept attainment. (CW)

This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…

The relationship between elementary operations underlying processing of numerical information and performance on psychometrically derived ability measures requiring processing of numbers but defining separate ability factors was studied for 102 Air Force recruits (54 males and 48 females). Patterns of convergent and discriminate relationships for…

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

Children in grades three through five and adults performed a number-matching task. Found that changes in the strength of arithmetic connections occurred with development and accounted for individual differences among adults. Individual differences among children were related to changes in the strength of number-line connections. (Author/GLR)

Described is a classroom activity incorporating a computer spreadsheet to study number patterns generated by the Fibonacci sequence. Included are examples and suggestions for the use of the spreadsheet in other recursive relationships. (JJK)

A variety of suggestions for making the mathematics curriculum more meaningful and interesting to students are described. Activities that incorporate real-world situations are provided for verbal items, common and decimal fractions, estimations and rounding off numbers, large and small numbers, geometry, probability, and statistics. (KR)

This study examined specific math practices utilized by 25 teachers in gifted preschool/kindergarten programs. Results indicated that most respondents used unstructured activities in small groups when providing math instruction. Although some concepts generally introduced to older students were taught, concepts of time and measurement were rarely…

Based on the cognitive psychological theories of Vygotsky and Davydov, discusses the establishment of connections between mathematical elements, and the algorithmic rules that govern them, and children's spontaneous mathematical concepts. Presents examples that establish connections involving addition and subtraction, comparing numerical…

Describes a teacher's experiences in a classroom where mathematics problems are presented in the context of aliens and other galaxies. (ASK)

Shares different students' solutions for a problem entitled How Much Film?, which appeared in the November 1997 issue of Teaching Children Mathematics. The problem has to do with how many rolls of film are necessary to take 687 pictures. (ASK)

Examines the incremental validity of Differential Ability Scales (DAS) factor scores in predicting standardized achievement scores in Word Reading, Basic Number Skills, and Spelling by using a nationally representative sample stratified on gender, ethnicity, geographic region, parental education, and educational classification. Results show that…

Presents building-up strategies and activities for preservice teachers to help students move from using informal strategies to expressing proportional relationships in algebraic terms. (ASK)

Describes four 50-minute lessons in which complex numbers are introduced to year-12 calculus students using hand-held calculators and laptop computers. (ASK)

Demonstrates examples, one of which is an extension of "guess and check," to include variables rather than numbers. The quadratic equation az2+bz+c=0, is solved by assuming a complex solution of the form z=x+iy. Explores the use of deMoivre's theorem in deriving trigonometric identities with other examples. (Author/ASK)