Describes a school-wide project using popcorn to gain number sense by learning more about a million. Used the books "How Much Is a Million?" and "If You Made a Million" to introduce the project. (MKR)

Discusses children's place-value understanding, including initial learning interference, vertical number lines, and planned discourse. Describes a learning activity that can guide children from a concrete to a symbolic understanding of place value. (11 references) (MKR)

This study illustrates the types of information microgenetic methods can yield. Ninety-seven 5-year olds who had not mastered number conservation were given training in conservation or in reasoning about conservation. Results elucidate how changes in thinking occur and demonstrate children's efforts to understand other people's reasoning. (SLD)

This case study of a 30-year-old woman with a developmental learning disability (including anomia, auditory processing problems, difficulty in learning reading and spelling skills, and a poor sense of number) suggests that all these impairments may be explained in terms of a sequential processing deficit. (Author/DB)

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…

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)

The teaching of negative numbers poses problems at the school level. A historical account of the intellectual difficulties in the evolution of negative numbers and a method of viewing negative numbers as an extension of the number system to help overcome these difficulties are presented. (MDH)

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)

Explores relative developmental influences of age, number-sense, and context on primary school children's ability to estimate measures. Finds that, although number-sense improved with age, estimation did not; ability to perceive number relations influenced ability to estimate area; and estimation was more accurate in textbook exercises than in a…