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Margolis, Eric; Laurence, Stephen – Cognition, 2008
Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap:…
Descriptors: Numbers, Learning Strategies, Number Concepts, Inferences

Biddlecomb, Barry D. – Journal of Research in Childhood Education, 1994
Uses work on children's counting schemes and a radical constructivist orientation to describe the development of computer microworlds for the teaching of rational numbers. Suggests that the design of complex software systems needs a strong theoretical background to provide direction for the design. Suggests that computer environments are the…
Descriptors: Computer Assisted Instruction, Constructivism (Learning), Elementary Education, Elementary School Mathematics

Steffe, Leslie P.; Wiegel, Heide G. – Journal of Research in Childhood Education, 1994
Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…
Descriptors: Computer Assisted Instruction, Constructivism (Learning), Elementary Education, Elementary School Mathematics
Orthogonal Reflections on Computer Microworlds, Constructivism, Play and Mathematical Understanding.

Kieren, Thomas E. – Journal of Research in Childhood Education, 1994
Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…
Descriptors: Computer Assisted Instruction, Constructivism (Learning), Elementary Education, Elementary School Mathematics

Kaput, Jim – Journal of Research in Childhood Education, 1994
Comments on the Fraction Project presented in this same issue. Examines the choice of appropriate perspectives on the phenomena induced and observed and the generalizability of the results. Investigates the phenomena as involving student attunement to constraints built into the computer-based learning environments and in terms of explicit…
Descriptors: Computer Assisted Instruction, Constructivism (Learning), Elementary Education, Elementary School Mathematics

D'Ambrosio, Beatriz S.; Mewborn, Denise Spangler – Journal of Research in Childhood Education, 1994
Comments on the Fraction Project presented in this same issue. Suggests that it has uncovered many implications for instruction. However, there are limitations as the proposed setting is restricted by the present school circumstances. Concludes that better learning will not come from finding better ways for teachers to instruct but from giving the…
Descriptors: Computer Assisted Instruction, Constructivism (Learning), Elementary Education, Elementary School Mathematics

Steffe, Leslie P.; Tzur, Ron – Journal of Research in Childhood Education, 1994
Interprets and contrasts children's mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. Proposes a superseding model based on the interrelations between the basic sequence of actions and perturbation and the interaction of constructs. Supports the model by describing how children used…
Descriptors: Computer Assisted Instruction, Constructivism (Learning), Elementary Education, Elementary School Mathematics

Olive, John – Journal of Research in Childhood Education, 1994
Proposes a new model of children's mathematics by composing aspects of the Fraction Project and critiques presented in the same issue. Argues that computer microworlds provide children with dynamic learning environments in which they are the primary actors and teachers with a medium for interact with children's mathematics while trying to maintain…
Descriptors: Computer Assisted Instruction, Constructivism (Learning), Elementary Education, Elementary School Mathematics

Duffin, Janet; Simpson, Adrian – For the Learning of Mathematics, 1991
Presents the reactions of a mathematics educator and a mathematician to a seven-year-old student's response for finding square numbers. Reflects on the mathematician's focus on the mathematics of the problem and the mathematics educator's focus on the student's systematic way of working, and discusses the common focus of student creativity. (MDH)
Descriptors: Cognitive Development, Cognitive Processes, Creative Thinking, Creativity

Scott, Judith – Montessori Life, 1995
Draws parallels between Montessori's mathematical curriculum and the evolution of numbers and counting. Suggests that children share with ancient Sumerians a basic human tendency to develop "the mathematical mind." Argues that children do not need to be surrounded by math; rather, the classroom must supply them with the means to explore…
Descriptors: Classroom Environment, Cognitive Style, Early Childhood Education, Individualized Instruction