Symbolic representation of environmental variables is a ubiquitous and often debated component of cognitive science. Yet notwithstanding centuries of philosophical discussion, the efficacy, scope, and validity of such representation has rarely been given direct consideration from a mathematical point of view. This paper introduces a quantitative…

Variability in strategy selection is an important characteristic of learning new skills such as mathematical skills. Strategies gradually come and go during this development. In 1996, Siegler described this phenomenon as ''overlapping waves.'' In the current microgenetic study, we attempted to model these overlapping waves statistically. In…

This study investigated the comprehension and effectiveness of teaching formal, probabilistic decision-making skills to middle school students. Two specific objectives were to determine (1) if middle school students can comprehend a probabilistic decision-making approach, and (2) if exposure to the modeling approaches improves middle school…

Investigates the effectiveness of utilizing analogies to effect conceptual change in students' alternative-probability concepts. Results indicate that analogies can be effective in producing desired conceptual change in high school students' probability concepts. (Author/CCM)

INVESTIGATED WERE JUNIOR HIGH SCHOOL STUDENT'S UNDERSTANDINGS OF THE CONCEPTS INTRINSIC TO PROBABILITY THEORY. THE SPECIFIC OBJECTIVES WERE TO EXPLORE (1) THE VARIATION AND CONSISTENCY IN USAGE OF QUANTITATIVE LANGUAGE TERMS, (2) THE ABILITY TO GENERATE POSSIBLE COMBINATIONS AND PERMUTATIONS, (3) THE RECOGNITION AND UTILIZATION OF THE CONCEPT OF…

Interviews of one child through grades one through five on several combinatorics tasks indicated the student's progress in classifying, organizing, and reorganizing data. Provides significant insight into the process by which the student learned to make proofs. (Author/MKR)

Arguing that the teaching of stochastic processes should reflect the experience and reality of the student, the author urges concentration on fundamental ideas. The development of intuition should be encouraged, and to this end continuity in teaching and a spiralled curriculum are important. (SD)

The inclusion of probability in the school curriculum is argued to be justified on mathematical, psychological, and social grounds. Contemporary teaching approaches are suggested as sufficient. (MP)

The contributions made by including probability theory in the primary grade curriculum are examined with respect to the day to day living of the developing child and his preparation for later life. In particular, language and decision making, misconceptions, research and systematic thinking, occupations, and the future are discussed. (MN)

Questions concerning probability which appeared on the General Certificate of Education test are analyzed in terms of the processes required to answer them. The relationships between these processes and cognitive development are discussed. (SD)

Digraphs, graphs, and task analysis were used to map out the content structure of a programed text (SMSG) in elementary probability. Mathematical structure was defined as the relationship between concepts within a set of abstract systems. The word association technique was used to measure the existing relations (cognitive structure) in S's memory…

Explores understanding of chance measurement and how this develops over time through the analysis of response data collected in 1993, 1995, and 1997. Analyzes this data to document changes in levels of observed student outcomes using the Structure of the Observed Learning Outcome (SOLO) developmental model. Results indicate no improvements in…

Presents research findings related to students' intuitive ideas about the concepts of chance to inform teachers how students form their concepts of probability and statistics. Discusses adolescents' conceptions of uncertainty, judgmental heuristics in making estimates of event likelihood, the conjunction fallacy, the outcome approach, attempts to…

Eighteen research reports related to mathematics education are abstracted and analyzed. Four of the reports deal with aspects of learning theory, five with topics in mathematics instruction (history of mathematics, exponents, probability, calculus, and calculators), four with teacher characteristics, and one each with testing, student interests,…

This study investigated young children's ability to solve probability problems and studied the cognitive processes proposed by Piaget and Inhelder as necessary to solve probability problems. The effects of tutorial and self-discovery training were measured and discussed. Results from 168 first-graders in five training conditions indicated that:…