To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

Normative discourse about probability requires shared meanings for disciplinary vocabulary. Previous research indicates that students' meanings for probability vocabulary often differ from those of mathematicians, creating a need to attend to developing students' use of language. Current standards documents conflict in their recommendations about…

The authors analyzed the development of 4th-grade students' understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. After observing the decreasing variation from the theoretical probability as the sample size…

This study is a longitudinal look at the different mathematics placement profiles of Black students and White students from late elementary school through 8th grade. Results revealed that Black students had reduced odds of being placed in algebra by the time they entered 8th grade even after controlling for performance in mathematics. An important…

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data…

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…

The purpose of this article is to sketch a hypothetical descriptive framework of statistical knowledge for teaching. Because statistics is a discipline in its own right rather than a branch of mathematics, the knowledge needed to teach statistics is likely to differ from the knowledge needed to teach mathematics. Doing statistics involves many…

This study investigates the effects on achievement of allowing students to ask questions before homework is collected v allowing questions only after homework has been graded and returned. Results indicate allowing questions before homework is collected is the superior method. (MK)

Examines possible differences in secondary students' conceptions of randomness before and after instruction in probability, which occurs for Spanish students between the ages of 14 and 17. Indicates that students' subjective understanding of randomness is close to some interpretations of randomness throughout history. Contains 16 references.…

Task analysis, learning hierarchies, and behavioral objectives for mastery learning were used to develop elementary school curriculum materials in probability and statistics. The feasibility of the unit was measured by pre- and posttests with an instrument specifically developed for the study; analysis of data is included. (JG)

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)

Seventy-one college students were taught probability and statistics for one month by one of three methods: MP, manipulative-pictorial; P, pictorial; and S, symbolic. Analysis of variance yielded significant differences (p.05) between treatment groups for selected subtests of an achievement test and generally favored MP and P over S.

Tests were given after instruction in probability and four weeks later to 25 sixth graders. Correlation between achievement scores for each student was .78. Retention ratios for individuals, total tests, each objective, and each item indicated high initial performance may contribute to high retention. (Author/DT)

Evaluates the thinking of third grade students in relation to an instructional program in probability which was informed by a research-based framework that included a description of students' probabilistic thinking. Reveals that overcoming misconceptions in sample space, applying both part-part and part-whole reasoning, and using invented language…