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Research

  • An analysis of the process of analogical thinking predicts that analogies will be noticed on the basis of semantic retrieval cues and that the induction of a general schema from concrete analogs will facilitate analogical transfer. These predictions were tested in experiments in which subjects first read one or more stories illustrating problems and their solutions and then attempted to solve a disparate but analagous transfer problem. The studies in Part I attempted to foster the abstraction of a problem schema from a single story analog by means of summarization instructions, a verbal statement of the underlying principle, or a diagrammatic representation of it. None of these devices achieved a notable degree of success. In contrast, the experiments in Part II demonstrated that if two prior analogs were given, subjects often derived a problem schema as an incidental product of describing the similarities of the analogs. The quality of the induced schema was highly predictive of subsequent transfer performance. Furthermore, the verbal statements and diagrams that had failed to facilitate transfer from one analog proved highly beneficial when paired with two. The function of examples in learning was discussed in light of the present study.

  • In the experimental study reported here we intended to examine possible differences in secondary students' conceptions about randomness before and after instruction in probability, which occurs for the Spanish students between the ages of 14 and 17. To achieve this aim, we gave 277 secondary students a written questionnaire with some items taken from Green (1989, 1991). with our results we extend Green's previous research to 17-year-old students and complement his results with the analysis of students' arguments to support randomness in bidimensional distributions. Our results also indicate that students' subjective understanding of randomness is close to some interpretations of randomness throughout history.

  • A key element in developing ideas associated with statistical inference involves developing concepts of sampling. The objective of this research was to understand the characteristics of students' constructions of the concept of sample. Sixty-two students in Grades 3, 6, 9 were interviewed using open-ended questions related to sampling; written responses to a questionnaire were also analyzed. Responses were characterized in relation to the content, structure, and objectives of statistical literacy. Six categories of construction were identified and described in relation to the sophistication of developing concepts of sampling. These categories illustrate helpful and unhelpful foundations for an appropriate understanding of representativeness and hence will help curriculum developers and teachers plan interventions.

  • This chapter reports on student performance with data and chance by examining individual 1996 NAEP items or clusters of related items and where available samples of student responses to constructed-response questions. The focus of this chapter is on four categories that are often interrelated: central tendency, reasoning with data, graphical data displays, and probability and chance. In addition to reporting and interpreting performance based on NAEP results, for some short and extended constructed-response items we also examined a set of sample student responses. This sample was not a representative sample of all responses; rather it was a convenience sample of non-blank responses. Some of the items described in this chapter were extended constructed-response tasks, a type of NAEP item that is discussed extensively in chapter 11 by Silver, Alacaci, and Stylianou.

  • Statistics educators have previously noted that university students experience some difficulty in knowing when to use statistical concepts they have encountered in their courses. In this study, statistics educators rated the importance of various descriptive and inferential statistical procedures for inclusion in an introductory statistics course. Items describing research situations were written (each item representing a different procedure) and presented to a sample of undergraduate and postgraduate statistics students. Students were asked to decide which procedure was appropriate for addressing each research situation. Results revealed that identifying appropriate statistical procedures in new situations is indeed difficult.

  • A probability-adjustment task was presented to 6-14-year-old children. In 2 experiments, children had to generate equal probabilities by completing the missing beads in a target urn with 1 type of beads presented beside a full urn with both winning and losing beads. The results indicate that only at around the age of 13 did most students proportionally integrate the 2 dimensions (i.e., the numbers of winning and losing beads).

  • The development of school students' understanding of comparing two data sets is explored through responses of students in individual interview settings. Eighty-eight students in grades 3 to 9 were presented with data sets in graphical form for comparison. Student responses were analysed according to a developmental cycle which was repeated in two contexts: one where the numbers of values in the data sets were the same and the other where they were different. Strategies observed within the developmental cycles were visual, numerical, or a combination of the two. The correctness of outcomes associated with using and combining these strategies varied depending upon the task and the developmental level of the response. Implications for teachers, educational planners and researchers are discussed in relation to the beginning of statistical inference during the school years.

  • The purpose of this study is to examine the use of computing technology in secondary school mathematics, particularly in the probability and statistics curriculum.

  • The objective of this study was to catalog undergraduate and graduate students' misconceptions in the area of power analysis, and to examine the efficacy of a computer simulation to remedy these misconceptions.

  • This descriptive ex post facto study analyzed conceptual understanding in descriptive statistics among 249 traditional age undergraduates at two northeastern universities after an instructional program which decreased the time spent on lecture and added activities, small group collaboration, and discussion that responded to students' varied learning styles.

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