Research

  • In this chapter, we present results from three studies that examined and supported 5th- and 6th-grade children's evolving notions of sampling and statistical inference. Our primary finding has been that the context of a statistical problem exerts a profound influence on children's assumptions about the purpose and validity of a sample. A random sample in the context of drawing marbles, for example, is considered acceptable, whereas a random sample in the context of an opinion survey is not. In our design of instructional and assessment materials, we have tried to acknowledge and take advantage of the role that context plays in statistical understanding.

  • The present study used both quantitative and qualitative methods to investigate the learning and motivational strategies used by students in a beginning-level statistics course. The research questions that guided the investigation are: (1) Do motivational variables account for unique variance in the academic performance of statistics students?, (2) Do deeper-level processing strategies account for unique variance in the academic performance of statistics students?, and (3) Do successful students report using different motivation and learning strategies than unsuccessful students in a beginning-level statistics course? Ninety-four students enrolled in six sections of the same course over a two-year period completed measures designed to assess attitudes about statistics, motivation and learning strategies use as well as previous math and statistics knowledge. In addition, randomly selected participants were interviewed about how they prepared for their midterm exam. The results of the study show that both motivation and learning strategies variables influenced performance in the introduction to statistics class. These results help to expand our understanding of what is involved in the process of learning statistics. Also, suggestions for teaching statistics are explored.

  • This study examined middle grades students' learning of concepts related to the use and interpretation of graphs. We view graphs as part of the process of statistical investigation. A statistical investigation typically involves four components: pose the question, collect the data, analyze the data, and interpret the results, in some order (Graham, 1987). The use of grpahis is linked to the "analyze the data" component of the statistical investigation process. Considering what it means to understand and use graphical representation is a part of what it means to know and be able to do statistics.

  • This study was designed to determine how middle grades students interpret data presented in a bar graph. Of particular interest was the nature of the explanations that students gave to support their answers to various questions. The data reported here are part of a larger study of students' understandings of graphs.

  • In this paper the initial results of a theoretical-experimental study of university students' errors on the level of significance of statistical tests are presented. The "a priori" analysis of the concept serves as the base to elaborate a questionnaire that has permitted the detection of faults in the understanding of the same in university students, and to categorize these errors, as a first step in determining the acts of understanding relative to this concept.

  • It is proposed that several biases in social judgment result from a failure--first noted by Francis Bacon--to consider possibilities at odds with beliefs and perceptions of the moment. Individuals who are induced to consider the opposite, therefore, should display less bias in social judgment. In two separate but conceptually parallel experiments, this reasoning was applied to two domains--biased assimilation of new evidence on social issues and biased hypothesis testing of personality impressions. Subjects were induced to consider the opposite in two ways: through explicit instructions to do so and through stimulus materials that made opposite possibilities more salient. In both experiments the induction of a consider-the-opposite strategy had greater corrective effect than more demand-laden alternative instructions to be as fair and unbiased as possible. The results are viewed as consistent with previous research on perseverance, hindsight, and logical problem solving, and are thought to suggest an effective method of retraining social judgment.

  • This study investigated two statistics classroom environments that a priori apeared to hold promise as being motivationally effective classrooms. One environment (2 classes) was at the high school level and the other environment (4 classes) was at the graduate level. In particular the study measured students' perceived situational interest in the learning environment, individual interest in statistics (with pre and post measures), and mathematics anxiety (with pre and post measures). The results indicate that both environments were high in situational interest, did substantially increase the mean individual interest of students, and had a beneficial but smaller impact in terms of associated decreases in mathematics anxiety. In addition, there did apear to be some gender effects-although these effects across the two learning environments were not consistent. Finally, the environments did appear to be particularly effective for students with previous low individual interests in statistics/mathematics. The study enriches our understanding of the "interest" construct primarily by providing evidence that the situational interest of learning enviornments may have a much greater impact on individual interests than researchers previously thought. While only two specific learning environments are provided as examples, the paper argues that we may need to pay as much attention to the motivational effects of statistics classrooms as we do to the learning effects. Students who have positive affective experiences will be more willing to continue taking mathematics/statistics courses or to use quantitative analysis techniques in their own research.

  • Concepts such as measures of center or graphicacy can be linked to the "analyze the data" component of the statistical investigation process. While a central goal is to understand how students make use of the process of statistical investigation within the broader context of problem solving, it also is necessary that we look at students' understanding related to concepts linked to this process. This has led us to consider what it means to understand and use graphical representations as a key part of what it means to know and be able to do statistics. Specifically, we have engaged in a process of developmental research that permits examination of middle grades learning of concepts related to the use and interpretation of representations. We have looked at how such understanding changes over time and with instructional intervention provided by knowledgeable teachers in order to develop a framework both for looking at students' knowledge of graphing (in the statistical sense) and for developing a research agenda related to this area.

  • This research examines an implementation of an activity-based constructivist perspective to teach the concept of a sampling distribution of a statistic. A correct conception and understanding of the sampling distribution of a statistic is crucial for students to be able to understand and correctly interpret hypothesis tests and confidence intervals. In particular, a comparison is made between this constructivist method of instruction and a traditional transmission mode of instruction in terms of student attainment of the concept of sampling distributions. In addition, qualitative research methods were employed to gain comparative data and extensive descriptive information on learning outcomes of students involved in the constructivist/reform instructional method. In terms of an overall empirical measure of student understanding of sampling distributions, the activity-based constructivist method implemented here, promoted a deeper and more complete understanding. Such a test, however, obscures an interesting phenomenon, the activity-based constructivist strategy, counter to typical constructivist claims, does not promote conceptual understanding for all students. Qualitative analysis seems to indicate a very complex interaction concerning the epistemology the student brings to the class, the connection between the students' epistemology and the epistemology inherent in constructivist instructional methods, the content of the activity, prior educational experiences, and the social/academic atmosphere of the class/institution.

  • The chapter does not provide an extensive overview of the use of technology in statistics. Rather, a detailed summary is provided of how one researcher has used technology to teach and assess statistics in grade eight. Both traditonal modes of assessment as well as technology-driven methods will be described in an attempt to demonstrate how multiple mediums of assessment can be used to provide a profile of students' statistical knowledge. The research reported here is grounded in cognitive theory with an emphasis on theories of learning that emphasize learning situations that are concrete rather than abstract. In other words, students learn better by "doing" statistics rather than just computing or reciting statistical equations or definitions. This research program is designed to provide authentic learning and assessment situations (Lajoie, 1995). The term authentic refers to meaningful, realistic tasks and assessments that validly assess what the learner understands.

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