An analysis of students’ initial statistical understandings: developing a conjectured learning trajectory

McGatha, Maggie B.; Cobb, Paul; McClain, Kay

doi:10.1016/s0732-3123(02)00133-5

Cited by 29 publications

(21 citation statements)

References 7 publications

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“…The best documented problem in this area is that students who have learned the arithmetic mean tend not to use it for comparing two groups (Konold & Higgins, 2003;McGatha, Cobb, & McClain, 2002;Pollatsek, Lima, & Well, 1981). In other words, we expect students to use the mean (or any other concept) within a process of reasoning, but they often use it purely descriptively or just calculate it out of habit.…”

Section: Three Challenges In Statistics Educationmentioning

confidence: 99%

Lessons from Inferentialism for Statistics Education

Bakker

Derry

2011

Mathematical Thinking and Learning

129

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Section: Three Challenges In Statistics Educationmentioning

confidence: 99%

Lessons from Inferentialism for Statistics Education

Bakker

Derry

2011

Mathematical Thinking and Learning

129

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“…The flow of classroom activities typically had the following structure, which might span two or more class sessions: (a) a whole-class discussion in which the teacher and students talked through the data creation process, (b) individual or small-group activity in which the students worked at computers to analyze data, and (c) a whole-class discussion of the students' analyses. The rationale for the first phase of this activity structure stemmed from our prior work with the students during their seventh-grade year (McGatha, Cobb, & McClain, 1999). In the prior design experiment, it proved crucial that datasets had a history for the students such that they were grounded in the situation from which they were generated and that they reflected the particular interests and purposes that had led to their creation (Latour, 1987;Lehrer & Romberg, 1996;Roth, 1997).…”

Section: Classroom Organizationmentioning

confidence: 99%

Learning About Statistical Covariation

Cobb

McClain²,

Gravemeijer³

2003

Cognition and Instruction

Self Cite

134

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In this article, we report on a design experiment conducted in an 8th grade classroom that focused on students' analysis of bivariate data. Our immediate goal is to document both the actual learning trajectory of the classroom community and the diversity in the students' reasoning as they participated in the classroom mathematical practices that constituted this trajectory. On a broader level, we also focus on the learning of the research team by documenting the conjectures about the students' statistical learning and the means of supporting it that the research team generated, tested, and revised on-line while the experiment was in progress. In the final part of the article, we synthesize the results of this learning by proposing a revised learning trajectory that can inform design and instruction in other classrooms. In doing so, we make a contribution to the cumulative development of a domain-specific instructional theory for statistical data analysis.Our purpose in this article is to report on a 14-week classroom design experiment conducted with a group of eighth-grade students that focused on statistical covariation. In presenting the analysis, we focus on both the trajectory of the students' learning and our own learning about the means of supporting the students' learning. This latter issue, the learning of the research team, is central to the design experiment methodology, in that conjectures about the trajectory of students' learning are tested and modified on-line while experimenting in a Requests for reprints should be sent to Paul A. Cobb,

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“…In cases where there is a conflict between intuitive estimates and formal measures, they should be encouraged to find the causes of the conflict rather than simply replacing their intuitive estimates with formal tools that usually produce the "correct" school-sanctioned answers. Too often, children are more concerned with school-taught statistical conventions than with critical analysis of data and context (McGatha, Cobb, & McClain, 2002).…”

Section: Discussionmentioning

confidence: 99%

An investigation of statistical thinking in two different contexts: Detecting a signal in a noisy process and determining a typical value

Groth

2005

The Journal of Mathematical Behavior

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The study describes students' patterns of thinking for statistical problems set in two different contexts. Fifteen students representing a wide range of experiences with high school mathematics participated in problem-solving clinical interview sessions. At one point during the interviews, each solved a problem that involved determining the typical value within a set of incomes. At another point, they solved a problem set in a signal-versus-noise context [Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33,. Several patterns of thinking emerged in the responses to each task. In responding to the two tasks, some students attempted to incorporate formal measures, while others used informal estimating strategies. The different types of thinking employed in using formal measures and informal estimates are described. The types of thinking exhibited in the signal-versus-noise context are then compared against those in the typical value context. Students displayed varying amounts of attention to both data and context in formulating responses to both problems. Suggestions for teachers in regard to helping students attend to both data and context when analyzing statistical data are given.

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An analysis of students’ initial statistical understandings: developing a conjectured learning trajectory

Cited by 29 publications

References 7 publications

Lessons from Inferentialism for Statistics Education

Lessons from Inferentialism for Statistics Education

Learning About Statistical Covariation

An investigation of statistical thinking in two different contexts: Detecting a signal in a noisy process and determining a typical value

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