This study explores the reasoning that emerged among eight high school juniors and seniors as they participated in a classroom teaching experiment addressing stochastic conceptions of sampling and statistical inference. Toward this end, instructional activities engaged students in embedding sampling and inference within the foundational notion of distributions of sample statisticspatterns of dispersion that one conceives as emerging in a collection of a sample statistics values that accumulate from re-sampling under essentially identical conditions.
The study details students engagement and emergent understandings in the context of instructional activities designed to support them. Analyses highlight these components: the design of instructional activities, classroom conversations and interactions that emerged from students engagement in activities, students ideas and understandings that emerged in the process, and the design teams interpretations of students understandings. Moreover, analyses highlight the synergistic interplay between these components that drove the unfolding of the teaching experiment over the course of 17 lessons in cycles of design, engagement, and interpretation. These cycles gave rise to four interrelated phases of instructional engagements:
Phase 1: Orientation to statistical prediction and distributional reasoning;
Phase 2: Move to conceptualize probabilistic situations and quantify unusualness;
Phase 3: Move to conceptualize variability and distribution;
Phase 4: Move to quantify variability and extend distribution.
Analyses reveal that students experienced significant difficulties in conceiving the distribution of sample statistics and point to possible reasons for them. Their difficulties centered on composing and coordinating objects into a hierarchical structure with actions in imagined re-sampling scenarios that involve: a population of items, selecting items from it to accumulate a sample, recording the value of a statistic of interest, repeating this process to accumulate a collection of values, structuring such collections and conceiving patterns within and across them in ways that support making statistical inferences.
| Identifer | oai:union.ndltd.org:VANDERBILT/oai:VANDERBILTETD:etd-07162004-083711 |
| Date | 26 July 2004 |
| Creators | Saldanha, Luis A. |
| Contributors | Kay McClain, Paul Cobb, Philip S. Crooke, Clifford Konold, Patrick W. Thompson |
| Publisher | VANDERBILT |
| Source Sets | Vanderbilt University Theses |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.vanderbilt.edu/available/etd-07162004-083711/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Vanderbilt University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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