Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling

dc.creator	Luis A. Saldanha
dc.creator	Patrick W. Thompson
dc.date	2007-10-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:10:31Z
dc.date.available	2015-07-20T22:10:31Z
dc.identifier	1306-3030
dc.identifier	https://doaj.org/article/e4b8886275c048c2b9ba721fe7b2517b
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/13694
dc.description	Construing a collection of values of a sample statistic as a distribution is central to developing a coherent understanding of statistical inference. This paper discusses key developments that unfolded over three consecutive lessons in a classroom teaching experiment designed to support a group of high school students in developing such a construal. Instruction began by engaging students in activities that focused their attention on the variability among values of a common sample statistic. There occurred a critical shift in students’ attention and discourse away from individual values of the statistic and toward a collection of such values as a basis for inferring the value of a population parameter. This was followed by their comparisons of such collections and by the emergence and application of a rule for deciding whether two such collections were similar. In the repeated application of their decision rule students structured these collections as distributions. We characterize aspects of these developments in relation to students’ classroom engagement, and we explore evidence in students’ written work that points to how instruction shaped their conceptions.
dc.language	English
dc.publisher	Gokkusagi Ltd.
dc.relation	http://www.iejme.com/032007/d9.pdf
dc.relation	https://doaj.org/toc/1306-3030
dc.source	International Electronic Journal of Mathematics Education, Vol 2, Iss 3, Pp 270-297 (2007)
dc.subject	Sampling
dc.subject	Variability
dc.subject	Sample Statistic
dc.subject	Population Parameter
dc.subject	Statistical Inference
dc.subject	Sampling Distributions
dc.subject	Teaching Experiment
dc.subject	Conceptual Operations
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.title	Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling
dc.type	article