Randomness, Sample Size, Imagination and Metacognition: Making Judgments about Differences in Data Sets

Autor/inn/en	Stack, Sue; Watson, Jane
Titel	Randomness, Sample Size, Imagination and Metacognition: Making Judgments about Differences in Data Sets
Quelle	In: Australian Mathematics Teacher, 69 (2013) 4, S.23-30 (8 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0045-0685
Schlagwörter	Secondary School Mathematics; Grade 10; Mathematical Concepts; Probability; Statistics; Sampling; Population Distribution; Statistical Distributions; Sample Size; Imagination; Metacognition; Visualization; Inferences; Statistical Analysis; Decision Making + Suchen Sie Ihr Suchwort? Wahrscheinlichkeitsrechnung; Wahrscheinlichkeitstheorie; Statistik; Demographical distribution; Bevölkerungsverteilung; Wahrscheinlichkeitsverteilung; Meta cognitive ability; Meta-cognition; Metakognitive Fähigkeit; Metakognition; Visualisation; Visualisierung; Inference; Inferenz; Statistische Analyse; Decision-making; Entscheidungsfindung
Abstract	There is considerable research on the difficulties students have in conceptualising individual concepts of probability and statistics (see for example, Bryant & Nunes, 2012; Jones, 2005). The unit of work developed for the action research project described in this article is specifically designed to address some of these in order to help students create visual and intuitive understandings of the issues of sampling, randomness and populations. The interweaving of concepts, combined with the technical skills, is intended to challenge teachers, students and researchers. Creating meaningful and deep learning experiences for students requires considerable teacher knowledge and skill, being able to weave together concepts with context and metacognitive thinking. In particular, it takes skill in helping students to draw out from diverse activities the central and connecting themes. At the end of the program the lead teacher said she had previously never thought of designing a unit around a key idea such as randomness or inference. Being able to use such big conceptual ideas as a theme for a unit provided a very valuable and interesting experience, certainly deepening her own experience of the nuances within the ideas and how to build more connective conceptual experiences for the students. For students who go on to study formal statistics, the hope is that the experiences with informal inference in memorable contexts such as the dolphin problem will provide a foundation for appreciating and understanding the formal statistics associated with t-tests and p-values. For those who do not go on to study formal statistics, it is hoped that they have gained an appreciation of randomness and its usefulness in decision-making, moving beyond seeing random only as haphazard. (As Provided).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2022/4/11