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Statistics, teacher knowledge, and effective teaching
Tim BurgessMassey University
National Numeracy ConferenceAuckland
20 February 2008
Why is someone giving a keynote address about statistics at a numeracy conference?
What is numeracy compared with mathematics?
What about statistics - is it part of mathematics, numeracy, both, or neither?
National Numeracy Conference
Numeracy Conference Themes and Objectives
•Pedagogical content knowledge•Effective professional
development in mathematics•Effective teaching of mathematics
for diverse learners
Mathematics vs. StatisticsMathematicsπ Deterministic; real life contexts may be useful for developing concepts but move towards the abstract
Statisticsµ ‘Reasoning under uncertainty’; real life contexts are essential to making sense of questions and issuesµ Move towards statistical thinking and reasoning (and away from just skills and procedures)µ Most research on teacher knowledge has been conducted away from the classroom.
Statistical ThinkingNeed for data
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Sherlock Holmes in The Adventure of the Copper Beeches by Sir Arthur Conan
Doyle.
Transnumeration changing the representation or form of the data
VariationReasoning with models
eg. graphs: look for the distribution of the data: this includes features of centre, spread, density, skewness and outliers
Integration of statistical with contextual knowledgeInvestigative cycle / Interrogative cycle
Dispositions
Mathematical Content Knowledge
•Common knowledge of content
•Specialised knowledge of content
•Knowledge of content and students
•Knowledge of content and teaching
Statistical knowledge for teachingContent knowledge Pedagogical content
knowledgeCommonknowledgeof content(CKC)
Specialisedknowledge ofcontent(SKC)
Knowledge ofcontent andstudents(KCS)
Knowledgeof contentand teaching(KCT)
Need for dataTransnumerationVariationReasoning withmodelsIntegration ofstatistical andcontextual
InvestigativecycleInterrogativecycleDispositions
Wild and Pfannkuch (1999):
Statistical thinkingHill, Schilling & Ball
(2004):
Mathematical content knowledge
Framework for examining teacher knowledge
Examples of common knowledge of content
Left handed
Right handed
Total
Whistler
2 15 17
Non-whistler
1 6 7
Total 3 21 24
Effective teaching
A teacher needs:
all four categories of teacher knowledge
across all components of statistical thinking.
Missed opportunities in the classroom
Gaps in the teacher’s knowledge will give rise to missed opportunities in the classroom.•Listening to, interpreting, responding to students•Posing questions for investigation•Guiding students with handling category and numeric data•Sorting data effectively, and moving from individual features to group features•Students’ difficulties with data based statements•Understanding variation, and development of inference
A solutionWhat was the problem again?•Pedagogical content knowledge•Effective professional development in mathematics•Effective teaching of mathematics for diverse learners
One solutionEngage and immerse teachers in investigations with real data - common knowledge of contentListen to students - real or video - specialised knowledge of content and knowledge of content and studentsWorkshops - knowledge of content and teaching
Timperley et al.’s best evidence synthesis of the professional development literature showed overwhelmingly that no professional development that focused solely on general pedagogy was successful in raising the achievement levels of students, and conversely that the most successful professional development, in terms of student achievement, involved the development of both the content knowledge and the pedagogical content knowledge of teachers (and that this latter category was particularly critical).
Timperley, H., Wilson, A., Barrar, H., & Fung, I. (2007 forthcoming). Teacher professional learning and development: Best evidence synthesis iteration [BES]. Wellington, New Zealand: Ministry of Education.
A challengeHow can we meet the challenge of involving teachers (pre-service and in-service) in investigating real data so that all categories of teacher knowledge can develop to an adequate level?Investigations
- physical manipulation of data- use of technology - eg Tinkerplots or
Fathom - who should provide these resources?
A challenge - continuedE-learning and pedagogyInformation and communication technology (ICT) has a major impact on the world in which young people live. Similarly, e-learning (that is, learning supported by or facilitated by ICT) has considerable potential to support the teaching approaches outlined in the above section.
For instance, e-learning may: …
* enhance opportunities to learn by offering students virtual experiences and tools that save them time, allowing them to take their learning further.
Schools should explore not only how ICT can supplement traditional ways of teaching but also how it can open up new and different ways of learning.
p. 36: The NZ Curriculum