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

Outline

NZ Curriculum Mathematics and Statistics learning

area Statistics

Teacher knowledge

Numeracy Conference Themes and Objectives

•Pedagogical content knowledge•Effective professional

development in mathematics•Effective teaching of mathematics

for diverse learners

Statistics in the curriculum in NZ

1969/72

1985/87

1992

2007

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

Examples of specialised knowledge of content

Examples of knowledge of content & students

Examples of knowledge of content & teaching

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