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Mathematical Thinking through a Statistical Lens, Part 1: Exploring Data

WILLIAM THILL NCTM HIGH SCHOOL SUMMER INSTITUTE 2016

ATLANTA, GEORGIA

Welcome !

If you came with somebody you know, find a new seat. Meet somebody new! Introduce yourself to your new colleague(s).

Introduce and share: What are you hoping to learn today?

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My Goals for you today

To experience statistical thinking. To communicate your thinking, and understand the thinking of others. To think how this differs from the thinking that might happen in a “typical math class.” To know where to explore more of this topic. To activate your curiosity and interest in statistical thinking.

Not my Goals for you

Tell you how to teach your kids in your class.

To defer to my perspective. This is discourse, not monologue.

To remain passive, polite, or obedient.

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NCTM HSSI Survey

http://bit.ly/NCTM_HSSI2016

I notice / I wonder / I suspect…

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Work with a partner…

Group Task: Mini Investigation

1. Question about the teachers that can be answered with THIS data set.

2. Visual display that will help you answer your question.

3. Answer your question, with evidence from your display in #2.

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Ideas for questions

• Compare entire distributions

• Is there a relationship between ___ and ___?

• Compare two groups

Visual displays: Keep it simple

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Senior Freshman

Agree Disagree

http://lock5stat.com/statkey/index.html

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What is this about?

Go to the spreadsheet of results

http://bit.ly/NCTM_HSSIresults

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Group Task: Mini Investigation

1. Questions about the teachers that can be answered with THIS data set.

2. Visual display that will help you answer your question.

3. Answer your question, with evidence from your display in #2.

GALLERY WALK

I like ___ because ___

I have a question about …

I wonder if …

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THINKING ABOUT OUR THINKING

• What was difficult?

• What did you like in other’s work?

• Any observations or surprises?

Statistical vs. Mathematical ThinkingGAISE Report, ASA 2006

Mathematics

The model (signal) is the focus.

Context is abstracted away. Abstraction elevated

Probability models accepted. P(three of four fair coins land H)

Statistics

Understanding variation (noise) is crucial.

Context is crucial. Context is valued. “All models are wrong, but some are useful”

Probability used to test claims. Are these four coins far?

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Doing Statistics means…

1. Formulate questions that data can answer 2. Design / employ a plan to collect data3. Analyze data with graphical / numerical

methods 4. Interpret results, respond to your question

Understanding Variability & Context

When did you use Statistical Practices?

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Another Task: Our Backpack Data

More Resources

GAISE Report Statistical Education of Teachers http://roughlynormal.com (coming soon) My Presentation and handout Lessons getting at statistical thinking StatKey : http://lock5stat.com/statkey/index.htmlFathom: https://fathom.concord.org

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