STATISTICS Day 1 AM

Day 1 AM Objectives: To develop the purpose of statistics in providing evidence for claims

To understand variability and distributions

To examine needs for shifts in classroom practice.

**1. TASK: What is Statistics? (30 minutes)**/

**Day 1 AM: 9:00 – 9:30**

**STANDARDS ACADEMY TASK NOTES**

Purpose: To introduce participants and surface ideas about statistics

Participants will respond to the following prompt in their journals.

Based on your experiences, what is statistics?

Have participants introduce themselves and give their response. /

**FACILITATOR NOTES**

PREPARATIONS: Have name tags on tables, mixing grade levels in each group. Have both levels of EU books at each table.

Have a chart paper available for vocabulary.

Summarize their responses on a chart.

Look for categorizations of

Calculations (mean, standard deviation)

Variability

Making Decisions

At this point, don’t try to summarize or define statistics.

**2. TASK: Homework & Bullying (30 minutes)**/

**Day 1 AM: 9:30 – 10:00**

TEACHER NOTES

Purpose: To use an outlandish claim to demonstrate the four-step GAISE process for a statistical study:

1. Ask a statistical question

2. Collect data

3. Analyze data

4. Interpret the results in answering the original question

**Core Standards Focus**:

7.SP: Use random sampling to draw inferences about a population

8.SP: Investigate patterns of association in bivariate data.

S.IC.3: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

S.ID.9: Distinguish between correlation and causation.

**Related Standards: S.IC.2, S.IC.6**

EU6-8: Statistics can be used to compare 2 or more groups of data.

EU9-12: 4. The way in which data are collected matters.

**Launch (Whole Class):**Begin by reading the statement aloud. Remind students that there are many different types of graphical displays and that they may use any they feel would represent that statement.

**Explore (Individual):**If a student does not know how to begin, ask them for a type of graphical representation (such as bar graph) and then ask how such a representation could look that would give the idea of association between homework and bullying.

Look for students who create two bar graphs versus a scatterplot. A common error for students is to create a separate representation for homework from bullying (a bar showing amount of bullying and a bar showing amount of homework). Ask those students how their representation shows the two are related. Encourage students to move on to the questions they would ask.

**Discuss (Whole Class):**Choose a student’s bar graph and a student’s scatterplot to show to the class. Question whether each shows an association between the variables as well as if it shows whether bullying is affected positively or negatively with homework. Make clear the difference between a representation that tells you something about each variable and a representation that tells how the variables are related.

Chart the questions students would ask. There should be a discussion of definition of variables, who was sampled, and how the data was gathered.

Ask several students for their conclusion. Possible choices are that homework causes bullying or that there can’t be a cause and effect situation. Discuss briefly the difference between a well-run experiment to determine cause and effect versus an observational study or an improper experiment. /

**FACILITATOR NOTES**

Allow only at most 10 minutes for participants to work on the task and share their graphs and explanations. This will allow at least 20 minutes for our other purposes…

**Purpose for our teacher participants:**To see the Big Ideas from Essential Understandings books. Make sure participants have copies of these books. We are as interested in participants have the “right” answers about which standards, and which EU are being demonstrated, as we are of having a healthy discussion of the standards, EU.

Debrief:

What are the standards this task is focused on?

Make clear that Grade 7 Math, as well as Secondary III, does include making inferences about a population parameter based on a sample.

Correlation is the Secondary I term; the word, “association” is used in Grade 8. Correlation versus causation will be a major idea throughout the high school curriculum.

Where would this task be in the learning cycle? [This is a quick formative assessment for participants’ understanding of the CMI learning cycle.]

Which of the Big Ideas from EU are surfaced with this task? (have participants look through their books (pg 10-12 in both books).

Take a few minutes to have participants share the big ideas from each grade level that they expected to see and ones they were surprised at or not sure about.

Refer participants to EU:6-8 p 8, Statistics as a Problem-Solving Process.

**PARTICIPANT ONLY TASK: The Future of High School Mathematics ( 30 minutes)**/

**Day 1 AM: 10:00 – 10:30**

**STANDARDS ACADEMY TASK NOTES**

Purpose: To have participants aware of the technique of a close read and to apply it to a persuasive mathematics education article.

Article:

*The Future of High School Mathematics*one for each participant

Explain what a close read is:

Essentially, close reading means reading to uncover layers of meaning that lead to deep comprehension.

Nancy Boyles

Educational Leadership, December 2012/January 2013 | Volume70| Number4Common Core: Now What?pp. 36-41

Close Reading Protocol: Read with a pencil. (20 minutes)

· Read each sentence

· Mark big ideas & key details

· Look for patterns, similarities, contradiction, word choice

· Ask questions about what you read

Focus Questions (10 minutes)

Instruct participants to go through article again to answer questions with justification from article

Group A: What do these authors want me to know or feel?

Group B: How does the perspective in this text compare with other’s perspectives on this issue?

Group C: What would I put in a response article?

Share out from each group – (90 seconds per group) / Have powerpoint available or post the protocol and questions.

Give 15 minutes for close reading with a pencil.

Assign 1 or 2 groups to each of the three questions.

Give 10 minutes for answering question as a group.

5 minutes for each group to report out.

**3. PARTICIPANT ONLY TASK: Progressions Task (30 minutes)**/ Day 1 AM: 10:30 – 11:00

STANDARDS ACADEMY TASK NOTES

Purpose: To become familiar with the statistics standards, the progressions, and the GAISE framework.

Divide into four groups. Give each group the 18 cards with tasks listed on them, and a piece of chart paper. Have them sort the cards by courses (Math 6 – Sec III) and tape to chart paper with the course highlighted.

After groups have sorted, have everyone shift to a different group’s work and compare their answers.

Return to the original groups and get out their copies of the Progressions and use them to resolve any debates.

Give answers (which based on the USOE Curriculum Guides): Math 6: 6, 8, 14 Math 7: 9, 11, 18 Math 8: 4, 15, 16 Sec I: 2, 3, 7 Sec II: 1, 5, 13 Sec III: 10, 12, 17

Handout the GAISE framework. Ask participants to respond in their journals to the prompt:

*Compare and contrast the Progression documents and the GAISE framework.*

/ FACILITATOR NOTES

Have cards cut out ahead of time.

Write url for wiki on board to locate progressions.

eucc2011.wikispaces.com

10 minutes to sort.

5 minutes to shift and consider others work.

Debrief:

Make clear that the GAISE framework does not correspond to grade levels and has only a loose association with the Progressions. For example, in mapping Progressions to GAISE, is it possible to be at GAISE Level C even at an earlier grade for some topics and concepts? [See EU6-8: p.94]

Relate the Gaise components to the Statistics as a Problem-Solving Process from EU:6-8 book p. 8

Make clear that the content in EU:6-8 is not exactly the same as the core for 6th, 7th, and 8th grade math.

4. TASK:The Case Against Homework Part I (30 minutes) / Day 1 AM: 11:00 – 11:30

TEACHER NOTES

Purpose: To understand the components of a statistical question and methods for collecting appropriate data.

Core Standards Focus:

6.SP:Develop understanding of statistical variability

7.SP: Use random sampling to draw inferences about a population

8.SP: Investigate patterns of association in bivariate data.

S.IC.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies

EU6-8: Statistics can be used to compare 2 or more groups of data.

EU9-12: 4. The way in which data are collected matters.

GAISE Components: Formulate Question and Collect Data

Launch (Whole Class): Ask students how many of you think teachers shouldn’t be allowed to give homework. So how can we convince either the teacher or administration of that belief? Here is your chance to set up such an opportunity. Read together the situation. Give students two minutes to write some questions on their own. Then move them into groups to choose a question and determine how to answer the question.

Optional Launch: Show the Chocolicious powerpoint. Ask what the purpose of the ad is. Discuss the purpose of the statistics and the actual statistical questions to achieve the company’s purpose. Analyze the charts and what the charts are saying compared to the claims.

Explore (Group): Groups that are struggling may need to be reminded of advertisements (drug or fitness commercials) that make claims and what statistics are used. Ask what kind of data they would want to gather (categorical versus numerical) and whether they would compare two groups or look for an association between the two variables. Questions about what type of representation they would want to see could also be helpful.

Discuss (Whole Class): If possible, have several groups present their ideas and try to have one that would use categorical data and one that would use numerical data. Discuss how the representations would look differently depending on the question and the process.

Make clear the difference between a statistical question and other kinds of questions. Sometimes a question anticipates a determined answer, but a statistical question anticipates an answer that is based on varying data. The questions “How tall am I?” is answered with a single height and is not a statistical question. The question “How tall are adult men in the USA?” is a statistical question because all men are NOT the same height. (GAISE report p 11)

Discuss the different forms of surveys/experiments. Students may present ideas such as using tests or quizzes to measure student learning and comparing two groups that do homework or don’t do homework. Make clear that it is important for there be definitions of the variables (what does it mean to not do homework) and a way to measure the results.

Depending on time and plans, it may be good to move into methods for collection and need for randomization. Next lesson could be Random Rectangles and creating some surveys or ways to measure a variable.

Discuss what allows us to make a claim of causation. [randomization and controls].

Follow up task: Buttons from Illustrative Mathematics / FACILITATOR NOTES

Allow only 5 minutes to write 1 or 2 questions and begin to consider methods individually without working in groups.

Debrief:

Discuss that in the classroom, need to allow students time to consider and see different ideas.

While there is not a standard that specifically says students will write a statistical question, the GAISE framework makes clear that formulating questions and how we design for differences in data collection is essential.

Make clear the difference between statistical questions and non-statistical questions. (Gaise report p 11). Discuss how formulate a statistics question matures through the levels (refer to Gaise framework.)

Other examples are on p 16 of Gaise report.

Refer to the three articles: How do the statistical questions change over the three grade levels?

Elementary:

*What is the most popular type of shoe in our class today? What is the number of goals scored by soccer teams on a particular weekend?*

Middle School:

*Do people tend to score higher on list A (real words) or list B (non-sense words)*

High School:

*What percentage of students in the school have a curfew?*

Make clear the possibilities for studies—sample surveys, observational studies, and controlled experiments.

What kinds of lessons follow this task?

Talk about why random sampling and/or random assignment to groups is non-negotiable in statistical studies.