A Wealth of Activities From the Statway and New Mathways Projects Colleen Hosking Gustavo Cepparo Mary Parker Austin Community College

To download activities See the slides at the end of this presentation for information about how to contact us and how to download the handouts for today’s presentation and ALL the activities.

Overview of the Course

Prerequisites and Expectations  Basic Math  The course length is 2 semesters Students are told in advance that they will be expected to work in groups, and that they will need to complete both semesters to earn credit for the college-level course.

Some of the design principles The next slide is from the Carnegie Foundation for the Advancement of Teaching. We include it here as a “teaser” for you to look at the websites.  Productive Struggle  Explicit connections to statistical concepts  Deliberate Practice

Statistics and Mathematics Proficiency: Flexible and stable knowledge of concepts, procedures, strategies; and productive disposition Explicit connections to mathematic al/ statistical concepts Struggle with important mathematics / statistics Deliberate practice applying concepts/ procedures to solving problems Students engage productively with learning opportunities: Believe they are capable of learning math, gradually over time See math as something that makes sense, that one can “figure out” Willing to invest persistent effort Primary Drivers Instruction / Learning Opportunities Teachers effectively implement curriculum with students to create learning opportunities: Belief that these students are capable of learning math and statistics See math as something that makes sense, that one can “figure out” Skills and knowledge to implement instructional system: engage students in problems; make concepts explicit in ways students can understand; provide emotional support Instructional resources that afford creation of learning opportunities: Relevant to students interests Statistics (as distinct from math, to allay anxiety) Focus on understanding/thinking with concepts Clear learning goals (concepts & skills) aligned with formative and summative assessments Lesson structure: struggle, then instruction Conceptual flows to structure instruction Secondary Drivers: How do these teachers use these Instructional resources to create learning opportunities for these students Learning Opportunities Stigler, Givvin UCLA 6

Activity From the student perspective Activity: Scatterplots and Correlation Investigating Consumer Reports Cereal Ratings

Rating Cereal: 0 to = unhealthy 100 = very nutritious

0 = unhealthy 100 = very nutritious Rating Cereal: 0 to 100

Student Handout PG 1

On what are you basing your decision? How would we decide what rating to give this cereal? Consumer Reports does this kind of work and provides it to consumers CR rated 77 cereals, but their rating formula is not available to the public. Rating Cereal: 0 to 100

Student Handout PG 2 What does each dot represent in this distribution? For this distribution, what seems to be an average rating? How would you describe the variability in ratings? How would you describe the shape of this distribution?

Your Mission: Crack their code! At the end of this lesson you will be designing a children’s cereal. You want your cereal to receive above average Consumer Report ratings but also taste good. Of course, we all know that what tastes good may not be the most nutritious. So this will be a balancing act. CLUES: We have the nutritional information from ingredients we think might influence the ratings for these 77 cereals and have created scatterplots.

Student Handout PG 2

Student Handout PG 3 Two new cereals are being rated by Consumer Reports. Cereal A has 10.5 grams of sugar in a serving and Cereal B has 2.5 grams of sugar. (1)Based on the data shown, predict the Consumer Reports rating for the two cereals. (2)For which cereal do you think your prediction is probably more accurate (more likely to be closer to the actual Consumer Report rating)? Why?

Student Handout PG 4 (3)Captain Crunch has the lowest Consumer Reports rating of the 77 cereals in the data set. How much fat is in a serving of Captain Crunch? (4)In this set of 77 cereals, Product 19 has the most sodium in a serving. What is the rating for Product 19? (5)All-Bran Extra Fiber is the cereal with the highest rating. How much sugar, fat, and sodium are in a serving of All-Bran Extra Fiber? Reading and Interpreting Scatterplots

Student Handout PG 5 (6) There are four cereals that have 3 grams of fat in a serving. Estimate the ratings for these four cereals. What might explain the variability in the ratings? (7) Imagine changing the recipe for a cereal that has 0 grams of fat in a serving and a rating of 60. Increase the amount of fat to 3 grams in a serving. Do you think the rating will probably increase, decrease, or remain the same? Or do you think that it is impossible to use the scatterplot to predict the impact of this change on the rating? How does the pattern in the data support your decision? Seeing Patterns and Relationships in Scatterplots

Student Handout PG 6 (8) Think about how the amount of fiber in a cereal might relate to the Consumer Reports rating. Here are three scatterplots with make-believe data from 10 made-up cereals. Which scatterplot do you think displays a pattern similar to what you may see in the actual data? Why? Seeing Patterns and Relationships in Scatterplots

Student Handout PG 6 (9) Suppose that carbohydrates are not used in the Consumer Reports rating formula. Sketch a scatterplot with make-believe data from 10 make- believe cereals to illustrate what the data might look like in this situation. Seeing Patterns and Relationships in Scatterplots

Get to it, cereal detectives! Now it’s your turn to design your cereal. List how much of each of the four ingredients your cereal will contain (fat, sugar, protein, sodium) and why you chose each amount. Estimate the rating of your cereal.

Activity From the teacher’s perspective

How students react  Eager : They are interested in the context and discussions are lively. Everyone has strong opinions about cereal!  Surprised: Not all ingredients are as influential as they might have originally thought. They see data can be surprising.

 Group dynamic: Some students who are unsure about concepts (ex. how to read a scatterplot) can ask their group in a low pressure situation. It’s not as big a deal to be corrected in your group than to be corrected by the instructor. In a lecture format they may never even feel comfortable enough to ask. Here they are not left behind.  Making connections: One student pointed out that in predicting ranges of ratings you could picture a vertical boxplot.

Instructor version of lesson  Rich task  Scaffolding  Wrap-up  Objectives Caution: The version here, 1.0, is a first version and there are some errors in answers

Organize around concepts

Examples: Module 2 and on. Distributions. “What are unusual values?” “What are usual values?” (hypothesis testing and confidence intervals) Module 2. Compare groups. (comparing two means) Module 1: Collecting data. (hypothesis testing)

Group Activity 1. What do you do now in an elementary statistics course that has some discussion of concepts well before you are “covering them? 2. What topics are hard for students and so it might be good to do this? 3. For each topic you identified, brainstorm ideas about how to do this.

Group Report Each group report as many of these as you wish.  Statistics “hard” topic.  Suggested activity / discussion / brief lecture to address that earlier in the course.  Nothing suggested – still looking for one.

What are the activities?

Resources  Table of Contents (blue pages in handout)  List of Activities (green page in handout) Both of these are version 1.0, upon which both Statway and the New Math Pathways is based.  Information from Carnegie Foundation (tan page in handout)

Impact on other courses we teach

Early introduction of concepts  Regular stat course - in the chapter on normal calculations, scale back the complexity of the homework and talk more about “unusual” and “usual” scores.  Regular stat course – early discussion of making decisions so that they are familiar with the main ideas of hypothesis testing.

Writing activities  Always write an instructor edition of the activity.  Always consider scaffolding.  Try to get other faculty members working on activities for developmental math to think in this way – that really sets us up for improving our activities. -- Mary

Style of activities  Incorporated these activities in place of more mundane activities in my stats course  The structure of the course with collaborative learning and struggling with a rich problem is so impressive I have started using this in my regular math courses --Colleen

Thank you! Thanks for attending today. If you have any further questions about this or how to find the materials, please contact us. Mary Parker Colleen Hosking Gustavo Cepparo

Downloading activities The activities themselves, Version 1.0, are on the website of the Charles A Dana Center. Read the copyright information to see how you can use and adapt them. Find links to the activities and other useful information from the website for this talk: