Adapting and Implementing Innovative Materials

Developing Lessons aligned with GAISE

PIs: Joan Garfield and Bob delMas

Project Staff: Andy Zieffler, Michelle Everson

Dept of Educational Psychology, University of Minnesota

Advisors:

Beth Chance, Cal Poly

George Cobb, Mt.Holyoke

Bill Finzer, Key Technology

Cliff Konold, U Mass, Amherst

Robin Lock, St. Lawrence U
Dennis Pearl, OhioState

Allan Rossman, Cal Poly

Dick Scheaffer, U of Florida

Evaluator:
Rob Gould, UCLA

STAT CHAT Outline

  1. Joan: What we plan to do
  1. Overview
  2. Products
  3. Alignment with GAISE
  4. Research foundations
  5. Lesson plan template
  6. List of topics
  7. Variables on our backs activity
  1. Andy: sample of what we have done
  1. A focus on developing inference
  2. Sample materials
  3. One lesson: Coke Pepsi Taste test
  4. Simulation graphical model
  5. A glimpse of Reese’s pieces activity
  6. A teacher’s perspective
  1. Bob: Where we are heading, next steps
  1. Evaluation and Research
  2. Making lessons portable
  3. Adapting to different formats
  4. Assessing outcomes/impact

Overview/Project Summary

This two year project will adapt and implement several types of innovative materials that have been produced in the past few years for introductory statistics courses. These materials include textbooks, software, web resources, and special simulation tools. Lesson plans and student activity guides will be developed for a series of lessons to transform an introductory statistics course into one that implements the Guidelines for Assessment and Instruction in Statistics Education (GAISE) for teaching introductory statistics courses. The innovative new lessons will involve students in lots of discussion, computer explorations, and small group activities. The lessons build on implications from current educational research.

Developing, testing, evaluating, and revising innovative lessons for our introductory statistics courses will enable us to not only improve the teaching and learning of statistics for students at our institution; it will also provide a model for other instructors who would like to see how these lessons work. In order to evaluate the adaptability of our lessons to another setting, and to do a comparative study on the effectiveness of the lessons, we will apply the activities to randomly selected sections of a second introductory statistics course taught in a different college.

AIMS and GAISE

  1. Emphasize statistical literacy and develop statistical thinking

We build students’ statistical literacy by having them read their text and complete study questions, complete lab assignments, and responding to literacy questions on take home quizzes.

  1. Use real data

We gather data from students (student survey data, body data) and analyze other real data sets of interest (admissions data)

  1. Stress conceptual understanding rather than mere knowledge of procedures

We focus on the following big ideas, and develop them throughout the course. Students first encounter them informally, and then as they revisit them again and again we move them to more formal understandings. These ideas include: data, distribution, center, variability, deviation, model, samples, and inference.

4. Foster active learning in the classroom

Our lesson plans suggest how teachers may guide students thought activities where they are actively engaged in making and testing conjectures, working in small groups, explaining their reasoning, and learning together. We incorporate versions of many innovative activities in our lesson plans.

  1. Use technology for developing conceptual understanding and analyzing data.

We use Fathom for data analysis and exploration, Tinkerplots to help students understand and reason about graphs, Sampling Sim to simulate data to make informal inferences, and several Web applets to illustrate abstract concepts.

  1. Use assessments to improve and evaluate student learning.

We use a variety of assessments and will suggest at least one assessment at the end of each lesson plan.

The Research Basis for AIMS Lessons

A. Instructional Design Principles used to create lessons

In developing lessons, we draw on guidelines for designing instruction based on educational research about how students learn and how to design effective instruction to develop statistical reasoning. Their design principles suggest lessons that:

  • Have students make conjectures about data that can be tested.
  • Are focused on central statistical ideas.
  • Are built on the investigative spirit of data analysis.
  • Are developed to enable teachers to achieve their instructional agendas by building on the range of data-based arguments that students produce.
  • Develop students’ reasoning about data generation as well as data analysis.
  • Integrate the use of technological tools that support students’ development of statistical reasoning and allow them to test their conjectures.
  • Promote classroom discourse that includes statistical arguments and sustained exchanges that focus on significant statistical ideas.

Components of Research-Based Lessons

  • Emphasize and revisit a set of major themes, making them explicit throughout the course (e.g., variability, model, and sampling).
  • Use Fathom and Tinkerplots software tools with carefully designed activities to explore data, visualize relationships between concepts, and to minimize routine calculations.
  • Use simulation tools (Sampling SIM and Web Applets) from the beginning of the course, to build formal ideas of inference from informal ideas.
  • Use a Simulation Process Model to help students become familiar with the simulation process and to move from informal to formal methods of inference.
  • Use carefully designed small group activities (adapted from those in Activity Based Statistics and the ISCAM materials) to develop reasoning, by building in opportunities for students to predict, test, and evaluate their predictions about characteristics of data and relationships.
  • Collect and analyze (throughout the course) real data sets of interest to the students to develop statistical thinking (e.g., first day of class survey, body measurements, admissions data).

We will also develop hypothetical learning trajectories for developing the big ideas, that are used to structure the scope and sequence of activities.

Lesson Plan Template

Student Goals for the Lesson: Specific learning objectives for this lesson.

Major Statistical Themes: Big ideas to be made explicit throughout the course (e.g., variability, model, sample).

Handouts: Handouts to guide students through activities with room for them to record predictions and results. Additionalmaterials to support lessons, such as guidelines for using software or information on data sets.

Computer files: Files of real data used in class activities, often generated by students (e.g., heights and arm spans).

URLs: Web sites to be used in class for activities and simulations.

Other materials needed: Supplies needed for activities.

Hook: A question to grab students’ attention and motivate the day’s topic.

Opening Discussion Questions: Questions to get students thinking about the topics, speculating about data, making predictions that will be tested out using the software.

Activities: The activities involve concrete materials (e.g., Sampling Reese’s pieces) and/or technology (Reese’s Pieces Web Applet), along with questions that prod students to speculate and make, test, and evaluate predictions. Questions are also given to guide small group discussions that are then shared with the entire class.

Whole Class Discussion: Questionsto bring the class together, share results, draw conclusions (e.g., how sampling distributions behave as the sample size gets larger).

Wrap-up: Revisiting original questions, questions to think about, summary of themain ideas, lessons to walk away with, what is coming next, etc.

Scope and Sequence of Lessons

Note:

1.These lessons do not necessarily “cover” an entire course.

2.We only need to produce 20 final lessons, more than the number listed below.

3.These lessons are not a textbook, but guides to what happens in a class period. They should be able to be used with any of the good textbooks.

4. Lessons include one or more activities. However, we know that class sessions vary form school to school, so some users might not be able to do all activities in a lesson.

5. Rather than have a set of activities, we use lesson plans to show the interweaving of discussion, activities, and summaries, and the absence of lectures.

6. We do not include reading or background materials or assessments in our lessons or materials.

Topics:

Data: 2 lessons on types of data, collecting data and simulating data to make inferences

Producing data: 3 lessons on experiments and surveys

Exploring data : 8 lessons on distribution, center and spread (intertwined), comparing groups with boxplots

Normal distribution: 1 lesson on empirical rule and z scores

Sampling variability and CLT: 3 lessons

Inference: 5 lessons on informal ideas of inference, tests of significance, confidence intervals, p-values

Bivariate data: 3 lessons on scatterplots, correlations, ideas of linear regression

Activities to develop ideas of Inference

  1. Simulating data to make predictions (day 2)
  2. Taking random samples: Gettysburg Address (Lesson 4)
  3. Coke and Pepsi taste test (day 5)
  4. Comparing two brands of raisins: is there a difference?
  5. Sampling Reese’s pieces: what is a surprising result?
  6. Body temperatures? When is a mean temperature unlikely?
  7. Balancing coins: are heads and tails really equally likely?
  8. Confidence intervals: estimating the chance of getting heads when balancing coins.

Experiments and Inference about Cause

Lesson Plan

Hook: Can you tell the difference between Coke and Pepsi? Can you correctly identify each brand in a blind taste test? How can you tell if somebody really knows?

Student Goals for the Lesson:

  1. To learn the characteristics of a well defined experiment
  2. To learn the difference between an experiment and an observational study
  3. To learn to recognize instances of confounding in an experiment.
  4. To learn that randomizing the assignment of treatments protects against confounding and makes cause and effect statements possible
  5. To build the foundations for understanding statistical inference, and judging whether a result is surprising, unusual, or due to chance.
  6. To understand how the Simulation Process Model illustrates the different levels of simulated and observed data.

Big Statistical Themes: Inference, Sample

Student Worksheet(s):

  1. Recording sheet for Coke/Pepsi experiment
  2. Coke/Pepsi Pouring Sheets
  3. Simulation Process Model (SPM) for Coke/Pepsi experiment

Other Materials/Resources Needed:

  1. Dixie cups (11 per group)
  2. 1 Big bottle each of Coke and Pepsi

Discussion: Who thinks that they can correctly identify Coke and Pepsi in a taste test?
How will you know if someone is just a lucky guesser?

How might you design a research study to determine if someone can correctly identify Coke and Pepsi in a taste test?
Would you give them more than one sample of each to test?

Activity #1: Coke/Pepsi taste test

Tell the students you have designed one study and you want them to participate and gather data to determine who can really identify coke and pepsi.

Ask for up to 8 volunteers to be the tasters.

(8) Tasters--those who think they can tell the difference (blind to test).

(8) Runners—those who run cups of coke from room to hall (blind to test)

(8) Recorders—they record and report results to the pourers who can grade

(8) Pourers—remain in the classroom as pourers/observers.

  • Tasters and runners leave the room and get a Dixie cup of water that will be used to cleanse their palette.
  • Pourers will be privy to the cola being tasted in each round as listed below.
  • After the Dixie cups of cola have been poured and laid out on the table by the pourers, the runners are called to bring one cup at a time to their assigned subject.
  • The recorder writes down the results on forms and reviews with pourer at end of test.

Discussion:

Was this an experiment or an observational study? Why?

Did we have all three elements of a good experiment (randomization, control, and replication)? What things could have confounded our results? Did we protect against this? How? What did we control for?

Based on these results, whom do you believe can tell the difference between Coke and Pepsi? Why?

What can we say about the group of students who took the taste test? On average, how well did they do?

What if I really couldn’t tell the difference between the two? How many would you expect me to get correct?

What if I did the taste test 10 times? How many would you expect me to identify correctly?

Write down 9 more results that you would expect IF I WERE GUESSING, so that you have 10 totals.

Pool your results with your group and create a dotplot. What does it look like?

Now imagine I took the taste test over and over and over again. How many would I get right if I were JUST GUESSING? What would the results look like?

Activity #2: Use simulation to simulate data for a Coke versus Pepsi experiment and to test our results (to see how surprising they were).

Open Sampling SIM:

For population, set: Measurement to Binomial, .5 = probability,

For Sampling Distribution window, set sample size = 10, # of samples = 5;

Open the samples window to show success (and failure) on each trial;

For Options: proportion below, one slider

Make sure ADD MORE is selected

“In actuality I got ‘2 right,’ i.e., 2 out of 10, or 20%. Where does my result fit in to our model based on chance?

Slide the slider to display the proportion expected based on chance.

Activity #3: Discuss the Simulation Process Model (SPM) in the context of this Coke versus Pepsi test. Display overhead of SPM on the white board and customize the model to reflect Coke & Pepsi. For example, start off with “What if you could not tell the difference, then what would you expect the results to look like?” 50-50?

Discussion:

What does the graph of the results look like?

Where does your actual result fit in?

Do we expect that result if you really couldn’t tell the difference?

‘So, based on your result should I believe that you can tell the difference between Coke and Pepsi?

Wrap Up

What problems were there in our experiment?
What could have been done to make it a better experiment?
What types of confounding were present? How could we have avoided that?

What type of study could we design next time that would give us more accurate results?

1

The Sampling and Inference Process / Simulation Process Model (SPM)
Coke Pepsi Taste Test / Levels of Data
1. Assume no one can really tell the difference, and is just guessing each time they taste a soda. / / Level 1: Population
Level 2:
Samples & sample statistics
2.Generate data based the model that everyone is guessing and can’t really tell the difference. How many would they get right just by chance? How many would they get wrong?
3.Compute the proportion of correct guesses for each sample of 10 guesses.
4.Graph these proportions (show the distribution). / / Level 3: Distribution of sample statistics
5.Show your result compared to distribution of guesses. Does it seem likely that you were just guessing?

1

Sampling from a Population: Reese’s Pieces

Part 1: Making Conjectures about Samples

Reese’s Pieces candies have three colors: Orange, brown, and yellow. Which color do you think has more candies (occurs more often) in a package: Orange, brown or yellow?

  1. Guess the proportion of each color in a bag:

Color / Orange / Brown / Yellow
Predicted
Proportion
  1. If each student in the class takes a sample of 25 Reese’s Pieces candies, would you expect every student to have the same number of orange candies in their sample? Explain.
  1. Make a conjecture: Pretend that 10 students each took samples of 25 Reese’s Pieces candies. Write down the number of orange candies you might expect for these 10 samples:

These numbers represent the variability you would expect to see in the number of orange candies in 10 samples of 25 candies.

You will be given a cup that is a random sample of Reese’s Pieces candies. Count out 25 candies from this cup without paying attention to color. In fact, try to IGNORE the colors as you do this.

  1. Now, count the colors for your sample and fill in the chart below:

Orange / Yellow / Brown / Total
Number of candies
Proportion of candies
(Divide each numberby 25)
  1. Now that you have taken a sample of candies and see the proportion of orange candies, make a second conjecture: If you took a sample of 25 Reese’s Pieces candies and found that you had only 5 orange candies, would you be surprised? Do you think that 5 is an unusual value?
  1. Write the number AND the proportion of orange candies in your sample on the board. Mark where each value should be on the two dotplots your teacher constructs (one for number of oranges, one for proportion of oranges).

Figure 1: Dot plot for the number of orange candies.