College of Education and Human DevelopmentUniversity of Minnesota

Setting the Stage for Students’ Conceptual Change in Learning

StatisticsCAUSE Webinar

June, 2008

Marsha LovettCarnegie Mellon University

Bob DelMasUniversity of Minnesota

College of Education and Human DevelopmentUniversity of Minnesota

Main Premise

• Much of student learning is driven by relatively few basic learning mechanisms

• An effective course/lesson creates the conditions in which these learning mechanisms work together to support the learning goals we have set for our students

College of Education and Human DevelopmentUniversity of Minnesota

Learning Principle #1

• New knowledge is acquired through the lens of prior knowledge

Students see things differently from the way we do What we intuitively feel will foster learning may not

even be understood by students (This is called the expert blindspot)

College of Education and Human DevelopmentUniversity of Minnesota

Implications

• Students often do not know: What features are important to attend to? How to find what is important in a problem, situation,

question? Which situations are similar to each other in important

ways? What ideas or concepts should be distinguished?

College of Education and Human DevelopmentUniversity of Minnesota

(x+1)2 - 8= x2 + 2x - 7 x2 + 2x + 1 - 8= x2 + 2x - 7

2x + 1 - 8= 2x - 7 2x= 2x x = x

Good, he’s shown that thestatement is true no matterthe value of x.

Find the set of values whichmay be substituted for x and whichmake the statement true.

Huh????There’s noanswer!!!

Okay, get this thing to look something like x = 4.

Solve for x : (x +1)2 −8=x2 + 2x−7

Solve forx

Illustration: Two Sides of the Elephant

Students don’t always see things the way we do

College of Education and Human DevelopmentUniversity of Minnesota

Illustration: Statistics Problems

• Data-analysis problems involve lots of details and real-world issues

• Experts know what to attend to, e.g., variables measured, study design, possible confounds, etc.

• Students may attend to other aspects, e.g., cover story, how the question is phrased, number of variables presented

College of Education and Human DevelopmentUniversity of Minnesota

Instructional Strategies

• Give students explicit direction about what features are important and what they should attend to

• Give students practice identifying (and explaining) what is important

Gradually build up the complexity of problems so students are not overwhelmed with too much information at once

College of Education and Human DevelopmentUniversity of Minnesota

Learning Principle #2

• The way students organize knowledge determines how they use it

Just as prior knowledge influences how new knowledge is interpreted, the organization of new knowledge influences how it is used

• Instructional strategies: Helping students see the connections and relationships –

both in new knowledge and between old and new - will create more links for effective retrieval

College of Education and Human DevelopmentUniversity of Minnesota

Learning Principle #3

• Learners refine their knowledge and skills with timely feedback and subsequent opportunities to practice

Without feedback, students often do not know their own gaps and inaccuracies

Without additional opportunities to practice, they cannot strengthen their refined knowledge and skill

College of Education and Human DevelopmentUniversity of Minnesota

Illustration: StatTutor Feedback

• As compared to a traditional statistics lab assignment, where feedback comes days after the error was made, StatTutor alerts students when they have made an error and offers multiple levels of feedback

College of Education and Human DevelopmentUniversity of Minnesota

StatTutor

College of Education and Human DevelopmentUniversity of Minnesota

Instructional Strategies

• Look for where you can give students feedback on key skills they are practicing

• Look for how to make the feedback timely

• Look for opportunities for students to get extra practice on the skills where they received feedback

College of Education and Human DevelopmentUniversity of Minnesota

Learning Principle #4

• Meaningful engagement is necessary for deeper learning

Applying what they have learned is one way to get students actively engaged with the material

Authentic practice motivates students and focuses their effort on important aspects of the task

• Statistics examples and strategies Students work on projects (often in groups) Students do activities in class (e.g., collecting data,

running physical simulations)

College of Education and Human DevelopmentUniversity of Minnesota

Main Premise

• Much of student learning is driven by relatively few basic learning mechanisms

• An effective course/lesson creates the conditions in which these learning mechanisms work together to support the learning goals we have set for our students

College of Education and Human DevelopmentUniversity of Minnesota

Adapting and Implementing Innovative Materials in Statistics:

The AIMS Curriculum• Transform an introductory statistics

course into one that implements the Guidelines for Assessment and Instruction in Statistics Education (GAISE) (http://www.amstat.org/education/gaise/)

• Use research-based design principles to adapt innovative instructional materials (Cobb & McClain, 2004).

College of Education and Human DevelopmentUniversity of Minnesota

Research Basis for Lesson

• Use of simulation throughout course• Revisit concepts throughout course• Informal to formal ideas of sampling• Making and testing conjectures• Simulation of Samples (SOS) Model:

Organizational scheme to support abstraction of important concepts across simulations

College of Education and Human DevelopmentUniversity of Minnesota

Outline of a Lesson• Statement of a Research Question• Whole class discussion• Activity 1

Students work in small groups, make conjectures

Generate or Simulate data Small group discussion of results Whole class discussion

• Activity 2: Repeat cycle• Wrap Up: Discussion and Summary of

Main Ideas

College of Education and Human DevelopmentUniversity of Minnesota

Sample Lesson: Reese’s Pieces• Part of Unit on Sampling and Sampling Variability

• Adapted from Rossman and Chance Workshop Statistics

• Initial whole class discussion :

If I get only five orange Reese’s Pieces in a cup of 25 candies, should I be surprised?

Out of 100, how many Yellow, Orange, Blue?

Conjecture: Expected count for Orange for each of 10 random samples, n = 25

College of Education and Human DevelopmentUniversity of Minnesota

Each student group takes a random sample of n = 25

Separates and counts each color

Then calculates and records proportion of Orange

College of Education and Human DevelopmentUniversity of Minnesota

Instructor creates dotplot of sample proportions

Students work in small groups to answer questions• Did everyone have the same proportion of

orange candies?• Describe the variability of this distribution of

sample proportions in terms of shape, center, and spread.

• Do you know the proportion of orange candies in the population? In the sample?

• Which one can we always calculate? Which one do we have to estimate?

• Based on the distribution, what would you ESTIMATE to be the population parameter, the proportion of orange Reese’s Pieces candies produced by Hershey's Company?

• What if everyone in the class only took 10 candies? What if everyone in the class each took 100 candies? Would the distribution change?

College of Education and Human DevelopmentUniversity of Minnesota

Activity with Reese’s Pieces Applet

Students work in groups of 3 to 4 to run the simulation, answer questions, and make and test conjectures:

How does this compare to the dot plot on the board?

Where does 0.2 fall? Where does 0.7 fall? [Informal idea of p-value]

Conjecture what will happen if we change to n = 10? n = 100?

Run the simulations to check your conjectures.

http://www.rossmanchance.com/applets/Reeses/ReesesPieces.html

College of Education and Human DevelopmentUniversity of Minnesota

Three dotplots

• For each sample size (n=10, n=25, n=100), how close is the mean sample statistic (mean proportion), to the population parameter?

• As the sample size increases, what happens to the distance the sample statistics are from the population parameter?

• Describe the effect of sample size on the distribution of sample statistics in terms of shape, center and spread.

College of Education and Human DevelopmentUniversity of Minnesota

Identifying the Important Parts & Immediate Feedback

Each time we do a simulation, we want to make sure we know what each part of the simulation represents.

Can you identify:

POPULATION

PARAMETER

SAMPLE

STATISTIC

Distribution of Sample Statistics

The Population?

The Sample?

The Sample Statistic?

The Distribution of Sample Statistics?

The Population Parameter?

College of Education and Human DevelopmentUniversity of Minnesota

Simulation of Samples (SOS) Model

College of Education and Human DevelopmentUniversity of Minnesota

More Practice with Follow Up Activities

• Next day: simulations of sampling coins, words

• Students discover the predictable pattern

• Third day: Students “Discover” the central limit theorem” using stickers and Sampling SIM software

College of Education and Human DevelopmentUniversity of Minnesota

Remember that . . .

It’s not teaching that causes learning. Attempts by the learner to perform cause learning, dependent upon the quality of feedback and opportunities to use it (Grant Wiggins, 1993).

College of Education and Human DevelopmentUniversity of Minnesota

ReferenceCobb, P. & McClain, K. (2004). Principles of instructional design for

supporting the development of students’ statistical reasoning. In D. Ben-Zvi and J. Garfield (Eds.), The Challenge of Developing Statistical Literacy, Reasoning, and Thinking (pp. 375-395). Dordrecht, The Netherlands: Kluwer Academic Publishers.

AIMS Lessons, Lessons Plans, and Materials will be available at the end of summer 2008 at:

http://www.tc.umn.edu/~aims/

More information on Principles of Learning available at:

http://www.cmu.edu/teaching/principles/learning.html