College of Education and Human Development

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Setting the Stage for Students Conceptual Change
in Learning Statistics

• CAUSE Webinar
• June, 2008

Bob DelMas University of Minnesota
Marsha Lovett Carnegie Mellon University
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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

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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)

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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?

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Illustration Two Sides of the Elephant
Students dont always see things the way we do
Solve for x
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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

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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

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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

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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

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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

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StatTutor
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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

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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)

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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

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Adapting and Implementing Innovative Materials in
StatisticsThe 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).

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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

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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

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Sample Lesson Reeses 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 Reeses 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

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Each student group takes a random sample of n 25
Separates and counts each color
Then calculates and records proportion of Orange
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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 Reeses 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?

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Activity with Reeses Pieces Applet
http//www.rossmanchance.com/applets/Reeses/Reeses
Pieces.html
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.
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Three dotplots

• For each sample size (n10, n25, n100), 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.

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Identifying the Important Parts Immediate
Feedback
POPULATION
Each time we do a simulation, we want to make
sure we know what each part of the simulation
represents. Can you identify
Distribution of Sample Statistics
The Population?
The Population Parameter?
SAMPLE
The Sample?
STATISTIC
The Sample Statistic?
PARAMETER
The Distribution of Sample Statistics?
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Simulation of Samples (SOS) Model
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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

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Remember that . . .

• Its 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).

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Reference
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/learnin
g.html
Cobb, 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.