Birth of an activity

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Birth of an activity

• Beth Chance
• Department of Statistics
• Cal Poly San Luis Obispo
• bchance_at_calpoly.edu

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Overview

• Common Vision project (PI Karen Saxe, Macalester
  College)
• AMATYC, AMS, ASA, MAA, SIAM
• Freeman report (2014) Active learning increases
  student performance in science, engineering, and
  mathematics
• Failure rates under traditional lecturing are 55
  percent higher than the rates observed under
  active learning
• When Monica asked me about this session, I was
  just finishing up creating a new activity
• Did I have any strategies that might be useful
  to other teachers?
• What does a good activity look like?

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Step One Pick a topic

• Identify an area in which students consistently
  struggle
• e.g. conceptual vs. procedural understanding
• Write out learning goals
• Make explicit what you want students to be able
  to do, remember afterwards
• What is your motivation for the activity?

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Step One Pick a topic

• Context
• In both my Stat 101 and Stat 201 courses, we
  have centered on randomization-based inference
  from the very beginning of the course
• Example Fourteen of 16 infants choose to play
  with a helping toy rather than a hindering
  toy indicating social evaluation (6 mos)
• Is that convincing evidence or could this have
  happened just by chance?
• Chance model toss 16 coins, is 14 an unusual
  outcome?
• Where does 14 fall on the null distribution?
• Binomial model
• Normal approximation/z-statistic more than 2SD
  away?
• So what conclusions can we draw from this study?

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Step One Pick a topic

• More Context
• What is probability?
• Descriptive statistics and inference for one
  proportion
• Two proportions (conditional proportions, bar
  graphs, randomization tests, normal
  approximation)
• 2nd midterm (week 7 of 10-week quarter)

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So whats the problem?

• Quantitative data
• How do I introduce importance and measures of
  variability with categorical data?
• Distributional thinking is difficult for many
  students
• How do I show them the richness of big data?
• Motivation
• Do more with quantitative data earlier in the
  course
• Catch up those who havent seen standard
  deviation before with straight forward example
• Use interesting data where students will be
  motivated to think about shape, center,
  variability

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Step Two Find interesting data

• Better yet find interesting research question
• Need to assess what your students are interested
  in (e.g., initial course survey)
• Use existing resources as much as possible
• Data and Stories Library, STEW websites
• Collect data on your students (anonymously)
• Listen to TV, NPR, news websites
• Set a time limit to how long you will spend
  tracking down the article
• Recent examples Early exposure to peanuts, Using
  lotteries to promote safe sex, Experiment
  investigating effectiveness of programs for the
  poor, Tylenol also dulls emotional pain

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Step Two Find interesting data

• Also wanted to give students a sense of the
  richness of data on the web
• Impacts of raising speed limits on driver
  safety
• FARS Encyclopedia

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Step Two Find interesting research question

• 2009 study

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Step three Context

• Summarizing background, motivation for the study,
  authenticity
• Students can be asked to read this outside of
  class
• Students can be asked to relate to the study
  personally
• Students can be asked to generate their own
  research questions
• Focus on restrictions, exclusion criteria (e.g.,
  rural vs. urban highways)
• Wikipedia page

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Step four Context
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Step four Classroom context

• Classroom layout, Class size
• Discussion among students?
• Lecture or Guided exploration or Open ended
• Access to technology
• Individually or in teams
• Expectation for participation from day one
• Student products/incentive system
• What do/should/might students know about this
  topic coming into class? (Stat 201)
• Watch for sensitive topics

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Step four Classroom context

• Computer classroom
• First day of class
• Didnt want to overwhelm them with technology
• Didnt want to assume any prior knowledge
• Mostly interested in exposure
• Data
• Variability
• Modern data science
• (a couple others along the way)

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Step five Scaffolding

• Hook students into the activity
• Start with learning goals
• Start with definitions, new terms?
• Start to build cognitive dissonance
• Get them to ask the next question?
• Habits of mind
• Surprise students!

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Step five Scaffolding

• From the table do you see any patterns or trends?
• What additional information is important to
  consider?
• What can you learn from the following plot?

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Step five Scaffolding

• Absolute difference vs. percentage change
• 1974 -17.14

Where is 1974? Why does it start in 1900? What do
you learn from the graph?
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Step five Scaffolding

• Other ways to compare 1974 to the other years?
• Dotplot
• How does this graph compare to the timeplot?
• How might you judge whether 1974 is unusual?

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Step five Scaffolding

• Introduce descriptors shape, center, variability
• Introduce formulas for mean, standard deviation
• Quick check of understanding
• Use technology to create own graph
• Dotplot vs. histogram
• 1994-1995 data (1.74)
• Extension/Application
• Investigate California, what year did CA repeal?
• Causation?
• Explore FARS website

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Role of technology

• Try to minimize unhelpful by-hand calculations
• Standard deviation once?
• Focus on comparing SD across distributions
• Be very conscious of learning curve of technology
• Added timeplot feature
• Use technology to explore
• Make more than one graph
• Histogram bin width
• Slider
• Critique, Dont use default settings
• Discuss limitations (e.g., axis labels)

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Step six Test the activity!

• Play the role of student
• Read the questions fresh
• Write out the answers (spacing, enough
  information, sequencing of ideas, reference)
• Ask another faculty member to review
• Ask a student to review
• Use R readHTMLtable to scrape data from Wikipedia
  page

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Step seven Use the activity

• Cross your fingers
• Advance planning
• Contingency plans
• Be proactive in monitoring student progress
• Make sure students realize what they are
  responsible for having learned from the activity
• Not only fun and games
• Resist repeating the lessons of the activity in
  lecture
• Get students to tell you the big idea
• Make sure students dont miss the gorilla

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Step eight Make notes

• Take 5-10 minutes to jot down notes to yourself
  (others?) on how the activity went
• Where did students get stuck
• Were students engaged in the context
• How was the timing
• What were the common questions
• How does this tie into previous/upcoming content
• What props do you need to remember to bring
  next time?

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One of my favorite activities

• Give students a copy of the Gettysburg Address
  and ask them to quickly circle 10 representative
  words
• Sample vs. Population
• Have students calculate the average length of
  their sample (statistic)
• Pool student results together to create a dotplot
  of averages (sampling distribution)
• Compare to the population mean (parameter)
• Repeat with random samples of 5 words and compare
  the results

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One of my favorite activities

• Compare distributions
• Move to technology, tweak inputs

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One of my favorite activities

• Common misconception Role of population size

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Evolution of the activity

• Activity-Based Statistics (1996)

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Workshop Statistics
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Measurement tip to tail
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Statistical concepts

• Population vs. sample, parameter vs. statistic
• Bias, variability, precision
• Random sampling, effect of sample size
• Effect of population size
• Sampling variability, sampling distribution,
  Central Limit Theorem (consequences and
  applicability)

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Critiquing the activity

• Did it make the best use of within vs. outside of
  class time?
• Multi-tasking, prepared ways to collect data
• Did it use real data?
• Real scientific question?
• Did it hook students?
• Were students actively involved?
• Were important statistical lessons clear?
• Does it connect to other parts of the course?
• Did it make effective use of technology?
• Tactile simulation vs. black box
• Learning curve
• Is there a clear way of determining whether
  students got it?

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Reminders

• Active learning ? Free-for-all
• Find engaging contexts (e.g., data on students)
• Elicit participation, prediction from students
• Promote collaborative learning
• Association ? Causation
• Get students to tell you the point
• Provide lots of feedback
• Follow-up with related assessments
• Inter-mix with lecture, as needed
• Do not underestimate the ability of activities to
  teach
• Have fun!