GAISE GAISE

Robin LockJack and Sylvia Burry Professor of Statistics

St. Lawrence Universityrlock@stlawu.edu

Guidelines for Assessment and Instruction in Statistics Education

COLLEGE REPORT

GAISE College GroupJoan Garfield Univ. of Minnesota

(Chair)Martha Aliaga ASA George Cobb Mt. Holyoke CollegeCarolyn Cuff Westminster CollegeRob Gould UCLARobin Lock St. Lawrence UniversityTom Moore Grinnell CollegeAllan Rossman Cal Poly San Luis

ObispoBob Stephenson Iowa StateJessica Utts UC DavisPaul Velleman Cornell UniversityJeff Witmer Oberlin College

The Many Flavors of Introductory Statistics

Consumer Producer

GeneralDiscipline-specific

Large lecture Small class

Year BlockSemester Quarter

H.S. (AP)

UniversityTwo year college

Four year

college

Challenge in Writing Guidelines

Give sufficient structure to provide

real guidance to instructors.

Allow sufficient generality to include good practices in the

many flavors.

Starting point: Cobb Report (1992)

Report from discussions of the Focus Group on Statistics Education in Heeding the Call for Change

Three Recommendations:

• Emphasize statistical thinking

• More data and concepts, less theory and fewer recipes

• Foster active learning

Statistically Educated Students

Should believe and understand why…• Data beat anecdotes.• Variability is natural and is also predictable

and quantifiable.• Random sampling allows results to be

extended to the population.• Random assignment in experiments allows

cause and effect conclusions.

Statistically Educated Students

Should believe and understand why…

• Association is not causation.

• Statistical significance does not necessarily imply practical significance.

• Finding no statistical significance in a small sample does not necessarily mean there is no difference/relationship in the population.

Statistically Educated StudentsShould recognize…• Common sources of bias in surveys and

experiments.

• How to determine the population (if any) to which inference results may be extended.

• How to determine when a cause and effect inference can be drawn.

• That words such as “normal”, “random” and “correlation” have specific statistical meanings.

Statistically Educated StudentsShould understand the process through which statistics works to answer questions. How to…• Obtain or generate data.

• Graph data as an initial step in analysis.

• Interpret numerical summaries and graphical displays (answer questions / check conditions).

• Make appropriate use of statistical inference.

• Communicate results of a statistical analysis.

Statistically Educated StudentsShould understand the basic ideas of statistical inference, including the concepts of• Sampling distribution and how it applies to

making inferences from samples.

• Statistical significance, including significance level and p-values.

• Confidence interval, including the confidence level and margin of error.

Statistically Educated StudentsShould know

• How to interpret statistical results in context.

• How to read and critique news stories and journal articles that include statistical information.

• When to call for help from an experienced statistician.

Guideline #1

Emphasize statistical literacy and develop statistical thinking.

Statistical literacy: understanding the basic language and fundamental ideas of statistics.

Statistical thinking: the processes that statisticians use when approaching or solving practical problems.

Statistical Literacy and Thinking

Suggestions for Teachers

• Model statistical thinking for students.

• Have students practice statistical thinking (e.g. open-ended problems and projects).

• Let students practice with choosing appropriate questions and techniques.

Guideline #2

Use real data.

Levels of Reality

Real: Data that were actually collected or generated to answer some question(s).

Realistic: Hypothetical data with a context that illustrate a specific point.

Naked: Numbers with no context (and thus no interest).

Suggestions for Teachers

• Search for raw data from textbooks, software packages, web data repositories.

• Use summary data from textbooks, articles, and websites with poll/survey results.

• Get data from class activities and simulations.• Make larger data sets available electronically. Practice

data entry on small data sets.• Return to a rich data set at various points in the course.• Use data with students to answer interesting questions

and generate new questions.

Guideline #3

Stress conceptual understanding rather than mere knowledge of procedures.

Concepts vs. Procedures

Many (most?) introductory courses contain too much material.

If students don’t understand concepts, there’s little value in knowing procedures.

If students do understand concepts, specific new procedures are easy to learn.

Suggestions for Teachers• Primary goal is not to cover methods, but to discover

concepts.• Focus on understanding of key concepts, illustrated by a

few techniques, rather than a multitude of techniques with minimal focus on underlying ideas.

• Pare down content to focus on core ideas in more depth. • Use technology for routine computations, use formulas

that enhance understanding.

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Guideline #4

Foster active learning in the classroom.

Types of Active Learning

Group or individual: problem solving, exploratory activities and discussion

Lab activities: physical and computer-based

Demonstrations: based on “live” results from students or software

Suggestions for Teachers

• Ground activities in the context of real problems.• Intermix lectures with activities and discussions. • Precede computer simulations with physical

explorations.• Collect data from students.• Encourage predictions from students anticipating

statistical results.• Plan sufficient time to do and wrap up the activity.• Provide lots of feedback and assessment.

Guideline #5

Use technology for developing concepts and analyzing data.

Types of Technology

Graphing calculators

Traditional statistical packages

Conceptual statistical software

Educational support

Applets

Spreadsheets

Suggestions for Teachers• Access large real data sets.• Automate calculations. • Generate and modify appropriate statistical graphics.• Perform simulations to illustrate abstract concepts.• Explore “what happens if...” scenarios.• Create reports• Consider

– Ease of data entry, ability to import data– Interactive capabilities– Dynamic linking between data, graphs, numerics– Ease of use and availability

Guideline #6

Use assessments to improve and evaluate student learning.

Types of AssessmentHomeworkQuizzes and examsProjectsActivitiesPresentationsLab reportsMinute papersArticle critiquesClass discussion/participation

Suggestions for Teachers• Integrate assessment as an essential (and current) component of

the course.• Use a variety of assessment methods. • Assess statistical literacy (e.g. by interpreting or critiquing articles

and graphs in the media).• Assess statistical thinking (e.g. by doing student projects or open-

ended investigative tasks).• For large classes

– Use group projects instead of individual– Use peer review of projects– Use multiple choice items that focus on choosing interpretations or

appropriate statistical approaches.

Six Recommendations

1. Emphasize statistical literacy and develop statistical thinking

2. Use real data3. Stress conceptual understanding rather

than mere knowledge of procedures4. Foster active learning5. Use technology to develop conceptual

understanding and analyze data6. Use assessments to improve and

evaluate learning

Making It Happen

Evolution through small steps:

•Find/develop a case study of statistical interest

•Find a new real data set

•Delete a topic from the list you currently cover

•Have students do a small project or new activity

•Integrate a neat applet into a lecture

•Try some new types of quiz/exam questions