Writing in an Introductory Statistics Curriculum John Harrison Princess Anne High School Virginia Beach, VA Beyond the Formula 2005

“Data is not the plural of anecdote.” Food for Thought Explain the following quote: “Data is not the plural of anecdote.”

Background Five years experience teaching AP Statistics Grown from 14 students to over 60 Historically about a 60% pass rate (3 or better) Large percentage of students get a 2 on the exam (30%) Looking for a way to decrease the percentage of 2s.

Areas Explored Changed textbook from a traditional statistics text to a more student centered text. Examined the number and type of hands on experiences Reviewed tests for level of difficulty Treisman model for challenge worksheets http://www.math.uiuc.edu/MeritWorkshop/uriModel.html Examined the number and type of writing exercises

Treisman Model Developed by graduate student Uri Treisman at UC Berkley in 1980s Working on the problem of high black failure rate in introductory calculus course Observed that most black students studied independently while most asian students collaborated with peers

Challenge Worksheets Attempt to force students to work in collaborative groups Challenging problems that push the boundaries of the course Typically Investigative Task type problems that require additional insight into the topic

Conclusion – More Writing Exercises Students cannot achieve top grades if their communications skills are weak (Peck) There were not enough evaluated writing exercises in my course Added Daily journal entries Writing component to Minitab exercises More frequent practice free-response questions

Communication in Statistics “The primary purpose of statistics is to provide analysts and researchers with methods for collecting data in a reasonable way and for making sense out of that data. As such, context is critical to statistics and helps distinguish it from mathematics.” Roxy Peck, “Calculations Aren’t Enough”, AP Central, 2003

“Data aren’t just numbers, they are numbers with a context.” George Cobb and David Moore “Mathematics , Statistics and Teaching” American Mathematics Monthly (1997)

Why is Communication in Statistics Important? The meaning of the results comes from the context of the problem. Interpretation of the analysis in context is the ultimate desired outcome. Statisticians must present their results to those who make decisions based on these results and who may not understand the underlying process.

What is Good Statistical Communication? Explanation of what was done. Explanation of why it was done. Interpretation of the results in context. Expressed in clear, concise, language that does not rely on jargon or specialized terminology to impart the information.

Communication Standards The College Board, in The Teacher’s Guide for AP Statistics, (1997) specified 5 levels of communications

Level 5 (Highest) Provides clear, organized, and complete explanation, using correct terminology, of what was done and why. States appropriate assumptions and caveats Uses diagrams or plots when appropriate to aid in describing the solution. States an appropriate and complete solution.

Level 4 Provides a clear but not perfectly organized explanation, using correct terminology, of what was done and why, but explanation may be slightly incomplete. May miss necessary assumptions or caveats. Uses diagrams or plots when appropriate to aid in describing the solution. States a conclusion that follows from the analysis but may be somewhat incomplete.

Level 3 Provides some explanation of what was done, but explanation may be vague and difficult to interpret, and terminology may be somewhat inappropriate. Uses diagrams in an incomplete or ineffective way, or diagrams may be missing. States a conclusion that is incomplete. Provides a minimal or unclear explanation of what was done or why it was done, and explanation may not match the presented solution. Provides no explanation of a legitimate strategy.

Level 2 Provides a minimal or unclear explanation of what was done and why it was done, and explanation may not match the presented solution. Fails to use diagrams or plots, or uses them incorrectly. States an incorrect conclusion or fails to state a conclusion.

Level 1 (Lowest) Provides no explanation or legitimate strategy

Why should we write in the statistics curriculum? Students are not accustomed to writing about “math”. Students are not trained to interpret results, rather they are trained that the numerical result is sufficient in most high school mathematics classes. Students need practice organizing their thoughts and using statistical terminology to express those thoughts.

How do we improve statistical communications? Proper communications is modeled by the instructor Parameter vs. Statistic Proper names of statistical tests and procedures vs. “calculator speak” Consistent application of language of statistics, especially in the interpretation of confidence intervals and tests of hypotheses. Students practice proper statistical communications.

How do students practice? Students conduct realistic statistical exercises Collect and analyze real data Use a variety of statistical tools such as calculators and statistical software Students present their results to other students

How do students practice? Students read realistic statistical information Case studies Newspaper and magazine articles Actual research Well written statistical texts

How do students practice? Homework must reflect variety of statistical processes. Simple calculation Descriptive statistics analysis Inferential statistics analysis Experimental design analysis

How do students practice? Students must be made to write about statistics As part of data analysis using either the calculator or computer software As part of homework assignments In daily journal entries

What is a statistics journal? Every day students are presented a writing prompt and given some amount of class time to write in their journal. Students are required to respond using the rules of proper written English including punctuation and capitalization and excluding slang. Answers must be in sentence form and should be a paragraph consisting of 3 to 5 sentences.

Where do you find writing prompts? From their homework assignments Describe the probability distribution used in question 2a. From class discussions State in your own words the Fundamental Rule for Using Data for Inference and explain why it is important. From the textbook Some books include writing prompts such as “Turn On Your Mind” segments in Mind on Statistics, (Utts and Heckard).

How do you assess student writing? Homework, journal entries, class work activities Informal assessment Grammar, on topic, complete thoughts Used to provide feedback to improve the process for formal assessments

Sample Journal Assessment Approximately every two weeks (5 journal entries), journals will be collected and graded. Journals which have all assigned entries, are neat, legible, and follow the standard rules of written English will receive a grade of 100. Missing entries will result in lowering the grade by the appropriate percentage of total assignments, i.e., if you are missing 1 of 5 assignments, the highest grade you can receive is 80. Journal entries missed due to absence must be made up. Minor grade reduction for neatness, grammar, and spelling (5 to 10 points).

How do you assess student writing? Projects, tests, practice AP Free-Response questions Formal assessment Use rubrics for consistency Clarity, grammar, on topic, complete thoughts, proper statistics vocabulary

Conclusion Communication is a vital part of the statistics curriculum Students need practice communicating about statistics Journals can play an important role by providing a practice field for statistical communications.

Questions, Comments or Personal Experience