How I learned to stop worrying and love statistics

I would like to propose a harmless exercise in fear-induction.

Approach 5 people at random and ask them their feelings about or experiences with statistics. Observe the signs of visceral reaction. Note the rapid change of facial expression: the anxious wrinkling of the forehead, the fearful widening of the eyes, and the distasteful downturn of the mouth. Behold the shoulder tensing, heavy sighing, and gut clenching. Steady yourself for the diatribes about how many majors were avoided or doctoral degrees went unearned because of the insurmountable obstacle of statistics.

As a statistics instructor for the past 3 years, I have been met with the entire spectrum of reactions, from disbelief to outright hostility to subdued dejection. In fact, I open my class each semester by recounting one such conversation to my students. Without belaboring the details, it involved an uncle at a family gathering, a long-winded account of his “college days” and an overturned bowl of soup.

Needless to say, the challenge of teaching statistics extends beyond the mere instruction of complex and abstract concepts. All statistics instructors must function as dual teachers and psychotherapists. Creating a safe environment, scaffolding implementation of new techniques, and working collaboratively to achieve goals are all essential to ensuring student buy-in and improving academic outcomes. In line with the Writing Across the Curriculum tradition and Karen Y. Holmes’ 2011 article, I argue that incorporating both formal and informal writing into statistics courses can serve three simultaneous functions that facilitate student learning and (dare I say) improve the blighted public image of statistics! I will argue that use of writing assignments can: 1) deepen understanding of course material, 2) improve statistical reasoning skills, and 3) reduce anxiety surrounding the material.

Low-stakes assignments to deepen conceptual understanding
There is perhaps no gentler tune to the ear of an anxious statistics student than the phrase “this will not be graded.” Incorporating low-stakes, informal writing assignments into your statistics course will increase students’ familiarity with course material, consolidate complex concepts, and reinforce the importance of clear and concise writing. By promising students that these assignments will not be graded for content, but rather for completion and/or effort, you can also help allay their anxieties while improving class participation and attendance. Here are several ideas for such assignments:

Entrance and Exit Slips (Stromberg & Ramanathan, 1996)
Pose short questions to students at either the beginning or ending of class to complete on index cards. Questions can cover course material, such as “Provide an example where the median would be a more appropriate measure of central tendency than the mean.” They can also probe for student understanding. For example, asking “What was one concept from today’s lecture you don’t understand” will help the instructor gauge students’ progress and allot class time to relevant topics. By writing in the small space allotted in an index cards, students will also become more adept at conveying ideas with brevity. Answers will be graded 0 (absent, completely off-topic) or 1 (attempts to answer topic, provides reasonable response). This practice has been shown to substantially increase class attendance and was positively received by 90% of students sampled in one class (Stromberg & Ramanathan, 1996).

Compare and Contrast Assignments (Holmes, 2011)
One of the common points of confusion in my statistics classes surrounds terminology. What’s the difference between Type I and Type II error? How does the alpha level relate to the critical regions? How do I differentiate between the independent and dependent variable? Writing is a wonderful tool for detangling complex relationships between concepts. Pose short writing assignments in class asking students to spend 5 minutes identifying the similarities and differences between related concepts. Have students swap assignments and peer review. Then review the correct answers together to ensure accurate comprehension and consider using visual aids, such as flow charts. To make the material stick, consider dividing the class into two groups; assign each group one concept (e.g., the independent variable group v. the dependent variable group). Ask them to list factors that identify their unique group and have the students engage in a mini debate about their relative value.

A Meaningful Paragraph (Jordan, 2008)
This short assignment can be posed two or three times during the semester. Created by the entomologist Elaine Backus, writing a meaningful paragraph involves crafting a paragraph that coherently incorporates several key terms. For example, ask students to write a paragraph using the following terms: population, sample, data and variable (Holmes, 2011). Ask them to couch the paragraph in a real context (e.g., in reporting on a recent study) that demonstrates they understand the relationship between these concepts. To grade, assign 1 point for each concept that was clearly explained.

Six O’clock Evening News Assignments (Beins, 1993)
How often have we heard students ask, “but how is this used in the real world?” Nip this line of questioning in the bud by providing students with a data set, asking them to perform the appropriate statistical analyses to answer the empirical question and then prepare a one-page press release that is entirely free of statistical terminology. Ask them how they would present this information on the six o’clock evening news. Setting the expectation that they are writing for the general public will help them minimize jargon and realize their role as daily consumers of statistical information.

Formal writing assignments to improve statistical reasoning skills
Many statistics courses include a formal paper assignment that involves conducting or proposing an experiment and writing an APA-style laboratory report. Stromberg and Ramanthan (1996) found that while poor grades in such assignments were at times related to students not understanding the material, more often, grades suffered because students did not read the instructions carefully, presented opinions rather than arguments, and failed to formulate facts into a coherent thesis. To address these issues, here are several tips:

1.  Improve students’ comprehension of empirical journal articles by providing a      worksheet that helps guide them through the process (Dunn, 1996). For example, enumerate several concepts they should identify throughout the paper: motivation/rationale, hypothesis statements, proposed methods to test aims, main statistical results, discussion of results couched in terms of significance etc. Provide a skeleton outline that they can complete with this information to help them become more familiar with the process of reading empirical articles.

2.  Scaffold the assignment through having students complete a skeleton outline of the paper. This will be worth 10 points of the final paper. Craft careful and thorough prompts to help them complete each section. Do not leave your students guessing about what kinds of answers you are seeking. Identify which sections should include numbers and which should be relatively free of statistical jargon. Provide feedback in the form of reflective prompts for incorrect answers (e.g., “What makes this the dependent variable? Is it being manipulated or measured?”).

3.  Spend one class session engaging in peer evaluation to review first drafts. Have students bring 2 copies of a draft to class. They submit one copy to the instructor for 1 point. The other copy is swapped with classmates. Provide students the same evaluation rubric you plan to use for grading and ask them to grade one another’s work. Award 1 point for completing a thoughtful evaluation of peers’ work. Peer evaluations have been shown to minimize the likelihood that students lose points for basic mistakes (e.g., not reading the instructions carefully) (Stromberg and Ramanathan, 1996). It also gives students a sense of their peers’ performance, which may be reinforcing for strong students or motivating for weaker students. Finally, it teaches students the process of writing more than one draft.

Self-Reflection to Alleviate Anxiety
Holmes (2011) proposes assigning a journal to students at the outset of a statistics class where they can engage in reflection on their progress in the course. By writing about their worries, particularly before exams, they are more likely to identify the areas where they are having the most difficulty and dedicate more time to studying those topics. They can also reflect back on their progress, noting whether their fears before exams and assignments were reasonable based on their performance or else catastrophized. Encouraging students to occasionally share their reflections will model that they are not alone in their anxiety and perhaps facilitate better class cohesion.

In summary, writing is a powerful tool for improving student outcomes, particularly in classes that have a negative stigma. Incorporating low-stakes informal assignments and scaffolded, clear and meaningful formal assignments will help foster greater depth of processing, organize related concepts into clear networks, and define how statistics can fit into a larger network of ideas reflected in the real world.

 

References:

Beins, B. C. (1993). Writing assignments in statistics classes encourage students to learn interpretation. Teaching of Psychology, 20(3), 161-4.

Dunn, D. S. (1996). Collaborative Writing in a Statistics and Research Methods Course. Teaching of Psychology, 23(1), 38-40.

Holmes, K. Y. (2011). Tips for incorporating writing into an introductory statistics course. Association for Psychological Science Observer, 25(1). https://www.psychologicalscience.org/observer/tips-for-incorporating-writing-into-an-introductory-statistics-course

Jordan, J. (2008). Writing assignments in an introductory statistics course. In CAUSE Teaching and Learning Webinar Series; May 13, 2008. https://www.causeweb.org/ webinar/teaching/2008-05/.

Stromberg, A. J. & Ramanathan, S. (1996). Easy Implementation of writing in introductory statistics courses. The American Statistician, 50(2), 159-63.