|Preparing to Teach Statistics
by Joan Garfield
University of Minnesota
||Practical Advice for New Teachers
What do you need to learn in order to be a good teacher of statistics? I've thought about this quite a lot in designing and teaching a new course at the University of Minnesota called "Becoming a Teacher of Statistics." This course is for teachers of introductory statistics at the high school and college level. I think it's important for those preparing to teach statistics to build on a strong understanding of statistics, especially applied statistical methods. However, knowing statistical content is not enough to be a good teacher, because there are so many challenges involved in teaching students.
Some of the challenges include these:
Given the challenges listed above, it is often a daunting task to prepare to teach a first course in statistics. Not only do teachers need a good understanding of statistics, they also need to develop pedagogical knowledge of how to teach statistics. That is what I try to provide in my course. Some of the topics that are included in this course are listed below, with references provided:
- Many statistical ideas and rules are complex, difficult, and/or counterintuitive. It is often difficult to motivate students to engage in the hard work of learning statistics.
- Many students have difficulty with the underlying mathematics (such as fractions, decimals, and algebraic formulas), and that difficulty interferes with learning the related statistical content.
- The context in many statistical problems may mislead the students, causing them to rely on their experiences and often faulty intuitions to produce an answer, rather than select an appropriate statistical procedure.
- Students equate statistics with mathematics and expect the focus to be on numbers, computations, and one right answer. They are uncomfortable with the messiness of data, the different possible interpretations based on different assumptions, and the extensive use of writing and communication skills.
- The language used in statistics includes many familiar words but with different or more precise meanings than students use. For example: normal, random, sample, average, variable, and distribution are introduced to students as new vocabulary words with statistical definitions, yet students often resort to their own familiar interpretations of these terms.
Recommendations on Teaching Statistics
There have been some important and influential papers written regarding teaching statistics. Some of these papers, by key statistics educators, include Cobb (1992), Moore (1997), and Scheaffer (1997). The recommendations in these papers discuss the role of using data and emphasizing concepts rather than computations, focusing more on applications and less on theory, and incorporating technology and active learning in statistics classes.
The Big Ideas of Statistics
Teachers must understand the big ideas of statistics: what they are and how to help integrate and highlight these ideas in a first statistics course. Some of these ideas are concepts, such as variability, distribution, trend, and model. Others are understandings, such as distinguishing causation from correlation, practical significance from statistical significance, and finding no effect from finding no significant effect (Utts 2003).
Data and Data Analysis
This topic includes the importance of data; types of data; how, when, and why to use data in teaching statistics; and good sources of data (e.g., Robin Lock's Web page, which, like many of the Web sites mentioned in this article, can be found below in "See also"). For good papers on data analysis, see Velleman and Hoaglin (1992) and section 2, "Teaching with Data," in Moore (2001).
Selecting and Evaluating Textbooks
It is important to know what to look for in choosing a textbook, characteristics of good textbooks, and how to best use them with students (e.g., how to get students to read their textbooks). For more information on selecting and evaluating textbooks, see section 4, "Textbooks," in Moore (2001) and Cobb (1987).
Technology for Teaching and Learning Statistics
Technology includes calculators and statistical software to graph and analyze data, as well as special types of software (e.g., Web applets, simulations) to illustrate abstract ideas. For example, the Sampling Sim software for illustrating sampling distributions and confidence intervals can be found online. For more information on technology, see section 5, "Technology," in Moore (2001) and Garfield, Chance, and Snell (2000).
Activities and Active Learning
There are many wonderful activities available, for example, see section 3, "Established Projects in Active Learning," in Moore (2001). These resources help guide instructors to effectively use activities in their statistics classes. This is important, because there is an art to using activities in a way to promote student learning and not just to give students an enjoyable experience during class. For other resources on activities, see the STAR Library, the Journal of Statistics Education, and Teaching Statistics.
What do we want students to understand and be able to do when they leave a first course in statistics? One way of describing these learning outcomes is to think of them as statistical literacy (understanding basic terms, graphs, and symbols and being able to interpret statistics in the media), statistical reasoning (understanding and being able to explain statistical processes and being able to fully interpret statistical results), and statistical thinking (understanding why and how statistical investigations are conducted and the "big ideas" that underlie statistical investigations). For papers that describe each of these learning outcomes, see Chance (2002), Garfield (2002), and Rumsey (2002).
Assessment of Student Learning
We need appropriate ways to assess students, to provide feedback to students and teachers to help improve student learning. Also important are student projects, different types of project assignments, ways to use projects effectively, and how to evaluate students' projects. For more assessment information and resources, see the Web ARTIST site.
Research on Teaching and Learning Statistics
The research literature includes studies that describe difficulties students have learning statistics and ways that statistical reasoning and thinking develop. For summaries of this research, see Garfield (1995) and Shaughnessy (1992). See also the new IASEStatistics Education Research Journal.
The Statistics Education Community
The statistics education community includes professional organizations. These include the American Statistical Association Section on Statistical Education, the International Association for Statistical Education, conferences (Joint Statistics Meetings, International Conference on Teaching Statistics, Beyond the Formula), and journals (Teaching Statistics, Journal of Statistics Education, STATS magazine).
The field of statistics education is a rather recent one, but one that is rapidly growing (see Scheaffer, 2001). As more and more students enroll in statistics classes, there will be an even greater demand for people to teach classes in introductory statistics at the high school and college level. I hope to see more courses develop and made available that are designed to prepare teachers of statistics.
Chance, B. L. 2002. Components of statistical thinking and implications for instruction and assessment. Journal of Statistics Education (online) 10 (3).
Cobb, G. W. 1987. Introductory textbooks: A framework for evaluation. Journal of the American Statistical Association 82: 321-39.
Cobb, G. 1992. Teaching statistics. Heeding the Call for Change: Suggestions for Curricular Action. Edited by L. A. Steen. (Washington, D.C.: Mathematical Association of America) MAA Notes no. 22: 3-43.
Garfield, J. 1995. How students learn statistics. International Statistical Review 63: 25-34.
How Students Learn Statistics
Garfield, J. 2002. The challenge of developing statistical reasoning. Journal of Statistics Education (online) 10 (3).
Garfield, J., B. Chance, and J. L. Snell. 2000. Technology in college statistics courses. The Teaching and Learning of Mathematics at University Level: An ICMI Study. Edited by Derek Holton, et al. (Kluwer Academic Publishers).
Technology in College Statistics Courses
Moore, D. S. 1997. New pedagogy and new content: The case of statistics. International Statistical Review 65: 123-37.
New Pedagogy and New Content (.pdf)
Moore, T., ed. 2001. Teaching Statistics. (Mathematics Association of America) MAA Notes no. 52.
Rumsey, D. J. 2002. Statistical literacy as a goal for introductory statistics courses. Journal of Statistics Education (online) 10 (3).
Statistical Literacy as a Goal for Introductory Statistics Courses
Scheaffer, R. L. 1997. Discussion. International Statistical Review 65: 156-58.
Scheaffer, Richard L. 2001. Statistics education: Perusing the past, embracing the present, and charting the future. Newsletter for the Section on Statistical Education 7 (1).
Statistics Education: Perusing the Past, Embracing the Present, and Charting the Future
Shaughnessy, M. 1992. Research in probability and statistics: Reflections and directions. Handbook of Research on Mathematics Teaching and Learning. Edited by A. Grouws. 465-94.
Utts, J. 2003. What educated citizens should know about statistics and probability? The American Statistician 57 (2): 74-79.
Velleman, P. F., and D. C. Hoaglin. 1992. Data analysis. Perspectives on Contemporary Statistics. Edited by D. Hoaglin and D. Moore. (Mathematical Association of America) MAA Notes no. 21: 19-39.
Joan Garfield is a professor of educational psychology at the University of Minnesota, where she heads a new graduate program in statistics education. She has taught statistics for 23 years at the undergraduate and graduate level, and has published several articles about teaching statistics and research on how students learn statistics. She is the editor or co-editor of four books, including The Assessment Challenge in Statistics Education and The Challenge of Developing Statistical Literacy, Reasoning, and Thinking. She is a fellow of the American Statistical Association and associate director for research of the Consortium for the Advancement of Undergraduate Statistics Education (CAUSE).