Preparing Teachers of Statistics: A Course for Graduate Students

and Future Teachers Joan Garfield and Michelle Everson

University of Minnesota

Overview• Discuss issues and challenges in preparing teachers of

statistics at the secondary and college level. • Present a case study of a graduate level course taught

at the University of Minnesota that:– Focuses on developing excellent teachers of statistics– Is based on the GAISE guidelines– Helps students develop both knowledge of teaching

(pedagogical knowledge) and specific knowledge about teaching statistics (pedagogical content knowledge).

• Explain how the course was transformed from a face-to-face setting to an online environment.

Challenges in Preparing Graduate Students to Teach Statistics

“Changing our understanding of what constitutes effective pedagogy, improving the use of technology, and placing an emphasis on working with data in elementary courses raise the standard that teaching assistants must meet. … Training programs should themselves be models of good pedagogy” (Moore, 2005, p. 1)

• Training programs in statistics departments

(Harkness & Rosenberg, 2005; Froelich et al., 2005)

• Few graduate courses for credit (e.g., Gellman, 2005)

Training vs. Development• TA Training: Prepares good teaching assistants to

assist faculty and teach recitation sections• TA (Teacher) Development: developing knowledgeable,

competent teachers of statistics.

EPSY 5271

• A teacher development course at the University of Minnesota– Unique graduate course offered yearly since

2002– “Becoming a Teacher of Statistics,” regular

and online– Serves graduate students across all

departments and teachers in the community

Goals for Students in EPSY 5271

– Develop into competent and effective teachers of statistics

– Become part of the statistics education community and utilize good resources

– Develop an awareness of and appreciation for the research, scholarship and best practices in the field

Goals in Teaching EPSY 5271– Model an effective and positive statistics

classroom. Teach the way we want the students to teach.

– Create a learning environment for developing a deep and meaningful understanding of statistics and help the teachers develop their ability to create this type of environment for students.

– Be a facilitator of learning by providing resources and activities and encouraging discussion and reflection.

What is needed to be an effective teacher of statistics?

• Teachers should: – Know their subject matter at a deep level

(content knowledge)– Have good teaching skills (pedagogical

knowledge)• Pedagogical content knowledge (PCK,

Schulman,1986) is also essential to promote student learning

Preparing Teachers for a Changing World, Darling-Hammond and Bransford ( 2005)

– The importance of preparing teachers to go beyond “covering the curriculum”

– Those who prepare teachers are encouraged to build on the growing knowledge base on learning and teaching to support teachers in meeting these demands.

– A model of professional practice that includes knowledge of subject matter and curriculum goals, knowledge of learners, and knowledge of teaching (the subject matter).

• Assume most graduate students preparing to teach introductory statistics have knowledge of the subject matter, they also need knowledge of curriculum, learners, and knowledge of teaching (both in general and specifically, of teaching statistics).

• Our course is designed to help prepare future teachers of statistics to become knowledgeable about each of these areas.

About the Course• A graduate-level semester long course

that met once a week for three hours at a time

• Each offering of the course has enrolled a variety of students representing different disciplinary backgrounds and teaching experiences.

• Students have had required textbooks (Moore, 2001; Gelman & Nolan, 2002) as well as weekly assigned readings.

Alignment with GAISE• Course is organized around the GAISE

recommendations.– Emphasize statistical literacy and develop statistical thinking;– Use real data;– Stress conceptual understanding rather than mere knowledge of

procedures;– Foster active learning in the classroom;– Use technology for developing conceptual understanding and

analyzing data;– Use assessments to improve and evaluate student learning;

• Readings and activities each focus on one if the guidelines.

• Each session or set of sessions are on a particular guideline.

Weekly Topics Introduction and Overview• Discussion of experiences learning and teaching statistics• Discussion of activities for a first day of class, types of first and

second courses• Introduction to the new and emerging field of statistics education• Introduction to GAISE recommendations

Use of real data

• Discussion of what statistics is and EDA is, how EDA is reflected in introductory statistics courses

• Discussion of importance of data, good data sets, how to use them and obtain them, how to explore them using statistical software

Weekly Topics Stress conceptual understanding rather than mere knowledge of procedures•Discussion of research on teaching and learning statistics•Introduction to Sampling SIM, causeweb.org

Emphasize statistical literacy and develop statistical thinking•Defining, teaching, and assessing statistical literacy, reasoning and thinking•Focusing on learning outcomes•Discussion of models and simulation

Weekly Topics Foster active learning in the classroom • Discussion of different teaching methods: Active

learning, cooperative groups, lab approaches• Discussion of what makes a good activity; students

spend time critiquing and improving different activities

Technology• Discussion of abstract concepts that technology can help

students visualize• Exploration of websites, web software, online courses,

and more

Weekly Topics

Assessment• Discussion of ways to develop tests for different

learning outcomes and concepts• Exploration of the ARTIST website• Discussion of student projects, critique of

different product guidelines and review of sample project ideas

• Discussion of assessment rubrics

Weekly TopicsA Statistical Reasoning Learning Environment (SRLE)•Discussion of what the SRLE is•Crafting lesson plans and activities for the SRLE

Innovative courses and projects•Discussion of AP statistics, ISCAM, CHANCE, AIMS, and online courses

Weekly Topics The Statistics Education Community• Students learn more about where the statistics

education field has been and where it is going• Discussion of different publications, journals,

organizations, conferences, websites, CAUSE, ASA, IASE, SRTL

• Discussion of ways to get involved in the statistics education community

Final weeks: Student Presentations

• Data set• Web resource• Group lesson plan

Assignments and Assessments• Presentation of a web resource

– Students find and share a favorite web resource that can be uses to support student learning in a unique way in a statistics course.

• Presentation of a data set– Students find a data set that interests them (one that

includes at least two variables and has both quantitative and categorical variables) and spend time exploring it and learning as much as they can about it. The data set is then shared with the class and discussion revolves around how the data set can be used in an introductory course.

Assignments and Assessments

• Group Lesson Plan Project– Students work in small groups to develop a

detailed lesson plan for one day in an introductory statistics course.

Assignments and Assessments

• Reflection Papers (4)– Their experiences as a student of and possibly

teacher of statistics– Observing a class period in a first course of

statistics– Reading, summarizing, and critiquing three

articles about teaching and/or learning statistics– Reflecting on the course and discussing the kind

of teacher they would like to become

Promoting Classroom Discourse

• Another important goal for the teachers in our courses is to develop an appreciation for the value of classroom statistical discourse. This is different from teachers asking questions and students responding. The kind of discourse we promote is dialogue where students learn to question each other, respond to each other’s questions as well as defend their answers and data-based arguments. The use of good activities and technology allows for a new form of classroom discourse.

Effective Classroom Discourse

• We try to model ways to create a classroom climate where our teachers feel safe expressing their views, even if they are tentative. We encourage them to express their conjectures, and ask other teachers to comment on these conjectures. Allowing questions that begin with “what do you think” or “what would happen if” can lead to good class discussions.

Challenges in the Online Class

• Desire to accommodate more students • Adapting from face-to-face• Changing activities and assignments• Role of discussion and promoting

discourse• A success, but changes will be made

Evaluating the Course• Midterm feedback • End of course evaluation

– Students in the course typically report on how amazed they are at the vast set of resources available for teachers of statistics and how appreciative they are of the course and what it offers them as future teachers.

• End of Course Reflection paper – Teaching philosophy statement that usually

documents their integration of course learning goals. • These statements suggest that the students in the course

take the teaching of statistics very seriously, have expanded their knowledge of statistics education, and have developed their awareness of good teaching and resources for teaching and learning statistics.

Success Stories• Participation in Stat Chat• Teaching awards• Academic positions after grad school• After course feedback of great success in introducing

activities into their classes and encouraging their colleagues to also enroll in this class.

• Six students from this course attended the US Conference on Teaching Statistics (USCOTS)

• In summary, the course appears to be succeeding in developing knowledgeable, competent, and enthusiastic teachers of statistics.

Summary• Unlike some of the teaching assistant training

courses or programs that focus primarily on administering large sections of introductory statistics, this course strives to prepare teachers to understand the challenges involved in helping students develop important learning outcomes,

• Focus on developing both pedagogical knowledge and pedagogical content knowledge.

Summary

• We continue to evaluate and revise our classes as we teach them each year.

• We hope more faculty will explore ways to develop courses for pre-college and postsecondary teachers and encourage them to consider the different types of knowledge needed by competent teachers of statistics.

Summary

• Moore (2005) offers four recommendations for preparing graduate students to teach statistics: – Borrow from existing programs,– Model good instructional practices,– Provide students with written materials to

study and carry away with them, and – Evaluate how well you are doing.

Summary• We concur with these recommendations, and are

happy to share our course materials with others who want to develop such a course:

– Lists of required and recommended readings, assignments, assessments

– Evaluation methods

• We encourage faculty who have the opportunity to work with graduate students interested in teaching statistics to consider developing and offering a course that goes beyond training to developing excellent teachers of statistics.

References

• Chance, B., Ben-Zvi, D., Garfield, J., & Medina, E. (2007, October). The role of technology in improving student learning of statistics. Technology Innovations in Statistics Education Journal, 1(1). Available: http://repositories.cdlib.org/uclastat/cts/tise

• Darling-Hammond, L., & Bransford, J.(2005). Preparing teachers for a Changing World. John Wiley and Sons.

• Cobb, P., & McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 375–396). Dordrecht, The Netherlands: Kluwer Academic Publishers.

References (cont’d)

• Franklin, C., & Garfield, J. (2006). The Guidelines for Assessment and Instruction in Statistics Education (GAISE) project: Developing statistics education guidelines for pre K-12 and college courses. In G.F. Burrill, (Ed.), Thinking and reasoning about data and chance: Sixty-eighth NCTM Yearbook (pp. 345-375). Reston, VA: National Council of Teachers of Mathematics.

• Froelich, A, Duckworth, W., Stephenson, W.R. Training Statsistics Teachers at Iowa State Universeity. The American Statistician. 59 (12), 8-10

References (cont’d)• Garfield, J. (Ed.). (2005) Innovations in teaching

statistics. Washington, DC: Mathematics Association of America.

• Garfield, J., & Ben-Zvi, D. (2005, May). A framework for teaching and assessing reasoning about variability. Statistics Education Research Journal, 4(1), 92-99. Retrieved December 26, 2006, from http://www.stat.auckland.ac.nz/~iase/serj/SERJ4(1)_Garfield_BenZvi.pdf

• Garfield, J. & Ben-Zvi, D. (2008). Developing Students’ Statistical Reasoning: Connecting Research and Teaching Practice. Springer.

References (cont’d)• Gelman, A. (1994). A course on Teaching Staiststics at

the University level. The American Statistician. 59 (12), 4-7

• Gelman, A., & Nolan, D. (2002) Teaching Statistics: A Bag of Tricks. Oxford University Press.

• Harkness, W., & Rosenberg, J. (2005)Training Graduate Students at Penn State University to Teach Statistics. The American Statistician. 59 (12),11-14.

• Moore, D. (2005). Preparing graduate students to teach statistics: Introduction. The American Statistician. 59 (12),1-3.