Before looking at research related to learning statistics, it is important to think about how students learn in general. Learning in a course is more complex than merely remembering what students have read or been told, and many of us have found that students don't necessarily learn by having us explain to them how to solve a problem. In fact, it is frustrating to work out a problem elegantly, explaining all the steps clearly, and then find out hardly any of the students understand it.

Many of us have informal learning theories that guide our teaching approaches. Some theories of learning are well defined and have recognizable names such as behaviorism, or cognitivism. In describing how students learn or think, theories of learning serve as a basis for theories of instruction that draw conclusions about how instruction should be carried out (Romberg and Carpenter, 1986). What happens in a particular course can be viewed as an interaction between the teacher's goals for what students should learn, views of students' characteristics and abilities, theory of how students learn, and assumptions about how students should be taught.

A recent theory of learning which has been widely accepted in education communities stems from earlier work by Jean Piaget, and has been labeled ``constructivism." This theory describes learning as actively constructing one's own knowledge (Von Glasersfeld, 1987). Today, this is the guiding theory for much research and reform in mathematics and science education. Constructivists view students as bringing to the classroom their own ideas, experiences, and beliefs, which affect how they understand and learn new material. Rather than ``receiving" material in class as it is given, students restructure the new information to fit into their own cognitive frameworks. In this manner, they actively and individually construct their own knowledge, rather than copying knowledge ``transmitted", ``delivered" or ``conveyed" to them. A related theory of teaching focuses on developing students' understanding, rather than on rote skill development, and views teaching as a way to provide opportunities for students to actively construct knowledge rather than having knowledge ``given" to them.

Theories of learning and instruction interact with teachers' particular goals for what students should learn in their courses. What are the skills and ideas teachers would really like their students to take away from their statistics courses? These goals do not necessarily correspond to what students are asked on quizzes or exams. If teachers were asked what they would really like students to know six months or one year after completing an introductory statistics course, most would probably not respond that students should know how to compute a standard deviation by hand, know how to convert normal variables to standard normal variables and look up their probabilities on the z table, or compute expected values. Many would indicate that they would like students to understand some basic statistical concepts and ideas, to become statistical thinkers, and to be able to evaluate quantitative information. A poignant way to think about this question is to ask ``what would you feel MOST bad about your former students not knowing about after completing a statistics course?"

Wed Jun 29 13:57:26 EDT 1994