Becoming
a Teacher of Statistics
Portfolio
by
Susan
Sexton
Probability and Statistics for Secondary
Teachers
STAT 6070
University of Georgia
Fall 2007
Instructor: Christine Franklin
Recommendation 2: Stress conceptual understanding rather
than mere knowledge of procedures.
Konold, C. (1995). Issues in assessing conceptual understanding in probability and statistics. Journal of Statistics Education, 3, Article 1. Retrieved October 23, 2007, from http://www.amstat.org/publications/jse/v3n1/konold.html
Abstract:
Research has shown that adults have intuitions about probability and statistics that, in many cases, are at odds with accepted theory. The existence of these strongly-held ideas may explain, in part, why learning probability and statistics is especially problematic. One objective of introductory instruction ought to be to help students replace these informal conceptions with more normative ones. Based on this research, items are currently being developed to assess conceptual understanding before and after instruction.
Konold addresses a familiar topic to all educators: addressing conceptual understanding. He bases his discussion on 15 years of research into Òstudent understandings of various probabilistic and statistical conceptsÓ (para 1). Traditional means of assessment is not enough in ascertaining studentsÕ understanding of material and statistics and probability is no exception. However, the concepts of statistics and probability pose a unique problem in assessing student understanding in that students already have preconceived understanding of concepts that are markedly and intuitively different than Òaccepted probability and statistical theoryÓ (para 1).
Konold finds it difficult to alter studentsÕ thinking and understanding of concepts for those students whose intuitions are in direct conflict with statistical theory. He discusses the constructivist view that students come to statistics with prior knowledge. He charges instructors with the responsibility to build on that knowledge. However, Konold has also found that assessing conceptual understanding is difficult and emphasis on procedural knowledge is not the avenue in which to take. Without Òtesting for conceptual understandingÓ Konold realized that he would have felt that Òthe curriculum [he] designed was magnificentÓ (para 22). Stressing conceptual understanding, rather than procedural knowledge, is one of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) recommendations. Both Konold and the authors of the GAISE report acknowledge that emphasizing conceptual understanding is a difficult undertaking and can prove to be ÒpoliticallyÓ (GAISE, 2005, p. 10) challenging.
Corresponding
with the GAISE
recommendation, Konold asserts that traditional forms of assessments (e.g.
tests and quizzes) Òassess competencies at the most rudimentary levelÓ thus
Òthe teacher inadvertently leads students to believe that routine skills and
memorized formulae are the important stuffÓ (para 24). Furthermore, the GAISE assessment
recommendation also claims, ÒStudents will value what you assessÓ (GAISE, 2005, p.13). Thus
setting up a learning environment that not only stresses but assesses
conceptual understanding will provide Òstudents with
a good conceptual foundationÓ so that they Òare well-prepared to go on to study
additional statistical techniques in a second course such as research methods,
regression, experimental design, or statistical methodsÓ (GAISE, 2005, p. 10).
In
illustrating his point on studentsÕ preconceived statistical and probabilistic
understanding, Konold provides two examples of how students do not understand the
concept of probability. In one example, he has found that many college students
understand a weather forecast to be a stated outcome rather than a
distribution. Undoubtedly students have been exposed to weather forecasting
considering that forecasting weather dates back before the invention of Doppler
radar systems; even before the farmerÕs almanac. Understanding how the weather
forecast is determined has probably never been formally discussed, just
constructed in the mind of a child as a way to determine the outcome of the
weather for a particular day of the year. Thus students have grown to have a
deeply rooted understanding of what it means to say Ò30% chance of rainÓ that
is in direct conflict with the statistical definition of chance and probability.
Statistics teachers should take the opportunity to discuss statistical concepts with students within those contexts with which students are already familiar (e.g. weather forecasts). Thus teachers can begin to build on this prior knowledge in hopes to alter those conflicting intuitive statistical and probabilistic conceptual understanding, enhance statistical thinking and understanding, and increase statistical literacy.
References
GAISE College Report. (2005). Guidelines for Assessment and Instruction in Statistical Education College Report. Alexandria, VA: American Statistical Association, http://www.amstat.org/education/gaise.
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