Development of a Tutoring System for Probability Problem-Solving

MF01/PC01 Plus Postage. College Students; *Computer Arsisted Instruction; Higher Education; *Intelligent Tutoring Systems; Mathematical Concepts; *Probability; *Problem Solving; Programmed Tutoring; Statistical Analysis; *Statistics; Tutorial Programs; Tutoring Interpreting information regarding health risks, crime statistics, and government polls requires some ability to use and interpret probabilities. Studies have shown that even after training or coursework in probability and statistics, people still have many difficulties solving probability problems. The thesis of this document is that helping students develop more efficient schema for solving probability problems will improve their performance on such problems, subsequently leading to a stronger and more lasting ability to use and interpret probabilistic information normatively. A proposed seven-step instructional model provides a description of steps involved and knowledge required for successful solution of many different types of probability problems. A computerized tutoring system which incorporates the model, investigates its success as an instructional aid in teaching and learning elementary probability concepts and procedures. A formative evaluation of the system was undertaken, but is not reported in this document. The development of the system, a description of the evaluation process, and future goals are reported. Additional information includes a table of type and frequency of observed errors in probability problem solving (n=50); a copy of the form used in evaluation, and a visual example of the computer program. (JBJ) ****************************************************** . **Mr Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** Development of a Tutoring System for Probability Problem-Solving by Ann Aileen O'Connell and Linda Bol University of Memphis t I t./1 PAM lit Nt (II I DuLAtior, IRA AlIt INAL RESOURCE t; INf ORN1AT ION CUNTFF1iER1Ct IT thi . do. umonl ha, holm reproduced a.. ret ed Itan the JIM...MI 0 all:la/awn 0111110.1111111 II 13 Miter Tilana... have Inn, made to Ill rtnc plain) bnn quallty P01011. of View 01 01,11110111) 1,1.111'd In 1111.. (10c do 1101 1101 reptet.rnt T din rai lir anit,on ITT part y PERMISSION TO REPRODUCE THIS MATERIAL HAS BEEN GRANTED BY L . bot. TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERICI Development of a Tutoring System for Probability Problem-Solving Ann Aileen O'Connell Linda Bol University of Memphis Paper presented at the Annual Meeting of the American Educational Research Association April 18-22: San Francisco, CA. Introduction An understanding of basic concepts regarding probability is essential in our society. Interpreting information regarding health risks, crime statistics, government polls, the likelihood of natural disasters such as earthquakes or hurricanes, all require some ability to use and interpret probabilities. Extensive research documents the existence of biases in people's reasoning about probability and probabilistic events (Tversky and Kahneman, 1974, 1983; Garfield and Ahlgren, 1988; Konold, 1989). Studies have also shown that even after training or completion of a formal course in probability and statistics, people still have many difficulties solving problems that require the use of probability or in making informed decisions under uncertainty (see, for example: Shaughnessy, 1981; Tversky and Kahneman, 1983). Therefore, preparing students for their future in education, business, the social sciences, biology, etc., and enabling them to become informed citizens and consumers would be facilitated if the process of teaching and learning basic probability concepts and procedures was better understood. The current project is a continuation of previous work in the area of probability problem-solving, which offered an instructional model for how people typically work towards successful solution during probability problem-solving (O'Connell, 1993a; 1993b). That research also indicated that nearly 23% of observable errors in probability problem-solving performance are due to errors in text comprehension, with an additional 45% due to procedural errors. However, many procedural errors result from a misunderstanding of text information. Our present project is based on the belief that helping students develop more efficient schema for solving probability problems would improve their performance on such problems, subsequently leading to a stronger and more lasting ability to use and interpret probabilistic information normatively. We argue that guiding people in the skills required to organize problem information accurately is important to the development of a reliable schema for probability problem-solving. Reasoning during problem-solving is highly dependent on the specific type of problem a subject is working through, since some problems are by nature more difficult than others and may require qualitatively different kinds of laiowledge. The proposed instructional model provides a description of the steps involved and the knowledge required for successful solution of many different types of probability problems. This seven-step model identifies key areas where probability problem-solving is likely to go wrong. The seven steps used in this model and incorporated into our tutoring system are described below: I. Understand the given information. In order to understand the information provided and develop a representation of the problem, or to interpret the given information as a mathematical or probabilistic expression, the student needs to have adequate knowledge of the natural language of probability, as well as an understanding of the concept of probability itself. 2. Identzfy what is being asked (the goal). Identifying the goal statement involves the ability to translate the question being asked into a probability statement suitable for solution to the problem. The student needs to distinguish between the faowing possibilities: is the question asking for a numerical solution to a problem, for the verification of an assumption, or for the verification of a particular formula (i.e., for conditional probability)? In addition, the student must know the meaning of 'at least', 'at most', 'no more than', etc. 3. Develop notation for the given information and the goal statement. C.) This step requires successful completion of steps one and two above, as well as an understanding of the formal, symbolic language of probability in terms of events being described as sets of outcomes. The