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• W41592542 abstract "ABSTRACT Teachers of probability often have to deal with their students' misconceptions that may interfere with instruction. Identifying and addressing these non-standard concepts is an important instructional goal that is often overlooked. The present paper is based on a workshop developed by the author with the objective to inform college teachers about common misconceptions of probability, methods of identifying misconceptions, and approaches and strategies used to correct them. The information included in this paper may be useful for instructors who teach introductory probability or statistics courses, as well as survey courses that have a probability component. A BRIEF OVERVIEW OF SOME PREVALENT MISCONCEPTIONS ABOUT PROBABILITY Students often have idiosyncratic concepts about probability. Many of their non-standard ideas were developed as a result of informal experiences while talking to their parents and friends, listening to the radio, watching television, and playing games of chance. Some ideas were formed as a result of an incorrect interpretation of what they studied in the classroom. These idiosyncratic concepts are often referred to in the literature as misconceptions [7]. What is a misconception? It is not simply a mistake. Mistakes can be made for various reasons, for example, because of a student's carelessness. A misconception is a student's erroneous concept that produces a systematic pattern of errors [7]. For example, a typical misconception in algebra is the belief that cancellation of fractions or rational expressions is simply the removal (crossing out) of what looks identical in me numerator and denominator. A student who holds this erroneous concept of cancellation would keep making the same mistake over and over; he or she will cross out a character common to the numerator and denominator irrespective of whether it occurs in a factor or term. A typical misconception in calculus is the belief mat me tangent line to a curve at point x^sub 0^ is a line that has exactly one point in common with the curve and does not split the curve. Students who hold mis misconception have a 'circle concept image' of tangent. They are likely to fail to identify correctly certain tangent lines mat have more than one common point with the curve or that split me curve. Likewise, students have misconceptions about probability. Common misconceptions include representativeness, the equiprobability bias, outcome orientation, availability, compound approach, confusing independent events with mutually exclusive events, and me conjunction fallacy. Describing all popular misconceptions is beyond me scope of mis paper, so we will limit our discussion to the first three mentioned here: representativeness, the equiprobability, and outcome approach. Representativeness bias is characterized by subjects estimating the likelihood of an event based on how well an outcome represents some aspect of me population. For example, in a family with 6 children the sequence BGGBGB is believed to be more likely than the sequence BBBBBG. The first sequence appears more representative of the nearly 5050 distribution of boys and girls in the population. In general, representativeness is a helpful heuristic used by people to estimate the quality of a sample; however, when misapplied it becomes a misconception. [6] The Equiprobability bias involves attributing the same probability to different events in a random experiment regardless of me chances in favor or against them. For example, when subjects are asked to compare me chances of different outcomes of three dice rolls, they tend to judge as equally likely the chance of rolling three fives and the chance of obtaining exacdy one five. In its most extreme manifestation, me equiprobability bias involves the belief that all random events are equiprobable by nature [3]. Outcome orientation misconception (also called the outcome approach) has its roots in a deterministic way of thinking; subjects do not see the result of a single trial of an experiment as embedded in a sample of many such trials. …" @default.
• W41592542 created "2016-06-24" @default.
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• W41592542 date "2008-10-01" @default.
• W41592542 modified "2023-09-25" @default.
• W41592542 title "Addressing Students' Misconceptions about Probability during the First Years of College" @default.
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