Illustrating Probability in Genetics with Hands-On Learning: Making the Math Real

Probability is an essential tool of genetics, and basic concepts of probability are usually included in introductory biology and beginning genetics courses. In spite of the central importance of probability for understanding and analyzing heredity, many students have difficulty with the subject. Part of this difficulty arises out of the quantitative nature of probability and the general problem that many students experience with quantification. Compounding the problem is the abstract nature of probability and statistics. In teaching introductory genetics to large numbers of college undergraduate students (200-250 per semester), we found that largely lecture-based instruction of probability concepts was ineffective; many students were disinterested in the topic and failed to understand and retain important concepts. McManus, Dunn, and Denig (2003) found that biology students who learned using hands-on manipulative activities had higher science achievement and science attitude scores than students who learned using traditional lecture, reading, and discussion activities. Considerable educational research demonstrates that cooperative learning within small groups leads to clear improvements in academic achievement, attitudes towards learning, and persistence compared with more traditional teaching methods in undergraduate science, math, engineering, and technology courses (Springer, Stanne & Donovan, 1999; Tanner, Chatman & Allen, 2003). To facilitate learning of probability for general genetics, we developed hands-on activities in which students in small groups actively and cooperatively learn probability. Teaching probability also can be facilitated through the use of electronic simulations of random events, which allow students to quickly collect large sets of empirical data to illustrate the predications of probability theory. A number of accessible and user-friendly Web-based tools are now available to simulate random events, such as tossing coins, rolling dice, and drawing cards from a deck (Table 1). Simulations of random events can also be produced through simple calculations performed by spreadsheets that are available on most personal computers. We have created four such spreadsheet-based simulation programs to accompany the probability exercises outlined in this article (Table 1, Figure 1); these are available free from the authors upon request. We believe that this combination of cooperative learning in small groups, with manipulative activities, and student-collected simulation data greatly enhances student interest in and understanding of basic concepts of probability. After we developed a laboratory exercise in probability based on manipulative activities and small group learning, approximately 70% of our students in an in-house survey agreed that this exercise was "helpful in understanding concepts taught in the lecture portion of the course. " The following laboratory exercise is appropriate for high school biology or advanced placement biology classes, as well as introductory college biology or genetics courses. Goals & Background We had four primary objectives for our students: 1. to understand the nature of probability and how it can be used to make predictions about the outcomes of genetic crosses 2. to understand and be able to apply the addition and multiplication rules of probability 3. to understand and be able to apply the binomial expansion to problems involving multiple outcomes 4. to know how to interpret probabilities associated with the chi-square test. [FIGURE 1 OMITTED] The addition and multiplication rules of probability are useful for calculating risk of inheriting genetic diseases as well as predicting the outcome of Mendelian crosses. For example, consider the following cross: AaBb x AaBb. One can quickly determine the probability of obtaining progeny with genotype aabb by using the multiplication rule. …