Guessing Answers to Pass a 5-item True False Test: Solving a Binomial Problem Three Different Ways

A binomial problem is examined through the use of three methods: a classical approach using the binomial formula, Pascal’s Triangle, and a frequentist approach using a Fathom ™ simulation. Using both physical and virtual coins, students explored the distinction between a coin-sequence and a coin-combination (where the order is not important) as a foundation for a 5-item True False test task. Pedagogy was based on general principles identified by probability education research as best practice and by Ma (1999), who emphasised deep understanding of concepts through the use of multiple approaches to problem solving. The Binomial Theorem is a well established topic in the senior high school curriculum. Normally taught using the binomial formula and Pascal’s Triangle, a computer simulation has the potential to offer an additional perspective and method of problem-solving. The study examined students ’ responses to a binomial problem using the three methods of the binomial formula, Pascal’s Triangle, and a Fathom ™ simulation, and whether the use of a multiple-method approach that included electronic simulation may assist student learning. Three student tasks from a two-week study are presented. The physical and virtual “Coin-sequence ” and “Coin-combination ” tasks provided an opportunity fo