Based on their belief that children in grades 3-5 possess the ability to make conjectures and have intuitions about probability and chance, Edwards and Hensien (2000) undertook three probability experiments with children. Their research aim was to determine whether mathematical concepts come to light naturally through students’ guesses or hunches about chance and probability; their lesson aims were for students to form an idea of “equally likely events’, assign a theoretical probability to events, and relate the theoretical probability of an event to the observed relative frequency of that event during the experiment” (p.525).
Twenty four fifth grade students were selected as subjects for the experiments, and were divided into 6 equal groups of 4, with each group working on 3 problems with “equally likely outcomes” (p. 525). Each group were required to work on 2 problems (flipping a coin and spinning a spinner with three colours) 25 times and the other (tossing a number cube) 30 times, resulting in a total of 150 or 180 recurrences of each experiment respectively, ensuring each figure could be divided by the number of potential outcomes.
Through discourse between the teacher and students as a class, and small group discussions, the students were able to perceive the concept of events that are equally likely, and were confident and at ease in using numbers to articulate chance; through elicitation and manipulation the teacher was able to introduce concepts of theoretical probability, closeness, fair chances, and experimental chance as probability.
Finally, the teacher evaluated their learning by setting a writing task, which illustrated differences between students; for example, by using numbers from one of the experiments some were able to correctly express the number of chances an event could happen; others thought it could happen only once in a total figure; yet others overgeneralized in the belief that there is equal chance for every event. The teacher however, had prepared a follow up lesson that would eliminate all false assumptions.
The benefits of utilizing such experiments as a means of exploring probability are quite obvious in that they allow students to work things out for themselves rather than the teacher providing the information. Teaching today focuses on student centered classrooms and this approach to teaching chance and probability adheres to that philosophy very well; it also takes account of the different learning styles of students and allows for individual learners to capitalize on their preferred learning styles and strategies.
Such an approach could be used to help upper-elementary students embark on the exploration of probability but it may be more appealing and thus more conducive to their learning to combine such experiments with simple probability issues or topics pertaining to everyday science that are specifically relevant to students.
An alternative would be a game such as ‘Rescue Mission’ (Illuminations) wherein students conduct a probability experiment with spinners and document results in tables and bar graphs, and use their findings to choose spinners with the maximum probability of assisting them to win the game; in doing so they learn about flight and its forces, such as drag, lift, weight and thrust.
The three experiments conducted by Edwards and Hensien (2000), although termed as experiments, illustrate how teachers can utilize activities that allow students to work through problems in a natural and logical way; many games and activities adopt the same principles and can be used within a math classroom to foster and nurture meaningful experiences for students that draw on their instincts and hunches that in turn assist them in making calculated guesses.
References Edwards, T. G. & Hensien, S. M. (2000) Using probability experiments to foster discourse, Teaching Children Mathematics, vol. 8 (8) 524-529 Illuminations (n. d. ) Rescue mission game, Retrieved 6 July, 2010 from http://illuminations. nctm. org/LessonDetail. aspx? ID=L296