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A great visual for Probability…not on the blog…just this picture

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FIDGET SPINNERS IN THE CLASSROOM STEM PROJECT

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Fidget spinners in the classroom driving you crazy? Learn how to put a positive "spin" on the fidget spinner trend with activities and free resources!

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1. Commutativity confusion. Students may think two girls and one boy is one possible out- come. But notice that if you list the eight possible combinations for three children, you have three girls only once (GGG), but two girls and one boy three times (GGB, GBG, BGG). Two girls and one boy is three times as likely. We refer to this as commutativity
confusion because students, knowing that 3 + 4 is the same as 4 + 3, think that that one boy and two girls is one event, not three. Students need to think about all the ways an event can occur when they try to determine how likely an event is.
2. Gambler’s fallacy. The gambler’s fallacy is the notion that what has already happened (two girls) influences the event. Students will argue a boy is more likely because there are already two girls. Similarly, students think that if a coin has had a series of 4 heads, it is more likely on the fifth flip to be tails (Ryan & Williams, 2007). But a coin has no memory, and the probability of heads or tails is still fifty-fifty, just as the probability of a girl is still fifty-fifty.
3. Law of small numbers. This misconception is like the gambler’s fallacy in that it relates to small samples but, with this misconception, students expect small samples to be like the greater population (Flores, 2006; Tarr, Lee, & Rider, 2006). This is discussed previously in the section “The Law of Large Numbers” (see Activities 22.11 and 22.12). So in the case of the three girls, it is not so unusual—it is just a very small data set, so it is not likely to resemble the larger population.
4. Possibility counting. In this case, students see what the possibilities are and assume each is equally likely. If a dice has a 1, 2, 3, then each has a 1 chance of occurring. Similarly, if a 3 spinner has a red and blue section, then each has a fifty-fifty chance of occurring, even if
there is more red on the spinner than blue. Activities 22.3, 22.4, and 22.5 are designed to help students focus on frequency rather than possible outcomes in determining probabil- ity of an event.