By: Megan Prats

03/15/2015

Problem-solving normally takes the student into the future as problem-solving is usually used to divert a future obstacle. Thus, it is important for the student to use the tool of probability as it quantifies the likelihood of a future event occurring. In short, probability is a rational way for the student to weigh the pros and cons of a hypothetical action to better avoid likely obstacles that will stand in her way.

For the student to adequately use probability in her problem-solving, she must first understand what it is. Probability is “the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences.” Thus, probability
is normally presented in a percent fashion. Because probability is frequently expressed in a vacuum (where circumstance is not factored into the calculations), conditional probability is probably the area of probability that the student will need to be more familiar with as it is more practical. Conditional probability is “the probability that an event will occur, given that one or more other events have occurred.” For instance, there is a greater probability that the student will not advance as quickly in her learning if she doesn’t do her homework than if she does. Thus, if the student wants to progress more quickly, conditional probability motivates the student to change her present behavior (not doing her homework) to avoid the future pitfall of slower progress.

Probability is an area of statistics that can be quite quantitative. However, for our purposes, the student doesn’t have to be well-versed in the quantitative side of probability to be able to use it effectively. If the student can assign ball-park figures to the likelihoods of different outcomes, that should be sufficient to make probability an effective tool in the student’s problem-solving. But, if the customized curriculum calls for it, formulas and more detailed mathematical calculations can be used in developing the tool of probability in the student.

For example, the student uses her critical thinking skills to arrive to several ways in which to express, “I think that Spanish is a beautiful language.”; in Spanish – “Creo que el español es un idioma bonito.” y “Pienso que el español es un idioma bonito.”. Both are grammatically correct
but, the student wants to use her sentence in conversation with her conversation partner. Because her conversation partner is exposed to Spanish as it lives in society, the student will likely be able to convey her meaning more clearly if she chooses the form that is in agreement with everyday Spanish. Because Spanish speakers use “creer” instead of “pensar” to express an opinion, conditional probability tells the student to go with the first sentence.

Probability is a powerful tool to effectively and safely navigate the future. Even though 100% probability doesn’t exist (the future is always uncertain) thus there is always room for error, more times than not, if the student applies probability in a sound way, her future will be a lot brighter. Because critical thinking is the gateway to the infinite realm of knowledge, probability is a tool of the critical thinker that should be used when the critical thinker believes that it’d be best. In order to develop this tool in the student, you should first explain to her what it is, and then teach her how to effectively use it. If the student can use probability to estimate the likelihood of a future event occurring rationally, like in the aforementioned example, it should be enough for her to use the tool effectively.