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# The Last Banana - A New Lesson for Teaching Probability

Updated: Sep 12, 2023

At the end of every year of AP Stats, we give a student survey. One of the questions asks them to identify the topic that was most challenging. The responses have been very consistent over the years: Probability.

## Why is Probability so Challenging for Students?

Too many students are getting through their math and science classes using the wrong approach: identify the right formula or equation, plug in the numbers, get an answer. The problem with this approach is that students rarely pause to make sense of their approach, to think and reason about the given information, or to consider the plausibility of their final answer.

In order to lead students away from a faulty reliance on formulas, we have tried to develop lessons for probability that rely more on thinking and strategies. We challenge students to use strategies like the sample space, Venn diagrams, two-way tables, and tree diagrams before jumping right to the formula approach.

## A Lesson to Get Them Thinking and Reasoning

One of our new lessons in the probability unit (inspired by a presentation we saw from AP Stats all-star teacher Doug Tyson) challenges students to make a decision based on probabilistic intuition. We start by showing them the first 38 seconds of this video:

A good majority of students (incorrectly) choose to be Player 1. What better place for learning than a situation that goes against your natural intuition.

Students will then play the game with a partner (virtual dice here), collect class data (use this Google sheet for remote instruction) and then work their way through the questions in the activity.

## Why We Love this Lesson

Instead of having students copy the statement of the Law of Large Numbers or just giving them a formula for using a sample space to find probabilities, students are engaged in a context that motivates and develops the need for such understanding. This is exactly the philosophy of the Experience First, Formalize Later (EFFL) approach to teaching statistics. Instead of students simply knowing the what, they now know the how and why.

From a technical perspective, this lesson has perfect alignment between the learning targets, the experience, and the formalization that happens when debriefing the activity. While students don't have to know the fancy vocabulary as they work through the activity, there is plenty of opportunity for teachers to introduce these terms (Law of Large Numbers, complements rule, sample space) in the debrief of the activity.

## But What Does This Look Like in A Virtual Classroom?

Check out this asynchronous video we created for our online students to engage in this activity. Hopefully you can pick up some new teaching strategies after watching Lindsey work through the debrief of the activity.

Activity: DOCX / PDF

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