# How to Teach Probability & Statistics

Probability and statistics are part of everyday life. Odds and percentages help people make life-changing decisions, from taking out a mortgage to choosing an appropriate medical treatment. Unfortunately, millions of students leave school with an inadequate understanding of statistical concepts, according to the journal "Psychological Science in the Public Interest." This impairs their ability to function in the real world and make wise decisions to protect their futures.

## 1 Emphasize Concepts, Not Processes

Although it's important to teach students how to crunch numbers to find the mean or the standard deviation of a data set, teaching the process of calculation does little to help students grasp important statistical concepts. Instead, instructors should supplement lessons in calculation with instruction in the underlying idea, according to the International Conference on Teaching Statistics. In a unit about measures of central tendency like mean and median, for example, you might ask students to guess mean and median income in their town. Ask what would happen if Bill Gates suddenly moved to town: The mean should skyrocket, while the median will remain unchanged. Use this as a starting point to discuss which measure is more appropriate for different problems.

## 2 Survey the Class

A reliable strategy for getting students interested in statistics is to poll them on their views about relevant issues. If student parking is tough to find, you might survey the class about whether or not seniors should get priority parking access, for instance. After calculating the results of the opinion poll, you can introduce concepts like margin of error. You can also discuss sampling bias and ask students what might happen to poll results if more underclassmen were in the course. By encouraging students to think about statistics as useful tools for thinking about issues relevant to their lives, you'll help students retain knowledge for the future.

## 3 Encourage Gambling

Probability underpins all games of chance, according to statistics professor John Croucher, so a little gambling in the classroom can help students cultivate an understanding of probability calculators. For a basic exercise, take a shuffle deck of cards and invite students to bet on the characteristics of a card drawn at random. Reward students with 2-to-1 odds for guessing the color correctly, 4-to-1 for guessing the suit, or 13-to-1 for guessing the rank. As you move through the deck of cards, explain to students that the relative probability of drawing a black card, a diamond or a queen changes as you eliminate cards. To avoid running afoul of your administration, have students play for candy or a bit of extra credit instead of cash.

## 4 Misusing Statistics

Misuse of statistics is an endemic problem in the United States, according to the Mathematics Association of America. Unfortunately, many students leave school with inadequate statistical literacy, leaving them unable to interpret statistical data and detect the abuse of statistics. A good statistical literacy exercise is to ask students to find examples of misused numbers in the media. As a homework assignment, ask students to find examples of media sources conflating correlation and causation, for example. Or get them to look for examples of biased poll questions or nonscientific polling samples. This exercise will help students develop an eye for misused statistics, protecting them from misinformation and improving their critical thinking skills.

- 1 Mathematics Association of America: Spinning Heads and Spinning News -- The Use and Abuse of Statistics in the Media
- 2 International Conference on Teaching Statistics: Beyond Calculation
- 3 Significance Magazine: Teaching Statistics? You Bet!
- 4 Psychological Science in the Public Interest: Helping Doctors and Patients Make Sense of Health Statistics