1.2 What Is Understanding?

Most of the math classes you have taken before focus on solving problems, not on understanding. Generally, in math courses you get introduced to a type of problem (e.g., a simple algebra problem), and then you are told the steps to solve the problem. If you are like most students, you memorize the steps, and use them to pass the exam! You might even have learned material in this way if you’ve taken a statistics class. You might have been given some data with instructions to calculate a statistic following a prescribed set of steps—steps you had memorized (and have now forgotten).

Although this seems perfectly normal—it’s the way most mathematics is taught, at least in the United States—it actually can prevent you from understanding mathematics. If you don’t understand, you won’t be able to generate the steps yourself, or apply them in new situations. As soon as you encounter a problem different from the ones in the book, you are in trouble!

Cognitive psychologists are beginning to uncover a lot about what understanding is, and how to get it. Here are a few things worth noting, because they will help you get your head in the right place to start this course.

Understanding Is a Skill That Can Be Practiced

Although we like to think that understanding is different from skills such as playing the piano, in many ways it is the same. Understanding, like many skills, is something that you can increase through practice. But, what you practice looks different from learning to play a musical instrument.

Understanding concepts such as the ones taught in this course requires you to practice thinking. What that usually means is practicing making connections. For example, you need to take an idea you learn about in this course and practice thinking about how it applies to new situations, and how it connects with other related ideas. This is what you need to do to understand.

Confusion Is Part of the Learning Process

Just like a musician starts out playing badly and gradually learns to play better, understanding works the same way. When you start trying to understand something that is hard to understand, you will initially be confused. This doesn’t mean you are stupid, it just means you don’t understand yet.

Because confusion is part of learning, we should say something about how to get less confused. You don’t want to just stay confused! The answer is: think hard, and don’t give up. Instead of thinking, “I can’t do this,” try just sticking with it, and be patient. Your understanding will grow.

Understanding Takes Time

These first two ideas naturally imply a third idea: understanding takes time. The concepts that underlie statistics are not things you understand in an instant, but things that will continue to develop over weeks, months, and even years.

We all know that learning skills takes time. No one expects to become an expert tennis player all at once—it can take years of practice. But many people think that understanding is something that happens in an instant—Eureka! As it turns out, that’s not true, at least for most things. So enjoy the process, be patient, don’t hurry.

Learning by Doing

With all this talk about understanding, you may think this course is going to be just a big discussion of ideas. It’s not. Because at the same time you are learning about the core concepts of statistics, you also will be learning how to analyze data.

The reason for understanding statistical concepts in the first place is to guide you as you learn to make sense out of variation in data. As you work through the course, therefore, you will be constantly putting your knowledge to use: organizing, analyzing, and interpreting data.

How This Course Supports Understanding

In this course you will be asked to do things on every page: analyze data and answer questions. You may feel like you are constantly being “tested.”

While in a sense this is true, it’s important for you to know that doing things is often the best way to learn things. So, answering a question is not just so your teacher knows how you are doing. It is also an important learning opportunity—a part of the learning design.

The main reason for all the questions you will answer as you work through the course is just to help you learn more. Don’t worry if you get questions wrong on the first try. Use the questions to help you figure things out. Working hard and thinking through these questions will result in learning, and that learning will lead to higher grades.