By NCTM President Linda M. Gojak

NCTM *Summing Up*, March 7, 2013

Have you ever spent time carefully planning a lesson only to find your students totally unreceptive? Several years ago, I participated in an outstanding problem-solving seminar and returned to my class eager to put many of the new ideas into practice. Despite my enthusiasm, my students rebelled! Why weren’t my students as excited about this as I was? Was it because they couldn’t solve the problem quickly that they gave up with loud moans of protest?

One of the most common concerns I hear from teachers is that their students aren’t motivated to do well in mathematics. Much has been written on the topic of motivation. There are motivational speakers, seminars on motivation, studies on motivation, and books on motivation. Key questions, however, remain: What motivates students to enthusiastically embrace learning mathematics, and how does our instructional practice affect student motivation?

Motivation can be intrinsic—we do something because we want to do it. We are intrinsically motivated, for example, when the task is interesting or we have a clear purpose for completing it. Extrinsic motivation, by contrast, implies that we have an external reason for performing a task, such as a reward, a grade, or a promotion. Ideally, we would like students to work hard in mathematics because they want to, they find it interesting, and they see the importance of learning mathematics. The reality for us as adults is that outside motivators, such as a promotion, job opportunities, or a higher salary motivate us, and similar rewards can be acceptable motivators for our students. However, these external rewards should never be the sole reasons that we offer as we encourage students to do mathematics to the best of their ability. Studies have shown that such rewards can eventually inhibit the development of intrinsic motivation.

Watch young children build with blocks. The intensity with which they approach the work is amazing. No assignment has been given to them. They do not have a particular task to complete. They are not worried about making a mistake. No reward, other than a construction that is personally satisfying, awaits the child. These children are highly motivated and their motivation is truly intrinsic. What can we learn about motivation from observing children at work? What are the implications for our mathematics instruction?

Young children are naturally curious about the world. When this curiosity is encouraged and students have the opportunity to explore mathematics in the context of their world, they are interested and want to learn. Too often, children enter school, and the gift of curiosity gets lost. In the student’s mind, the goal becomes getting the correct answer or doing what the teacher says to do. From preschool through high school, we must think about how we structure our lessons and present tasks in ways that encourage students to maintain their inherent curiosity.

Motivated students are persistent. They stick with a task, trying various approaches and strategies, asking themselves and others questions until they reach a solution that they find acceptable (intrinsic satisfaction), whether it is correct or incorrect. When necessary, they return to the task willing to rethink their solution process until they reach an accurate solution. To encourage persistence in our students, our lessons should present optimal challenge. Tasks should challenge students without overwhelming them. We must provide adequate time for students to work on the task. Good tasks are likely to take more time. Classwork and homework assignments must be carefully selected, ensuring that they allow students to reason about and make sense of the mathematics that they are learning. When possible, we should provide students with choices so that they can select an assignment that is particularly interesting to them.

Students enter school confident and eager to learn. When students are confident about their ability to do mathematics, they are motivated to explore new concepts even if they are not immediately successful. As self-efficacy wanes, so does motivation. If the mathematics doesn’t make sense to students, they often get frustrated and lose interest. As teachers, we must provide the support that each student needs to be successful. An encouraging word following a good effort can go a long way. Scaffolding tasks and asking probing questions that move students who are stuck (without telling them what to do), foster understanding and sense making.

In “Lesson from the TIMMS VideotapeStudy”* *(*Teaching Children Mathematics*, November 2000), Eugene Geist identifies seven characteristics of mathematicians as they go about solving problems. Mathematicians—

- often work for a long time on a single problem;
- collaborate with their colleagues and study the work of others;
- must prove for themselves that their solutions are correct;
- work on complex problems;
- get satisfaction from the process;
- gain a sense of pride in attaining solutions;
- use unsuccessful attempts as stepping stones to solutions.

Share this list with your students. Encourage them to believe that they can become mathematical thinkers. Discuss with colleagues how this list can influence your teaching practice. Although we cannot force students to be motivated in our classes, we can provide a learning environment that encourages students to be curious, persistent, and confident.

By the way, I did not give up on my students and the importance of persistence in doing (and teaching) mathematics. In subsequent lessons, I included more scaffolding and intentional opportunities for my students to be successful. As their confidence grew, so did their eagerness to try various strategies to solve problems. I knew we had all grown a great deal when a group of students came to me in April and asked, “Why did you save all of the easy problems for the end of the year?” They had become problem solvers, and I was a better teacher!