President Linda M. Gojak
NCTM Summing Up, March 7, 2013
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?
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?
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.
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?
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.
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.
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
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—
work for a long time on a single problem;
with their colleagues and study the work of others;
prove for themselves that their solutions are correct;
on complex problems;
satisfaction from the process;
a sense of pride in attaining solutions;
unsuccessful attempts as stepping stones to solutions.
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.
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!