Motivating students to be (enthusiastically) receptive is one of the most important aspects of mathematics instruction and a critical aspect of the Common Core State Standards. Effective teachers should focus attention on the less interested students as well as the motivated ones. Presented in this blog post are nine techniques, based on intrinsic and extrinsic motivation, which can be used to motivate secondary school students in mathematics.
Extrinsic motivation involves rewards that occur outside the learner's control. These may include token economic rewards for good performance, peer acceptance of good performance, avoidance of "punishment" by performing well, praise for good work and so on.
However, many students demonstrate intrinsic goals in their desire to understand a topic or concept (task-related), to outperform others (ego-related), or to impress others (social-related). The last goal straddles the fence between intrinsic and extrinsic.
With these basic concepts in mind, there are specific techniques which might be expanded, embellished and adapted to the teacher's personality and, above all, made appropriate for the learner's level of ability and environment. The strategies are the important parts to remember -- examples are provided merely to help understand the techniques.
Strategies for Increasing Student Motivation in Math
1. Call Attention to a Void in Students' Knowledge
This motivational technique involves making students aware of a void in their knowledge and capitalizes on their desire to learn more. For instance, you may present a few simple exercises involving familiar situations, followed by exercises involving unfamiliar situations on the same topic. The more dramatically you do this, the more effective the motivation.
2. Show a Sequential Achievement
Closely related to the preceding technique is that of having students appreciate a logical sequence of concepts. This differs from the previous method in that it depends on students' desire to increase, but not complete, their knowledge. One example of a sequential process is how special quadrilaterals lead from one to another, from the point of view of their properties.
3. Discovering a Pattern
Setting up a contrived situation that leads students to "discovering" a pattern can often be quite motivating, as they take pleasure in finding and then "owning" an idea. An example could be adding the numbers from 1 to 100. Rather than adding in sequence, students add the first and last (1 + 100 = 101), and then the second and next-to-last (2 + 99 = 101), and so on. Then all one has to do to get the required sum is multiplying 50 X 101 = 5,050. The exercise will give students an enlightening experience.
4. Present a Challenge
When students are challenged intellectually, they react with enthusiasm. Great care must be taken in selecting the challenge. The problem (if that is the type of challenge) must definitely lead into the lesson and be within reach of the students' abilities.
5. Entice the Class with a “Gee-Whiz” Mathematical Result
To motivate basic belief in probability, a very effect motivation is a class discussion of the famous "Birthday Problem," which gives the unexpectedly high probability of birthday matches in relatively small groups. Its amazing -- even unbelievable -- result will leave the class in awe.
6. Indicate the Usefulness of a Topic
Introduce a practical application of genuine interest to the class at the beginning of a lesson. For example, in the high school geometry course, a student could be asked to find the diameter of a plate where all the information he or she has is a section smaller that a semicircle. The applications chosen should be brief and uncomplicated to motivate the lesson rather than detract from it.
7. Use Recreational Mathematics
Recreational motivation consists of puzzles, games, paradoxes or facilities. In addition to being selected for their specific motivational gain, these devices must be brief and simple. An effective execution of this technique will allow students to complete the "recreation" without much effort.
8. Tell a Pertinent Story
A story of a historical event (for example, math involved in building the Brooklyn Bridge) or contrived situation can motivate students. Teachers should not rush while telling the story. A hurried presentation minimizes the potential motivation of the strategy.
9. Get Students Actively Involved in Justifying Mathematical Curiosities
One of the more effective techniques for motivating students is asking them to justify one of many pertinent mathematical curiosities. The students should be familiar and comfortable with the mathematical curiosity before you "challenge" them to defend it.
Teachers of mathematics must understand the basic motives already present in their learners. The teacher can then play on these motivations to maximize engagement and enhance the effectiveness of the teaching process. Exploiting student motivations and affinities can lead to the development of artificial mathematical problems and situations. But if such methods generate genuine interest in a topic, the techniques are eminently fair and desirable.