A teacher might also stir curiosity by demonstrating a mathematical trick with an unusual result that prompts students to wonder why and how this trick works. Try this "trick": invite students to pick a number (x), then multiply it by 2 [2x]. Then have them add 9 to that [2x + 9], add in the original number [3x + 9], and divide by 3 [x + 3]. To this students will add 4 [x + 7], and as a final step, subtract the original number (7). No matter what original number is chosen, the final result will always be 7.

Invite students to try several numbers to see that this "trick" does, in fact, work every time. Algebra will then reveal the "trick."

#### A Choice to Learn

The desire to act on something as a result of one's own volition is often a motivating factor in the general learning process. Students will be more motivated if they can determine for themselves what is to be learned, rather than learning merely to satisfy someone else or to attain an extrinsic reward (Reeve, 2006).

There are motivational activities to support autonomy and encourage students to want to learn (Reeve, 2006). To do this, a teacher can provide a problem that students may not know how to solve, such as factoring a binomial or a trinomial. Students can be reminded that every math skill they develop is based on knowledge and strategies they already know. In this case, the teacher can suggest that they factor two- and three-digit sums and differences to find the strategies they already know. Then students can be encouraged to use these known strategies to factor the binomial or trinomial.

#### Desire for Challenge

Some students are more eager to do a challenging problem than a routine one.

It is not uncommon to see this type of student begin homework assignments with the most challenging problem. If a test has an "extra credit" item, these students might tackle it before looking at the remainder of the test, even if the time spent on the item prevents them from completing the required portion.

This drive to know more seems to go hand in hand with achievement. According to Gottfried, "Academic intrinsic motivation was found to be significantly and positively correlated with children's school achievement and perceptions of academic competence and negatively correlated with academic anxiety" (Gottfried, 1985).

Helping students achieve intrinsic motivation contributes to the positive learning environment. Here, teachers can introduce the lesson with an example that will challenge these students. In addition, the lesson presentation can be followed with an enriched problem to further allow students to develop their competencies.

**SOURCES OF MOTIVATION FOR A LESSON INTRODUCTION**

- Innate Curiosity
- A Choice to Learn
- Desire for Challenge
- Need for Acceptance