Effective Techniques to Motivate Mathematics Instruction

Alfred S. Posamentier, Stephen Krulik

• Verlag: Routledge
• Jahr: 2016
• ISBN:
  9781317248279
• Auflage: 2
• Thema: Bildung
• Thema: Bildung Allgemein

Effective Techniquesto MotivateMathematics Instruction offers pre-and in-service teachers best practices and techniques that can be used to motivate students in the first few minutes of any lesson in mathematics. Veteran teacher educators Posamentier and Krulik show how a bit of creativity and planning up front pays back by enabling a successful lesson on even the most challenging mathematics topic. Organized around nine different motivational techniques, each chapter includes a variety of illustrative examples of how the technique may be applied. Designed to complement any methods textbook, this practical, accessible guide helps future math teachers ease the transition from successful student to successful teacher by developing the tools needed to create motivational introductions in their classes.

1
Indicate a Void in Students’ Knowledge

The desire to complete has always been part of human nature. A person is usually most satisfied when a task has been fully finished. Stamp collectors, for example, often spend years searching for that single elusive stamp that completes a particular set for their collection. Similarly, most students have a natural desire to complete a task or complete their knowledge of a particular topic. Awareness of these voids awakens a desire to fill them.

Beginning at a young age, children may inquire about a particular topic until it is fully explained. Although a simple answer may be sufficient at one time, more questions may arise at a later point, and a person may not rest until these, too, have been answered. This process is in reality lifelong, and possibly one of the most decisive drives that pushes humans to learn and develop. In the same way, students have a natural need to complete and expand their existing knowledge.

Often, it is very effective and motivating when a particular gap in knowledge is subtly indicated, such as with a topic that will be discussed to complete students’ understanding of a specific area in mathematics. If a teacher acts cleverly, students can be made to discover this gap themselves, and thus their efforts to research this gap will increase until the gap is closed—their curiosity and attention have been awoken.

Naturally a teacher must be aware that it is important to reinforce recently covered subjects through well thought out examples before drawing attention to new topics, perhaps by indicating further knowledge gaps. It is also important to keep the curiosity and ambition of the students awake, so that formerly posed questions that may still have gaps can be discussed.

In this chapter we present some examples of how this motivational technique can be used for a variety of secondary-school topics. For instance, you might present a few simple examples involving familiar situations followed by an example involving an unfamiliar one, but on the same (or closely related) topic. Students should be led to the notion that they are actually lacking in a certain area where they previously (with the success on the first few familiar examples) felt comfortable. This tends to build a desire in the students to complete their knowledge of the topic at hand. This is different from telling students they are lacking information about a topic. Rather, through clever presentation, they are led to that feeling by themselves. This can be highly motivating, if done correctly. The more dramatically you do this, the more effective the motivation. Guiding students to discover this void in their knowledge plays a large role in making this motivational technique work well. We will examine a number of such motivators that lead the students to realize that they have reached a point where they must fill a void in their mathematical knowledge in order to complete their understanding of a topic.

Topic: The Introductory Lesson on the Tangent Ratio

Materials or Equipment Needed

Prepare the drawing below in advance, either on paper or computer, for presentation to the class at the start of the lesson.

Implementation of the Motivation Strategy

This activity is intended to motivate students for the first lesson on the tangent ratio. The design here is to indicate a void in the students’ knowledge about trigonometric functions without telling them that they are not familiar with this concept. Please bear in mind this is to be done without the aid of the Pythagorean Theorem.

Begin by having students find the value of x for each of the following:

Figure 1.1

Figure 1.2

Figure 1.3

Students should have been introduced to the sine and cosine functions in an earlier lesson, and now they are to be motivated to learn about the tangent function. The value of x in figures 1.1 and 1.2 can easily be found by using the two trigonometric functions with which students should now be familiar. Namely, for figure 1.1,

, then x ≈ 55°, and for figure 1.2,

, then x ≈ 37°.

Presented properly, the students should now feel comfortable about finding an angle of a right triangle, where the sine and cosine function can be applied, that is, when the lengths of the hypotenuse and one leg are given. However, when confronted with the right triangle in figure 1.3, where the length of the hypotenuse is not given, while the length of one leg is given and the measure of an angle is also given, students will be made to realize that they cannot apply the cosine and sine functions to find the side of length x. (Please remember that the Pythagorean Theorem should not be used here.) Suddenly they sense there is a void in their knowledge of trigonometric functions. Presented properly, they ought to be motivated to fill this void. They might realize that the teacher has this missing piece of information to fill this void—in this case, the tangent function. Applying the tangent function now allows students to determine the value of x in figure 1.3, namely:

, then x ≈ 4.

The technique of having students realize that there is a void in their knowledge base is effective, because of the natural tendency to complete an understanding of a topic. When it can be applied, it is particularly motivating and will have a favorable effect on the remainder of the lesson—in this case the study of the tangent function.

Topic: Special Quadrilaterals

Materials or Equipment Needed

A chart (figure 1.4), which should be on display for the class...