Need for Acceptance

Students' social needs, particularly by middle school, influence their relationship with the teacher, as well as with peers, thereby affecting how students learn. For instance, students tend to seek the approval of teachers, and tend to view higher grades as marks of approval, and conversely, lower grades as disapproval (Fehr, 2007).

Students also develop a need to perform well in front of their peers (Wolters, 2004). A teacher's awareness of these developing attitudes is integral in planning effective motivation and positive interactions with students.

Techniques for Engaging Students

Active engagement helps students to make knowledge their own and enables them to think about new situations. There are many techniques the teacher can use in the mathematics classroom to engage students, including:

Find Patterns

Patterns are inherent in mathematics; they are fundamental to algebra. Selected properly and presented enthusiastically, patterns can be an effective device for generating a concept and stimulating students' interest.

For example, consider a lesson on multiplying two negative numbers. This concept can be introduced by presenting a pattern similar to the one below by having students predict the next three numbers-in this case, 5, 10, and 15. Students can be asked to specify a general rule about this pattern and then complete a table to demonstrate the rule.

 Factor 1 X Factor 2 = Product -5 X 3 = -15 -5 X 2 = -10 -5 X 1 = -5 -5 X 0 = 0 -5 X -1 = ? -5 X -2 = ? -5 X -3 = ?

Teachers can use the table as a basis for a discussion on the pattern in the "Product" column, engaging them as active learners. The teacher can guide students' thinking through modeling or questioning to help them understand the underlying rule and justify it through common usage: "two negatives imply a positive."

For example, "I will not withdraw (two negatives) money from the bank." To further engage students, the pattern can be extended- in this example, to -15, -10, -5, 0. Students then work to predict the next three numbers.

A similar table can lead students to generalize that the product of two negative numbers is a positive number. They may also discover that their responses are to be addressed as the focus of the next lesson, thus increasing anticipation and interest. In this activity, the chart might appeal to field-dependent learners, who, states Whitefield (1985), "love to graph, map, illustrate, draw, role-play, create charts, invent games, make things, etc."