Page 293 - ABCTE Study Guide_Neat

Mathematics Instruction

Lesson Objective

Now that we have learned all of these mathematical reasoning and problem-solving techniques, we
can hopefully fulfill our goal of being able to teach these techniques to students. So let's go over
some strategies and tips for successful mathematical instruction.

Previously Covered

In the previous pages we looked at some simple problem solving techniques, as well as some common
missteps in mathematical reasoning. We also brushed up on some basic types of proofs.

Systematically Sequence Mathematics

Example: Consider the situation where a teacher wants a student to learn how to multiply two fractions.
How would this teacher systematically sequence instruction in order to achieve this goal?

Assuming that a student is already familiar with basic mathematical operations (addition, subtraction,
multiplication and division), the teacher would want to teach the students about fractions:

A fraction is a rational number , where a is a real number called the numerator, and b is a real number
not equal to zero called the denominator.

Then the teacher would want to define the product of two fractions and :

( )( ) =

where the numerator of the product of the two fractions is equal to the product of the numerators of the
two fractions, and the denominator of the product of the two fractions is equal to the product of the
denominators of the two fractions.

To end the sequence of instruction, the teacher would want to go over an example illustrating the concept
of multiplying two fractions:

Tailor Your Instruction to the Skill Level of the Student

For any given group of students, it is most likely the case that they are coming from very different
backgrounds—some of these differences being levels of knowledge, aptitude, and interest in the subject
being taught.

Therefore, it is important to structure lessons in order to accommodate all of these students. How would a
teacher do this? Here is a possible course of action: