Memorizing and Understanding Mathematics

Symbols, definitions, rules and algorithms must both be  memorized and understood.

We learn best when what we are learning has meaning to us.

The more we review, practice and think about a topic, the better we can understand, make connections  and apply the concepts and methods.

Understand, do not memorize!

In mathematics a reason exists for everything that we do.

In order to succeed we must understand the problems and the reason we solve the problems the way we do.

In general, mathematics is to be understood, not memorized.

A Topic: Addition of Integers

Prerequisite Skills:

Add and subtract whole numbers.

Identify and graph integer numbers using the number line.

 

Objectives:

Add integers with the same and opposite signs.

Translate verbal expressions into mathematical expressions and simplify.

Identify properties of addition.

Motivation: Real-life problems

Example: The temperature rises 3 degrees from 8:00 to 9:00 am and 5 degrees from 9:00 to 10:00 am. If the beginning temperature was 65 degrees, what is the new temperature?

Example: The balance in a checking account is $265. A check for $120 is written and later a deposit of $200 is made. What is the new balance?

Problem Solving: Steps

A discussion will be promoted in order to understand the problem.

Students will be encouraged to verbally describe what they think they have to do.

Words will be translated into numerical expressions containing addition of signed numbers.

Lecture/Practice will follow on the following topics:

Adding integers with the same and opposite signs.

Translating verbal expressions into mathematical expressions and simplifying.

Identifying properties of addition.

The problem(s) presented as example(s) at the beginning of the class will be collectively solved and the solution(s) discussed.

Homework will be assigned.