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Tuesday, January 23, 2007

Mathematics Tips: General Math Tips

Read the book

Read carefully over the assigned sections and look carefully at the sample problems. Decide if you benefit more by reading before or after the instructor covers the material. More information about reading math texts will soon be provided in a separate section of this page.

Develop a sound math foundation

Because most math courses are cumulative, in other words new concepts are added to and build upon previous concepts, it is very important that the early material be mastered thoroughly. Similarly, mastery of material from previous courses makes success in later courses more likely, so continually review and practice concepts from prior math classes.

Time management

Complete all readings and especially homework assignments as soon after they are announced as possible. And definitely complete all assignments before new material is covered since math is cumulative. This insures that the inforamtion is fresh in one's mind and linked to prior, more fundamental information. Do your assignments early enough that you can get help with the things you do not understand.

Calculator

Learn how to use your calculator effectively and efficiently, especially if exams are timed and you have trouble completing tests in the allotted time. Check with the instructor about suggestions for the appropriate calculator to purchase for a class. Be sure the machine comes with an instruction manual and read the manual. Learn how to use important function keys. Get in the habit of carrying the calculator with you. It is better in the long run to become proficient with your own calculator rather than borrowing other people's calculators.

Show your work

Avoid the temptation to skip steps when solving a problem unless you are quite clear about how to proceed. This is a good habit to get into with your math homework. And definitely don't skip steps on an exam no matter how well you know the material. Why take chances (unless you're running out of time)? Showing your work allows you to locate logical or calculation mistakes more easily, and sometimes partial credit is given for the correct portions of an answer.

Organize your work and write legibly

Write all numbers and variables clearly so they may be easily distinguished. Pay particular attention to 4 and 9, 1 and 7, x and y.

Spaces are as important in math equations as are the numbers and variables themselves. Allow enough space between different terms in an equation so it is easy to distinguish them.

Be sure to line up terms in each step of the solution, and write steps one below the other rather than to the right or left. Use lined paper or graph paper to help organize the problems on your page. Don't scrunch! Use plenty of paper to work each problem. Recycle the paper at the end of the term if you are concerned about wasting paper.

Support services and materials

Find out about the support services and materials available to you. Support services include workbooks, study groups, self-help videos and cassettes, peer tutors, professional tutors, and instructors' office hours. Using the resources from the start of the course may help your confidence and get you off on the right foot. Minimally, make use of these resources as soon as you feel uncomfortable with the material - do not wait until it is too late!

Preparation and supplies

Being prepared for each course involves several important factors:

  • complete any previously assigned homeworks
  • compile a list of questions about the previous assignments to ask the instructor
  • preview the material to be covered that day
  • take your textbook and/or workbook to class
  • carry the proper supplies to each class - calculator, pencils, erasers, lined or graph paper, etc.

Information organization

Math information - including definitions, symbols, equations, and steps for solving problems - may be organized using flash cards, running concept lists, flow charts, and matrices (D. Applegate, CAL).

Flash cards

Flash cards are useful for organizing all forms of math information. Two examples are given below.

Running concept lists

Running concept lists organize all forms of math information.

Flow charts

Flow charts are useful for organizing sequential information such as the steps for solving a problem.

Matrices

Matrices may be used to organize math symbols, equations, and definitions.


TERM

DEFINITION

EXAMPLE

numerator

top number in a fraction

the 1 in
1
5

denominator

bottom number in a fraction

the 5 in
1
5

reciprocal

the inverse of a fraction (flip it)

2
3

the reciprocal is

3
2


integer

any member of the set of positive numbers, negative numbers, and zero

1, 2, 3,
-1, -2, -3,
0


PROBLEM

EQUATION

perimeter of rectangle

P = 2L + 2W

area of rectangle

A = L * W

volume of a rectangle

V = L * W * H

perimeter of square

P = 4s

area of square

A = s * s
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