I will give you strategies about mathematics to improve your confidence about all things mathematical—plus all things logical. This pretty much covers everything. That is the nature of mathematics. The structure is ancient, and the scope is comprehensive.
The tips, instructions, techniques, and patterns I teach are what I use to do well on mathematics tests—despite my stronger background in language arts. As I mention in many of these columns, most of the strategies I use in language arts sections of SAT and other tests relate to checking the answers by eliminating all the other answers. There are tests related to aptitude and math questions that have nothing to do with eliminating the incorrect answers.
First, a review of the OTHER type of strategy—the one involving connotations and emotional intelligence, as well as logic:
I call the questions and answers related to the language arts sections on the SAT ‘racecar’ questions and answers for three reasons:
1) The procedure for answering, including reading the passage, is usually fast and streamlined.
2) The choices are brief—one word, a pair of words, or the letter of the answer.
3) The word ‘racecar’ is a palindrome to remind me that my scores will be higher on the language arts section if I use the fact that these are easier for me to pace to read them ‘frontwards and backwards’—like a palindrome.
Second, a review of the general method to manage mathematics and quantitative questions (such as the ones on the Graduate Records Examination):
Reword the question in your mind while jotting down an illustration for yourself on your ‘scratching’ area. Now, attempt to find the correct answer and to eliminate two wrong answers.
Eliminate two wrong answers. I advise NOT eliminating every answer you believe to be incorrect. That is too time consuming. Instead, the elimination strategy relates to knocking out the obviously incorrect answers –especially when you are somewhat lost in a more difficult question.
Because most of the elimination of ‘wrong’ answers as a strategy has to do with moving on and the time pressure of the test, I am not going to begin this section about mathematics with all of the ‘elimination’ tips especially for math. To be sure to get the answers you know correctly chosen and marked, let’s start with some predictable aspects of this section.
As you plow through the minutes of this section, you will encounter terms for numbers. Keep looking at some of those terms.
Integers is the term you will see again and again: Integers include zero, whole numbers, negative and positive numbers…--Keep noticing more things about integers and why this term is used instead of one of the other definitive ‘sets of numbers’ such as:
Natural or counting numbers {1,2,3,4,5,…11,12,…}
Whole numbers {0,1,2,3…10,11,12,13…}
This would be a good time to go to a text and to find examples and definitions to make cards, PowerPoint presentations, and games from the definitions, spellings and examples for :
Integers
Natural or counting numbers
Whole numbers
Rational numbers
Irrational numbers
Real numbers
Imaginary numbers
Complex numbers
Today, the only other overview of EVERYTHING that I am going to mention is the Order of Operations. There will be questions on the math test that are only about whether you know which operation to do first. Otherwise, the computation will be simple for those questions. The answer will be correct ONLY if you do the operations in order.
From left to right, you look to see if there are
operations to do within parentheses,
then you handle the exponents, if any
Multiply
Divide
Add
Subtract
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
PEMDAS—Please Excuse My Dear Aunt Sally is the mnemonic often used. Put this on the same page with the formula information on your test booklet.
When I begin a mathematics test, I look for the page with the formulae. And I write this mnemonic for my quick review—even for a short problem like : 5+2x4= Is the answer 13 or 28?
(The answer is 13 because you multiply before you add.)
Commutative and associative properties are rules reminding you to realize that order of operations is paramount; HOWEVER, numbers may be added in any sequence; and they may be multiplied in either order to get the same result.
(See more about this later.)
Today’s Summary: Mathematics strategy is different from other strategies.
Keep practicing exercises with the terms. One term can change in meaning across the subject areas and even within an area.
Practice doing the operations (multiplication, division, addition, and subtraction) in the proper sequence. Before anything, do the operations within parentheses, then do the multiplication of the exponents—then: multiplication, division, addition, subtraction.
The mnemonic is PEMDAS: Please Excuse My Dear Aunt Sally.
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
(Come back to do more mathematics. We will return to the ‘racecar’ questions and answers, too.
Judiethcarol&Rocketcat march 2010
