If you want to become a teacher, I think that’s great! I have devoted my life to education, and I think teachers are wonderful people who do extremely important work. Of course, one of the challenges you will have to face in becoming a teacher is the Praxis Core Mathematics Test.
If you have studied something quantitative in college, the Praxis Core Mathematics Test probably will not pose much of a challenge. You should look over the topics and do a little practice just to make sure that you are familiar with everything that could be asked. Folks in this situation typically don’t need strategies for studying math.
This post not written primarily with those good-at-math folks in mind. This is written for the folks who are not lovers of math, for the folks who, if they had a choice, would never do math again. Typically, these folks drop math like a hot potato as soon as high school requirements are done, and they blissfully ignore it in college. Now, these good-hearted folks want to pursue a a career in teaching, but—alas!—the ogre of math rises again in the form of one of the Praxis Core tests! Heavens to Murgatroyd! This post is written especially with these anxious math-phobes in mind.
Here are five points of strategy to keep mind.
1) Practice mental math
This point is so important that I made it the first of my Praxis Study Tips. If you are someone who doesn’t like math, chances are very good that you try to do as little math as possible. There’s a problem here.
Suppose I knew that, for some reason, I had to run a marathon in a few months. Suppose I didn’t like running much at all. If I don’t do any practice at all, then try to run the marathon, I will in all likelihood hurt myself and not be successful. Much in the same way, if you ignore math until you have to do on the Praxis Core Math Test, you are not likely to perform at your best. Much as with running, you need to practice every day and get those “math muscles” in shape!
My first math tip is to practice ordinary arithmetic in your head every day. Make yourself add, subtract, multiply, and divide one-digit and two-digit numbers in your head every day. Make yourself compute calculations such as (38 + 27) or (91 – 57) or (3 × 19) or (78 ÷ 13). Have a friend or roommate hold a calculator, do calculations on the calculator, and ask you to do the same calculation in your head.
In the Magoosh math lessons, I created a few lessons about tricks you can use to make mental math easier, and throughout the lessons, I make clear ways that you can solve problems with mental math.
2) Don’t rely on the calculator
On the Praxis Core Mathematics Test, you get an onscreen calculator, to which you have access throughout the test. One of the biggest mistakes folks make on the Praxis Core Mathematics Test is to reach for the calculator on virtually every problem. The calculator can be a huge time-sink if you don’t use it carefully.
On the Core Math test, there are 56 questions. Let’s say your goal should be to use the calculator on no more than 5 questions. Practice mental math and other problem-solving skills so that you don’t need the calculator. Toward this end, don’t touch a calculator anywhere in your life between now and when you take the test. Especially as you do practice problems, force yourself to do the practice without a calculator. You will need the practice to develop the problem-solving skills that will allow you to solve these problems without a calculator, and that’s what you need to be practicing. When you get the real test, you should be able to do just about everything without a calculator, and the fact that you get the onscreen calculator on test day should be a bonus at that point.
3) Ask why questions
When folks study math, especially folks who are not very comfortable with math, get stuck in “what”-mode. These folks simply want to know what to do—”what do I have to do to get the answer to this problem?” Very literal, very practice, very business-like. Often these folks just want to know the bare minimum in math to get the job done.
Obviously, shooting for the bare minimum is not a winning strategy in any pursuit. Mathematical understanding deepens when one gets curious and asks “why”-questions. These are questions about the underlying mathematical logic: tapping into this logic makes everything easy to understand and remember.
For example, consider the problem of adding two fractions. How do we add fractions? In other words, what do we have to do in order to add fractions? Of course, we have to find a common denominator. If we have two fractions with a common denominator already, then we can simply add them:
That’s a simple “what”-level math factoid. Now, the “why”-level: why are we allowed to add two fractions that have the same denominator? Well, one way to say it is that when we write the fraction 4/5, one way to think about that is that we have four of these objects called a fifth. Well, if I have four of these objects called a fifth, and then add three of these same objects, I naturally will have seven of these objects. This is simply the Distributive Law, one of the fundamental laws of mathematics: four of anything, plus three of that same thing, equals seven of that thing!
That’s just a small example. You see, if you think about the “why”-level, that makes it much easier to remember what you have to do in this problem, and in a new problem, it may give you insight about how to proceed. In the Magoosh math lessons, I explain many of these “why”-level points as I cover the material, and if you pay attention to all that, you will develop much more confidence with math.
4) Don’t overuse formulas
A small number of formulas are necessary for success on the Praxis Core Mathematics Test. Students sometimes think that if they know a formula, then they thereby understand everything they need to know for that chunk of math. First of all, to extend the conversation of the previous point, formulas are still at the “what”-level of math, and understanding occurs only at the “why”-level. Another way to say this is as follows: each formula is a useful tool, and under the right circumstances, the right formula could provide enormous time-saving help. The flip side, though, as the psychologist Abraham Maslow said: “. . . it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.” Some students, emboldened by the supposed mathematical power a formula appears to give them, decide to apply the formula beyond what is appropriate. Knowing the formula itself is 10%—the other 90% is knowing exactly when to use it and when not to use it!
5) Think like the test writer
Think, for a moment, about the job of the folks who write the Praxis Core tests and other tests. A question that everyone gets right is not a good question, nor is a question that everyone gets wrong: the job of a test, and each question, is to separate those who have the skills from those who don’t. A good math question is one that folks get correct or incorrect for the right reasons: that is, the people who get the question correct do so because they understand the underlying mathematics, whereas the folks who get the question incorrect do not have this understanding.
One way the test writers achieve this is to include typical mistakes: mistake that folks with a superficial understanding of math make, but which those who have deep understandings of math tend to avoid. Folks who struggle with math tend to make a large number of these typical mistakes, so simply by learning to spot the typical mistake patterns, you can improve your performance. Magoosh math lessons cover many of these typical mistakes.
Summary
Finally, a sixth tip for free: sign up for Magoosh! We have a large library of math video lessons that cover everything you need to know about Praxis math from square one. We also have over 100 math practice questions, and each question comes with its own video explanation: the immediate feedback of a mini-video-lesson right after each question accelerates learning and helps people arrive at mastery. If a student using Magoosh has a question, he can send in his own question and get personalized help. When it comes to Praxis math, Magoosh has your back!
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