Powers of 2

From my early days as an undergrad math student, I knew that powers of 2, the numbers of the form 2ⁿ, have many properties, and are very important in many areas of mathematics.
However, it was only after I became a math tutor that I realized how common questions involving powers of 2 are in standardized tests.

Before becoming a math tutor I had held positions at colleges and high schools as an associate professor, adjunct professor, math teacher, and teaching assistant. Up to that point I had memorized only the first six natural powers of 2, from 2¹ to 2⁶, these are:
2, 4, 8, 16, 32, and 64, the powers of 2 that are two-digit numbers.

Later, when I became a math tutor, and I realized how often standardized tests present students with questions involving powers of 2, then I memorized larger powers of 2, up to 2¹², or:
128, 256, 512, 1024, 2048, and 4096.

It is really a big advantage at test time, for a student to be able to recognize a power of 2 when they see such a number in a problem, because then they can write that number in its exponential format, and use the algebraic rules of exponents to work out the problem’s math easier and faster than dealing with the number in its decimal form, using only arithmetic operations, because the longer route is more time-consuming, and more attention-intensive, therefore riskier and less efficient.

So, if you are preparing for a standardized test, from the CBEST or the ASVAB to the GMAT or the CSET, know your powers of 2. Memorize them well from 2¹=2 to at least 2¹⁰=1024, and you’ll increase your chances of scoring a few extra points in the exam.

To like or dislike math is an individual choice

Helping students regardless of whether they like math

One basic way I help my students is by respecting their right to dislike math. I do not try to make them like math. I refrain from insinuating, or even thinking to myself, that they should like math, because I believe they are free to make that choice by themselves. I am no longer one of those teachers who are always telling students how wonderful, important, or beautiful math is, and that they should like it. I personally love math but I very well know it is one of the least popular subjects among students. As a math tutor, I see my students as human beings first, then as clients, then as students. I know they hire me to help them pass their exams with a good score, not to make them like math, and I totally respect that. Often my students start their first session telling me they are not good at math, or they have always had problems with math, or they do not understand math, or they do not like math, or they hate math. I always listen to them, I acknowledge what they say, and I tell them that it is O.K., meaning, I have no problem with them hating math; I do not feel offended that they do not like math; I do not think they should like math; and I am not going to judge them, or criticize them, or give them a hard time just because they do not like math. Most times I do not even have to say it. Just a nod of the head, and a brief comment like “Yeah, that’s alright” make them feel comfortable with me from the very beginning because they perceive my attitude is sincere. Somehow they realize that, plain and simple, I could not care less whether they like math or not. It is their choice. I am still going to help them to the best of my ability. I do not believe there is anything wrong with them just because they do not like math, or are having problems with math. Once this basic understanding is established, that I am not going to try to change them, they trust me, and they are much more open to what I have to say to help them. In this way I can help them much better.