Tutoring For All Ages

Every year I work with science and math students who come to me thinking they just need help learning the material, without realizing that their main problem is that they don’t know how to study. They’re generally very good students who make the common mistake of assuming that the methods that work for them in history and literature classes will work for them in chemistry or geometry. In fact, these are such different classes that the same study habits rarely work for both.

So if you’re taking your first hard math class, or your first physical science class, here are some tips to help you study more efficiently:

• Know when to stop memorizing. Every subject in school involves some amount of memorizing. Sometimes you have to spend hours a night drilling dates and names into your head, and sometimes you just have to memorize the Central Limit Theorem. Memorization is a skill that will serve you all your life in some capacity or another, so don’t neglect it.

  However, another important skill you need to learn is when to put down the flash cards and pick up a pencil and some scratch paper. In math and the hard sciences especially, there is just no substitute for practice problems. (more…)

We hear a lot of reasons for why students don’t like to write down their intermediate steps on standardized tests. Sure, it may not be necessary to show your work in the same detail as when you’re graded on that work, but you should think twice before leaving your test booklet blank. Our most commonly-heard excuse is:

Habit. It’s just what I’ve always done.

Now, sometimes this is just another way of saying, I’ve never been allowed to do it. Students taking statewide standardized tests aren’t always allowed to write in their test booklets. That’s because some schools re-use their test booklets from year to year, and erasing is time-consuming and can be damaging to the paper. (Whether or not we think that’s a good policy is a subject for another post.) So when students go from using separate scratch paper to having no separate scratch paper at all, they often just think they’re not supposed to write anything down.

If this sounds familiar to you, know that the ACT, AP, ISEE, SAT, and SSAT exams all expect that you’ll be using your test booklet as scratch paper. Part of your test fee is paying for that test booklet, which will be thrown away after you take the test. So, write away!

But for those students who are just in the habit of doing all their work in their head, consider the adage: “If you always do what you’ve always done, you’ll always get what you’ve always gotten.”

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Students often think that just because nobody will be checking their work on a standardized test, that means they won’t be punished for leaving the test booklet free of scratch work. To that end, we’re continuing our series on the most common reasons that students fail to “show their work” on standardized test day:

Pride. I should be able to go without.

We see this a lot from students who are taking a test that they expect to get a high score on, and it’s also a favorite excuse from people who like to get to an answer fast.

Unfortunately, standardized tests don’t care about your ego or your impatience. You don’t get bonus points for turning in a blank test booklet, or for turning it in early. If you missed a negative sign, no one but you is going to know that you made a simple, careless error. Careless errors get the same score as errors of knowledge or understanding.

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When it comes to homework and in-school tests, the vast majority of our students don’t have to be reminded to show their work (at least, not more than once or twice). Getting credit in school isn’t usually about getting the right answer; it’s about demonstrating that you know how to get the right answer.

But when it comes to standardized tests, many of the same students, who painstakingly write out every line of algebra or underline every important line in their history textbook, won’t touch pencil to paper except to fill in a bubble. We’ve yet to see a student who can get away with doing it on every question of a test — it inevitably leads to careless mistakes.

And yet, sometimes a student, despite just having seen the results of those careless mistakes, continues to leave a blank workspace again and again while working through practice problems.

Why does this happen? There are likely many reasons, but we’ll address a few of the more likely causes in a series of posts, starting with:

Time. If I write out my work, I won’t be able to finish the whole test.

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A student at an Ivy League university is taking a final exam in an advanced Astrophysics course. She reads a problem similar to the following:

What is the mean free path of a photon through a cloud with optical depth T = 1, electron number density D = 10¹⁶ cm^-3, and scattering cross-section s = 0.6 ×10^-24 cm²?

A sense of panic comes over her as she realizes that, for all her studying, she has no idea how to do this problem. She reads it once more and notes that if she just multiplies the numbers together and takes the reciprocal, the units work out so that the answer has the unit of length, which is what she knows the unit of the answer should be. Knowing that time is running out and she still has to do other problems on the final, she multiplies the numbers (showing her work) and writes down the answer.

Two weeks later, she gets her final exam back and sees that she earned full credit for the problem.

The moral of the story: units are a powerful problem-solving tool. Use them. Units are your friend.