Tutoring For All Ages

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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The Pareto Principle, applied to standardized tests, states that 80% of the results you get come from 20% of the work you do. If we use the SAT as an example, this can be applied to much of the test. On the essay, for example, the actual writing may take the most time, but the ideas behind the essay form the foundation of your score, and they typically come together in the first few minutes of the section. Within the Critical Reading sections, students tend to spend most of their time on a few really hard questions.

And the 80/20 rule can be applied to most of the math questions on the test, too. Here’s a sample math SAT question: (more…)

Okay, so maybe you don’t love ‘em. But you also can’t leave ‘em, at least not if you’re taking geometry.

What is a proof? Fundamentally, it’s a puzzle. You’re given the answer, but you have to figure out how to get there. Once you figure that out, then comes the hard part: writing it all down.

Theoretically, there should be only one right way to do a proof. Math is absolute, right? …wrong. Different teachers have different requirements for even simple proofs. Some teachers want you to write down every little step you take, right down to the “AB = AB: Reflexive Property” steps. Other teachers find that a complete waste of time and will even take points off your work. Your path to good grades: learn what your instructor wants.

Once you’ve learned the nuances of your teacher’s requirements, the hard part is over. From then on, you can concentrate on the math.

Set a timer and see how long it takes you to answer this hard SAT problem:

The price of 10 pounds of apples is d dollars. If the apples weigh an average of 1 pound for every 6 apples, which of the following is the average price, in cents, of a dozen such apples?

A) 20d
B) 50d/3
C) 5d
D) d/5
E) d/20

There are several ways to approach the right answer here. Some take more time, others, less. (more…)