Why are the standardized math tests difficult?
The standardized tests such as the SAT and ACT serve a few essential purposes. For one, they provide a piece of the student’s total package for college recruiters to assess, along with GPA, references, and extracurricular activities. They also compare a student’s scores with all of the other cohorts applying at that time, regardless of what school they are from.
The standardized tests have come under some criticism lately, with studies suggesting that performance on the test does not necessarily predict future "success" in college or beyond. Considering almost 70% of Americans do not have a college degree, such a finding could use some qualifications. An ambitious student who may not be particularly strong academically, but bound and determined to succeed, is more likely to do well once they get in. And there are options to getting in without the standardized test – the community college route being a highly recommended one.
My goal however, is to improve math problem-solving abilities. From my years of experience as a personal tutor, I see a value in the ability to do well with these problems, regardless of a student's intended major. Using the rules and processes to work such math problems could improve your problem-solving skills in any vocation you pursue. I have taught how to work thousands of these problems, and I do feel that these tests provide a good assessment of a student’s math skills. With instruction and effort, a student can significantly improve their math ability, and this would be reflected on these tests, as well as those taken in school.
So why are these standardized math tests (SMTs) difficult for the typical student? Unfortunately, they are supposed to be, as most tests are. As a college professor, I prefer to give a more difficult exam than an "easy" one to get a clearer picture of which students paid more attention, studied harder, prepared better, retained more, etc, and are therefore most deserving of an A. But with respect to our current system and student behavior, it is worth addressing four primary reasons how and why students are generally unprepared for these tests. (This does not include what might be the most important reason: that their parents have not been actively involved in their math progress.)
First, students have not been accustomed to dealing with such an assortment of problems in one sitting. Students take a geometry class and are shown how to work geometry problems, then move on. A couple of years later, they are confronted with the college admissions test, which may have a circle problem, then a function problem, followed by a ratio problem, then a volume problem, followed by an exponent problem, and so on. Surprisingly, the math concepts required for these tests are not sophisticated; by Algebra II, a student has covered the basics required to do well on the standardized tests. However, they are not served this material in such a smorgasbord manner over the years; they are fed one item at a time until it is digested and passed (pun fully intended). Unfortunately, our school systems tend to herd the students through regardless of whether or not they have retained any of that material.
Second, many students are fundamentally weak at using a process to solve math problems. Classroom teachers – of which I am one - are limited in their ability to provide tailored individual instruction to their students who have not retained the concepts. This would require meeting outside of the class, or setting the student up with a tutor (as well as the student communicating their difficulties before the test, which most don't). Students are typically shown the process, asked to regurgitate the process, and move on as a group. Many of the students I tutor individually are not able to systemically figure out how to solve a math problem. Many are instead rampant guessers, looking for patterns or connections as to which answer choice looks best. Students often punch in the numbers on their calculators, in various combinations until something looks close. Or they work backwards from the answers. (Occasionally this is an option, but on average takes longer than solving the problem). Multiple choice answers unfortunately encourage all these behaviors.
A third reason is that many of the SMT problems are structured as word problems – whether a short sentence or full paragraph - in order to explain it. Many students are not typically assigned such problems to work for homework, or on tests. They are generally presented problems in their raw equation form, where the students perform the necessary steps to reach the answer. The hardest part of many SMT problems is figuring out how to set up the equation, not working the equation. The SMTs assume that operations such as "combining like terms" and "isolating the variable," for example, are automatic. What they are testing is the student’s ability to recognize what the problem is and how to approach it.
Fourth, students often have difficulty finishing these tests. Practice is the most important factor for increasing speed, and there are useful tips to improve efficiency. But because of the time pressure, many students mistakenly perceive that they won't have time to completely work the problems to a definitive answer. This enables them to maintain bad habits of guessing or looking for patterns. Many students have not accepted the counter-intuitive idea that by systematically solving the problem, not only will they get more right, it effectively speeds them up! By actively engaging and visualizing the problem, a student is stimulating the thought processes. Writing out the pertinent equations, or labeling the givens, or sketching out a figure, this reinforces an understanding of the problem, and sparks ideas on how to approach it. Many students waste time mulling over the problem, primarily for the purpose of guessing strategies, not typically for the purpose of solving it.
As much as I hate taking and giving tests, they are not likely to go away any time soon. They provide a method for assessing what the student knows, or understands, or has retained, or has memorized at that moment. But I do prefer a more integral, long-term approach, similar to an old proverb: Getting the right answer feeds a student for the day, but teaching them how to solve the problem prepares them for a lifetime.
RKL for MAXimatician.com
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