After several years of helping students prepare for standardized tests, I noticed a common trend. Motivated students often worked through many practice tests but made limited progress. They weren’t learning from their mistakes. So, I decided it was time for a more structured approach.
The obvious place to begin with with a diagnostic test. Where are we beginning. What do we know and, more importantly, what knowledge are we missing? What topics will we need to focus on first? What bad habits do we need to adjust?
Now that we understand what we’re working with, it’s time for review. This may seem surprising, but this is the step that most students skip when working on their own. We need to actually go back to the material and make sure we have all the mathematical knowledge required for the test.
There are several possible approaches to review. First, we could start with high-priority topics that the diagnostic test revealed as lacking. Sometimes, students know they have a big gap and are eager to set about filling it. Second, some students can make the best use of a comprehensive review so we set about it in an orderly fashion and go all the way through.
A skilled and experienced teacher will be able to sort through all the math material and highlight the gold nuggets that appear on the test and that a student might be missing. Reviewing on their own, students often struggled to know what to review. After 16 years of observing common errors, I can tell you exactly what key knowledge students usually need to be refreshed.
After reviewing a topic, it’s critically important to practice. Just talking about a subject isn’t enough. In math, knowing isn’t enough - you also need to be able to use what you know to solve problems. In fact, this is often the most difficult part of most standardized tests which try to design problems such that students have to actually understand how to apply their knowledge.
A mixture of targeted guided and independent practice is essential. After reviewing the rules of exponents, say, we need to jump straight into using them. There are many different ways to practice and I like to harness different tools. Computer-aided learning, for example, is much more effective than traditional worksheets.
First, in some areas students tend to need practice with the basic mechanics. When solving systems of linear equations, for example, we should start by making sure that we know and can execute reliably the standard methods of elimination and substitution.
Second, we extend our practice problems to more creative test-style questions that aren’t as straight forward. Can we apply the techniques to actual test questions? Can we solve systems of equations when they are presented in word problems? We probably need to practice that.
After reviewing and practicing specific topics, let’s bring it all together with some mock tests. There’s no substitute for actually sitting down in a proper test-taking environment and working through the (often) hours-long exam. The mock tests can tell us how we are doing, how close we are to our goals, and what we still need to work on.
A proper score report and analysis from a qualified teacher can expedite the score-polishing process. A score report that simply shows a student missed several algebra problems doesn’t tell us why they missed those problems. Is it a lack of knowledge? Maybe. But perhaps it’s a careless mistake? Does that mean we need to review algebra? Perhaps, but which part? Or maybe we just need more skills-based practice focused on being more careful. Even better, we might need a more deliberate approach to problem-solving which will reduce errors overall.
In the last phase of test preparation, it’s time to focus on technique, tips and tricks, time management, and learning how to relax and summon your full potential on test day. It’s extremely useful to have a tutor or mentor to guide you through this last phase of preparation. Mindset and critical and we often need direction.
