Modeling as a Math Skill
Critics of standardized tests often paint those assessments as aloof from everyday exercises of knowledge and learning, conveniently ignoring the primacy of reading and written communication in most activities. That’s right: tests like the SAT and ACT evaluate the kind of reading and writing skills that matter in school, work, and life. Math, however, seems to be more of a disconnect; how often do you need trigonometry or geometric theorems in your non-scientific day-to-day? However, tests like the SAT and ACT do assess math skills and knowledge that matter beyond high school, from broad conceptual quantitative literacy to creative problem solving. One more oft-overlooked skill that carries into real life is modeling, the application of math skills to answer questions about real world situations. What are some common examples of modelling? How much does a shirt with a retail price of $40 cost during a 30%-off sale? How long will…
How is a Test Like a Climbing Wall?
I’ve been happily immersed in ACT Certified Educator training over the last week. This is a great program with terrific trainers. Jason Derby, for example, is a true educational triple-threat, teaching high school classes, ACE courses, and private test prep. No wonder so many of his insights resonated with my own experience of testing. For example, who could argue with this analogy? The ACT is like a rock wall: there are usually multiple ways to climb to the top. Jason hits the nail on the head here. Great climbing walls are designed to challenge a wide range of complementary skills and strategies along a spectrum of successful outcomes. Great tests do the same. Neither trial is necessarily designed to allow every competitor to attain the summit but still permits numerous paths to the highest levels of success. The comparison doesn’t end there. Solving a tough test question is a lot…
Looking Back
Have you ever had the experience of driving somewhere, but then forgetting how you got there or even when you arrived? Most of us know that disorienting feeling. In fact, the more senior among us sometimes forget how–or why–we walked into a room! If you spend more time on the road than in a classroom these days, you may not recall that this phenomenon plays out every single day in schools and on tests around the world. Students diligently toil on math problems to arrive at solutions they suddenly forget how they found. George Pólya, the influential mathematician who authored How to Solve It: A New Aspect of Mathematical Method, knew all too well how quickly people abandon and encapsulate their efforts: Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing…
SAT Math Tips from Real Test Experts
Happy Pi Day! I can think of no better way to celebrate this magical mathematical holiday than by talking math, specifically the most challenging aspects of one of the most challenging math tests any American student ever takes. Make no mistake: since its most recent revision, the SAT is more of a math test than it’s ever been. If you’re looking for tips on tackling math on the SAT, you already know how much this exam differs from math tests in school. You may already be aware that the SAT tests math from basic arithmetic through advanced topics in algebra 2 and trigonometry. If you’re lucky, you’ve also learned that SAT math focuses heavily on problem solving, particularly through tricky word problems. Still, real success on the SAT Math section requires much more in the way of content knowledge and strategic insight. To speed your progress, I asked a few…
Doing the Work
Life comes with few guarantees, but you can always count on problems. In a long life, you’ll encounter lots and lots of problems, some easy, some hard, but all requiring solutions. In this regard, George Pólya’s How to Solve It: A New Aspect of Mathematical Method doesn’t simply serve as a guide to tackling math problems but also as a handbook for managing challenges in any area. Polya wisely recommends that we always begin by understanding the problem, followed by carefully devising a solution. Unfortunately, the process does not end there. We still have to do the work to implement the solution. “To devise a plan, to conceive the idea of the solution is not easy. It takes so much to succeed: formerly acquired knowledge, good mental habits, concentration upon the purpose, and one more thing; good luck. To carry out the plan is much easier, what we need is…
Cannot Be Determined From the Information Provided
“Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved…” Certainty in this complex and confusing conditions can be hard to come by. Sometimes, we cannot know definitively whether we possess sufficient evidence or understanding to make correct choices, yet still we must choose. Such is the uncertain fate of those who tackle standardized test math! Math on exams like the SAT and ACT frustrate test takers for a myriad of reasons, from convoluted word problems to complex or unexpected concepts. Sometimes devising the right solution to a problem seems impossible, while, at other times, we don’t even fully understand the problem. These levels of extreme uncertainly can be considered features of standardized test design, rather than flaws. After all, the test makers channel tremendous knowledge, expertise, and…