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 a trip of 500 miles take at an average speed of 60 mph?
- How many square feet of wallpaper is required to cover the walls of two 10×12 rooms?
Life doesn’t get more real than that, which is why modelling means so much. In fact, mathematician John Berry describes mathematical modelling as among “the most quoted generic skills that should be developed as an outcome of a programme of mathematics in school, college and university.”
The SAT and ACT both test modelling heavily through word problems. The ACT presents Modeling as a separate Reporting Category, but doesn’t feature questions that only evaluate modeling. Instead, the ACT bases the Modeling score on achievement on those Higher Math and Essential Skills questions that involve producing, interpreting, understanding, evaluating, and improving models. The SAT also presents modeling as an overarching skill set rather than a discrete question type or subscore. The College Board’s stated philosophy is that questions on the Math Test “are designed to mirror the problem solving and modeling you’ll do in college math, science, and social science courses, the jobs that you hold, and your personal life”
What should test takers and teachers alike know about solving modeling problems? Rachel Levy in American Scientist describes a process in which problem solvers “make assumptions, choose a mathematical approach, get a solution, assess the solution for usefulness and accuracy, and then rework and adjust the model as needed until it provides an accurate and predictive enough understanding of the situation.” If this sounds like the process people use every day to deal with problems, you get the point. Modeling is all about real life, which is either refreshing or scary, depending on your perspective. Don’t over-complicate the modeling process, and avoid unhelpful abstraction or excessive calculation. Deal with modeling math problems the way all obstacles in life should be overcome: quickly, easily, and accurately!
Mike Bergin