The Paradox of Longer Problem Solving 

Jack Nelson, Staff Writer

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The high school mathematics core curriculum has been marred in the same cycle for decades; introduction to the new material, extensive techniques to solve new problems, quicker ways to solve those problems, and assessment of that newly attained knowledge.  Each district’s high school revolves around this practice when it comes to their math subjects– predominantly Algebra, Geometry, Precalculus, and Calculus. The material is not what’s in question though, as history tells us, these subjects will remain the four cornerstones of high school math for decades to come. The critical flaw is the manner in which they are taught.  Teaching the long way of solving math problems undermines the efficiency of student learning and merely serves as a time-burner to fill the length of the school year.  

On the surface, teaching these longer methods as opposed to only teaching shortcuts seems counterintuitive.  Introduction to and practice of longer methods can sometimes take an entire school week, yet learning about shortcuts for those same problems often takes one or two classes, at most.  Why take a few classes to explain how to find a derivative in 3 minutes instead of taking one class to demonstrate how to find that same derivative in half the time? That’s a question I found myself asking in my AB Calculus class last week, and given the competitive nature of today’s students, I am not alone in my confusion.  Wasting away class time that could be spent on quicker problem solving characterizes the high school math curriculum as a deterrent for advanced learning. That’s a reputation that high schools should want to reverse immediately.

Unless you’re a math wiz who finds satisfaction in completing a long problem, extensive techniques for problem-solving are becoming increasingly unappealing.  Digital services like Photomath, Khan Academy, and the sacred TI-84 Calculator offer a variety of shortcuts and tricks that can make even the most complex math problems seem easy.  As a result, today’s students are gravitating toward the use of these quicker methods, especially when it comes to crunch-time for in-class assessments and homework. In the past, some of these shortcuts have even found their way into the curriculum and are now formally taught, but high schools have yet to fully commit to them.  The time to do so is long overdue.

The main argument against burying longer problem-solving techniques is the belief that mathematics is about reasoning, not memorization.  Many claim that the ability to do extensive problem solving is invaluable in real-world scenarios. This argument loses relevance when one considers the future at stake.  The pace of technological innovation is so rapid that almost anything that can be made more efficient will be made more efficient in years to come. By the time today’s high school students will have begun their careers, digital platforms will likely be able to solve any math problem, and access to them in the workplace is unlikely to be restricted.  I see lessening the emphasis on longer problem solving as essential in preparing students for this technologically-dominated future. Teaching them efficiency and focusing on a clever approach keeps up with the fast-paced world, allowing them to be more successful with their schoolwork and opening up class time for other subjects to be addressed.

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