Showing Your Work When There's Nothing to Show

Does your visual-spatial child answer math problems accurately, but never show the steps taken? Can your child solve complex long division or algebraic equations, but is not able to tell you how the answer was obtained? For visual-spatial learners, those who think and learn in pictures, rather than in words, there are few requests more frustrating than, "Show your work.." Because this type of learner intuitively grasps the "big picture" rather than taking what would be a painfully slow series of steps to reach a conclusion, the demand to "show your work," is nearly an impossible task. Visual-spatial learners (VSLs) very often just see the correct answer-and they're right. They cannot tell you how they know, they just know. They cannot tell you how they got their answer, they just get it.

In no subject is this a greater problem than in math. Because most teachers are sequential thinkers, they teach in a step-by-step manner and expect their students to solve math problems in a step-by-step fashion. They also tend to anticipate that their students will be able to demonstrate their work by detailing the steps they took to arrive at their answers. The same is true for textbook developers and those who construct state achievement tests. But, for someone who thinks in pictures and sees the correct solution without ever taking a step, this could result in a devastating outcome. Every day, students are admonished, even accused of cheating, because they are intuitively able to reach accurate solutions to complex math problems but absolutely unable to explain how they got there. Most of the time, they lose partial or full credit for their answer because they did not show their work. At a time when "thinking outside the box" is a revered ability in the business world, when to be able to find solutions to complex problems is highly regarded (and don't we need answers to today's complex problems?), it's time we stop penalizing these students for their innate gifts and begin honoring what comes naturally to them.

Until that day, however...

It is quite likely that visual-spatial students sitting in math classes at all different levels, are being docked credit for answers they cannot support with detailed steps. Nearly every standardized achievement test in the United States deducts credit when the steps are not shown to solve a particular problem. So, I propose it's time we teach visual-spatial learners to fight back! "Show your work," doesn't have to mean "complete the problem exactly as I, a left-hemispheric, auditory-sequential thinker would." It means, teach me, the left-hemispheric, auditory-sequential thinker, how you did this so I can do it myself. Show me, in the way I learn best (step-by-step) how to do this. When students know the material well enough to teach it, they really know it. If we help our visual-spatial students learn how to explain their answer to someone who does not think in images, then we've succeeded in teaching them to show their work, how to offer the smaller details, and, hopefully, to cease the unfair practices of losing credit on their tests and assignments.