Since we started doing math in kindergarten, we’ve been taught to show our line of reasoning, whether it’s moving blocks from one pile to another, to taking the derivatives of polynomials. Making students show work is one of the most widely accepted methods of teaching math in the United States for a number of reasons. For one, it requires students to carefully consider every step of the process they’re completing, which helps eliminate mindless calculational errors in solving problems. For another, it helps the teacher examine how a student is solving a given problem. This, in particular, is beneficial as it allows teachers to gain a better sense of how to structure lessons in order to target their students’s strengths and weaknesses in a few ways. If a teacher can see a student’s train of thought, it’s easier to fill in gaps in reasoning in future lessons. It’s also useful if a teacher is trying to build a particular skill and would like students to solve the problem using that specific method.
However, showing work can also be incredibly stress-inducing for students, particularly on tests. With the clock ticking, every second is precious and every second wasted on showing work for a problem already solved feels meaningless and aggravating. Even without time pressure, plugging numbers into formulas and rote mathematical operations can seem menial and tedious, especially for students who like creative problem solving. Furthermore, this stress only increases when the command on the test is stated vaguely, with directions such as “Show work” or “Justify.” Standards are not made sufficiently clear and a student could waste time showing steps they don’t have to or take too little time, assuming that their line of reasoning was clearer than it actually was. This makes tests a trial of stress and time management, rather than a clear demonstration of skills.
Showing work also discourages creative thinking in mathematical scenarios. When students are taught to learn formulas by rote, write them down on paper, and plug in the numbers given, it becomes difficult to learn to problem solve without an obvious formula provided for the situation. Teaching students to trust their intuition and work things out in their heads, even if they can’t translate it to paper, will be beneficial overall for strengthening their creative math skills. And though showing work and writing things down will often be necessary for solving complex problems, the emphasis during classroom learning should always be in-depth understanding of why things work and how to apply them, as opposed to simple memorization of formulas. Even just for the sake of reframing a problem when you get stuck, being able to reason about it even before you get anything down on paper is vital.
Clearly, there is some balance to be struck between the benefits of showing work (organization, checking solutions, and accountability) and the above drawbacks. To me, the answer seems to be that there is a time and place for showing work. On particularly complex, multi-part problems, students should naturally show their work if only just to keep track of all of the numbers. When there is a particular skill a problem is testing, it is within the teacher’s right to request that students demonstrate how that method would be used to solve the given problem. However, if students are getting less than full credit on problems for which they provide the correct answer because they don’t show work, the motives and method behind the request to “Show work” or “Justify” should be examined. Was it clear exactly what the teacher was asking of their students? Was it clear why the teacher was asking this of their students? If not, further discussion between teachers and students is necessary for the welfare of both them and the subject of mathematics as a whole.