“Show your work.” A common theme on math worksheets and tests. Yet, despite the frequent refrain, it’s actually quite difficult for teachers to describe what good examples of “showing work” actually look like. It’s been called a “good and hard question to answer” by a college math instructor. Middle school math teacher Michelle Russell wrote an entire blog post about why this is difficult to describe. However, if we go back to the “why” question, it might give us a glimpse into the “how.”
Students should show their work in math so that
- the teacher can identify understanding and misunderstanding
- teachers, students, parents, and tutors can identify errors and tailor tips accordingly
- some varieties of learning accommodations and needs can be unmasked and addressed at the most beneficial times
- students learn to communicate procedural steps while the stakes are lower and the problems are shorter
- students can identify and use patterns and efficiencies of thinking
- students can learn to correct errors along the way rather than having to start over each time
- students can demonstrate their brilliance to the adults around them
Why should students show their work in math?
- Shown work helps the teacher know what concepts a student understands an what misunderstandings a student has. This allows the teacher to know what they might need to go over individually or, when many students have the same misunderstandings, reteach.
- Shown work allows a teacher to know what types of errors students are making. This allows the teacher to give study, test-taking, and other tips targeted specifically to the types of errors the student makes.
- Shown work can help a teacher identify when a student might benefit from learning accommodations or different types or learning strategies.
Have you ever heard a list of directions or instructions that were either too short (leaving you with questions) or too long (leaving your eyes and brain swimming from too much information)? Learning to show work well helps us learn what’s important and what’s unimportant to tell someone any time we have to communicate a step-by-step process to someone else.
Attempting to follow the “show work” instructions in a college engineering class, my friend Ward received the demoralizing feedback that the amount of minute detail he showed demonstrated that he either “didn’t study enough” or “had no aptitude in mathematics.” To a young engineering student, you can imagine how this must have hit his heart and his dreams, especially since he only did this in an attempt to follow the instructions given. I hope this is increasingly unusual among even university faculty, and I can not excuse this professor of this unfeeling feedback. However, it does illustrate the idea of how learning the skill of balancing detail with big picture while young and while the problems are short can pay off by helping avoid awkward moments like my friend Ward faced.
- Showing work builds the student’s communication skills. Communicating mathematics can be one of the hardest parts of the subject. But the communication skills built in this process go beyond mathematics.
- Showing work organizes the student’s thinking.
- Showing work allows the student to make corrections along the way rather than starting over each time.
- Showing work allows the student to use efficiencies in and notice patterns of similar problems.
Parent’s or Tutor’s Perspective
- Shown work allows a parent or tutor to help the student find any errors, correct them, and avoid them in the future.
- Shown work allows a parent or tutor to see into the processes and procedures students are learning and using in class. Thus, the parent or tutor can speak to the student at the level they’re prepared to understand and build the student’s mathematical confidence.
- Shown work helps a parent or tutor recognize common errors the student makes. They can then strategize together how to avoid this general type of error in the future (eg, helping the student know when to slow down, when to check arithmetic on a calculator (if allowed), etc.)
- Shown work can help a parent or tutor identify when a student might benefit from learning accommodations or different types or learning strategies.
- Shown work can help a parent or tutor get to know the student better by showing a glimpse into the student’s brain and how they think.
What happens when students don’t show their work?
- The teacher does not know what the student understands and doesn’t understand, only whether the student can recite rote facts.
- The student has to recreate the entire process from the beginning whenever a followup or similar question is asked.
- Student needs for reteaching, for accommodations, and other indicators are buried and/or hidden.
- Parents are frustrated with not understanding or knowing how math is being taught to their children in class.
- Students may make patterns of error types that are masked by the lack of work, but could be identified and corrected if work is shown.
- Students may make memory errors in the middle of a problem.
- Instead of learning the skills to explain processes in these smaller settings, students may struggle to know how to explain larger processes in situations where the results matter more.
- The student may miss out on partial credit if the final answer is wrong, or be penalized for not showing work.
- The student may struggle with alternative question types: “we know / we’re pretty sure the answer is _____. Can you prove it?”
What if my student is neurodivergent or has physical or fine-motor limitations?
You know your child best! Hopefully, you and your child’s teachers have access to the technology and support they may need. I encourage you to seek out solutions that do allow your student to show their work. Many of the reasons above apply just as well to students with non-standard needs. In addition, many of these students are very smart, though it unfortunately takes the right communication tools to be able to demonstrate that to teachers and others. Help them unmask the intelligence you know is there. Finding a way to allow your child to show their thinking, even when it’s difficult, can show off their brilliance. Take advantage, as much as you can, of the advances in both learning research and in technology that allow students to communicate mathematically in ways that are accessible to them.
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