Many math teachers ask their students to show their work or to write a sentence or two explaining their thinking. Some teachers even mark math homework as incorrect or only give partial credit if the student doesn’t show their work or explain their thinking.
It’s understandable that some learners might find it frustrating to have to explain how they solved a math problem. After all, some learners just get it, and some can even solve problems in their minds without writing anything on paper. Why should these intuitive math learners spend extra time showing how they figured out that 4 x 4 = 16 or that a 15% tip brings the total cost of a meal to $25.00?
The truth is that even though these learners may sometimes feel frustrated, it’s usually still worth it for math learners to show their work. Here are three reasons why:
Showing work can help you figure out where you made a mistake.
Let’s imagine that Marisol the math student’s teacher gave the class a two-step word problem that involved first finding out how many students were at school on a service project day and then dividing these students into 7 equal teams. The school has 126 students total, but 14 students were absent the day of the project. The teacher wanted Marisol and the other students to show their work by drawing a tape diagram or picture and clearly demonstrating every step they took to solve the problem.
Marisol solves 126 ÷ 7 in her head and then quickly writes down an incorrect final answer of 18. She feels confident in her answer because she knows she has to divide to get equal teams, and she is great at mental math. Unfortunately, because she never drew a tape diagram or picture to show her thinking process, it may be hard for her to see why she got the question wrong. Her picture or diagram would probably have helped her realize that she skipped an important step by not subtracting the number of students absent from 126.
Seeing how a learner solved a problem helps a teacher, tutor, or caregiver know what the learner does or does not understand.
Let’s imagine that Mica the math student’s teacher asked the class to solve this multiplication problem: 26 x 38.
Mica understands how to multiply two-digit numbers really well but sometimes flips numbers in his mind. Mica solved 26 x 83 and got the answer 2,158. If Mica only writes down the final answer, the teacher might assume that Mica doesn’t know how to multiply two-digit numbers.
But if Mica shows his work or explains the steps he took, the teacher will see that Mica knows how to multiply but just mixed up two digits. The teacher may also give Mica partial credit on homework or a test. They may also help Mica by reminding him to check the order of the digits when doing math work.
Showing work or explaining process builds critical thinking and communication skills.
It’s true that not every math problem requires lots of shown work or a sentence explaining how the student solved it. A learner may just know that 4 x 4 = 16, for example. And in an in-person class, a teacher can circulate and ask students to explain their thinking verbally rather than in writing. However, developing the ability to describe—in numbers, words, or both—how you solved a problem is beneficial in at least two ways.
First, being able to clearly show or explain step-by-step how to do something is a skill that transfers to many real-life situations: from sharing a recipe to writing a protocol for scientific research.
Second, becoming aware of your own thinking process and learning habits helps you tackle learning tasks in all subject areas at all levels. For example, if Marisol knows that she is a quick thinker who tends to miss details when she hurries, that awareness can help her become a stronger reader. Recognizing that she reads math problems a bit too quickly, she might start to read more slowly and carefully in her science, social studies, and language arts classes, too.
Math is about more than just finding quick answers. Math is a language, and part of being fluent in a language is communicating your thoughts to others. Math is also about more than final answers. Math is a process and an opportunity to build self-awareness and problem-solving skills that can be applied both inside and outside the classroom.
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