James Shuls: Students Display Deep Understanding by Getting Answers Correct

by James V. Shuls, Ph.D.
Director of Education Policy, Show-Me Institute

Fill in the blank: In math, what matters most is the ______. If you answered "the process," you picked the answer supported by mainstream colleges of education and teachers throughout the country. If you replied "the answer," give yourself a pat on the back because you are correct.

Think about it. When your accountant does your taxes, when the carpenter builds your home, when scientists conduct experiments, what matters most? I can tell you, it is not the process. If the accountant gets the wrong answer, you could be in big trouble with the IRS. If the carpenter's measurements are off, your house could crumble. And if the scientist's calculations are amiss, their findings are invalid. The answer matters most.

Unfortunately, too many in the field of education have given correct answers a bad rap and held up the process as king. Let me illustrate with an example. My second grade daughter has been working on many word problems this year as part of her school's push to give "real world" examples. In the problem below, she correctly identified that the answer could be found by doing subtraction. That is, she needed to find the difference between the two numbers.

She used a standard algorithm and she got the answer correct — or did she? Not according to her teacher.

Grades are not assigned in second grade at my daughter's school, but students are given a rating of one through four. These numbers coincide with: does not meet expectations, developing, meets expectations, and exceeds expectations. The problem solving skills that she displayed here probably deserved a "meets expectations." Instead, she received the lowest rating possible.

Why? She did not follow the process. Interestingly, there have been other problems where she reached the wrong answer, but received a higher score.

This is not the first time I have taken issue with the math instruction at my kid's school. Two years ago, when we were in a different school, in a different state, I pulled my children out of a school because of the math program. At that school, they used a discovery learning approach and shunned standard algorithms. When we moved, we chose our current school because the district embraces standard algorithms and explicitly teaches concepts. Though the curriculum and instructional strategies are completely different at the two schools, there is one underlying principle to which they both subscribe. They believe that getting the correct answer does not imply "deep understanding." In the former school, students had to display their thinking in some form besides the standard algorithm. In the latter, students have to demonstrate their problem solving skills by following the prescribed process.

Both schools are amiss. When a student gets an answer correct, they are displaying deep understanding. They are displaying problem solving skills. Of course, there are times when a student may haphazardly stumble into a correct answer. That is not what I am referring to. What I mean, is that when a student can correctly identify the type of problem and can solve for the answer using some type of process, they understand the concept.

All of this is not to downplay the role of the process. The process matters tremendously. But as educators, we should not be so dogmatic about it. When we do so, we send mixed messages to kids and we prevent them from enjoying math. There are few things as discouraging as knowing you have done something right and then getting criticized nonetheless. Rather, we should celebrate correct answers and, when necessary, demonstrate more efficient methods or other ways of thinking about problems. This should be done while keeping in mind that what matters most is that our students have a method that works and is transferrable to other problems.

We continually tell students to "think like scientists" and "act like mathematicians." Do you know what good scientists and mathematicians do? They get the answer correct. It's time we elevate correct answers to their appropriate level of prominence and put the process in its place. The best way for students to display "deep understanding" is by getting answers correct.

James V. Shuls, Director of Education at the Show-Me Institute, earned his Ph.D. in education policy from the University of Arkansas. He holds a bachelor's degree from Missouri Southern State University and a master's degree from Missouri State University, both in elementary education. Prior to pursuing his doctorate, James taught first grade and fifth grade in southwest Missouri. His primary research interests are in the areas of school choice and teacher quality. His work has been featured in numerous media outlets, including: Phi Delta Kappan, Social Science Quarterly, Education Week, The Rural Educator, Education News, the Arkansas Democrat-Gazette, and the St. Louis Post-Dispatch.

James Shuls

James Shuls

James V. Shuls, Ph.D., is an assistant professor of educational leadership and policy studies at the University of Missouri–St. Louis and a fellow at the Show-Me Institute.
02 13, 2014
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