How to Grade & Evaluate Student Math Solutions

Instructor: John Hamilton

John has tutored algebra and SAT Prep and has a B.A. degree with a major in psychology and a minor in mathematics from Christopher Newport University.

In this lesson, we explore the difference between a mathematical procedure and a concept. We'll also discuss how teachers can grade and evaluate math solutions for the purposes of student assessment.

Assessing Math Solutions

Back in the olden days, a teacher would present a student with a math problem and then mark the student's answer as correct or incorrect. But standards have changed. Common Core standards demand that students do more than just determine answers; students must also explain their answers.

So, nowadays, teachers to do more than just grade the solutions to math problems. They also evaluate math solutions to assess students' understanding of how and why they arrived at their answers.

Assessments that reflect math standards accomplish several goals for you as a teacher. They:

  • Foster general academic growth
  • Promote equity in regards to students and standards
  • Promote student learning
  • Determine whether the student gets the answers correct
  • Reflect whether the student truly understands and grasps the material

Math students should be given formative and summative assessments. A formative assessment occurs during a lesson or unit to assess student understanding and determine whether or not instruction needs to be modified to improve comprehension. A summative assessment is given at the end of a lesson or unit to test student understanding and compare the learning outcome to the standard. Many teachers use a standards-based rubric, or scoring guide, to grade and evaluate math solutions and to determine whether or not the solutions meet the standards.

Mathematical Concepts vs. Mathematical Procedures

When you grade and evaluate math solutions, it's important to distinguish between mathematical concepts and mathematical procedures. A concept can represent a strategy as well as a big idea or an understanding. A procedure is a rule, series or steps, process.

Knowing a procedure does not necessarily lead to conceptual understanding. For example, a student might be able perform the procedure of adding 1/3 and 1/3 and arriving at the answer of 2/3. But the student might not truly grasp the concept that a fraction is part of a whole. In other words, if we take a whole apple pie and cut it up into three sections, the student might not actually understand that each section of the pie is 1/3 or that two slices is 2/3.

So, as you are grading and evaluating math solutions, consider ways to assess students' ability to complete a procedure as well as their understanding of the concept. For example, you could ask them to complete a numerical math problem and then explain, in words, how they arrived at the answer.


A good assessment can tell you where students are in relation to the standards. Let's look at a few examples to gain a better understanding of how this might work.

Subitizing Assessment

Being able to subitize (pronounced soob, not sub) is an important mathematical standard for elementary students. This skill requires an understanding of concepts. Students who can subitize can recognize a collection of items without having to count. For example, if you held up three fingers on one hand and two on another, a student who can subitize would tell you that you are holding up five fingers without counting each finger one at a time. You can teach students to subitize with manipulatives, or objects that can be handled to facilitate the understanding of a math concept, like dominoes, dice, or flashcards. These same tools can be used to assess students.

Iteration Assessment

Math standards require students to understand how to choose the correct unit for measurement and how the chosen unit influences the number of units required to measure something. For example, measuring a large parcel of land in inches would result in a large number of units, while measuring the length of a baby carrot in feet is a conceptually difficult idea.

Students who understand unit iteration, in which a length is measured by repeating the length of a single unit, often have an easier time choosing units and making accurate measurements. For instance, take your students out to the school soccer field and have them measure off a 35-yard kick with a yardstick. Do you see how the students would have to lay down the yardstick to measure the first yard, and then flip the yardstick over 34 more times as they walked in a straight line?

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