How to Grade Math: A New Perspective for Homeschool Parents

If you are a homeschooler or a teacher, there is one task that most of you dread: Grading! This article aims to take the dread out of grading and give you a different perspective on grading, specifically grading math (although the principles can apply to other subjects as well.) 

So, what makes grading daunting? 

Often times homeschoolers (and even teachers!) think you need to grade every single assignment. Multiply this by the number of kids, and you’ve got a whole lot of grading to do! Counting how many correct, how many incorrect, figuring up a percentage grade…it can get very daunting and tedious very quickly. 

But what is the alternative? 

It’s simple, really: just don’t grade practice work!

Now, don’t get me wrong, it’s important to check work for accuracy. But if all you are doing is skimming the work checking to see if the answers are correct with an eye towards misunderstanding rather than counting how many correct and incorrect, you don’t use up near as much time. Checking for accuracy only allows you to spend more time on the most important thing: helping your student master the material he/she missed. 

If I’m not grading practice work, what should I grade? 

The purpose of grades should be to asses mastery and learning. Therefore, you don’t grade practice work, but you DO grade any quizzes, tests, and exams. Those are given to see how much a student has understood/retained, and therefore give a more accurate picture of what a student actually knows. But here is the kicker: late penalties and timed tests should have NO place in graded exams, especially math! Why, you ask? Let’s use an example.

Say you have two kids, Tom and Joe. They were given the same 15-question math test. Tom finished his test in 25 minutes with all questions correct. Joe finished his test in 45 minutes with all correct answers as well. They both had all correct answers, but one student was much slower than the other. Does that mean one student hasn’t mastered the material? Does it mean the fast student is “smarter” than the slow student? No! It just means one student works slower. Fast does NOT equal smart, ESPECIALLY in math. Some of the greatest mathematicians worked the slowest! 

Let’s Look at an Example

Let’s take those same two students and give them the same test, but this time they have a 30 minute time limit. Tom finishes his test in 25 minutes, and still gets all questions correct. Joe, on the other hand, runs out of time, and only answers the first 9 questions, but he got those questions correct. However, Tom got an A, while Joe got a D because he didn’t answer the last several questions. They both have the same understanding but Joe is just slower, so he wasn’t even able to try the last several questions. Does that seem like a fair an accurate grade to you?

Let’s take it one step further and give you a bit more insight into Tom and Joe and the test. The test consisted of 5 computation problems and 10 word problems. Tom is a fast reader and quick writer, so he can handle any problem with ease. Joe is a slow reader and slow writer because he has a few added challenges: he has dyslexia and ADHD, but his ADHD is undiagnosed so he doesn’t have any accommodations for math. He understands the math computation easily and excels in math,  but struggles with the word problems because reading is difficult and staying focused through long word problems is doubly difficult. Now how does the grading seem? Is it fair to treat Joe the exact same as Tom? Of course not! Students don’t need documented disabilities to put them at a disadvantage during a timed test. If you TRULY want to know how much a student knows, they should be given as much time as they need (within reason). Leaving timed tests behind is an easy way to meet ALL students where they are at, regardless of their learning challenges, documented or not. 

Okay okay, you say. Time limits aren’t helpful. But what about late assignments? If I don’t count students off if they are late, won’t they just never turn in their work on time? Think about it this way: You have a deadline to finish a project by Thursday and it’s Monday. You start on it, get some of it done, but life happens, it’s Wednesday, and you aren’t going to have it finished. What do you do? Do you turn in a sub-par result or do you ask for an extension so you can turn in your best work? As a boss, what would you prefer? Sub-par work on time, or your best work a little bit late? 

A student’s goal is to learn and master the material. Sometimes that takes a little longer than anticipated. I don’t want students doing just enough to qualify and turning in crappy work. I want students taking a little more time and giving their best. Students are still learning responsibility and time management. They aren’t small adults with all of the tools needed to be on time all the time. Our goal as teachers (and parents, you are teachers too!) should be to help them learn and practice those skills, not punish them for not being perfect. A math grade should be just that: a grade that tells you how much math they have mastered. If you knock a student’s grade for late work, does that grade really reflect how much they have learned? Will the late penalty teach them how to avoid a repeat occurrence in the future? It seems counterintuitive, but students are more likely to work hard and follow deadlines when they aren’t penalized for missed answers on practice work and late penalties. If they still struggle to meet deadlines, it is up to you as the parent/teacher to figure out WHY they are struggling in that area and teach them strategies to overcome it. 

A Different Perspective for Grading Tests 

We talked about how you shouldn’t grade practice, you shouldn’t give timed tests, and you shouldn’t give a late penalty. So what SHOULD you do? 

Most people think that math is as clear cut as you got it right or you didn’t. For some questions that is true, but for most there are varying levels of understanding/correctness, so when it comes to math, I prefer to grade using a rubric system. 

Above you see the rubric that I use to grade my students’ tests, quizzes, and exams. Here is how it works: 

• First, I tell all my students ahead of time to show ALL THEIR WORK. If they don’t show their work, they don’t get full credit. I do that for two reasons: 
  1. If they don’t show their work cause they are lazy, then they aren’t proving understanding and giving it their best, so they don’t get full credits. A correct answer but no work would get a 4.
  2. If they don’t show their work because they know how to get the right answer in their head don’t know how to write it out, that means they don’t fully understand the concept, and thus haven’t earned the full credit 5.
• Second, I use the rubric to give each question a rating 1-5 based on how they answered it, what they got wrong, and why they got it wrong. It takes a bit longer to grade this way, but it gives you a far more accurate picture of what they need to work on (i.e., computation, attention to detail, the math concept itself, which step of the question is confusing them, etc) so its much easier to correct and practice any misunderstandings. 
• Third, I tally up how many points they got and divide that by the total number of points, and you get a percentage. This is what goes in the grade book. 
• Fourth, and this is THE MOST IMPORTANT STEP, I go back and reteach/practice anything they didn’t get correct, or, if attention to detail was the main issue, we do ‘detail challenges’ where we practice following directions with lots of detail that requires focus and attention. 

And there you have it! That is how I grade my students’ work. Especially when you get into upper level math where some problems have 5+ steps, having a rubric instead of a simple yes/no is so helpful. Imagine a student working a long polynomial problem correctly, only to miss the last step. To grade that with a zero because the answer isn’t correct doesn’t reflect the student’s knowledge. Giving a student a 4 out of 5 for that problem much more accurately represents their level of understanding. 

Have any questions? Reach out and let me know!

Lastly, I’ll ask YOU a question: 

What did you think of this article? Do you agree? Disagree? Have you ever heard of this grading philosophy? I’d love to hear from you!

- Mrs. Holman 

About the author: My name is Carolyn Holman and I've been a math teacher and/or tutor for over 10 years. I have a bachelors in mathematics and a masters in teaching, and I am currently a certified teacher for grades 4-12 math! I have always had a passion for teaching, and I LOVE seeing the lightbulbs go off in students eyes when they finally UNDERSTAND math. If you have a middle/high schooler and you don’t want to teach or grade their math, I’ve got you! I teach both live and self paced Pre-Algebra, Algebra 1, and Algebra 2 classes, tutor, and have a Get Ready for Pre-Algebra self-paced course. I'd love to meet you and your students! To see all that I offer, you can check out my profile here on IndyEd or on my website at mrsholmansclassroom.com. To get the latest news and updates, subscribe to my email list! I love keeping in touch will all of my students!