June 4, 2020

## Should Partial Credit Be Awarded on Math Tests?

This is a debatable subject. Math teachers seem to be on one side or the other. When asked for reasoning, I hear things such as, “No partial credit should be given because the real world doesn’t allow for things to be wrong.” Other teachers are very busy and don’t have the time to look at a student’s work in the detail needed to figure out where their mistake was or what their thinking was, so they could correctly award partial credit; it is much easier to just grade it as 100% right or 100% wrong. On the other side of the coin, teachers who award partial credit encourage students to “show their work” and want to encourage students for getting conceptual parts of the problem correct and not penalize them for making one tiny mistake in a multi-step problem that demonstrates that they have actually learned what they were being taught. We are all human after all.

So – what is the correct approach? Should partial credit be awarded? If so, how much should be awarded? When should it be awarded? Do teachers have the “right” to choose the 100% right / 100% wrong approach? Is it fair for some teachers to grade students this way, hence awarding a B or C to a student that might actually have a good grasp of the content when another teacher who gives partial credit would give that same student a grade 10 points higher – and hence the “unlucky” students who get the non-partial credit teachers look like they understand less (when in fact they don’t) than another student who happens to have a teacher who awards partial credit?

Are all math teachers flawless? If they were not to use a calculator at all, would they never transpose a number or accidentally make a mistake? Of course not, all teachers (myself included) have been corrected by students when we occasionally make a mistake during our lessons. Yet, we are willing to subtract 8-10 points off a test grade if the student does the same?

What if the problem is testing a very difficult concept and the student gets all the concept correct, showing they clearly understood everything taught to them but they accidentally transpose a number or maybe made a silly arithmetic mistake or even lost a negative sign in all the written work required as they were focusing on the difficult concept. Are we then to reward them with no credit when in fact they clearly learned what we were trying to teach them?

Here is a quote from Brian Boley, “Avoid the “partial credit” trap when teaching middle school and high school students. Someday you may drive over a bridge which one of your students designed. Do you expect him to have calculated the loads correctly or should he get “partial credit” for getting a close answer? And all because you taught him that using the right equation was worth 90% of the problem — and adding 2 + 5 = 8 was only 10% off.”  His argument is sound, right?  Who would want to be on that bridge?  Yet, is that what partial credit is promoting?  Would we give credit for 2+5 = 8?  Of course not, that is wrong.  The entire concept that is being taught is wrong and hence no partial credit should be award in those cases.  When the student misses the concept, they do in fact lose all credit for the problem.  If they do a math problem in Algebra and have no understanding – just a few random ideas – that is not a time to offer partial credit.  We are talking about giving credit to the student who made a careless error but who clearly understood what they were doing.  Remember, we are not building a bridge, if we were, we wouldn’t have a new student learning something for the first time doing the math for it – that is not how the real world works – school is a time for learning.  A “close answer” does not equal credit, what equals credit is a demonstration of the concept being tested or a partial demonstration of that concept that shows you got 1/2 the concept and you missed 1/2 the concept so we will award you credit for the 1/2 of the concept you got correct and take away credit for the 1/2 of the part of the concept that you still need to learn.  It is just a way to break up the scoring of a problem with multiple steps into multiple scoring which is a fair and reasonable thing to do.  So, when you hear arguments like Brian’s, don’t immediately think – yeah, I don’t want to be on that bridge – don’t worry, brand new Algebra students or middle school students don’t build bridges.

What is our goal in teaching mathematics? Don’t we want people to stop saying, “I am not any good in math.” Well, we will just continue to perpetuate this problem by not rewarding students with partial credit especially when it is obvious that they grasped the concept being taught and the mistake was elsewhere! Why don’t math teachers care about our students’ perceptions of mathematics? How can you choose to be a math teacher when you don’t care enough to make students want to feel good about math. Now, don’t get me wrong, I am not a proponent of teachers who give grades for undeserved work! I met a woman who wanted her students to feel positive about math so she gave everyone a B or higher – no matter what they did. That won’t help them either. They must earn their grades but if you give them positive feedback, encouragement (which includes acknowledging their efforts and what they have learned and accomplished with partial credit), they will respond with a better self-image about mathematics which in return will improve their efforts, attitude, study habits, and hence their grades.

I also don’t agree that life only allows for Right and Wrong answers. If that were the case, we would all be in a lot of trouble. We are human, we make mistakes, it is a great thing for kids to learn that we acknowledge that we all make mistakes and don’t expect perfection and that the world does not expect perfection. Even working a job, people will make mistakes, if you do, you figure out where your mistake is, you communicate with others, you realized the solution is not working so you rework the problem and find your own mistake, etc. Very few people do everything perfect the first time in the real world. Why would we penalize our kids psychological well-being as well as their future (see grade issue above based on the 100% wrong teachers vs. the partial credit teachers) because they made a small arithmetic mistake even though they correctly integrated this very long function?!

I also think we owe it to them to look at their work and try and find their mistakes or if teachers don’t have the time, get creative. Mark it wrong and let the student come back with a test correction where they show the teacher where their mistake was and offer them partial credit back at that point based on WHY they got the problem wrong. It makes the student go back and find their own mistakes and yet still gives them partial credit.

Award partial credit appropriately. If the mistake was just arithmetic and the concept was Algebra – they lose a little. If they transpose numbers but did the whole problem right with the transposed numbers – they lose almost nothing! If they make a partial Algebra mistake – they lose much more credit, depending on how much of concept they were able to get. For example, if solving an Algebra word problem, if they got the equation right but then had no idea how to solve the equation – they would get half (or more than half as finding the equation is really the hard part) credit – if they got the equation and just made a “mistake” solving the equation but seemed to know the general process, they lose less. So partial credit is not awarded equally. If a student is solving an order of operations problem and they do the order of operations correct but state that 4^2 = 8 instead of 16, they should be awarded a large part of the credit since the problem was testing order of operations but lose some for not knowing how to evaluate an exponent. If they make that same mistake again in future problems but again solve the problem correctly, the amount lost should be minimal since obviously they will continue to make that same mistake but you already took off for it and the teacher should be looking for the main idea of the question, not marking every problem on the test wrong just because the student missed this one concept of how to evaluate an exponent even though they can solve everything else about the other problems correctly.

So, to answer the question – Should partial credit be awarded on a math test? The answer is a resounding YES. I hope this article points to the many reasons why it is important to award partial credit to students on their tests.

Author: Lynne M. Gregorio, Ph.D. in Mathematics Education
Owner: Triangle Education Center and Educator for over 23 years.