Chapter 9: Marking - Behind the Scenes

Marking a math solution is fairly straightforward, right? You take a student's response to a question, you compare it to the actual solution, and you give marks according to how well their response compared to the actual solution. But is it really just that straightforward? I would argue strongly that it is not. 

Take for instance, a mathematics problem that can be solved in more than one way (otherwise known as any math problem). If a student were to be evaluated against an "answer key" that differs in structure from their response, they would not receive full credit, despite getting to the correct answer. 

What about students who use manipulatives or geometric representations to discover a solution? If they solve a question using pictures, is their "full solution" any less valid? For example, lets examine the question below:

A online store called Amathon is running an "add-on" promotion. The promotion states that if you order an item that costs $25 or more, they will "add-on" a free gift. If you place an order with two items that cost $25 or more each, they will "add-on" three free gifts. If you place an order with three items that cost $25 or more each, they will "add-on" five free gifts, and so on.

1) If you placed an order with ten items that cost $25 each, how many free gifts will you receive?

2) Write a rule that could be used to determine the number of free gifts you would receive for any order containing items of $25 or more. 

This answer could be solved in a number of ways. Most academic math students would simply model the situation using listed values, or values in a table. However, some students may want to use of a graphical or geometric representation of the situation (see example below) in order to make conclusions. 

original image 

Are any of these methods more valuable than the others? Again, I would strongly argue that no, they are all equally valuable assuming they lead to the correct answer. There is no way that a "marking scheme" could prepare for all of these possible solutions, so how can we fairly and accurately mark this question? The situation becomes even more complicated when we consider that a student may get only some of the question right. 

I believe that we need to revise the way we think about marking. A solution to a problem is not a static set of steps, but rather a fluid group of mathematical processes that lead to a final conclusion. Although a "mark scheme" can help us determine whether a student was able to get the correct answer, it should not be used to dictate whether a students' thinking process is right or wrong. When marking math questions, educators should take more of a holistic (for lack of a better word) approach. The final solution is important, but the process a student takes to get there is just as, if not more, important. Sure, it might be hidden within a graph, a seemingly random group of numbers, or a drawing that might look like a doodle, but it is our job to extract a students thought process and evaluate it accordingly. 

Thanks for reading!