This semester to explore a statistics minor, I enrolled in the introductory course, STA 215. To learn course material, we have a couple different mediums, such as online assignments or textbook work.

The other day we had a worksheet for homework, which we didn’t go over in class yet. I overheard on student ask the professor if he had an answer key to check his work. The professor replied that he didn’t, but if the student was unsure about his answers, he should work through the problems with a peer.

This small interaction made me think about the effectiveness of answer keys in math-based classrooms. Although there is some creativity in the technique used to get from the question to the answer in subjects such as statistics, this flexibility is very minimal.

Despite some variation in methodology being possible, there is typically only one correct answer. If there is any freedom in answer possibilities, it will be contained in a calculated range. It is not subjective. In consideration of this, should students be provided with answer keys to confirm they are reaching the right conclusion in order to learn?

One problem teachers might come across if the key is handed out prior to collection is that students may just copy answers. They many not even attempt to complete the assignment on their own. They might wait until five minutes before class to scribble down the correct answers, and if the answer key only provides the conclusive answer, the product might even be absent of copied work. It will just simply be a question with an answer. There will be no technique at all. This is certainly not learning.

However, students on the opposite end of the spectrum who don’t have those answer keys and are still scribbling quick responses before class for credit in participation are not learning either. They’re not even truly participating. They’re just handing in a sheet. It’s all for looks.

Is that student any better off than a student that didn’t write anything at all? Did they learn more? No, of course not. They only thing they demonstrate is good behavior. They turned in the assignment they were supposed to. Whether an answer key is present or not, these type examples will not teach methods of solution.

Answer keys can be effective when they provide not only an answer but also model techniques to reach that conclusion. Modeling is essential in many classrooms but especially in math-based ones. If it is used with some as an example, then students try very similar problems independently. They are beginning to exercise some learning. Then, they can relate these models to more complex versions for example problems where different variables are included or excluded.

The questions need to be phrased in a new way in order to actually test comprehension. Repeated practice is essential, but it can’t be done without something to reference. We need models as a foundation to build our skills and we need to practice concepts constantly.

While answer keys can’t always be used, it may be helpful to have a model on the homework for a specific type of problem at least in the beginning. This could also be incorporated into online assignments by having each step outlined, then actually showing your work as a progression instead of just giving a final answer.

Whether answer keys are implemented or not, the focus of instruction should be shifted from what is the answer to how we get there.