I have been giving out worked out answer keys to my math students for years. These are handwritten PDF keys that I have made showing how I would do the problem. Homework assignments and review assignments all had a worked out answer key online. At the end of last year, I started having second thoughts about my answer keys. And this year, I have completely abandoned them. Why? Mostly, I felt like I have been robbing my students of the typical thought process that should happen with any good math problem. You know, problem solving stuff like creating patterns, accessing prior knowledge, discovery, conjecture, failure and so on. So here is my list of 6 reasons why I have stopped making worked out answer keys. Also, at the end of this post, I have a couple of things that I'm now doing to replace the worked out answer keys.
1. Worked Out Answer Keys Eliminate "The Struggle"
What is "The Struggle"? I think of it as the tension of which path to take while solving a problem. This is a good thing. It is a natural thing. We all have "The Struggle" with math. It is the "uncomfortable" part of math. I love the fact that Brene Brown tells her students that they SHOULD BE UNCOMFORTABLE in her class. Why? Because learning is stretching, growing, and being vulnerable to say I don't know. If we eliminate this "Struggle", we will be taking away the "Joy" of mastering the problem. And yes, there is "Joy" in a high school math class. However, with no struggle, there is no joy. And the typical high school math class nowadays is just that... BORING.
Students often use each other to collaborate. When students have the worked out answer key in front of them, they don't need to work with anyone else to get at the solution. As a matter of fact, students don't even want to talk to another student for fear that it will mess up their thinking with incorrect advice. I think it is good for a student to listen to another students advice and be able to discern what is correct and what is not correct. It is a life skill.
3. Worked Out Answer Keys Create the Fear of Being Wrong
Another problem is that when we create a key, we are telling the students that you must do it MY WAY. Whether we intend that or not, we are sending a message. Do the problem my way or you will be wrong. Students get this right away and will not proceed until they know they are on the right track. They become afraid to try. Have you ever had a math student say they don't know what to do or where to start? I think this is a classic "I'm afraid to try something and be wrong".
4. Worked Out Answer Keys Stifle Creativity and Promote Memorization
I'm coming to the realization that creativity comes from the need to be creative. If we never give our students the opportunity to be creative, they won't do it. My own most creative moments have arisen because I had thought long and hard about some problem and couldn't get anywhere. Then, I would usually be doing something else, or exercising and think...VIOLA, I need to do it this way. The worked out answer key never gives our students the a chance to think long and hard on a question. It gives them the answer. It really never gives them the chance to be creative.
One thing I have been trying to avoid is having my students just remember the steps of how to do a problem. When students are memorizing the process, they are not really understanding the math. Typically this type of math memorization does not last too long either. Students might be able to repeat it for the test the next day, but is not in their math "tool box". When students see answer keys, they try to remember the steps of a problem instead of actually thinking through how to do it.
Can you imagine if someone EXPLAINED the solution to Towers of Hanoi to you before you actually tried it? That is not the idea of a puzzle. The idea of worked out answer keys is so that students will work out the problem on their own, and then check with the worked out answer key to see if they are correct. This doesn't usually happen. What end's up happening is the students will have the problem and the answer SIDE BY SIDE. So when the student gets even the least bit anxious about not knowing what to do, they look at the worked out answer key. Go ahead and try the puzzle below. Towers of Hanoi I almost can guarantee that after you tried Towers of Hanoi the first time you realized right away there is a better way. You worked at it. You figured it out. And you tried something different. This is called LEARNING! Giving worked out answers is like explaining the solution to Towers of Hanoi to someone BEFORE they try it.
I have found that when students have the worked out answer key, they don't need to ask questions. Worked out answer keys make it easier for us, but not so good for students in the long run. Questions are the essence of learning. We want our students to ask questions.
Two Alternative Ideas to Worked Out Answer Keys
1. ANSWER POOLS
Answer pools are the answers to the problems in RANDOM order. First of all, the answer is not worked out. Secondly, they know that if their answer is not in the pool, they have made a mistake. Then the students will keep trying. Click here for an example of an answer pool. Many times I put too many answers in the answer pool.
2. Public Posting of Student Answers
Students answers are different than the teachers answers. That is because the student is not sure if another students answer is correct. It gives our students the analysis skills. They look at another students work and glean anything that they can from it. Sometimes the student might consider different approaches to problems depending on the solution given. Example of a Padlet with student answers posted. I like Padlet to post answers. However you can use any discussion thread to accomplish the same thing.
What are your thoughts?
4 comments:
Hello! I'm a college student studying to be a Middle School or High School Math Teacher. One of my Math Education teachers encouraged us to start following Math Blogs to gain knowledge and insight for our future classrooms. Until I read this post, I never realized the disadvantages to providing students with worked out answer keys. Something I really hope to foster in my future math classroom is finding different and unique methods to finding the answers. Without worked out answer keys, students do not have to worry about having to follow a set procedure every single time. I do agree about the collaboration portion, but I would be nervous that if one student posted the answer on Padlet everyone else would copy off of that student. Have you had this issue yet in any of your math classes? The answer bank is a great idea since it tells students whether or not they are on the right track. Overall, I really enjoyed this post about alternatives to worked out answer keys. Thanks for sharing!
I'm going to try the answer pool idea for my class tomorrow. It sounds like a great solution for me, not wanting to give them all the answers (they do give up way too soon), yet it seems like just enough to encourage them to keep going if they find their answer in the pool. Thank you
I teach high school math in PA. I have always provided my students with an answer key, but not a "worked-out" solution key. It is important that students know if they are getting problems correct. When they do, it builds confidence and when they don't it facilitates their problem solving strategies. In this way, students can undergo a meta cognitive process - they are thinking about their thinking. It also takes the burden off of me to provide the answers to them in person, say, the next day in class. This accelerateds their learning curve. Some of my colleagues only provide answers to the odd numbered problems, not the even ones, to encourage student confidence.
Providing a worked out solution to one problem in a problem set, may be useful for some students as a way to scaffold their learning.
I am a high school math teacher in Maine and love the idea of having students submit their answers. I am trying to use more tech in my classes and I think it would be a great way for students to engage in problem solving via written communication. It's a great way for them to show what they know and try to practice speaking and writing mathematically.
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