Wrong Answers Only

A popular trend on various social media platforms or websites is to post a picture or image and invite people to post “wrong answers only.” The creativity in the wrong answers is often brilliant. There is a level of cognitive gymnastics that a person does in making an answer wrong, but also close enough to have some humorous connection. Here is an example of naming this movie (Iron Man) with wrong answers only.

A sample response would be Feman in reference to the word Iron, which the chemical symbol Fe replaces.

People who view this type of meme, must analyze the picture and determine how the wrong answer is connected to find the humor. Developing connections and analyzing information is an integral part of being a mathematician.

I’m not too fond of some of the standardized questions students are presented with in math class. Students will often guess the correct answer or get the answer incorrect by making a computation mistake even if they have a rich understanding of the concept. As a teacher, I would ask students to explain their answers to understand the student response further and would often get an explanation such as, “I used this formula” or “multiplied these numbers,” which did not offer insight into student critical thinking. It often felt like a regurgitation of steps without much thought.

Instead, what if we removed the correct answer and gave students “wrong answers only” and asked them to analyze this situation, similar to the response to the meme at the beginning of this post?

The following is an assessment question related to transformations. Fully acknowledge that a question such as this is necessary to prepare students for standardized testing, but let’s try to improve it using a “wrong answers only” approach with the prompt that all these answers are wrong, please select one and tell me why. (Note: If you desire for students to tell you the correct answer, that can be the final step in the problem. Or better yet, discuss the right answer as an epilogue to sharing explanations of the wrong answers.)

Why I like this shift in problem structure:

1. Placing Value on Wrong Answers

As a student, I often learned more from wrong answers than correct ones. In particular, when I took the time to unravel why they were wrong. I like the idea of promoting this instruction practice of students dissecting why something is not working. Furthermore, there is a subtle nod of students developing some familiarity with the potential “traps” test writers might include in developing wrong answers as part of standardized assessments.

2. Promoting Student Choice and Varying Strategies

I love the idea of students picking which answer choice they want to analyze. There is potential for rich discourse alone in asking students which one they selected to explain, not to mention the actual explanations. Also, the number of strategies will most likely vary greater than if I had asked students to explain the correct answers. With many standardized questions, there is usually only one way or strategy to be accurate as apposed to the varying wrong answers. At the same time, there are probably more ways an answer may not fit that will demonstrate some student understanding of the concept.

3. Concept in Progress

Students may not fully understand how to answer a question, or their understanding of the concept may still be in progress. If we focus only on the correct answer, we may not uncover what a student knows about the concept. Students either get the problem wrong or guess the correct answer, leaving little evidence of their thought process if they have not developed the concept yet. In the example above, a student may not be able to find the rotation of the point 180 degrees about the origin. Yet, if a student picks one of the wrong answers and can describe a reflection, we can build from it to help them understand the concept of rotation.

It is important to note that I am not saying that determining the correct answer is not necessary. Finding the right solutions is part of developing mathematical proficiency that we frequently do in math class. However, I love the idea of pressing on student understanding and mathematical connections through “wrong answers only” as a twist to standardized test questions.

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