At the end of each unit we complete, I write and distribute practice tests for my students to complete. The practice tests provide an opportunity for students to review and synthesize the material, see the types of questions they will encounter on the actual test, and develop their test preparation skills.

For me, the creation of a practice test usually means the creation of a solution key — a document that not only contains the correct answer, but also a step-by-step, sometimes annotated solution that shows how I arrived at the answer.

There’s no question that students want solution keys. They want to know if they’ve gotten the right answer. Or they want to see how they “should” complete a problem. But recently, I’ve begun to ask myself: do we undermine student learning by providing solution keys? More and more, I find myself answering: Yes.

My response to this has been to shift toward creating opportunities for students to crowdsource their own solution keys using Google Docs. But before we get into that, let’s consider some reasons why providing students with solution keys can have unintended and negative consequences for student learning:

  1. Solution keys allow students to “give up” sooner than they should. Despite all of my advice about persisting through challenging problems and trying different approaches, I find that students give up too quickly when they know a solution key exists. 
  2. Solution keys direct students’ focus to the “right answer.” Whether I intend this to happen or not, when students look at solution keys, the first thing they do is look at the answer. They want to know whether they are right or wrong. If they are right, they rarely look at my proposed solution; they simply move on. If they didn’t get the correct answer, they look at the worked-out solution, and then move on. Either way, there’s very little engagement in this process. 
  3. Solution keys inadvertently communicate that there is one right way to get the right answer. Even though I repeatedly remind students that they are many different ways to approach a problem, I generally provide one when I create a solution key. And because I do that, students who do study my solution walk away thinking that my approach is the only approach. (With that said, I generally provide the most efficient approach, but how many students actually take the time to try multiple approaches in order to determine efficiency? If students only look at my solution and then look at theirs without doing any additional work, the efficiency argument often takes a back seat to getting the right answer.) 
  4. Solution keys do not teach students how to check their own work. We want students to be able to assess their own work. I often ask students to determine whether their solution is reasonable, or I ask them to try to approach the problem in a different way to check their solution. But when I provide a solution key, I take away the need for students to practice these strategies. Come test day, students must possess the ability to assess their own work, so we must ensure that they practice this skill ahead of time. 
  5. Solution keys reinforce students’ tendency to view the teacher as the person who determines correct vs. incorrect. Connected to #4 above, I want students to assess their own work. I also want students to assess one another’s work. I work really hard to create a learning environment in which everyone in the room is both a teacher and a learner. By providing solution keys, I emphasize my role as teacher and I take away students’ opportunity to be the teacher. 

So what can we do instead? In my classes, I often tell my students:

  1. I ask them questions that I believe they can answer. They may have to work at it, but the problems are within their range of ability.

  2. Collectively, my students are capable of much more than they are as individuals. Their combined intellect, observations, questions, and conclusions will lead to much greater insights.

These two beliefs have led to a new exercise when helping students prepare for a test. I still write and hand out a practice test, but provide a solution key only to the first few tests, largely to model for students how to organize and present their work. In place of the solution key, I create a Google Doc that contains each question on the test; every student can access this document, allowing the entire class to work together to crowdsource a solution key.

Here is a screenshot from one crowdsourced solution to a problem reviewing similarity and quadrilaterals. After one student proposes a solution, other students add their comments and questions, and a discussion ensues:

Screen Shot 2017-07-26 at 23.08.07

Student 1 took a straightforward approach, typing a two-column proof to address the prompt. However, Student 2 then offered some feedback and a question about whether or not one can fully answer the question, followed by Student 3, who responded to Student 2. All of the students in the class can watch the discussion unfold and join in if they want to contribute. (Note that Student 2 uses the “∆” notation, and Student 3 has used the Insert Equation feature in Google Docs to create proportions.)

The next diagram is a continuation of the discussion, as Student 4 responds to Student 2. In this case, I’ve decided to add a comment in order to push this student’s thinking further.

Screen Shot 2017-07-26 at 23.08.16

So far, the outcomes have been terrific. In no particular order, here are some observations that I’ve made with multiple experiences with this process:

  1. Although initially anxious about whether or not they’d arrive at the “right answers,” my students are now better able to assess their own work without needing me. 
  2. Together, the students create their own solution key. I don’t have to do this for them. 
  3. The only way to know if someone has completed a problem correctly is to try it for oneself. Students can engage one another, ask questions, debate, and gain clarity. 
  4. The students teach one another, reinforcing the idea that we can all teach one another and we can all learn from one another. 
  5. There is a learning curve in terms of teaching students how to use various features to communicate their ideas. They can draw diagrams, insert symbols, and Insert Equations to format their writing using mathematical notation. Other students complete their work using pencil-and-paper, or on an iPad, and then upload a screenshot of their work.

  6. This process helps students understand the importance of providing clear explanations so that their peers can fully understand their arguments. 
  7. I don’t entirely remove myself from this process. Instead, I occasionally add a comment, ask a question, or provide a hint, using my contributions to push students to think about the question in a different way. However, I do not contribute by telling students whether they are right or wrong. 
  8. Whereas small groups of students might work together outside of class, this format allows all students to engage with one another. Limitations to students’ ability to get together due to time or physical space do not exist with this exercise. 
  9. I have not yet figured out a way to ensure that all students contribute meaningfully, rather than simply lurking or providing brief responses such as “I agree.” But I have also not yet decided whether everyone must contribute meaningfully.
  10. There has been a lot of attention paid to how we engage more introverted students. This approach provides quieter students with a forum to share their ideas.
  11. The GoogleDoc serves as a permanent record of students’ work and the evolution of their thinking throughout the year. I sometimes direct their attention back to work they have completed so that they can see how much their thinking and ability to communicate has changed.

I am still tweaking this approach, and thinking about ways to make it even more effectively. But I have seen deeper understanding from students who engage in this process, which in turn encourages more hesitant students to jump into the fray. Moreover, the benefits from this type of exercise spill over into our day-to-day classroom experience. Students arrive with more confidence, greater willingness to engage with one another, and deeper appreciation for their own agency and ability to solve challenging problems together.