- Documented Problem Solutions
- Description
- Students document all the steps they applied to solve a problem.
- Purpose
- Assess how students solve problems
- Assess how well students can communicate how they solve problems
- Development student awareness and control of problem solving routines
- Step-by-Step Procedure
- Select 1 – 3 representative problems for students to solve. If you select 3, you can pick:
- one problem ALL students can do
- one problem MOST can do
- one problem that will challenge NEARLY ALL students
- Document problem solutions for each of the problems. Be sure to follow all the expectations you intend to set for students.
- Give students time in class or assign problems for homework.
- Explain that documenting the steps and their rationale is more important than getting the problem right.
- Select 1 – 3 representative problems for students to solve. If you select 3, you can pick:
- Analysis Steps
- Analyze steps in correct solutions and in solutions that had correct steps but arrived at the wrong answer
- Try to diagnose the types of errors and wrong turns students took when arriving at the wrong answer
- Distill what was learned to 3 to 4 key observations
- Share observations with the class
- Extension Ides
- Assign a low and medium level problem as a diagnostic pre-assessment so you know how to start the next problem solving lesson
- Create heterogenous teams and ask students to explain their solutions to each other. Document mistakes and how students learned from these.
- Ask students with strong solutions to present their solutions to the class.
- Make this a regular part of homework. Example: students document at least one problem in their homework set this way
- Pros
- Makes problem solving thinking processes visible
- Makes students aware of a range of problem solving approaches
- Promote content-specific metacognitive skills
- Cons
- Students may struggle at first to explicitly comment on their problem solving steps
- Some mistakes are hard to explain
- When students are solving problems at many varied levels, general feedback may not be helpful
- Caveats
- Model the skill a lot – especially in the beginning
- Don’t expect very good solutions on the first couple tries
- May need to give credit for responses because they are time consuming
- Try not to get overwhelmed by grading but try to develop feedback insights that feed students at all problem solving levels
- Description
- Audio- and Videotaped Protocols
- Description
- Students create a video or audio recording of them solving a problem
- Purpose
- Assess in detail how well students solve problems
- Assess how well students are able to communicate problem solving processes
- Step-by-Step Procedure
- Select or create a problem that is worth talking through: involves multiple steps and students can be expected to solve it
- Decide whether to video or audiotape the solution – both can be done fairly easily with most cell phones. Educreations is also a good tool for this.
- Decide in advance what you will look for in responses and how you will assess them
- Draw up a problem sheet with the problem and criteria for taping the solution. Be sure to include time limits and what they are supposed to learn from the exercise
- Make students aware of the types of feedback they can expect to get from their recordings.
- Analysis Steps
- Create a model solution.
- Create a checklist that describes model solution.
- Use the checklist to notice features that student solutions have right, incorrect, or are missing
- Extension Ides
- Ask students to work in teams to create individual recordings.
- Provide students with a checklist for providing feedback on the videos and let students use it to give their teammates feedback.
- Pros
- Recordings are accessible and can be viewed multiple times.
- Recordings can be stopped and rewound to focus in on key steps.
- Students and teachers work closely together on problem solving processes.
- Teachers gain insights on student’s problem solving points and can identify stuck points to address in class.
- Students become more aware of their problem solving routines which gives them better control over them.
- Cons
- Takes time to create and assess.
- Students can’t be anonymous.
- Solutions will be diverse – hard to compare to other solutions.
- Some students who are good problem solvers are not good at communicating their thinking.
- Caveats
- Time associated with this can’t be justified unless the skill being practiced is critical to the course or future employment
- Students will expect a grade on this because of the time expended.
- Teachers need to be open-minded to various valid solutions to problems.
- Description
The solution documentation strategies describes in this article can be used to make students’ problem solving processes more visible. Students can learn more about how they solve problems which can help change their processes as they learn new things. Although these artifacts take longer to assess, teachers can learn a lot about students’ problem solving skills by evaluating these artifacts.
Preparation Steps
- Analyze problem solving skills in upcoming projects.
- Decide whether any of the problem solving skills are critical and subtle enough to be looked at closely.
- If so, decide which of the strategies listed above you would like students to use to document their solutions.
- Create a model solutions of the type your students are about to create.
Early Implementation Steps
- Show students a model solution that demonstrates what they are about to create.
- Emphasize the key features of the model solution and how these were created.
- Give students time in class or outside of class to document solutions.
- Analyze solutions using one of the approaches described above.
- Share feedback with students.
Advanced Implementation Steps
- Teach students how to use checklists to find common flaws in their documented solutions.
- Have students reflect on the lesson they are learning as they correct flaws in their solutions.
- If you repeat the strategy multiple times, have students reflect on how their problem solving routines are changing over time.
