Group Problems on Tests

This term, I have been giving group problems on my tests, and it has been fruitful.

Giving group problems as part of an assessment helps students treat group work during class time more seriously. In the past, I have tried to get students to work on problems in groups during class time, but they most often gravitated to working individually in the groups. This was because they knew that in the end, they were going to be tested individually.

This term, I noticed a point in time when there developed a resistance against group work. A colleague suggested that I try putting a group problem on a test to show that I value group work. I tried it, and it worked! No longer do I need to convince students to work in groups. Sure, there are still a few who just want to work on their own, but the majority have come to value working together and learning from each other.

I am still tinkering with the logistics. I have tried giving a problem for them to work on and then getting them to come up and ask for the rest of the test on which they will then write up the problem they solved together on their own. I have also tried giving a similar problem as the test for them to work on right before the test so that they will be ready for it when they complete their test. Finally, I included a group problem on the last midterm as described below:

Students were to in groups build a three dimensional object out of parts that I provided. They would then each describe and draw the object on their papers and give the object to another group to work on. The other group would then describe and draw the shape they received, and then work together to find the volume and surface area of the shape. Each student would then hand in a write up of the activity and then complete the rest of the midterm. The activity was graded as one of the midterm questions.

In giving such a task, I worried that students would just come up with simplistic objects in order to take the easiest possible route. However, the drive for most groups was quite the opposite. They challenged themselves with the most complicated shapes they could come up with! They even surpassed the outcomes of the unit in creating shapes such as:

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Because they had created their own shapes, they had this drive to engage themselves in figuring out the volume and surface area regardless of how complicated it got! Many fruitful ideas and questions came out of their discussions.

If the stage is set right, group work can be very productive. However, I am constantly searching for new ways to switch up my group work strategies because too much of a good thing can take a hit. I have found that if I organize my class in the exact same way too many times in a row, students lose interest and it is no longer a novelty.

“Keep it fresh” is the advice I like to follow and remind myself of every time I plan a lesson.

Student Generated Examples

Since I have much more class time available for students to engage in learning material, I have been playing around with various types of tasks. One of which is getting students to generate examples of questions they may be asked. Any teacher who has developed their own questions knows that doing this is more difficult that it seems. A lot of knowledge is required to make a question to which a solution may be found using prerequisite knowledge. I was teaching a unit on using properties of exponents to simplify exponential expressions. I asked students to generate a question in groups and give the question to another group to solve. I also asked them to create a potential unit test in order to build study skills. I was afraid that students would choose to create extremely simple examples and that they wouldn’t learn enough from the task. However, I didn’t realize how difficult it can be for a student to create a “simple” example. In order to know that it will be simple to solve, they need to be fluent with their knowledge. In my class, all the students decided to try to make the most difficult problem they could think of! I was shocked. It led to a lot of good discussion and I was able to clarify several key points to them through analyzing how they would solve the problem. For example, a lot of them threw in addition signs but didn’t realize how much more difficult it is to simplify rational exponential expressions with several terms in the numerator and the denominator! This stemmed from the fact that they were still unsure of the difference between multiplying exponential variables and adding exponential variables. Other nuggets came out as well. This task was so useful that I ended up putting a question on their unit test to create an example and solve it. The fact that they had to solve it themselves forced them to try to stick to using properties they understood.

I’d like to share my favorite student generated example from the group work activity:

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This is truly brilliant. Is it not?