“Did you check your calculations? Which operation did you use? Please show your thinking!”

Math teachers frequently find themselves repeating the same suggestions over and over. Students enjoy and thrive with this level of teacher support, but having immediate access to a teacher for each problem is typically not feasible. This issue got the Magma team thinking. What are the most common mistakes that students make? What does it mean for a student to show their thinking in a meaningful way? And lastly, is there a way to automatically detect what type of feedback a student should receive based on what they did when solving the problem?

It turns out that the answer is yes! After working hard on the detection part, we started to roll this out in the format of hints. Here are some examples of hints that your students might have already encountered when showing their thinking in Magma.

That’s right, Magma has started to recognize and celebrate students who show their thinking. It is noteworthy here that the system does not simply check if the drawing area was used or not. It performs a deeper analysis and *understands* that it was done in a meaningful way. If the drawing area on the other hand is used for random scribbles, the additional encouragement will not appear.

Okay, but what if your student did show their thinking, but got the answer wrong due to some misunderstanding or mistake? After researching large quantities of data on student submissions, we learned that the vast majority of mistakes made are not unique but common among peers. This got us wondering – if a lot of students are making the same mistakes, can we somehow train our system spot the patterns of when a certain mistake has been made?

According to our research, this is in fact one of the most common mistakes done by students calculating the perimeter of rectangles. They mix up the concepts of area and perimeter and calculate the answer to a different question than the one that was asked. For these situations, Magma now has the ability to go beyond just correct/incorrect in its feedback. It takes things one step further by identifying that a common mistake has been made, and generates a message to nudge the student in the right direction.

When showing this error catching feature to teachers, we learned an interesting fact about student mistakes. They can actually be a valuable asset for math discourse. So the natural next step of this was to display a mistake not only to the students, but also to the teacher.

The box of common errors will show if 3 or more students have made the same mistake. How teachers choose to act on this will of course vary greatly, but some cases we have heard about include:

- Having a small group instruction with the students having this misconception.

- Class-wide discourse comparing the common mistake with a correct solution. Why not have your students spot the differences, and brainstorm tips for avoiding the pitfall in the future?

We at Magma are just getting started in our mission of making data around student thinking useful in your classroom. The examples above merely scratch the surface of what is possible, so we are eager to hear your feedback. Is there a particular mistake that you would like Magma to cover? In what shape or form do you think student feedback is most useful? If you have ideas or reflections, please don’t hesitate to reach out to kristoffer@magmamath.com.