Providing formative feedback to linear equations

María Sanz Ruiz, Universidad de Cantabria, Spain

The AuthOMath Project combines GeoGebra and STACK. It allows us to present multiple representations of the same mathematical object. STACK is especially useful to create different approaches to feedback.

This task is about solving linear equations step by step. Whenever the students make a mistake, STACK is able to identify it and provide specific feedback to it. Below is an empty question ready for a student.

A blank question
Figure: A question in which student should write their answer.

The image below shows feedback generated automatically by the system. Notice some lines are correct, but the student has made one mistake.

A blank question
Figure: A question in which student should write their answer.

These formative hints can be delivered in many ways. Some students are more receptive to symbolic feedback, while others appreciate written comments. It is also possible to combine both.

A blank question
Figure: A question in which student should write their answer.

This is a useful way to distinguish the characteristics of the different feedbacks and determining which are more helpful and effective in fostering mathematical abilities and learning.