Wolfram Computation Meets Knowledge

Wolfram Summer School


Andrea Griffin

Educational Innovation

Class of 2016


Andrea recently received a master of science in computer science from Rivier University in Nashua, New Hampshire. Previously she received a bachelor of arts in applied physics with minors in mathematics and secondary education from Saint Anselm College in Manchester, New Hampshire. Andrea has spent the past several years tutoring students from young to old in a wide variety of subjects, ranging from drawing lines to advanced calculus in many settings.

Project: Algebra Feedback System

Teachers are faced with an immense amount of tasks, many of which could be automated to help them do as little as possible and focus on interactions with individual students, which is crucial to the students’ development. In an attempt to help teachers, I developed a system that provides students feedback on their work for mathematics classes. These systems already exist in the market and are highly used by teachers. The difference between the system I developed and these other systems is that my system provides feedback on more than just whether the student’s final answer is correct.

My system runs on a microsite and provides students feedback on where their work goes wrong line by line on single-variable equations with zero, one or infinitely many solutions. The microsite initially asks the student for the question he or she is currently working on, checks the entered question to be sure it is a question the system can return feedback on and proceeds to provide input lines for the student to enter his or her work, checking each line along the way to make sure it is mathematically equivalent to the previous line of work. When the student gives a correct final answer, a summary of his or her work is displayed. The response from the system allows students to be aware of when their work is no longer mathematically correct and stops them from moving further along in the question. This project heavily utilizes the Wolfram Language Ask and AskFunction functions.

The image below shows what a student’s work might look like if graded by the current feedback systems versus this system. The red outlines are the pieces of work that would be avoided with the algebra feedback system. The green outlines are the pieces of work that are commented on by other feedback systems. In questions 2 and 10, the student made the same type of error. If the student had received feedback when they were doing question 2, they could have fixed their response (learned from their mistake) and later completed question 10 correctly on the first try. That is what this system does: it stops students when they make mistakes, gives them the opportunity to fix it and encourages them to learn from those mistakes before repeating them later.

A system of this kind is highly complicated, and for this reason there are some aspects that I intend to continue to work on beyond the Wolfram Summer School. I would eventually like the system to read handwritten lines of work so students could essentially take pictures of their handwritten work on their phones and be provided teacher-quality feedback. The system also needs to be expanded to address other math courses/math topics. To provide better feedback, I’d like the system to collect student answers so I can analyze common mistakes, and improve the system to provide more detailed feedback to the student than it currently does.