MathCEP Director Receives Wolfram Research Innovator Award

I was honored earlier this month to be recognized by Stephen Wolfram as one of the recipients of the Wolfram Innovator Award at the annual Wolfram Technology Conference.   (Here is the official announcement of the Award Winners.) This award is given annually to educational and scientific pioneers that use Wolfram’s Mathematica™ software to bring the future to today.

 

The awarded project was the result of a large number of people at the University of Minnesota working to lower the cost of college attendance by replacing expensive textbooks with technology better suited to the needs of 21st century students. In addition, this technological innovation has improved the way we deliver instruction at MathCEP.

The project, now known as the Minnesota Online Learning System (MOLS), delivers assessments to students using the Mathematica platform. It replaced a publisher’s automated homework system initially, and then expanded to house the University of Minnesota’s math placement exam. One major feature of MOLS is the ability for instructors to author questions.

The history of the MOLS project began in 2013, when I first taught a pre-calculus course using a ‘flipped classroom’ approach. We used a publisher’s textbook and associated homework system, with mixed results. On the one hand, it is important for students to receive instantaneous feedback on their homework, as they can immediately learn from their mistakes and plan how to study. However, test results didn’t seem to be affected by the homework; students who hadn’t completed the homework prior to the exam performed as well as students that had. My conclusion was that the choices of questions I had available from the publisher didn’t align well with the concepts I was trying to teach. I made suggestions to the publisher for questions that could be added, but the process to add new questions would take months. I needed something more responsive.

The design of MOLS, (and in my mind, the design of all automated homework systems), would need to include these four features:

1. Question Bank – Pre-authored questions from a publisher is a good starting point, but there are advantages for an instructor to be able to author their own questions quickly. In addition, when multiple instructors author their own questions, the question bank becomes more robust.

2. Student Interface – The students need to be presented questions and have the ability to input an answer. In mathematics, this can be a challenge. Fractions, exponents, square roots, and integrals are commonplace symbols that students write on paper in introductory collegiate math courses, but they are not presented in the same way using a QWERTY keyboard. A tablet interface that allows students to express mathematics in the same way that they write is necessary.

3. Evaluation Engine – The system must correctly decide whether the mathematical object the student proposed as the answer matches what the author claimed the answer to be in the answer key. For example, when simplifying in a calculus class, one student may get the answer 2sin(x)cos(x), while another gets the answer sin(2x). It is beneficial to have a system that recognizes those two answers to be the same.

4. Gradebook – Student scores need to be reported in a secure fashion to the instructors.

5. 
   

The system has improved my instruction in the following ways. First, the questions represent my notation, my formatting and my points of emphasis. The content is aligned with a video textbook used in my pre-calculus courses. Students are able to make sense of my examples in completing their homework. Second, class time can be spent on higher order thinking skills, focusing on the problem-solving process instead of routine calculation algorithms. We have found that students can perform routine calculation without much human interaction. Students watch videos to learn the procedures, attempt the homework; where they don’t succeed, they figure out their mistake, or return to the video content, or occasionally make use of office hours, but for the most part, they are able to figure out those things on their own. This frees up class time for deeper discussions about mathematics. Finally, students have control over their own learning. They seek out the information that is most helpful to them, sometimes working with other students, sometimes seeking other internet content, sometimes working ahead and returning to difficult material when they have developed the skills to handle it.

There is much work yet to be done. Teaching students how to do routine calculation is important, as it is the foundation upon which the rest of their understanding is based. However, there are many other ways in which technology can be used to improve math education. Interactive applets that allow students to discover important principles can be embedded with written and video content and assessments. Technology can aid in student-student collaboration. For example, a lesson on parametric equations can begin with a simple Etch-a-Sketch task of two students working together to draw a circle where one student controls a dial which determines the x-coordinate while the other controls the y-coordinate. The underlying principle now comes to life as students struggle to coordinate their efforts.

MathCEP is committed to continuing to work on improving technologies for math education through several projects, from the MOLS project to the Distributed Open Educational Network (Doenet), which is an educational research tool that will make it easy to author and share interactive educational content. We hope to strengthen and enhance all learners’ problem-solving and communication skills by advancing the available educational technologies, and creating new ones to better meet their needs.