Immersive Exercises are mini-apps that replace and combine traditional textbook examples and exercises. Students learn problem-solving skills by actually working a problem in real time while the IE does the routine, low-level  calculations that can interrupt and even thwart the problem-solving process. Immersive Exercises associated with the text Interactive Linear Algebra were designed by Plaut Pedagogy and coded by software engineers Abhi Ravi and Kishan Taylor at our partner company, MathMentorApp.

AI tutors are the shiny new object in math pedagogy. They use large language models to find and explain solutions to mathematical problems. But finding a solution is not the same thing as solving a problem, and every mathematics instructor knows that developing problem-solving skills is the most important learning outcome of any math course. Learning to solve mathematical problems requires actual practice and repetition, not simply reading or listening to someone else’s solution. Immersive Exercises facilitate problem-solving (rather than bypassing it) by engaging students in decision-making in real time.

Let’s compare two approaches to Immersive Exercises (IEs). One approach is to find a solution online, then figure out how to adapt that solution to the input format of the IE, including the requirement of fractional input, and enter every problem-solving step in real time. This approach assumes that the online solution even matches up with a solution path embedded in the IE. Because IEs allow students to solve problems rapidly by avoiding manual arithmetic, instructors can assign far more repetitions of exercises. Students quickly learn that inputting the steps from internet solutions in real time is a comparably inefficient way to complete all those repetitions. They are highly motivated to take the second approach, which is to just learn the problem-solving steps so they can practice rapidly without accessing and inputting new solutions for every repetition.

Many “supplemental materials” for traditional math textbooks, including ebooks, send students to external software to do computations that are too complex to do with pencil and paper. The problem with this strategy is that the external software is a black box that hides the mathematical process the student is learning. It gives an answer, but the student learns little about where the answer came from. External software can also consume instructional time and add headaches for the instructor, and for what pedagogical purpose? In contrast, Immersive Exercises (IEs) are highly intuitive and have essentially no learning curve from a user standpoint, so that the student can focus on learning what is most important: solving problems.

If you’re an instructor, you will be using Dr. Plaut’s text Interactive Linear Algebra together with the MathMentorApp software, which consists of Immersive Exercises for each topic in the text. The text includes a QR code (paper copies) or links (e-book) to Immersive Exercises called “Math Pauses” (MPs). All MPs should be assigned for the material that is covered in the course, due shortly after the corresponding textbook material is introduced in the class.

Students can purchase the textbook and licenses for the accompanying software online.

Instructors obtain information for each student on their rate of completion of each Immersive Exercise. Students who make correct decisions will get the correct answer, and therefore it is the student’s progress that matters, not their answer. Instructors may also assign supplemental written exercises from the text, most of which concern applications or mathematical proofs. A special exam mode is available for most of the Immersive Exercises. Depending on the learning objectives of the course, instructors may give additional written test problems as part of a hybrid online/written exam. Data on students’ progress on the MPs, which is subject to Family Educational Rights and Privacy Act of 1974 (FERPA) regulations, is kept private and secure on our partner MathMentorApp’s website.

The distinction between an “answer” and a “solution” is often lost in the day-to-day pedagogy of mathematics courses. A solution is the process of solving a problem, and an answer is the result  of that process. Mathematics teachers or professors will likely agree that the most important learning objective of any mathematics class is that the student becomes proficient at solving mathematical problems. Yet our courses and the materials that we use are still oriented around answers, which often depend on the kind of rapid, flawless, low-level calculation that hasn’t been required of STEM professionals since the 1970s.  It’s common to see student solutions that are perfect except for a 5th-grade-level arithmetic mistake. If we only look at the answer, the student’s work is “wrong”. If the answer is all that matters in the evaluation of the student (e.g., in a multiple choice exam), then the fact that the student actually understood how to solve the problem is completely lost.

Interactive Linear Algebra is an integrated set of materials, with Immersive Exercises linked directly from the text (e-book version). Rather than providing “interactive” widgets that demonstrate how to solve problems–which are simply a software implementation of traditional textbook examples–the Immersive Exercises  accompanying Interactive Linear Algebra actually replace both traditional examples and exercises. Students learn by solving problems rapidly within the Immersive Exercises, initially supported by hints, while the software handles routine, low-level calculations. Students can practice far more solutions, unencumbered by 5th-grade arithmetic that is incidental to, but not important for, the actual solution.

There is no evidence that AI “solves” any problems, as opposed to simply finding a solution to an essentially identical problem. STEM professionals, more than ever, will have to be problem-solvers for more advanced problems that are at the cutting edge of science. For example, AI is great at writing bits of code, leading to the unemployment of people who are simply good at writing bits of code. But design of truly innovative software requires human oversight. The Interactive Linear Algebra companion software allows students to develop mathematical instincts on basic problems that will benefit them when they tackle much more complex ones in the future.

All student data is encryted and FERPA compliant. Please see our webpage detailing our data security and privacy policy.