When I first asked an upperclassman for advice on how to prepare for the GRE, he chuckled and said “good luck on the math section!” I didn’t understand - both of us were engineering students and had taken plenty of higher-level math classes. What could be so bad about a general math exam?
After taking my first practice test, I realized it wasn’t the content of the test that made it difficult – and generally uncomfortable – it was the actual design of the math section. The GRE, like other computer-based math exams, has test-takers work out math problems on scrap paper provided by testing centers while interacting with a computer screen for question prompts and answer submissions. The cognitive load of reading a math problem on a screen, solving it on a flimsy erasable sheet, and then selecting the appropriate answer on the computer may seem small but it really adds up, breaking student focus and increasing anxiety.
After that adventure, I started thinking more about how improvements in technology could impact math education. While there are already great apps that effectively teach and assess students on math concepts, there is a serious challenge that tech applications have not solved yet: how do you bring the complexity of solving math equations, most intuitively done by hand, into the digital world?
This is the same question developers of the original word processor struggled with. When my grandfather first started using a PC in the early 1990s, he saw the task of typing as unnecessarily time-consuming since he could write swiftly and efficiently by hand. The task of booting up a PC and identifying appropriate characters on a keyboard to communicate the same message seemed foreign and cumbersome. However, there were clear advantages to typing – mainly the ability to save information as a digital asset and share it with others.
In the years since, the industry has continued to build on that core functionality, creating countless new platforms around revision and collaboration opportunities for typed words.
The equivalent of a word processor revolution is about to happen, this time bringing mathematics online.
Optical character recognition (OCR) has been around for years but we haven’t seen identification and interpretation solutions for math handwriting yet because the subject contains an extremely large character set and the meaning of each equation is greatly dependent on the spatial relationships between symbols.As a result, our current options are either type-centric (such as LaTex and Microsoft Word with which you type out math characters using code or an online keyboard) or screen-focused (using which you draw out problems using apps such as MyScript on a tablet or phone).
These solutions fall short of truly bridging the gap between free-form handwritten problem solving and the digital ecosystem. What we need is a way to connect to the digital environment that captures the same nuances as handwritten math, but with a scale that allows for sharing, search, and collaboration.
Solving this problem isn’t easy since the technology needs to recognize a variety of handwriting styles, accept different backgrounds, and successfully omit noise in images. However, if done well, bridging this divide would bring math online in a more authentic manner. It would also have a massive impact on students and educators.
Make Math Tutoring More Personal
For academic support, many students use WolframAlpha - a well-designed computational knowledge engine that solves all kinds of academic problems. It was truly instrumental in helping my friends and I learn difficult math concepts through school.However, Wolfram hasn’t tackled the screen-paper divide with its web or mobile products: students have to use a math symbol set to type out equations and then proceed to solve them by hand or navigate back to a different learning management system. This disconnect feels inauthentic and generally impedes learning.Former Stanford PhD student Nicolas Jimenez created Mathpix, a mobile app that reads and interprets math handwriting, to make the process of doing math calculations more seamless. The app enables users to take a picture of any (printed or handwritten) math problem and graph it or get a solution.
While this is great as a new-age digital calculator, such technology holds much greater potential. As a company like Mathpix collects the data to improve image recognition and analysis, it could create many new opportunities in education delivery and assessment.
Provide students with timely feedback on problem solving strategies
Most edtech products tout their immediate feedback functionality. What is overlooked is that immediate feedback is not necessarily a good thing - it bases the platform’s response solely on one element, the answer, and ignores the (often long and tedious) process to get there.
We shouldn’t teach students to just focus on getting an answer – modern computational advances make getting an answer easy, but the nuance is setting up the question and using critical reasoning to get there.
With the current screen-paper divide, even the most advanced personalized platforms only provide binary feedback around what is correct, rather than teasing out where along the problem solving path a user goes astray. We should instead aim to advance every student’s understanding of the problem solving approach.
“The computer’s feedback logic is brittle and inflexible, which teaches the untruth that math is brittle and inflexible.” -Dan Meyer, Chief Academic Officer at Desmos
In college, a math tutor once recognized that I wasn’t struggling with a Differential Equations assignment because I didn’t understand the concepts in that class, but rather because I didn’t know a small yet significant property of calculus (from two semesters ago). That gap in knowledge inhibited my ability to solve a much larger problem a year later. The math tutor had me sit with underclassmen to solve a dozen of their problems to learn that concept. In the future, technology will have greater visibility into a student’s work and be able to intervene at critical learning points.
The next iteration of edtech products will provide this level of personalization. Once technology can pinpoint the concepts students struggle with by identifying which steps in a solution a student struggled with, it will be able to more effectively suggest relevant practice problems.
These advances will only happen when we get greater insight into how a student thinks and behaves - by looking into what work happens on their paper before they input an answer on the screen.
Help educators create authentic, more frequent assessments
The only people who experience the difficulty of the screen-paper divide more than students are their educators. Responsible for creating math assessments for students, teachers tend to use Microsoft Word or LaTex. Unfortunately, LaTex is not simple to learn and using MS Word for creating math questions is quite painful. If teachers had a simpler way of creating math problems, they would more frequently - and accurately - assess their students.
The pain point of creating assignments is also felt in grading student work, line-by-line, by hand, which often takes hours upon hours for each class and each assignment. There is a real tradeoff between providing more authentic assignments and detailed feedback to students on an infrequent basis versus rapid, real-time, but shallow feedback through multiple-choice assessments that can be graded automatically. Students dislike the all-or-nothing factor on their grades and teachers worry that having few authentic assessments could impact the college-readiness level of their students.
In the future, with sufficient data and the right amount of intelligence, a technology tool could identify student mistakes (to help teachers grade faster) and find recurring themes (to prevent cheating).
What’s Next
Bridging the screen-paper divide for math is a massive opportunity area. If done well, we will not only solve critical education problems but also introduce collaboration and manipulation mechanisms that open up growth areas in teaching and learning that we have yet to even fathom.
Are you building an interesting product in this space? Reach out @siiyeah.