Denise Garcia knows that her students sometimes cheat, but the situation she unearthed in February seemed different. A math teacher in West Hartford, Connecticut, Garcia had accidentally included an advanced equation in a problem set for her AP Calculus class. Yet somehow a handful of students in the 15-person class solved it correctly. Those students had also shown their work, defeating the traditional litmus test for sussing out cheating in STEM classrooms.
Garcia was perplexed, until she remembered a conversation from a few years earlier. Some former students had told her about an online tool called Wolfram|Alpha that could complete complicated calculations in seconds. It provided both the answers and the steps for reaching them, making it virtually undetectable when copied as homework.
â€‹Pippa Biddle is a writer interested in culture, complex systems, and making sense of the world.
Sign up to get Backchannel’s weekly newsletter.
For years, students have turned to CliffsNotes for speedy reads of books, SparkNotes to whip up talking points for class discussions, and Wikipedia to pad their papers with historical tidbits. But todayâ€™s students have smarter tools at their disposalâ€”namely, Wolfram|Alpha, a program that uses artificial intelligence to perfectly and untraceably solve equations. Wolfram|Alpha uses natural language processing technology, part of the AI family, to provide students with an academic shortcut that is faster than a tutor, more reliable than copying off of friends, and much easier than figuring out a solution yourself.
Since itâ€™s release, Wolfram|Alpha has trickled through the education system, finding itâ€™s way into the homework of college and high school students. Use of Wolfram|Alpha is difficult to trace, and in the hands of ambitious students, its perfect solutions are having unexpected consequences. It works by breaking down the pieces of a question, whether a mathematical problem or something like "What is the center of the United States?", and then cross-referencing those pieces against an enormous library of datasets that is constantly being expanded. These datasets include information on geodesic schemes, chemical compounds, human genes, historical weather measurements, and thousands of other topics that, when brought together, can be used to provide answers.
The system is constrained by the limits of its data library: It canâ€™t interpret every question. It also canâ€™t respond in natural language, or what a human would recognize as conversational speech. This is a stumbling block in AI in general. Even Siri, which relies heavily on Mathematicaâ€”another Wolfram Research product and the engine behind Wolfram|Alphaâ€”can only answer questions in programmed response scripts, which are like a series of Mad Libs into which it plugs answers before spitting them out of your speaker or onto your screen.
Using Wolfram|Alpha is similar to executing a Google search, but Wolfram|Alpha delivers specific answers rather than endless pages of potentially relevant results. Anyone can go to the Wolfram|Alpha website, type a question or equation into a dialogue box, hit enter, and receive an answer. If youâ€™re trying to solve x2 + 5x + 6 = 0, Wolfram|Alpha will give you the root plot, alternate forms, and solutions. If you are looking for a step-by-step explanation, there is a pro version available for $6.99/month with discounted options for students and educators.
I first heard about Wolfram|Alpha in my parents’ kitchen. My father had come home from his job at a private school in Dobbs Ferry, New York. He dropped his bag on the floor, and asked me what I thought about Wolfram|Alpha. Earlier that day he had been confronted by STEM teachers who were frustrated with their students’ use of the tool. It was, they said, blatant cheating. My father had left the office unsure of how to proceed. Should the school crack down on Wolfram|Alpha? Or did the school need to catch up to this new beat in education?
Iâ€™d never heard of it, but a quick post to Facebook revealed that many of my friends hadâ€”especially those studying math. Some had used it to get through college calculus, while a few were still using it at their jobs as engineers or quantitative analysts. The rise of Wolfram|Alpha had completely passed over my humanities-minded head, just as, for millions of minds, it had become ubiquitous. Turning to the tech for answers was, they said, normal. At the same time, all made it clear that they didnâ€™t want their use of Wolfram|Alpha to be made public.
Though Wolfram|Alpha was designed to be an educational assetâ€Šâ€”â€Ša way to explore an equation from withinâ€” academia has found itself at a loss over how to respond. What some call cheating, others have heralded as a massive step forward in how we learn, what we teach, and what education is even good for. They say that Wolfram|Alpha is the future. Unsurprisingly, its creator agrees.
Stephen Wolfram, the mind behind Wolfram|Alpha, canâ€™t do long division and didnâ€™t learn his times tables until heâ€™d hit 40. Indeed, the inspiration for Wolfram|Alpha, which he released in 2009, started with Wolframâ€™s own struggles as a math student. Growing up, Wolframâ€™s obsession was physics. By 12, heâ€™d written a dictionary on physics, by his early teens heâ€™d churned out three (as yet unpublished) books, and by 15 he was publishing scientific papers.
Despite his wunderkind science abilities, math was a constant stumbling block. He could come up with concepts, but executing calculations was hard. His solution was to get his hands on a computer. By programming it to solve equations and find patterns in data, he could leave the math to the machine and focus his brain on the science. It worked. In 1981, Wolfram became the youngest person to ever receive a MacArthur Fellowship. He was only 21.
Yet the tool that helped Wolfram build his reputation with physics ended up pulling him away from science. Wolfram became obsessed with complex systems and how computers could be used to study them. Five years after receiving his MacArthur Fellowship, Wolfram began developing Mathematica, and in 1988 Wolfram Research announced the release of its flagship product.
Wolfram never planned for his tool to become highbrow CliffsNotes, but heâ€™s not too concerned about it, either. â€œMechanical math,â€ Wolfram argues, â€œis a very low level of precise thinking.â€ Instead, Wolfram believes that we should be emphasizing computational thinkingâ€”something he describes as â€œtrying to formulate your thoughts so that you can explain them to a sufficiently smart computer.â€ This has also been called computer-based math. Essentially, knowing algebra in todayâ€™s technology-saturated world wonâ€™t get you very far, but knowing how to ask a computer to do your algebra will. If students are making this shift, in his mind, theyâ€™re just ahead of the curve.
Alan Joyce, the director of content development for Wolfram Alpha, says that cheating is â€œabsolutely the wrong way to look at what we do.â€ But the staff understands what might make teachers uncomfortable. Historically, education had to emphasize hand calculations, says John Dixon, a program manager at Wolfram Research. Thatâ€™s because there wasnâ€™t tech to fall back on and, when tech did start to appear, it wasnâ€™t reliable. Only recently can computers calculate things automatically and precisely, and itâ€™ll take some time for curriculums, and the teachers that are beholden to them, to catch up. Wolfram Research, Dixon says, wants to engage with teachers like Garcia, who are frustrated by the tool, to help them understand how it can help their students.
Indeed, the people who are directing the toolâ€™s development view it as an educational equalizer that can give students who donâ€™t have at-home homework helpersâ€”like tutors or highly educated and accessible parentsâ€”access to what amounts to a personal tutor. It also has enormous potential within the classroom. A "show steps" button, which reveals the path to an answer, allows teachers to break down the components of a problem, rather than getting bogged down in mechanics. The "problem generator" can pull from real datasets to create relevant examples. â€œWhen you start to show educators the potential,â€ Dixon says, â€œyou can see points where their eyes light up.â€
For every teacher whoâ€™s converted to Dixonâ€™s camp, there are multitudes of students who have been there for a while. As Alexander Feiner, an aspiring engineer and high school freshman told me, Wolfram|Alpha is a study aid, not a way of avoiding workâ€Šâ€”â€Šsomething that Dixon insists is the norm when it comes to out-of-classroom student use.
Still, the prevailing notion that Wolfram|Alpha is a form of cheating doesnâ€™t appear to be dissipating. Much of this comes down to what homework is. If the purpose of homework is build greater understanding of concepts as presented in class, Joyce is adamant that teachers should view Wolfram|Alpha as an asset. Itâ€™s not that Wolfram Alpha has helped students â€œâ€˜get throughâ€™ a math class by doing their homework for them,â€ he says, â€œbut that we helped them actually understand what they were doingâ€ in the first place. Dixon believes that Wolfram|Alpha can build confidence in students who donâ€™t see themselves as having mathematical minds. Homework isnâ€™t really about learning to do a calculation, but rather about learning to find and understand an answer regardless of how the calculation is executed.
Thatâ€™s the route down which education appears to be headed. Once upon a time, education was all about packing as much information as possible into a human brain. Information was limited and expensive, and the smartest people were effectively the deepest and most organized filing cabinets. Today, itâ€™s the opposite.â€œThe notion of education as a transfer of information from experts to novicesâ€”and asking the novices to repeat that information, regurgitate it on command as proof that they have learned itâ€”is completely disconnected from the reality of 2017,â€ says David Helfand, a Professor of Astronomy at Columbia University.
The technology isnâ€™t going anywhere: Like copying out of the back of a book or splitting a problem set among friends, students arenâ€™t likely to stop using Wolfram|Alpha just because a teacher says so. Even Garcia can see a future where Wolfram|Alpha fits in. â€œI think, in an ideal world, teachers, myself included, need to do a better job of incorporating technologyâ€¦and finding ways of using it in productive ways,â€ she says.
Just as robotics has transformed manufacturing, tools like Wolfram|Alpha are forcing us to rethink an educational system by challenging it to rise to the new technological standard. Either we reshape our schools to embrace tools like Wolfram|Alpha, or we risk becoming living artifacts in a rapidly progressing world.