Fractions, Unlocked

Why fractions matter and how technology can help.

GUEST COLUMN | by Krista Marks

credit-woot-mathI often argue that learning fractions is the single biggest pain point in American education. I understand that making this argument is probably provocative (that’s part of why I make it), but it is not without basis. First, fractions are a very specific point within the curriculum. Second, they are of crucial importance for later mathematics, and without facility with fractions many of the subjects central to STEM, and more broadly, fully participating in the modern world, are simply out of reach. Third, they are the point at which far too many students go off the rails. The National Math Panel said it clearly in 2008: “…knowledge of fractions is the most important foundational skill not developed among American students.” Lack of this foundational skill remains equally evident in recent national testing.

It is not that technology is a silver bullet, but in the hands of a capable teacher, a research-based, adaptive learning platform can help students gain mathematical confidence, competence and fluency – especially on the topics that present the most critical stumbling blocks.

The importance of learning fractions has been the subject of a great deal of research. To argue my case with a single title: “Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents” (Torbeyns, Schneider, Xin, and Siegler, 2015).

I also like to argue that technology can make a difference. Here, I am arguing with skin in the game, because I run an edtech startup on a mission to prove whether technology can help move the needle on fluency with fractions. I personally believe that we as a nation have never been in such a strong position to enable all students to succeed with fractions.

Today, technology has reached a level of both capability and adoption to have a genuine impact on differentiated learning in K-12 classrooms. It is not that technology is a silver bullet, but in the hands of a capable teacher, a research-based, adaptive learning platform can help students gain mathematical confidence, competence and fluency – especially on the topics that present the most critical stumbling blocks.

There is no better example of how technology can be useful for learning critical topics than when working with fractions. Students need experience making connections among different representations of fractions in order for them to make sense of fractions and learn how to use them in flexible ways. Typical visual models for fractions include area models like fraction circles or fraction bars, a number line, or even a set model.

As students gain proficiency they can move fluidly among these representations as they begin to build mental images of fractions. Digital manipulatives that allow students to explore problems in flexible and connected ways help students develop stronger mental images. Rather than just see a picture of one fourth, a student can build a model of one fourth. Rather than simply read a number line, they can use a bar model to partition and experiment with one.

Another advantage of technology is the ability to adaptively tailor content and instruction to each student. The most powerful forms of adaptivity go beyond analyzing whether an answer is right or wrong and look at the reasoning behind the response. Take this example of four students comparing a fraction to the benchmark ½. The screenshots of actual student work show that each student has modeled the fractions correctly, but each has entered the wrong answer.


By analyzing not only the answer, but the actual student work, an adaptive tool can detect that the models are correct and tailor the real-time help to acknowledge the successful modeling and then depending on the work, review the meaning of the inequality symbols or the underlying concepts of order and equivalence. As students struggle to make sense of fractions – as with all mathematics – they often get more right than wrong. Adaptive technology is able to detect and acknowledge the right and the wrong in student reasoning and in the process build the confidence they need to succeed.

Of course, adaptive technology can only be effective if it leverages quality supplemental content; it is essential that such technology is based on sound research in math education and backed with rigorous trials demonstrating efficacy. While we have invested years into the technology behind Woot Math, it would not be effective without the decades of fraction research from organizations like the Rational Number Project and without funding for research from organizations like the National Science Foundation.

We can move the needle on fractions in this country. From the research, we know it’s possible, and for our students, we know it’s essential. While I am still trying to understand what the solution will look like, I do know that there isn’t one person, one organization or one company that holds the answer. It will take a community of teachers, researchers and developers working together. Together we can make a difference for all students.

Krista Marks is the CEO and Co-founder of Woot Math, Inc.


  1. I agree also with the article on many levels. However, as a teacher, time is of the essence and my most valuable commodity which must be stretched beyond its means. All this is to say, I want avenues to assist and aid and enhance learning with my students that doesn’t require a huge amount of time to set up or go through to ensure it is what I need. With so many programs… like Woot Math ..who made it personable by coming in to meet with us and ask us what we need, we saw the human side and we got immediate responses.

    Thank you for woot math and for making it “more human” by meeting with us.
    I would like one aspect where they draw or configure what one-half or 3/4 of something actually looks like after the practice.

  2. I agree with both of your points here: A. The learning of fractions is fundamentally important to future STEM learning. B. Technology, when used appropriately, can support this learning. I believe that when technology is used effectively it can support any learning. However, at the same time, if technology is used ineffectively it can be detrimental to learning. One of the most important things that must be done is to correlate effective Websites with particular learning objectives. My company, A Pass Educational Group,has a service in which we do just this: correlate curriculum maps or syllabi with freely available digital resources. Take a look:

    Andrew Pass

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