As they practice, students are expected to develop automaticity, meaning they can retrieve answers from long-term memory without conscious effort.
This Behind the Scenes article was provided to LiveScience in partnership with the National Science Foundation.
When Kelly McNamara, a fifth-grade teacher in the Burrillville School District, Rhode Island, recently asked her students, "What is a common denominator for 4 and 7?," and they all instantly responded "28!," she smiled. "This was the first year that I could worry more about teaching the content rather than waiting for students to figure out their math facts," she says.
This year McNamara's class used Reflex, an online system from ExploreLearning that has students learning math facts within a game-based environment. Launched in 2011, the program has won a CODiE award for Best K-12 Instructional Solution. Hundreds of thousands of students across the U.S. are using the program each week.
Under the hood, the system's adaptive software applies data-driven pedagogy and technology that ExploreLearning pioneered with National Science Foundation (NSF) funding.
NSF funding enabled startup's research
"Generations of students are all too familiar with the traditional methods associated with math facts — a seemingly endless ritual of timed table drills, flashcards, timed worksheets, followed by more times table drills — repeated ad infinitum and ad nauseam," said Paul Cholmsky, ExploreLearning's head of R&D and principal investigator on the NSF-funded research. The problem, he says, is not just "the mind-numbing boredom" of these methods. "[S]tudies have also shown that they just don't work at all for many students," he says. When students labor in vain, it can seem like evidence to them that mathematical proficiency must be some kind of innate talent — one they just don't have, he said. This can become a self-limiting belief that individuals will hold throughout their schooling and into their careers.
Enter Reflex. Almost a decade ago, ExploreLearning began a research program to look at how it might use the wealth of data generated by students' interactions with online games and simulations, to continuously adapt the content and pedagogical methods to each student's specific needs. At that time, ExploreLearning was a small startup in Charlottesville, Va., with a growing reputation based on its award-winning library of online math and science simulations, Gizmos. To pursue a new line of research, it applied for and won a series of grants through the NSF's Small Business Innovation Research program. "The NSF's funding was critical to our being able to undertake the kind of speculative prototyping and experimentation required to go after this exciting new area in educational technology," Cholmsky said. ExploreLearning was subsequently acquired in 2006 and is now part of Cambium Learning.
Getting to automaticity
Cholmsky explained that the goal extends beyond getting students to correctly answer simple expressions in addition, subtraction, multiplication and division. Over the course of elementary school, students typically progress from methods like finger counting through a series of more advanced mental strategies that reflect their developing numeracy. For example, a student who is unsure of 5 x 7 but knows that 5 x 6 = 30 might find the answer by realizing that 5 x 7 is equivalent to 5 x 6 + 5. Thinking of multiplication as repeated addition in this way enables the student to correctly answer 35, albeit with some mental effort.
As they practice and evolve these mental strategies over time, elementary students are expected to ultimately develop automaticity with these basic facts, meaning they are retrieving answers from long-term memory without conscious effort or attention. Recent brain imaging studies have shown how this progression is reflected in the regions of the brain that are involved in mathematical computation. By achieving automaticity, students free up their working memory so that it can be devoted to problem-solving and learning new concepts and skills.
The challenge for math educators is that many children in the United States never attain adequate automaticity with basic math facts. Those who do develop automaticity tend to do so later than their peers in nations with higher math achievement. Students who continue to use effortful methods to answer math facts tax their working memory, impeding their ability to learn more advanced material such as fractions and algebraic equations. To address this issue, new national curriculum standards and research-based classroom guidelines have focused on automaticity as one of the critical benchmarks in elementary mathematics education.
High-speed game environment
Cholmsky explains how an adaptive system works in this context. "Reflex uses a range of data-gathering 'sensors' to monitor each student's developing fluency across the entire range of math facts, constantly looking for opportunities to leverage their current abilities to help them learn new facts more efficiently. A student who has begun confidently recalling 7 x 3 = 21, for example, can be coached to apply the commutative property to answer 3 x 7, and then given a series of practice environments that place increasing demands on them."
Ultimately, students enter a high-speed game environment whose elements place a load on their working memory. In one game, they might have to answer math facts to navigate through a maze and avoid pursuers; in another, they might answer facts to serve ice cream to space aliens or to fly a hot-air balloon. The goal is to develop their abilities to effortlessly retrieve facts from long-term memory while they are focused on a different, complex task. This is precisely what you want happening in the classroom when students are learning, say, how to add fractions with unlike denominators. "You want them focused on the new procedure they are learning, not on struggling to answer all the math facts required as part of applying it. Provided the game difficulty is accurately matched to their current ability with each fact, students can make tremendous progress in relatively short amounts of time."
The program also is designed to help students learn important concepts like the inverse relationship between multiplication and division, by actually applying the concept as a bridge from known to unknown. The data-driven, individualized process builds on each student's current proficiency, whatever it might be, and is designed to work for even the most struggling student. "It's the Goldilocks approach," said Cholmsky, "not too hard, not too easy, just the right difficulty at that point in time to challenge and engage the student without frustrating them."
Success for all
ExploreLearning wrapped the Reflex technology within addictive online games. Says Cholmsky, "Here's something else that's really exciting: Students are choosing to use the system in their free time. We've studied many schools where Reflex is assigned as homework, say, three times a week, and students go well beyond that, regularly logging on five, six or even seven days a week to play games and work on their fact fluency."
Teachers are pretty happy when the class average is to do more homework than assigned, he says.
"This past summer, we also saw summer school students who already use the system on an intensive basis every day in class choose to log in again from home during the evening or over the weekend. That's something I'm really pleased about, since many of these summer students have been struggling with mathematics in general and giving them a positive experience before the next school year is important. We're even getting fan mail, which is pretty cool. Remember that this is for a system for practicing math facts!"
Since its launch last year, students have already answered over a billion facts while playing Reflex games.
Teacher McNamara says, "I experienced amazing results with Reflex. I taught nearly 60 math students this year and all but eight students were 100 percent with the lowest fluency over 80 percent." The program has "changed my teaching life!"
Editor's Note: The researchers depicted in Behind the Scenes articles have been supported by the National Science Foundation, the federal agency charged with funding basic research and education across all fields of science and engineering. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. See the Behind the Scenes Archive.