Strong math skills are important if students hope to succeed in high school and beyond—and many school leaders are finding that software that delivers hands-on, personalized instruction can help.
K-12 math instruction is undergoing fundamental changes as individualized adaptive learning programs combine with lessons meant to keep students of all ages engaged and interested.
For example, DreamBox Learning provides more than 500 elementary-level lessons to help students develop computational fluency, conceptual understanding, and problem-solving skills through an online gaming platform. Students can choose a game character and theme, and they progress through different levels of the experience, earning rewards for their progress.
Meanwhile, teachers are able to review the advancement of each student, receiving detailed reports that indicate when a student needs extra attention or when a student successfully passes the lessons.
When companies describe their software as “adaptive,” they typically mean that students progress through the same levels of instruction in the same sequence, albeit at a different pace, said DreamBox President Jessie Woolley-Wilson. But with DreamBox, it’s truly adaptive learning that is taking place; although students start at the same point in the assessment, their experience with the software will be completely different based on their individual abilities and interests.
“Technology allows for mass customization in a way that teachers don’t have time to do,” Woolley-Wilson said. “This is exciting, because it’s going to change the velocity of learning.”
“We can blend great teachers and great technology and create an individualized adaptive educational environment to meet the needs of kids [in a way] that hasn’t been done before,” said Mickelle Weary, director of instructional design.
Formerly a teacher, Weary said the program responds to a child’s struggles or successes as a teacher would.
“When we actually sit down and plan the way lessons are going to behave, we take into consideration, ‘What would I be doing if I was sitting next to that child and [he or she was] struggling?’” Weary said. “In sitting shoulder to shoulder with our developers, we would talk to them about how we teach, how we would react to students in the classroom, and they would take that knowledge and they would build our platform.”
West Seattle Elementary special-education teacher Elizabeth Raymond said DreamBox offers huge benefits to instructors.
“What I like about it is it gives me immediate feedback. … I can go into the teacher reports and really see what specific concepts certain students are struggling with,” Raymond said.
DreamBox is unique in its ability to appeal to students, she said, adding: “I really think it can reach those students who have been resistant to traditional teaching styles. It’s a format they’re already familiar with from playing so many video games and things like that at home.”
Raymond said she has trouble keeping her students away from DreamBox.
“This is a program that I don’t have to coax students onto; they actually pester me during the day, [asking:] ‘When is it my turn to go on DreamBox?’ I only wish that I had more computers in the classroom, so I could have more [students] on at a time,” she said.
The results of consistent play on the software are staggering.
“We took a fall test before I began using DreamBox … and then we tested again at the end of December,” Raymond said. “My students averaged a 40-point gain in mathematics on this test. And I really think that’s a testament to the efficacy of the program.” She noted that for special-needs students, these numbers are even more impressive.
With the success of the program for grades K-3, DreamBox is planning to expand its content to grades four and five, while increasing the content available for third graders.
Cooperative, hands-on learning
While DreamBox Learning focuses on students in the youngest grades, Pitsco Education has seen remarkable success with a math program of its own, this one specializing in algebra instruction for grades 7-10.
With diagnostic assessments, targeted remediation, individualized lesson plans, and one-to-one computer-based instruction, Pitsco’s Algebra Academy has produced some incredible results in one South Carolina high school.
The Algebra Academy has computer-based elements, but it functions as a multipart program. It combines individualized curriculum; small-group activities; cooperative, hands-on learning projects; and diagnostic assessments to deliver its progressive, three-phase system.
Students in Phase I work their way through a series of Individualized Prescriptive Lessons (IPLs) after completing diagnostic assessments. Based on their test results, they are prescribed lessons in math concepts for which they need remediation, each of which begins with a practice test and concludes with a mastery test. After demonstrating a mastery of basic math concepts in Phase I, students then progress to a project-based curriculum in Phases II and III.
“We … realize the need for individualization, because [students are] going to be all over the board in terms of their range of current abilities—so we utilize individualized software instruction as one of the first interventions for students,” said Pitsco’s director of education, Matt Frankenbery.
Pitsco follows up these individualized, computer-based lessons with cooperative, hands-on learning projects to help keep students engaged.
Students “spend time doing a lot of [work] with actual materials in their hands, versus just experiencing something on the screen,” Frankenbery said.
Phase II involves teacher-led, small-group activities, and in Phase III, students work in pairs to solve challenges. In a module called “Unsolved Mysteries,” for example, teams of students are tasked with solving a crime, and in the process they learn algebra concepts and how to apply them.
In one of the mysteries, a cup of coffee is found at the crime scene. By determining how long it takes a similar-size cup of coffee to cool, the students can estimate when the crime took place. So, students take part in a lab experiment in which they periodically measure the temperature of a cup of coffee as it cools to room temperature, then plot the data on a graph. In the process, they learn about scatter plots and linear regression.
The three-phase system distinguishes Pitsco’s Algebra Academy from other products.
“We’ve utilized three different methodologies in the overall solution, so we’re really meeting the needs of pretty much every student,” said Frankenbery. “We feel like it’s this blend … of methodology that’s really what is connecting the students” to the lessons.
At Carolina High School and Academy in Greeneville, S.C., 71 percent of the students passed the most recent state math exam—but among students who took algebra using Pitsco’s curriculum, that figure was 94 percent, said Assistant Principal Michael Delaney.
What’s more, at least 40 percent of the students who experienced Algebra Academy made some kind of jump to the next level of math instruction in the following school year, Delaney said—and 19 percent moved from the lowest level to honors-level math.
Applying math to real-world challenges
While Pitsco and DreamBox have developed new ways to teach math fundamentals, the Society for Industrial and Applied Mathematics and The Moody’s Foundation have joined forces to demonstrate to older students how these skills can be applied in the real world.
“We really hope to shed light on a lot of the exciting careers and applications of mathematics,” said M³ Challenge project director Michelle Montgomery.
The M³ Challenge, which took place March 5-6 this year, provides thousands of dollars in incentives to encourage high school students on the East Coast to participate. This year, 717 teams from more than 5,000 high schools registered for the M³ Challenge, which is designed to pique high schoolers’ interest in real-world applications of mathematics.
“There’s a lot of data, statistics, projections, graphing—all kinds of math stuff, but it also involves a real issue,” said Montgomery of the contest.
The M3 Challenge, which is in its sixth year, has always been built around a newsworthy issue. This year, the problem was based on the drought in the Colorado River Basin, and it involved making projections and a hypothetical report to the Department of the Interior.
The web-based challenge gives participants 14 hours to solve a legitimate real-world problem. Teams gather data, develop assumptions, and establish mathematical models. The teams then upload their solutions, which consist of papers that can be up to 20 pages long, and are judged by more than 80 Ph.D.-level mathematicians.
Judging occurs in three stages. The first pares down the field to 100 teams, while the second round of judging identifies the top 40 and the final round chooses the top six. The top 40 teams are recognized as honorable mentions or finalists and receive prizes of $1,000 or $1,500, respectively, while the winners receive scholarship prizes totaling $100,000.
“If you’re going to high school and you’re taking math and you’re saying, like lots of kids say, ‘When am I ever going to use this? What am I ever going to do with this?’—we’re trying to show through these math modeling programs, these applied math problems, that there’s tons of stuff you can do with this, and lot of it is really exciting and current,” Montgomery said. “I think we’re really illustrating how math, applied math, and STEM fields can contribute to a better society for the world.”
This year’s winners will be announced April 28; for more information, go to http://m3challenge.siam.org.