As the emergence of a new global economy continues to drive wholesale instructional changes in the nation’s classrooms, the demand for solutions designed to teach higher-level mathematics concepts such as calculus and engineering is growing.
With President Bush making math and science instruction a point of emphasis in his State of the Union address and Education Secretary Margaret Spellings calling on schools to “raise the bar” on math instruction, K-12 institutions are looking for ways to help students understand–and even appreciate–tough math concepts.
And it’s technology, not textbooks, many experts say, that will make much of this transformation possible–along with a shift in teaching strategies and an emphasis on professional development.
“Used well, technology can open the door to mathematics for more students than it ever has in the past,” said Cathy Seeley, president of the National Council of Teachers of Mathematics (NCTM).
With that thought in mind, NCTM recently teamed up with executives at Texas Instruments (TI) and producers for the hit CBS television drama Numb3rs to launch a new classroom companion web site and curriculum based on topics discussed during the show, which features a mathematician who employs complex theories to help the FBI solve crimes.
The idea, according to TI’s Linda Beheler, is to take what students often see as abstract mathematical concepts and make them more relevant to their daily lives. The television show, she said, serves as an example of how math is used every day to solve real-world problems.
“We always get the same question,” said Beheler. “Students always want to know, “How are we ever going to use this stuff in the real world?'” And that’s the idea behind the Numb3rs initiative–“to show them how these [concepts] apply to what they do in life.”
Mathematicians and educators from NCTM are working with the show’s writers and producers to develop lesson plans and activities centered on the different mathematical concepts encountered during each episode. Topics touched on already this season include continued fractions, Benford’s Law, probability, direct variation, ellipses, and randomization.
Before each episode airs, teachers, students, and parents can go the Number3s web site and download the corresponding activities, giving them an opportunity to play along with investigators as the characters try each week to solve a new crime. Students then return to class prepared to talk about the concepts used during the show; teachers, in turn, provide corresponding problem sets to reinforce the topics. The activities from each episode remain on the site throughout the entire season, so teachers can return to them and use them as they deem fit, Beheler said.
The activities also are designed to integrate well with TI’s handheld Navigator and graphing calculator products, she said, giving educators another opportunity to integrate technology into the learning process.
Like the show, Beheler said, the Numb3rs activities are a hit. Since September, as many as 21,000 people reportedly have registered to take part in the program. She said CBS reports as many as 6,000 new activity downloads per week from the site.
“We’re seeing a real groundswell of support for the program,” she said.
Proponents attribute much of its success to a renewed focus by President Bush and other U.S. leaders on the importance of high-quality, advanced mathematics instruction in the nation’s schools. It’s a need, many say, that has become particularly acute as U.S. students continue to lose ground to their academic counterparts in developing nations such as India and China.
“It’s really echoing what a lot of us have been saying for some time,” NCTM’s Seeley said of the program and the call for better math instruction in the nation’s high schools. “That is, whether you want to become a scientist or an astronaut & you’re really going to have to use and understand math skills that weren’t even being talked about a decade ago in terms of workforce preparation.”
Looking to the future, experts agree a majority of the jobs that will be in high demand are likely to have a strong technical focus. From computer engineering, to science, to design, Seeley said, math plays an increasingly central role in all facets of the modern workforce.
But while educators in foreign nations have been aggressively pursing curricula with a focus on higher-level, 21st-century-type math skills such as calculus and engineering, U.S. institutions, by and large, have been slow to adapt, she said.
“A problem that we’re having is that a lot of folks around the country haven’t been paying attention to the growing importance of math,” she explained. “The role of math in the world is growing.”
Through interactive initiatives such as the Numb3rs program and others, Seeley said, NCTM aims to make higher-level math more accessible to more students.
According to TI’s Beheler, that’s a large part of why her company–one of the nation’s leading technology providers–signed on to sponsor the program.
“Even if you don’t go into a technological field, studying math is going to give you more [career] options,” she said. “We’d encourage every high school student to take at least one math course each and every year.”
Seeley expanded on that point, saying that if America is going to remain a leader in the global economy, it’s imperative that educators find effective ways to reach even the most reluctant students. And more and more, this involves the use of technology tools.
“Teachers are going to need to change the way that they teach…to use technology well,” she said. “We need to use the tools that will allow us to teach better, smarter.”
It’s that kind of thinking that is driving innovation and research at places such as Pittsburgh, Pa.-based Carnegie Learning.
Born in 1992 out of a research lab at Carnegie Mellon University, the technology-centered educational services provider operates under the philosophy that students learn best not simply by memorizing methods of operation, but by understanding the process through which answers to mathematical problems are achieved.
“[H]aving a deeper understanding is important [because] it helps you remember long-term, so that when you enter into the workforce you still retain enough of the information to help you in your job,” said Steve Ritter, a co-founder of the company and senior vice president of research and development.
Fifty years ago, Ritter said, U.S. schools were ahead of the pace when it came to teaching mathematics. But in recent years, a widening body of domestic and international evidence–including reports from the American Institutes for Research, the Program for International Assessment, and the Trends in International Mathematics and Science Study, or TIMSS–has given rise to increased concerns over American students’ inability to keep up with students in other industrialized nations.
“The biggest challenge in mathematics is getting to the deeper understanding of how and why do I want to solve a particular problem,” Ritter said. “Why is a particular operation the right thing to do?”
Every student thinks differently; as a result, Ritter said, each student also learns differently.
For teachers, he said, the key is to identify the difficulties faced by each individual student–and then teach to those weaknesses. And that’s where technology can help, he said–by differentiating instruction.
For example, Carnegie’s software “does more than tell a student what is right or wrong,” Ritter explained. “It follows the thought process of the individual student. It asks, ‘How do you want to solve [the problem]?'”
Using word problems fashioned after real-world situations and accompanying graphs, he said, Carnegie’s line of advanced math software aims to integrate the kinds of true-to-life thinking skills that students are likely to encounter in the workforce.
For instance, he said, in one of Carnegie’s algebra programs–each of which includes a combination of computer simulation and face-to-face instruction taught from an accompanying textbook–students are asked to envision working for a company where they’ve been tasked by their boss to choose the most cost-effective employee cell-phone plan. Using a set of predetermined variables–from cost per minute, to permanent charges–the students are asked to use their math skills to determine which plan best suits the needs of their imaginary employer.
“Districts really are starting to take this very seriously,” Ritter said of the real-world approach. “We find that questions like these really resonate with students and with teachers.”
Ritter said his company’s products are now used in 750 school districts across the nation, reaching some 350,000 students.
But given the much-publicized struggles of U.S. students in the areas of math and science, he acknowledged, innovative solutions alone probably won’t be enough to prepare students for the challenges of the global economy.
For this shift in thinking to occur, Ritter said, teachers–and parents–also have to buy in to the philosophy that math is a life skill that needs to be learned, not memorized.
To do that, schools have to change not just how they approach their students, but how they train their instructors, too, he said.
“We have to provide teachers with the essential and guiding questions to take the kids to the next level,” explained Sandy Bartle, Carnegie’s director of educational services and head of the company’s professional development division. She added, “We’re trying to align teaching to the way students learn.”
National Council of Teachers of Mathematics
NUMB3RS educational web site
Texas Instruments Education Portal