Making Math Add Up
By John Lucas
Why do American kids, plus long-established teaching methods, sometimes equal struggle in math classrooms? A UW-based project is studying that equation.
More than a decade later, I'll still have an occasional nightmare about my third period advanced algebra class. It's always the same scene: I'm sitting alone, before school, in the dark, deserted "math resource area" of my suburban Chicago high school. I'm there to retake a test loaded with equations, graphs, and functions. As I stare at the jumble on the page, it slowly dawns on me that it's not even a matter of not knowing the right answers. I can't begin to comprehend whether the right answer would take the form of a number or an equation - or what type of math operation would get me to the general neighborhood of an answer.
My "didn't study for the test" nightmares don't stray far from real life.
Why do American kids, plus long-established teaching methods, sometimes equal struggle in math classrooms? A UW-based project is studying that equation.
More than a decade later, I'll still have an occasional nightmare about my third period advanced algebra class. It's always the same scene: I'm sitting alone, before school, in the dark, deserted "math resource area" of my suburban Chicago high school. I'm there to retake a test loaded with equations, graphs, and functions. As I stare at the jumble on the page, it slowly dawns on me that it's not even a matter of not knowing the right answers. I can't begin to comprehend whether the right answer would take the form of a number or an equation - or what type of math operation would get me to the general neighborhood of an answer.
My "didn't study for the test" nightmares don't stray far from real life.
I never really clicked in class with my algebra teacher, a stocky football coach with a long beard and a blunt teaching style. He seemed to be a nice enough guy, but to me, the lessons were deadly dull. I'm a word person, I reasoned, so why bother?
From his perspective, I probably seemed like one of his worst students. It's true that I spent a good chunk of third hour chatting with classmates, discussing sports or music. Of course, my indifference caught up with me in the end; I flunked most of my quizzes and tests. For all his faults, my teacher graciously allowed me a handful of early morning retakes - which I also proceeded to flunk - hence, my psychological scars. Much to the dismay of my parents, I ended up with a D - and an appointment to retake the class with a remedial section the next semester.
It's a simple equation that is still repeated day after day in classrooms across America: uninspired teacher, plus unmotivated student, equals math failure.
From his perspective, I probably seemed like one of his worst students. It's true that I spent a good chunk of third hour chatting with classmates, discussing sports or music. Of course, my indifference caught up with me in the end; I flunked most of my quizzes and tests. For all his faults, my teacher graciously allowed me a handful of early morning retakes - which I also proceeded to flunk - hence, my psychological scars. Much to the dismay of my parents, I ended up with a D - and an appointment to retake the class with a remedial section the next semester.
It's a simple equation that is still repeated day after day in classrooms across America: uninspired teacher, plus unmotivated student, equals math failure.
But help is on the way. Since November, a forward-looking research and development consortium based at UW-Madison's Wisconsin Center for Education Research, a department of the School of Education, has been looking at ways to improve math teaching.
The five-year, $11.5 million project, funded largely by a grant from the National Science Foundation (NSF), is concentrating on methods for teaching math to a diverse group of students at levels at which they can find success. Organizers hope their efforts will influence the field over the next decade.
Known as DiME/CLT - for Diversity in Mathematics Education Center on Learning and Teaching - the consortium is one of the first programs to take a concerted and serious look into how differences in race, gender, and class affect the teaching and learning of mathematics.
Many underprivileged students, for example, struggle with math, often leading them to lower-track classes that won't prepare them adequately for college, says Walter Secada, a UW-Madison professor of curriculum and instruction who is directing DiME. Less clear are the best ways to solve the problem.
The five-year, $11.5 million project, funded largely by a grant from the National Science Foundation (NSF), is concentrating on methods for teaching math to a diverse group of students at levels at which they can find success. Organizers hope their efforts will influence the field over the next decade.
Known as DiME/CLT - for Diversity in Mathematics Education Center on Learning and Teaching - the consortium is one of the first programs to take a concerted and serious look into how differences in race, gender, and class affect the teaching and learning of mathematics.
Many underprivileged students, for example, struggle with math, often leading them to lower-track classes that won't prepare them adequately for college, says Walter Secada, a UW-Madison professor of curriculum and instruction who is directing DiME. Less clear are the best ways to solve the problem.
"In too many middle and high schools, you can tell what track of math class you're looking at by simply noting the color of the students' skin or the quality of their clothes," he says. "And that is abominable."
Through the years, testing has shown that, as a whole, older American students are lagging behind other nations in math and science. As recently as 1998, the Third International Mathematics and Science Study (TIMSS) showed that American eighth-grade students scored well below average and twelfth-grade students performed near the bottom relative to their peers around the world.
Consistently poor results have fed into the "math wars," an ongoing controversy over "old" versus "new" math, and "hard" versus "soft" math, among others. Much of the discussion centers around whether the value of drilling and procedures (old and hard) outweighs conceptually based (new and soft) methods.
According to Secada, these wars and the labels that the media use miss the point. "We want students to know skills and to understand them; society also needs students who can apply what they know to solve problems that are becoming increasingly complex," he says.
Through the years, testing has shown that, as a whole, older American students are lagging behind other nations in math and science. As recently as 1998, the Third International Mathematics and Science Study (TIMSS) showed that American eighth-grade students scored well below average and twelfth-grade students performed near the bottom relative to their peers around the world.
Consistently poor results have fed into the "math wars," an ongoing controversy over "old" versus "new" math, and "hard" versus "soft" math, among others. Much of the discussion centers around whether the value of drilling and procedures (old and hard) outweighs conceptually based (new and soft) methods.
According to Secada, these wars and the labels that the media use miss the point. "We want students to know skills and to understand them; society also needs students who can apply what they know to solve problems that are becoming increasingly complex," he says.
At the same time, Secada, who is Hispanic, says there's been a growing recognition that America's culturally, socially, and linguistically diverse K-12 student population plays a major role in the nation's scores and its future economy. A significant math "achievement gap" exists between white students and students of color, and the gap relates to how teachers instruct - or fail to instruct - students of differing languages, cultures, and economic classes.
What's worse, math - and algebra in particular - is viewed as a key academic "gatekeeper" subject. Students who do poorly are more likely to be placed in lower-track courses and are less likely to go to college and be competitive in the job market.
"If a student leaves high school having been taught just checkbook math, that person won't have a checkbook worth doing math in," Secada says.
What's worse, math - and algebra in particular - is viewed as a key academic "gatekeeper" subject. Students who do poorly are more likely to be placed in lower-track courses and are less likely to go to college and be competitive in the job market.
"If a student leaves high school having been taught just checkbook math, that person won't have a checkbook worth doing math in," Secada says.
"Our society's demands for math literacy are going up and up," says Secada, who visited the White House during the Clinton administration for the release of the twelfth-grade TIMSS results. "It's not the case that schools aren't improving," he says. "They are - but they are not improving fast enough to keep up with the increased demands for technical skill and mathematical knowledge."
When the NSF decided to commit millions of dollars toward rebuilding the nation's math and science leadership, Secada, along with UW-Madison colleague Thomas Carpenter PhD'71 and their colleagues at the University of California-Berkeley and the University of California-Los Angeles, seized the opportunity.
Their approach underscores the significance that diversity plays in teaching and learning math. They propose training experts who will do research, apply ideas in the classroom, and teach college students. In the process, they will discover more about the reasons behind the "achievement gap" and develop ways to close it.
When the NSF decided to commit millions of dollars toward rebuilding the nation's math and science leadership, Secada, along with UW-Madison colleague Thomas Carpenter PhD'71 and their colleagues at the University of California-Berkeley and the University of California-Los Angeles, seized the opportunity.
Their approach underscores the significance that diversity plays in teaching and learning math. They propose training experts who will do research, apply ideas in the classroom, and teach college students. In the process, they will discover more about the reasons behind the "achievement gap" and develop ways to close it.
The idea of training a new generation of math teachers is designed to address some sobering facts:
- One-third of mathematics teachers in grades seven through twelve have neither a major nor a minor in the field, yet they teach one in four of all mathematics students.
- During the next decade, the nation's schools will have to replace more than two-thirds of current teachers due to attrition.
- More than half of university faculty in mathematics education will be eligible for retirement during the next two years, and almost 80 percent will be eligible for retirement within the next ten years.
One major component of the DiME center's work is a plan to produce thirty new doctoral students in math education research and teaching. In the future, the group will eventually develop its own research and ideas on diversity issues, particularly relating to the teaching of algebra. Teachers already in the classroom will also receive ongoing professional development along with college students at the consortium's partner institutions.
"We want to close those achievement gaps," Secada says. "How we get there, we don't know all of the details, but we want our best and brightest minds to be a part of it. It's a challenge."
"The project will create new research, new tools, and more importantly, a generation of researchers capable of making significant strides on issues of diversity in mathematics education," says Rogers Hall, an associate professor of education at UC-Berkeley and an associate director of the new consortium. "If we are successful, the field will be changed fundamentally by this new generation of scholars."
"We want to close those achievement gaps," Secada says. "How we get there, we don't know all of the details, but we want our best and brightest minds to be a part of it. It's a challenge."
"The project will create new research, new tools, and more importantly, a generation of researchers capable of making significant strides on issues of diversity in mathematics education," says Rogers Hall, an associate professor of education at UC-Berkeley and an associate director of the new consortium. "If we are successful, the field will be changed fundamentally by this new generation of scholars."
DiME represents just one of the substantive contributions that UW-Madison's math education experts have made to their field. Over the years, Carpenter and others in the School of Education, including emeritus professors Thomas Romberg and Elizabeth Fennema, and active faculty such as Richard Lehrer, Leona Schaubel, and Andy Porter, have been instrumental in curriculum reform, standards development, and many other innovations in math education.
Until the new generation of DiME scholars emerges, the consortium is likely to have immediate beneficiaries in the teachers and students in the Los Angeles Unified School District, the Berkeley Unified School District, and the Madison Metropolitan School District (MMSD). These districts have partnered with UW-Madison to become learning labs for diversity education.
Through in-services and workshops, Secada and Carpenter have already been active in the Madison public schools, supporting dozens of teachers as they explore ideas on the diversity components of math, says Mary Ramberg, teaching and learning director for the district.
"We have a wonderful symbiotic relationship with UW-Madison," she says. "We've learned a lot from each other. We believe that all kids can learn math, and a focus on kids who have been left behind is sorely needed."
In spite of the small amount of systemic research in the field, Secada says he has ideas on how to teach math to diverse populations. Among them:
Until the new generation of DiME scholars emerges, the consortium is likely to have immediate beneficiaries in the teachers and students in the Los Angeles Unified School District, the Berkeley Unified School District, and the Madison Metropolitan School District (MMSD). These districts have partnered with UW-Madison to become learning labs for diversity education.
Through in-services and workshops, Secada and Carpenter have already been active in the Madison public schools, supporting dozens of teachers as they explore ideas on the diversity components of math, says Mary Ramberg, teaching and learning director for the district.
"We have a wonderful symbiotic relationship with UW-Madison," she says. "We've learned a lot from each other. We believe that all kids can learn math, and a focus on kids who have been left behind is sorely needed."
In spite of the small amount of systemic research in the field, Secada says he has ideas on how to teach math to diverse populations. Among them:
- A focus on smaller class sizes for students who are on the bottom tracks.
- A more balanced curriculum, stressing understanding and skills, operations, applications, contextual problems, and how they all relate to each other.
- More real-time assistance in which students can get immediate help to understand a problem.
- The development of student reasoning based on problem-solving strategies that are often different from standard, by-the-book procedures.
Some of Secada's ideas are playing out every day in the classroom of Chris Stafslien '98 at La Follette High School on Madison's east side. At 9:40 on a January morning, students in her basic algebra class listen to school announcements before slowly beginning to focus on the day's lesson: functions and absolute value.
Stafslien, a third-year math teacher, is also pursuing her master's in education. For the past three years, she has participated in a seminar for mathematics teachers of low-track students run by Secada, his graduate students, and the MMSD.
"At first, I wasn't sure what kids were thinking about or what they were understanding," she says. "The goal is to get them involved and get them to take ownership of their math. The idea is to take kids with really low math esteem and show them what they're capable of."
Stafslien, a third-year math teacher, is also pursuing her master's in education. For the past three years, she has participated in a seminar for mathematics teachers of low-track students run by Secada, his graduate students, and the MMSD.
"At first, I wasn't sure what kids were thinking about or what they were understanding," she says. "The goal is to get them involved and get them to take ownership of their math. The idea is to take kids with really low math esteem and show them what they're capable of."
The twenty students in her racially mixed group have been recommended for the class by their previous teachers because of difficulties they experienced in pre-algebra or other algebra sections. Her task is to devote as much time as it takes on each key topic until students seem to "get it." On this morning, the class members happily grab graphing calculators and dig into practice problems. After a few minutes, Stafslien reviews homework and then begins an "investigation," an activity in which the class pairs off with partners and begins working together to solve problems on a graph.
Talking about the problems with classmates makes them easier to solve, says freshman Ashley Huff. "Most other teachers move too fast," she says. "But [Stafslien] moves slowly, and she's always around to help. It's gotten to be fun, because it comes easier to me."
With the "investigation" complete, Huff and a few other students show their work on the board before getting a jump on homework problems. Stafslien circulates through the room, asking questions about each student's progress on the assignment.
Talking about the problems with classmates makes them easier to solve, says freshman Ashley Huff. "Most other teachers move too fast," she says. "But [Stafslien] moves slowly, and she's always around to help. It's gotten to be fun, because it comes easier to me."
With the "investigation" complete, Huff and a few other students show their work on the board before getting a jump on homework problems. Stafslien circulates through the room, asking questions about each student's progress on the assignment.
Stafslien says her approach is designed to encourage students to think through the concepts they find most difficult to understand. Following Secada's idea on the importance of how students learn to reason, she says she keeps in mind that many may approach the problems differently than she does.
"We've made a lot of progress," she says. "These kids have failed before in the system. They've always looked at math as a dry set of rules and theorems they didn't want to memorize.
"At the beginning of the year, everyone was unhappy with math and kind of resigned to being here," she adds. "Now they're getting excited."
Maurice Dean, a freshman, says he doesn't expect to ever have test retakes, let alone nightmares about algebra.
"It's become my favorite class," he says. "I love the way she teaches."
"We've made a lot of progress," she says. "These kids have failed before in the system. They've always looked at math as a dry set of rules and theorems they didn't want to memorize.
"At the beginning of the year, everyone was unhappy with math and kind of resigned to being here," she adds. "Now they're getting excited."
Maurice Dean, a freshman, says he doesn't expect to ever have test retakes, let alone nightmares about algebra.
"It's become my favorite class," he says. "I love the way she teaches."
