Divide and Conquer
Not long after professor Isabel Rodríguez-Dehmer brushed up on her rusty algebra skills, she stood before a class and discussed the seven steps of factoring polynomials, a type of algebraic expression made up of constants (numbers with fixed and defined values) and variables (such as x and y).
You wouldn’t expect to see a mathematics teacher relearning one of the most fundamental concepts in algebra before giving it as a lesson. But Rodríguez-Dehmer doesn’t teach math. For the past 15 years, seven of which she’s been at Miami Dade College, she’s taught reading.
“Reading is the foundation and the backbone of all courses,” the North Campus professor said.
Rodríguez-Dehmer is a die-hard reading specialist. Yet about two years ago, she took an interest in polynomials when she became part of MDC’s progressive initiative to teach mathematics across disciplines, including reading.
At that time Rodríguez-Dehmer learned of a grant the College had received from the National Science Foundation’s Mathematics Across the Community College Curriculum (MAC³) Project.
The three-year project is led by the American Mathematical Association of Two-Year Colleges in partnership with Miami Dade College and Washington State’s Edmonds and Seattle Central community colleges.
The goal of the project, according to the association, is “to create a mathematically literate society that ensures a workforce equipped to compete in a technologically advanced global economy.”
MDC has served as an integral part of the collaboration by hosting more than a dozen two-year colleges from around the country for the project’s winter institute, which has been held in Miami Beach for the past three years.
Through MAC³, the College has developed course connections between math and several disciplines, including art, biology, chemistry, computer science, economics, student life skills, music, nursing and reading.
Excited about the concept, Rodríguez-Dehmer, who had experience in teaching reading across disciplines, contacted math professor Lourdes España to collaborate in a learning community, a practice in curricular design of linking courses to create a shared experience for students.
España already had some experience in the cross-pollination of disciplines. Since she arrived at the College eight years ago she has been teaming up with professors in several subjects to teach math. Her first collaboration was combining algebra with a psychology class.
“The psychology instructor’s lessons helps students learn to overcome math anxiety and how to relax in order to take a test,” España said.
The reading-math collaboration would require the same approach, España knew. If she and Rodríguez-Dehmer were going to be successful, they would have to first address math anxiety among some first-time college students.
Together, they developed “The Circle of Life,” a project that combines a developmental reading class with a developmental algebra class.
Their collaboration resulted in a dramatic increase in student pass rates in both subjects and earned them the 2007 Florida Department of Education Chancellor’s Best Practice Award. The award is given annually to showcase exemplary programs at local institutions and to further promote those initiatives to state and national audiences.
“The State was asking institutions to try something new,” Rodríguez-Dehmer said. “They wanted us to help with retention and to stress different ways of thinking. This program has allowed MDC to be among the first to pioneer and be a part of this curriculum.”
Improving the Odds
According to Patrick Bibby, professor emeritus of mathematics and the College’s principal investigator on the MAC³ project, only 15 percent of entering students are able to start with college-level mathematics courses. Sixty-four percent of students entering MDC test into developmental or college prep math, for which they earn no credit. And, 21 percent test into intermediate math, for which students can earn credits that do not count toward the math requirement for graduation.
One explanation is that many students enter the College after an extended period of no math instruction. Some non-traditional students enter MDC after being in the workforce full time and not seeing an algebra text book in a decade. Then there are the graduating high school seniors who fulfilled their math requirements as sophomores and who may need a refresher.
Whatever the case may be, Bibby said, College research indicates that students who take math courses in sequence are more likely to succeed than those who wait a year or more.
Furthermore, Bibby said, research conducted at MDC shows developmental math, intermediate algebra and college algebra are serious obstacles to graduation and program completion for many students.That is why MDC is taking math education more seriously than it ever has before.
“Mathematics can be found in just about everything,” said Bibby, who has been teaching mathematics at MDC for 33 years. “We want to teach our students how it can be used and applied so they can have a greater appreciation for math and for society in general.”
MDC successfully completed its most recent accreditation review by the Southern Association of Colleges and Schools (SACS) three years ago. SACS, the regional accrediting body, now requires its member institutions to submit a quality enhancement plan (QEP) that focuses on student learning outcomes. MDC chose mathematics as its QEP topic.
“It was a bold step because math is such a difficult area,” Bibby said. “We chose to take it on and try to do something creative and innovative to help students through it.”
Besides teaching math across disciplines, other strategies for the QEP initiative include frequent testing, e-mailing interim progress reports, supplemental instruction for developmental course repeaters and establishing a training program for tutors who work in the math lab.
The new tutor training program – which requires that all tutors receive seven hours of training – was certified by the College Learning and Reading Association.
Additionally, MDC was chosen to host a recent meeting of the National Mathematics Advisory Panel. The panel, which was created by President George W. Bush in April 2006, advises the president and the secretary of education on the best use of scientifically based research to advance the teaching and learning of mathematics.
The Algebra Project
On a recent evening, Dr. Robert “Bob” Moses and his co-instructor Dr. Jermaine Brown stood before a developmental math class at InterAmerican Campus. When solving polynomials, Brown told the class, you can only add like terms.
Moses took it further. “Another way to think about it,” he said while marking an equation on the dry erase board, “is to think of the way we add our 10s.”
Then Moses demonstrated in simple arithmetic terms. You can’t add x3 to 2x2 and 5x. To simplify matters further, he made x equal 10, and he wrote the equation on the board:
5x + x3 + 2x2
x3 = 1,000
2x2 = 200
5x = 50
When adding up these numbers, you wouldn’t add the 1 in 1,000 to the 2 in 200 or the 5 in 50 because “we add our numbers in powers of ten,” he said. “All of that gets carried over to polynomials.”
Moses’ process is simple yet effective. He was brought on board to teach developmental math using the Algebra Project, the nationally revered school reform effort for math that he founded.
“Dr. Moses is teaching math from the social perspective,” said Alex Salinas, assistant professor in the communications, arts and philosophy department, who was instrumental in bringing Moses to the College.
“The project teaches that math is a civil right. There is a civic connection there that goes back to the idea of education being a form of empowerment,” Salinas added.
In the 1960s Moses was a civil rights activist, leading voter registration drives in Mississippi. Since the early 1980s, when the Algebra Project was founded, Moses has sought to build the demand for math literacy across the country, especially in poor and minority communities. “Dr. Moses wants to work with students at the bottom,” Salinas said. “It’s his mission.”
Moses’ philosophy is not that those students don’t have the ability to do college-level math, but that they were never given the opportunity for a proper math foundation.
Some students need more help than can be offered in a three-credit course. So faculty members have created learning communities in which two courses are taught back to back, each reinforcing the other.
Math professor Miguel Montañez and biology professor Juan Morata have formed such a community at Wolfson Campus.
Montañez and Morata developed a curriculum that requires their students to tackle a project that brings together elements of math and science. Besides tests given throughout the semester, the project counted for a considerable percent of the grades students earned in each course.
“The project is great because they have to use the scientific method, which has a systematic series of steps to come up with a conclusion,” Morata said. “And, they have to use math to explain their conclusions.”
When coming up with the project concepts, the professors agreed they should make it something in which students could relate and have an interest. “We wanted to make math more tangible and palatable,” Montañez said.
They developed five modules that the students, divided into five groups, would tackle.
One group had to analyze the exploding population in Miami-Dade County and how the numbers were going to affect South Florida’s socioeconomic and environmental outlook.
“From the math perspective they were going to collect the raw data, organize the data, find functions and draw conclusions,” Montañez said. “And they were also going to focus on the scientific methods of observation, drawing a hypothesis and doing research to validate or kill that hypothesis.”
The professors met regularly to discuss their syllabi so that their daily lessons complemented each other. “We are in constant communication,” Montañez said. “We want our students to see the constant collaboration and communication.”
Also, classrooms were set up so that students sat at tables rather than desks, forcing them to work together – a shift that has had more than a strictly educational benefit.
“They’re all good friends now because they worked cooperatively throughout the semester,” Morata said. “And what they learned in those classes will definitely be used again in other classes.”
Connecting the Three R’s
On the whole, MDC’s approach to math education is based on a simple idea: In order for students to conquer the subject, they have to believe it is a subject in which they can excel. Philosopher Karl Popper called this idea the Oedipus effect – “the effect of a prediction (or a similar piece of information) upon the events or objects to which the prediction refers.”
That means translating formulas and equations into everyday parlance to convince students that they can learn math, said Bibby, the veteran math professor.
Bibby spoke of the geometric shapes that have been used throughout history in art and architecture. The golden ratio or divine proportion, for example, is said to be found in works like the Mona Lisa and in ancient buildings like the Parthenon. “It’s very mathematical,” he said. So is music, he added, referring to musical terms like octaves and scales. “It’s amazing how you can pluck a string to get a note, and if you cut that string in half you’ll get the same note but one octave higher.” The places where one can find math, Bibby said, are endless.
Rodríguez-Dehmer helps students reduce tension in math and reading comprehension by using España’s algebra text book in her classes. “In reading you are trained to see patterns and bring those patterns together into a whole picture,” she said.
And seeing the whole picture – the interconnectedness of math with every other subject – is what MAC³ is all about.
— Pilar Ulibarri de Rivera