Making Connections
Between Math and the Real World

"What makes it so exciting is that it really makes mathematics come alive," says Steve Leinwand, mathematics consultant with the Connecticut State Department of Education. "What makes it so exciting is that it provides real-world situations and real-world contextto make sense of big mathematical ideas."

So what is it that Leinwand is so excited about? It is Math Connections, a new math curriculum, a math curriculum that's exciting, Leinwand adds, because it's an attempt to implement the new NCTM [National Council of Teachers of Mathematics] standards.

"It's wonderfully gratifying," says Leinwand, "to finally be able to say that there are published quality materials now available that in fact begin to answer the dream that we had for a long time -- the dream of being able to have accessible, sensible, coherent materials like Math Connections."

MATH CONNECTIONS: THE BACKGROUND

Math Connections was developed through a National Science Foundation grant to the Connecticut Business and Industry Association (CBIA). The secondary school program is a collaboration among mathematicians, scientists, businesspeople, and educators in the fields of math, science, and technology. It shows students how math is used in other academic subjects such as science, history, art, and music. It also introduces students to technology through the use of computers and graphic calculators, and requires team projects that will build the students' communication skills.

"Using these real problems, students can see how math is used every day in the working world instead of asking, 'What am I ever going to use this for?'" says Kenneth O. Decko, president and CEO of CBIA. "Math Connections is at the very forefront of the math revolution in the United States. It was developed because many students were completing high school unprepared to perform the math functions that would be required of them in higher education and in the world of work. We've succeeded in getting students tuned into math."

"Connecticut students who have used the curriculum are outperforming those who have taken a traditional math curriculum," Decko adds. "Now, that same opportunity will be available to high school students nationwide."

Decko notes that the curriculum helps students apply their knowledge, critical-thinking skills, and problem-solving skills -- all of which will be crucial either in college or when they eventually get jobs.

A "BLENDING" OF MATH CURRICULA

Math Connections integrates algebra, geometry, trigonometry, probability, and statistics to show students how these math topics are interrelated.

"Topics are blended," explains June G. Ellis, project director for Math Connections. "They are covered in the order in which they are needed, and are revisited over the course of the three-year program."

"Students learn to look at mathematics as a whole, rather than piecemeal," adds Ellis. "This shows students how the different mathematics are connected to each other and to the real world."

The three-textbook series written by mathematics professors and teachers is being published by It's About Time, an Armonk, N.Y.-based company.

"It's been amazing to see students who were having difficulty with mathematics suddenly become excited about working with math as a way of finding answers to all sorts of problems," said Ellis. "Math Connections shows them how they can use mathematics in their daily lives, as well as how they could use it in their future careers."

SO WHAT KINDS OF PROJECTS ARE STUDENT WORKING ON?

"The Math Connections philosophy is to encourage students to have fun using math by showing them its relevance outside the classroom," says Ellis.

So what sorts of projects are students working with in the classroom? Students analyze real data -- from Consumer Reports studies to pro ball players' salaries -- and use that data to solve real-world problems. Among the situations students might investigate are these:

• Students are given electric bills and asked to use algebra to figure out a missing piece of information -- the amount of electricity used by a family or the amount of the bill, for example. The constant in the equation is the usage rate the electric company charges. In addition, students might be asked to study the impact that an increase in the usage rate might have on a family's budget.

• Students are asked to "build" a new police station in their town. Using population figures and data from neighboring towns (the size of the police forces and the square footage of the police stations, for example), students figure out how many square feet of space will be needed for their town's new station.

• In a hospital, two patients are wheeled into an emergency room about the same time. Doctors measure blood pressure and heart rates to determine which patient should be treated first. Students are provided with information and then asked to put themselves in the doctors' shoes. Who will be treated first? Why?

Math Connections incorporates a lot of writing too. In traditional math programs, students get the right answer and go on to the next problem. But in Math Connections students are asked to prove how they got their answers by explaining, often in writing, their thinking processes.

IS THE PROGRAM SUCCESSFUL?

"Math Connections is an attempt to create classroom tested materials that reflect the spirit of the NCTM standards," says Steve Leinwand in the July 1996 issue of the National Council of Supervisors of Mathematics (NCSM) newsletter. "And according to independent evaluation it has."

One study took a look at the test scores of two groups of students. One group took Pre-Algebra and Algebra in grades 9 and 10; the other group took Math Connections I and Math Connections II. The study compared test results from those two groups of students on the Connecticut Mastery Test (CMT), given in the fall of grade 8, and the Connecticut Academic Performance Test (CAPT), given in the spring of grade 10. The mean test score results are shown on this chart.

External evaluation conducted by Don Cichon Consultants compared the numbers of Math Connections participants who met or exceeded the state goal of 266 on the CAPT. For the matched sample, 53 percent of the Math Connections participants met or exceeded that goal compared to 43 percent of the non-participants.

Another study indicates that Math Connections students have more confidence in learning mathematics and perceive it to be more useful.

Leinwand, president of the NCSM, is on a campaign now to broadcast the results of these studies. He hopes the data will silence some of those who are critical of (and win over some who have expressed skepticism about) the reform movement that has resulted in the new standards. He refers often to the mean score data (above chart). "But," Leinwand says in the NCSM newsletter, "since mean scores don't tell the entire story, we created a scatter plot of the data for all 56 students. What a wonderful picture of the impact of the alternative program on 10th grade scores at nearly every level of grade 8 achievement."

THE TEACHERS AND STUDENTS SPEAK

"It's math in a whole new light. It makes sense," says Amy Shibles, a student at Oxford High School in Norway, Maine. "I don't say to myself 'Why am I doing this? I'm not going to use this' because it shows me how I'm going to use itBefore it was pure numbers. This is pure situations. And that's the way I need to learn."

"My friends and I have found ourselves talking about math," Shibles adds. "We'll be talking about this program and we'll be saying 'Well what did you think about that?' and we'll be relating it to real-life and all of a sudden we'll stop and say [incredulously] 'We're talking about math!'"

"I never liked math so much," adds Travetta Walker, a student at Crosby High School in Waterbury, Connecticut. "Before Math Connections, I really didn't like math so much so I wasn't putting in the effort."

"I was a little nervous at first," Carl Bujaucius, a math teacher at Manchester (Conn.) High School. Math Connections was a big change from the traditional curricula. But he changed his mind when he saw how students reacted to the new program. "A higher percentage of kids are trying to do the homework," he adds.

Rosalie Griffin, a math teacher at Crosby High, was "a traditional teacher" for 30 years. "I gave a lecture, went over problems, asked them to do homework," she says.

"Math Connections was a big change for me," says Griffin. "It's active learning almost 100 percent every day, with everyone involved."

"The students think math is fun," she says, "which is something we didn't traditionally hear from these students. They say it makes sense. I think they see the relevance of math to the real world."

Henry Kopij, math department chairman at Montville (Conn.) High School agrees.

"Instead of learning the theory of some algebraic concept, students organize data and gather information and from that generate some kind of equation," Kopij told the New London Day. "They see the uses of algebra rather than just learning the theory."

FOR MORE INFORMATION

To learn more about Math Connections or to get a copy of a Math Connections text, check out the Math Connections Web site.

Article by Gary Hopkins
Education World® Editor-in-Chief
Copyright © 2008 Education World