Think your math skills are up to snuff? Try these word problems, geared for 7th to 9th graders (answers at end):
1) You plan a train trip from Chicago to Portland, Ore. The distance between the cities is 1,790 miles, and the average train speed is 42 m.p.h. How many hours will the trip take?
2) The wheel axles of a train turn both wheels at the same rate. When a train travels around a curve, the distance traveled by the inner wheel is less than the distance traveled by the outer wheel. Using your knowledge of a train wheel’s structure, explain why trains don’t derail when going around a curve. Use diagrams to support your answer.
If you’ve got some gray hair, you probably recall the first type of word problem, and not so fondly. Many students didn’t care about when the train arrived. Many of their teachers focused on the equation needed to solve it and the answer rather than whether students understood why the question was asked in the first place.
The second represents a new-style word problem, which involves more than an algorithm. It’s meant to make math interesting and relevant by getting students to analyze, visualize and offer an explanation rather than just a number answer.
Turned off to math
The impetus for the change, affecting classrooms nationwide, has been the recognition that many students take only required math courses in high school because they don’t like or understand the subject and do poorly in it. Yet, when they move into the work world, they need numerical competency because of the importance of technology, even if they’re not in math fields.
Parents may not help, experts say.
“Parents read to their children, but few do math problems with them,” said Chicago math educator Norman Lederman. “Students learn formulas, but they aren’t sure why they use them. Sometime, often in middle school, something happens to turn many off about math, especially females. They opt out of taking math as an elective. Students should be taught how useful math can be–to buy CDs or decide how much carpet to buy.”
The acknowledged need to make math less abstract and more relevant has spurred educators to change how it’s taught.
Additional factors fuel this effort. Fewer students major in math. A critical teacher shortage will increase, given that twice as many math teachers leave the profession yearly (to retire or out of frustration) as enter it. Industries complain that new employees don’t possess basic skills, and math content has changed.
Many ways to achieve goal
“What was basic 40 years ago is no longer taught,” said Johnny Lott, president of the National Council of Teachers of Mathematics, which sounded a warning 14 years ago. “Our goal is to have more students study more math with more qualified teachers in every class. There’s no single way to achieve the goal.”
Andy Issacs agrees.
“Decisions should be made locally because 1 million factors go into what makes a good math program,” said Issacs, who holds a doctorate in math, works as a research scientist at the University of Chicago and helped to write one of the math “reform” programs known as Everyday Mathematics. It’s designed for pupils in kindergarten through 6th grade but is part of a larger program that addresses reform through 12th grade.
Issacs estimates that as many as 20 comprehensive math reform programs have emerged since the late 1980s, as educators reacted to the 1970s back-to-basics curriculum, which focused too much on computations or paper-and-pencil arithmetic. If less comprehensive programs, supplemental materials and teacher workshops are added, he estimates hundreds of new efforts may be under way.
Starting at the top
Universities such as the Illinois Institute of Technology are among those that believe the first step is to make teachers more knowledgeable and get them to teach differently. IIT set up an education department that focuses on specific subject matter–i.e., math–rather than general education courses.
Lederman, who was brought in to chair the new department and revise the curriculum 1 1/2 years ago, said, “We want kids to love math and science, but we’re strong believers that first teachers need to know far more than their students. That seems intuitive, but there are places where those who teach don’t have college degrees in math.”
The department’s approach is multifaceted and includes a variety of programs rather than one curriculum, plus an internship with a practicing researcher and use of community resources such as museums and zoos.
Andrea Gorss, 24, is among IIT’s first crop of students planning teach math the new way.
She did well in math growing up but majored in civil engineering in college because she thought it would prove more useful. After working for an engineering firm, she found her profession not social enough. She entered IIT to complete math and education coursework.
“I think I’ll be good at explaining concepts and encouraging male and female students,” she said.
Making the subject real
In Chicago and elsewhere around the country, new programs are being used. Evanston/Skokie School District 65 likes Everyday Mathematics because it requires more thinking and relates better to everyday life, said Randee Blair, curriculum coordinator.
Another program that has growing appeal, but for older students, is Interactive Mathematics, developed at the University of California. It presents information on a compact disc, using video, graphics, animation and audio components, plus text materials.
Consultant Edward Landesman, involved with Interactive Mathematics, said the use of a computer helps bashful students who hate being called on and those who need extra time.
Educators also encourage the use of support materials, whether games such as Equate and PrimePak, which Mary Kay Beaver invented for a family to play, or lesson plans such as the Chicago Architecture Foundation’s “Schoolyards to Skylines,” a 500-page curriculum that incorporates math lessons and field trips.
Kimberly Folkening, a 3rd-grade teacher at North Kenwood/Oakland Charter School on Chicago’s South Side, has used the foundation’s lessons for the past three years.
On one field trip, students learned why buildings stand up. In a unit this spring on the 1893 World’s Columbian Exposition, they’ll see layouts of the buildings and have to find their areas and perimeters. Down the road, they’ll design a building for a hypothetical client’s budget.
“Kids are fascinated by their physical environment, yet they’re not given enough time to explore it. Doing this has also opened a new world for me as a teacher,” she said.
There are many highly specialized programs as well, such as Go-Girl, a math enrichment program for 7th-grade girls that meets at Wayne State University in Michigan and is funded by a National Science Foundation grant. The program helps improve middle-schoolers’ interest, competence and confidence.
Progress hard to measure
How useful are these approaches? Many say it’s too early to judge because students are now graduating from high school.
“Most data is anecdotal and situation-specific,” Lederman said.
Nevertheless, some teachers are optimistic because they already witness greater interest and improved test scores.
“I’ve worked with schools on probation because of their students’ math scores, and after using Everyday Math the scores are no longer a problem,” said Cheryl Moran, a former Chicago teacher who consults in classrooms.
More still needs to be done. Lott’s long-range goal is to have certified math teachers in every classroom, even at the elementary level. “A recently passed federal law said that will occur by the year 2005,” he said.
But he is concerned whether it will get implemented so fast. That number may need to be revised, he said.
Answers to problems
The answer to problem 1 is 42.62 hours. The equation used is T=D/R. Divide the number of miles, 1,790, by the m.p.h., 42, and you get the hours, 42.62.
The answer to problem 2 requires more visual and cognitive analysis. The outer edge of a train wheel has a ridge that makes its circumference greater than the circumference of the inner edge. When the train goes around a curve, the outer wheel travels on the ridge. So, even though the inner and outer edges of the wheel turn at the same rate, the outer edge covers a greater distance. If the outer wheel on a curve doesn’t cover a greater distance in the same time as the inner wheel covers a shorter distance, the train could not possibly remain on the track, and the outer wheel would fall off the track, making it derail.
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Want to tackle more problems? Go to the National Council of Teachers of Mathematics’ Web site at www.figurethis.org, which features about 80 for parents and children to do together.
