The U.S. Department of Education recently released a national report that suggests that secondary students who take rigorous math classes are more successful in college and in the work force. Several faculty members at the University of Michigan’s School of Education also have conducted research that addresses significant issues related to mathematics education in America today. Here are some recent U-M studies:

? Although the percentage of American high school students taking rigorous math courses has steadily declined throughout the 20th century, this long-term trend has been sharply reversed in the 1980s and 1990s, says U-M education Prof. David L. Angus.

In “Mathematics Enrollments and the Development of the High School in the United States, 1910-1994,” Angus and colleague Jeffrey E. Mirel say that the concept of a “differentiated curriculum”?one that is tailored to the abilities and desires of different students?resulted over time in the development of “high-interest, low-ability” alternatives to more rigorous math courses like algebra and geometry.

“In the 1970s, many Americans were shocked by the news that their school system was perhaps not the best in the world,” Angus says. “The highly publicized international comparisons of educational achievement in which the United States ranked behind such nations as Korea and Taiwan in mathematics achievement jerked us out of complacency and focused attention sharply on the state of mathematics education.”

According to Angus and Mirel, the mathematics share of all credits for U.S. high school graduates increased from 12.1 percent in 1982 to 13.7 percent in 1994?nearly a full additional year of math for all high school students. Further, enrollment in general math courses has declined from 29.5 percent in 1982 to 16.1 percent in 1994, while enrollment in geometry has risen from about 46 percent to 70 percent during that time.

Angus, whose work will appear in a forthcoming volume on math education by the National Council of Teachers of Mathematics, can be reached at (313) 647-2466 or by e-mail at [email protected].

? In her study “High School Curriculum Structure: Effects on Course-taking and Achievement in Mathematics for High School Graduates,” U-M education Prof. Valerie E. Lee says that schools that offer a great number of courses in math are not necessarily doing their students any favors.

Students who attend high schools with fewer lower-level math courses to choose from?courses less demanding than algebra, geometry and calculus?progress further through the math curriculum and achieve at higher levels than students at schools offering more options in basic math classes, she says.

“Offering too many low-end courses keeps many students from moving very far into the more academic end of the curriculum,” she says. “If schools stop offering so many undemanding courses, if the curriculum becomes narrower and more academic, our research suggests that all students would take math courses that would be advantageous to them in terms of achievement on important gateway tests.”

Lee and her colleagues studied 3,430 students in 184 public and private high schools in and around the nation’s 30 largest cities. They found that students at “high-progress” schools?those where students complete many advanced math courses, such as pre-calculus and calculus, and few lower-level classes?attain scores on a 12th-grade math test that are more than 40 percent higher than the test scores of students at “low-progress” schools.

Lee can be reached by e-mail at [email protected].

• Students who need the most help in math are the least likely to ask for it, says U-M education Prof. Paul R. Pintrich.

In their study of 203 seventh- and eighth-graders in southeast Michigan, Pintrich and U-M graduate student Allison M. Ryan found that students who are unsure of themselves, both academically and socially, are more likely to feel threatened when asking their peers for help and are more likely to avoid seeking help.

“When individuals believe in their abilities, they are less concerned that others will think their need for help indicates that they are unable,” Pintrich says. “Further, feeling comfortable and skillful in relating to others lessens the perception that there will be negative fallout?a negative reaction from the helper or feeling dumb?from help-seeking.”

Students who do their math work primarily to gain understanding and mastery are likely to perceive help-seeking as beneficial, while students who are focused on goals external to the task itself?receiving rewards, avoiding punishment, desire to demonstrate high ability?are more likely to feel threatened by asking their teachers for help, Pintrich says.

The study also found that students’ attitudes influence their willingness to seek help. If students think that asking for help will benefit them by helping them learn, then they will seek help. If they fear that they will appear dumb, they will avoid seeking help.

Pintrich and Ryan’s study “‘Should I Ask for Help?’ The Role of Motivation and Attitudes in Adolescents’ Help-Seeking in Math Class” appeared in a recent issue of the Journal of Educational Psychology. Pintrich can be reached at (313) 647-0611 or by e-mail at [email protected].

U-M News and Information Services University of Michigan

[email protected]Valerie E. Lee[email protected]Paul R. PintrichJournal of Educational Psychology