8th-Grade Math Achievement Tied To Focus on Algebra, Geometry
Eighth graders' achievement in mathematics may be linked to how much teachers emphasize algebra and geometry in their classrooms, an analysis of results from the National Assessment of Educational Progress suggests.
The study, prepared by the Council of Chief State School Officers, is scheduled for release this month. It uses state-by-state data from the NAEP math tests given in 1990 to look for patterns linking 8th graders' performance to other conditions in the classroom, such as the kind of instruction students had received or the training of their teachers.
As part of the NAEP examination, students' teachers were asked to indicate whether they had given heavy, moderate, or little or no emphasis to particular aspects of mathematics in their classrooms. Those aspects were: numbers and operations, measurement, data analysis and statistics, geometry, and algebra and functions.
In states such as Alabama, Hawaii, and North Carolina, where larger percentages of teachers said they had maintained a traditional focus on numbers, operations, and measurement in the classroom, students tended to score low on the NAEP exam. In contrast, students from states in which more teachers said they emphasized algebra and geometry fared better on the assessment.
For example, in the nine states whose students scored in the top fifth on the test--North Dakota, Montana, Iowa, Nebraska, Minnesota, Wisconsin, New Hampshire, Wyoming, and Idaho--an average of 37 percent of teachers surveyed said they had focused heavily on algebra and geometry. This compares with an average of 31 percent of teachers in those states whose students ranked lowest on the tests.
Moreover, in most of the high-performing states, teachers also said they had placed little emphasis on more basic mathematics.
Researchers said the correlations were significant.
"If teachers are addressing more ambitious, complex math, there seems to be a clear relationship with kids doing better,'' said Ramsay Selden, the director of the council's state education-assessment center, which conducted the analysis.
"This is going to be really important for the states.'' he added. "We're beginning to get to a point where all of this hangs together.''
'On the Track'
The results also appear to provide some statistical backing for the kind of teaching advocated by the National Council of Teachers of Mathematics. In 1989, the council published national standards for mathematics instruction that favor reducing the traditional emphasis on teaching students how to add, subtract, multiply, and divide. Rather than spending year after year on such basic mathematical functions, the standards suggest, students should be introduced early on to so-called "higher mathematics,'' such as algebra and geometry.
Although the standards have been widely praised, they have also become the focus of controversy in recent years. Some educators and parents have begun to express concerns that in the new emphasis on more complex mathematics, students may fail to learn basic calculation skills.
But the council's study suggests that "we're on the track,'' said Mary Lindquist, the president of the N.C.T.M.
"The standards didn't come out of the blue,'' she said. "They reflect good practice in a balanced curriculum that was there all along.''
She also pointed out that, by 1990, the NAEP exam had just begun to reflect the kind of mathematics curriculum suggested by the standards.
In a similar vein, the researchers found that allowing students to use calculators in class and on tests did not hurt their performance on the NAEP exam. Students from states where calculator use is allowed tended to score higher on the exam than their counterparts in states that prohibited the practice. Students were not allowed to use calculators on more than 60 percent of the examination.
The study also found that:
- Even though 41 states had incorporated the N.C.T.M. standards into state-level curricular guidelines, the dominant approach to teaching math in most states in 1990 was still the traditional emphasis on numbers, operations, and measurement.
- Students taught by teachers certified in mathematics tended to be more proficient on the tests than those whose teachers were certified only in elementary education.
- Students scored higher in states where more teachers reported having had two or more days of in-service training in mathematics over the past year.
- States with more teachers who said they lacked the resources and materials for teaching math had lower overall math proficiency as assessed by NAEP.
Copies of the report are available for $12.50 each from the Council of Chief State School Officers, State Education Assessment Center, One Massachusetts Ave., N.W., Suite 700, Washington, D.C. 20001-1431.