Indicators of Precollege Education in Science and Mathematics A Preliminary Review (1985) / Chapter Skim
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5. Student Outcomes
5. Student Outcomes
Pages 110-134
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From page 110... ...
STUDENT ATTITUDES Both NAEP and TEA collect information from students on their attitudes toward mathematics and science. Mathematics seems to be better liked than most subjects, but its average popularity drops as students grow older.
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; favorable attitudes towards science teachers increased by over 2 percentage points (from 63.6 to 65.9) ; and favorable attitudes regarding science careers increased by over 4 percentage points (from 47.8 to 52.2)
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Further research could help to establish the extent to which schooling affects student attitudes towards mathematics and science and preference for a college major, as well as the significance of attitudes for such goals as improved student achievement, future performance, and eventual career choice.
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Hence, grades are not satisfactory to compare the achievement of students in different geographic areas or over time. Some university admissions offices maintain data banks that compare high school grades with university performance and then use the results to calibrate the grading in the high schools.
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At the international level, IEA conducts assessments at several age levels and for key instructional areas. Unfortunately, the most recent published IEA findings on mathematics achievement in various countries are 20 years old, and the IEA science results date back to 1970.
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The need to base tests on what almost all students are likely to have learned in their classes eliminates the possibility of assessing achievement not deemed part of the common core. Consequently, especially in the case of national assessments, few of the mathematics topics taught beyond 10th grade are included, and science topics tested tend also to sample what is deemed to be a common core in the biological and physical sciences.
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. Norm-referenced tests, which relate individual raw test scores to the scores of a comparison group, provide data that make possible the ranking of test-takers.
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. evidence that tests do influence teacher and student performance and that multiple-choice tests tend not to measure the more complex cognitive abilities The more economical multiple-choice tests have nearly driven out other testing procedures .
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to conclude that "students improved most on easier knowledge and skill exercises, least on those that required a more complete grasp of mathematics or more sophisticated skills." In particular, students appear to be able to perform arithmetic operations but do not know which algorithm to use or how to apply their answers to the solution of practical problems. Seniors participating in the 1972 National LongiTABLE 24 Mean Performance Levels on Three Mathematics Assessments, Common Items, Ages: 9, 13, 17 Number Mean Percent Correct Percent Change, Age of Items 1973 1978 1982 1973-1982 9 23 39.8 39.1 38.9 -0.9 13 43 53.7 52.2 56.4 2.7 17 61 55.0 52.1 51.8 -3.2 SOURCE: National Assessment of Educational Progress (1983:2)
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From page 119... ...
were given a 15-minute mathematics test intended to measure their ability to solve problems involving quantitative skills; the test did not include any items involving algebra, geometry, trigonometry, or calculus. On the 18 items that were virtually identical in the two tests, the mean score declined by one-sixth a standard deviation between 1972 and 1980 -- about the same amount as the decline in average mathematics SAT scores over the same period (National Center for Education Statistics, 1984c)
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There was a decline of 3 percentage points, from 48 percent of the items answered correctly to 45 percent answered correctly, between the two assessments. Achievement in arithmetic
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12th-grade achievement with international scores: the total sample of U.S. students performs at a level considerably lower than the median level of performance found in the terminal year of secondary school TABLE 27 International Achievement Comparisons, Second TEA Mathematics Study 13-Year-Olds (180 Items)
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However, this comparison must be treated with considerable caution because at that level of education there are great differences among countries with respect to curricula, student populations, and a host of other factors. Preliminary IEA results for the last year of secondary school in Japan indicate continuing high achievement, with Japanese students ranking second of the 14 participating countries in all areas of mathematics.
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The number of courses taken was, in fact, strongly correlated with achievement for the Illinois students, but the investigators caution that requiring more mathematics courses for high school graduation will not necessarily increase achievement because of varying course content. It should be noted that there is TABLE 29 Mathematics Achievement Means and Standard Deviations for High School Students from Japan and Illinois Japan (N:1,700)
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Wolf (1977) analyzed the changes in country rankings that result from comparisons of the science scores of seniors representing the top 9 percent of the total age group in each country rather than those of the scores of all students enrolled in the final year of secondary school.
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Figure 8 shows different rankings of achievement scores by country as different proportions of the age-group are considered, together with school retention rates as of the time of the science assessment. IEA conducted a second international science study in 1983.
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_ _ _ ~ LL N — _ a, C: .~ ~ a' 11 m L L t __' -.e.' r—— ...... 1 1 levels FIGURE 8 Mean scores in science of students in terminal year of secondary school for top 1, 5, and 9 percent of the total senior age group and for all seniors enrolled.
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Both the College Board and the American College Testing Program administer tests in mathematics and science. About one-fifth of the one million students who take the SATS each year also take the College Board's Achievement Tests in one or more of 13 academic areas, which include two levels in mathematics.
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. ACE conducted a sample survey of senior academic officials in 486 institutions with undergraduate programs and in 383 with graduate programs; the sample was designed to be representative of the more than 3,000 institutions of higher education in the United States.
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Much of this generally observed but small increase is due to increasing achievement scores for black students, especially for mathematics in the lower and middle grades. · Analysis of the most recent NAEP mathematics assessment yields evidence that gains have been made on computational skills but that there is either no improvement or a slight decrease in scores on test items that call for a deeper level of understanding or more complex problem-solving behavior.
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· International assessments in mathematics and science education such as those sponsored by TEA need to be carried out at least every 10 years. Tests · Developmental work on tests is needed to ensure that they assess student learning considered useful and important.
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This work will require careful research on the content of instruction, tests constructed with a common core of items, and alternative sections of tests to match curricular alternatives. · Assessments should include an evaluation of the depth of a student's understanding of concepts, the ability to address nonroutine problems, and skills in the process of doing mathematics and science.
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