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IMP® Students Demonstrate High Achievement
Studies Target Twenty-First Century Skills and Needs
The development of the Interactive Mathematics Program parallels many important changes taking place in the American workplace. Computers and calculators are now considered part of our basic toolkit. Rapid technological innovation has increased the demand on students to acquire mathematical skills in data analysis and problem solving. Surveying the effects of these changes, distinguished mathematicians and educators, including the National Research Council's Mathematical Sciences Education Board (MSEB), have published extensive commentary on the demands of the Information Age, and the need to shift priorities in K12 mathematics education.*
These reports point to the need to update mathematics curricula to include statistics and probability, topics usually reserved for college-level work, as well as to increase emphasis on problem-solving skills and quantitative reasoning. IMP fulfills these recommendations, by providing students with a curriculum that adds these new content areas, while maintaining essential content knowledge found in traditional high school courses of algebra I and II, geometry, trigonometry, and precalculus.
Previous evaluation of IMP student achievement has focused on norm-referenced, standardized tests, which do not cover these new content areas and skills. IMP has reported several studies demonstrating that on standardized tests, IMP students do as well as, and sometimes better than, students in traditional mathematics course sequences.
In order to measure student success in the recommended new content areas, IMP's external evaluator, Dr. Norman Webb of the Wisconsin Center for Education Research (WCER) conducted a series of three studies. Each study was designed to examine content knowledge and skills in one of these areas:
The tests were conducted in grades 9, 10, and 11, respectively.
In all three studies, IMP students demonstrated substantial knowledge and proficiency in these topics, doing significantly better than students who were enrolled in a traditional mathematics course sequence.
This bulletin gives details of these studies, describing the student populations tested, the assessments used, and the achievement results.
Overall Design of the Studies
Each of the three studies was conducted in a separate school, at a different grade level, with a different testing instrument. The three tests used came from sources independent of IMP. Within each school group, both IMP and non-IMP students took the same test under identical conditions.
Schools selected for each of the three studies were located in different regions of the country and were considered sites where the IMP curriculum was being implemented as intended. An adequate number of students with pretest scores had to be available to participate.
In each of the three schools, IMP students were matched with participating students from the traditional course sequence on the basis of grade 8 achievement test scores. Gender and ethnicity were also used in matching student groups, when it was possible to include these factors and also match scores. Such matched group analyses for each test ensure that students in the groups being compared had comparable mathematics abilities and skills when they entered high school. Testing was done in spring, 1996.
School No. l: Statistics Test
On the statistics test, grade 9 IMP students demonstrated the ability to develop and interpret statistical information. Chart No. 1 shows the results of the statistics test data through a matched group analysis. The two groups differed significantly in mean test scores, with IMP students showing significantly higher achievement. The findings identify additional content that students learn from taking IMP, compared to the traditional algebra I course.
The statistics test used the statistics items from the Second International Mathematics Study (SIMS), which was originally administered to grade 12 students in the 198182 school year. The items were modified from the multiple-choice format used in SIMS to an open-response format. Tasks included interpretation of information in graphical form, computation of a weighted average, effect of a linear transformation on the mean and standard deviation of a distribution, and application of properties of the normal curve.
School No. 2: Problem-Solving Test
On the problem-solving test, grade 10 IMP students demonstrated a high degree of proficiency in solving complex problems. In comparing test scores of matched groups (Chart No. 2), IMP students had a significantly higher mean test score than the geometry students.
A separate analysis compared IMP students specifically with geometry students in Honors classes. This comparison showed gains for IMP from a new perspective. Although grade 8 test results indicate that students in the Honors Geometry group entered high school with significantly higher achievement than the IMP group, the grade 10 IMP students scored higher than Honors Geometry students on the problem-solving test. Taking the grade 8 scores into account, the difference on the problem-solving test was statistically significant.
In other words, through the use of the IMP curriculum over a two-year period (grades 9 and 10), the IMP students were able to perform on these problem-solving activities at a level higher than honor students who had performed at a significantly higher level in grade 8.
The problem-solving test was composed of two performance-assessment activities that were originally developed for the Department of Public Instruction of a midwestern state. Test items required students to solve problems, develop and test conjectures, and write clear explanations of solutions.
School No. 3: Quantitative-Reasoning Test
In the quantitative-reasoning test, IMP students were successful in finding correct answers to problems involving numerical data. The matched group analysis (see Chart No. 3) shows that the IMP group significantly outperformed the algebra II group.
The test was based on ten items from a practice version of a quantitative-reasoning test developed for a prestigious university. The test is customarily administered to entering first-year students. Knowledge measured by the test items included data and graph interpretation, probability of independent events, and statistical concepts of mean and standard deviation for a distribution. None of the items asked a question in the same form as it appears in the IMP curriculum. Half the items required some understanding of probability and statistics, which are areas emphasized in the IMP curriculum. The other five test items required knowledge of rate of change and the interpretation of slope of a graph, which are topics that receive as much attention in a traditional curriculum as in IMP materials.
While the numbers of participants in these three studies are small, the results are sufficiently dramatic to be significant from an educational standpoint. These tests highlight the high degree of flexibility and mathematical reasoning that IMP students are capable of attaining. While students still need to know their basic math facts, today they also need to be fluent in applying their mathematical knowledge to solve problems that require extensive development and quantitative reasoning skills. The IMP curriculum prepares students to meet these demands.
*Reports from the Mathematical Sciences Education Board of the National Research Council include Everybody Counts: A Report to the Nation on the Future of Mathematics Education, 1989; Reshaping School Mathematics: A Philosophy and Framework for Curriculum, 1990; On the Shoulders of Giants: New Approaches to Numeracy, 1990.