E. Jean Gubbins
Catharine F. de Wet
Robert J. Sternberg
Tonya R. Moon
Carolyn M. Callahan
Catherine M. Brighton
Section A: University of Connecticut and Yale University Algebra Pilot Research Study
(University of Connecticut Research Study: Schools 1 and 2 and Yale University Research Study: Schools 3, 4, and 5)
The University of Connecticut and Yale University sites for the research study entitled Unclogging the Mathematics Pipeline Through Access to Algebraic Understanding involved grade 6 students for 30 hours of an after-school pilot research study in Algebra. Students who earned at least a B in mathematics were eligible for participation in the screening process, which included the Iowa Tests of Basic Skills, Mathematics Problem Solving and Data Interpretation (grade 8) subtest, and the Iowa Algebra Aptitude Test (grade 8).
The after-school pilot research study occurred for 10 weeks (1½ hours, twice a week). Teachers used Connected Mathematics 2, Variables and Patterns, a unit typically designed for grade 7 students. Of the 110 students assessed for the University of Connecticut research site, 73 participated in the program, with 30 students working with two teachers in School 1, and 43 students with three teachers in School 2.
A total of 90 students from 3 schools participated in the program for the Yale University research site, with 32 students working with 2 teachers in School 3, 31 students working with 2 teachers in School 4, and 27 students with 2 teachers in School 5. Schools 3 and 4 were in the same district. Students were thus divided into two groups at each school. Each group worked with one teacher who used technology or one teacher who did not use technology.
The pilot research study attempted to determine if involvement with above grade level curriculum would impact achievement, and attitude and interest toward mathematics. Student achievement in mathematics was assessed using four pre/post measures: Iowa Tests of Basic Skills, Mathematics Problem Solving and Data Interpretation subtest; Iowa Algebra Aptitude Test; Connected Mathematics Unit Test; and Connected Mathematics Unit Extended Test.
University of Connecticut Research Site Findings
All paired samples t tests on each achievement measure across and by schools yielded statistically significant differences.
Participation in the Algebra research study did not affect students’ self-efficacy, and positive attitude and interest in mathematics. Students were positive about mathematics before and after their involvement in the after-school pilot research study. Their perceptions of the mathematics classroom practices in the after-school program indicated that the majority found the intensive Algebra program fun, interesting, and exciting. Many noted that the work differed from the regular classroom because it was more difficult. Yet, the students in this study found hard, difficult, and challenging work in Algebra to be fun and exciting.
Teachers and administrators shared their perceptions of teaching and learning mathematics. They recognized the importance of effective instruction in mathematics and were familiar with the characteristics of mathematically talented students. Challenging these students was important to the continuation of their learning.
Classroom observations provided a complete perspective on the research study as planned and as implemented. These observations confirmed teachers and students’ adherence to the philosophy of the Connected Mathematics Program, and documented students’ ability to understand and apply advanced-level knowledge and skills related to algebraic understanding. The dynamics within the classes were definitely determined by the teachers and students’ commitment to learning how to think algebraically. Students mastered above grade level content and concepts and achieved representational fluency, which is the ability to solve problems using tables, graphs, words, or symbols. Algebraic reasoning prepares students for future accomplishments in mathematics, and the 73 students and their 5 teachers at the University of Connecticut pilot research schools were certainly successful in achieving the goals of this pilot research study.
Yale University Research Site Findings
Data analysis showed a gender x treatment interaction, with technology benefiting female students more than males.
Participation in the Algebra research study did not affect students’ self-efficacy, and positive attitude and interest in mathematics. Students were positive about mathematics before and after their involvement in the after-school pilot research study. Their perceptions of the mathematics classroom practices in the after-school program indicated that there were mixed opinions, students liking some aspects of the program and not others. There was no consistent agreement on the difference between regular classroom practices and the after-school program.
Section B: University of Virginia Algebra Pilot Research Study
This pilot research study attempted to determine whether varying the form in which mathematical material is presented creates greater equality of opportunity. The particular mathematical material studied comprised types of Algebra word problems that typically are presented in the logical/mathematical mode and that utilize spatial visualization (e.g., mixture, work, and time-rate-distance problems). The design investigated whether presenting such material in a narrative mode with spatial aids can equalize opportunities for mathematical achievement in Algebra. The ultimate goal of the project was to increase students’ math achievement and students’ attitudes toward and interest in mathematics.
Section B: University of Virginia Algebra Pilot Research Study summarizes data from the summer intervention program. Some of the quantitative data presented include students’ scores from a subset of the Yale University data. All of the qualitative results are from the University of Virginia dataset only.
The following research questions guided the pilot research study:
- Do students who participate in the mathematics intervention outperform control students on a measure of mathematics achievement after taking into account pretreatment mathematics achievement differences?
- Do students who participate in the mathematics intervention outperform control students on a measure of mathematics achievement after taking into account pretreatment Algebra aptitude differences?
- What are students’ perceptions of the mathematics classroom practices in the mathematics intervention?
Although there were no statistically significant differences between treatment and control groups on achievement, aptitude, or attitudes, three important findings emerged from the qualitative data that merit consideration. Each will be considered separately below.
- One interesting finding emerging from the study was that all teachers unanimously expressed liking being provided with a prescribed curriculum that was easy for them to follow. All perceived the curriculum to be high-level, challenging, and engaging for students, as well as enjoyable to teach. As a result, all teachers maintained a high level of fidelity to the treatments.
- Students in both the treatment and control groups expressed thoroughly enjoying the math program. Students from both groups cited the small class size, the “fun” and interactive math activities, and the high level of challenge as the primary reasons for enjoying the program. None mentioned the technological components as contributing to their enjoyment of or engagement in the program. This is interesting in light of recent attention focused in the literature on the use of technology to engage students in learning math.
- Students in the study indicated a clear preference for learning at a faster pace and at greater levels of challenge than they normally got the opportunity to do in their regular math classes. Nearly all of the participating students indicated that they learned better under the conditions of a quickened pace and increased challenge.
The findings suggest that while technology provides a useful pathway to understanding for students, it alone does not necessarily encourage or ensure student engagement. Instead, it seems that for the students in this study at least, high-level challenge, one-on-one time with the teacher, and hands-on activities are what is needed to engage advanced students in learning math.
Nearly all participating students indicated an eagerness to learn more math than they were able to do during their regular school year classes. This signals a need for a consideration of the match between the challenge level of the mathematics curriculum offered in our middle classrooms and the needs and abilities of the adolescents populating these classrooms. It begs the questions, Are we underestimating the level of mathematical ability and interest of many of our middle school students? Are we limiting the possibilities for able math students by the lack of fit between the curriculum and instruction offered in our middle school math classes and their mathematical abilities and interests?