Ed 333 Ruhi Vasanwala-Khan
July 13, 2002
Motivating Students to Learn Algebra
Stanford University
Learning Problem and Goal
Recently we asked a college graduate “Do you still use algebra?” and he responded “not anymore.” Such a response from an educated individual is common, and illustrates the obstacles that face current algebra and math curriculum design. This response testifies to the fact that algebra “students believe math has little or nothing to do with the real world (Bruning et al., 1999).” In fact, alarming statistics on math and algebra education in the United States support this statement. For example, only 80 percent of students take a first algebra course, and less that half of these students take a second. Moreover, less than 10 percent of all students enroll in calculus. Additionally, there are cultural and gender differences dividing those students who continue mathematics education beyond algebra and those who are left behind. Fewer girls than boys and fewer African American and Hispanic students take classes beyond algebra. Although these trends are improving, students’ disinterest in continuing mathematics study beyond algebra is still a tremendous problem (Bruning et al., 1999).
Why do so few students incorporate algebra as a tool to use in their daily lives and why do so few students lose interest in studying mathematics after algebra? Greeno et al. (1996) conclude that lack of real world application of algebra demotivates students to learn more advanced mathematics. In addition, they showed that algebra textbook exercises are boring and ungeneralizable.
We believe that one way of combating these problems with algebra education is to reform the current trends. We propose that reworking curricula according to the design principles of the situative approach to learning will promote algebra as an affordable, useful tool and will help them realize the true value of mathematics in their lives. To increase student understanding and applicability of algebra, we wish to connect specific algebraic concepts to real-world situations. For example, performing everyday tasks such as making lemonade or shopping or even planned curricula such as the African Drum and Ratios Curriculum (website) give students opportunities to practice ratios and percentages.
Design Principles – A Situative Approach
Teaching a student that 3x= 9 and therefore x= 3, will probably not make a profound impact on that student’s life. However, teaching a student who is perhaps interested in running a lemonade stand that for every 3 glasses of lemonade that they sell they yield a $.09 profit. By learning mathematical concepts in this applicable manner, the student would conceivably become motivated to extrapolate other mathematical relationships predicated on this basic algebraic construct.
Creating this type of a demonstration or environment uses the design principles of situative learning. Here, a student, group, or class is taught to learn by associating pieces of knowledge and information from their environment to practical applications in their personal community. Greeno et al. explain that the situative design principle incorporates seven components (S1 – S7) that foster learning within one’s environment and within groups to promote inquiry and response through the knowledge transfer process.
The seven components are spread across the three categories of situative learning. The first category speaks to the design of learning environments. The focus of this category, which includes the S1 (Environments of participation in social practices of inquiry and learning) and S2 (Support for development of positive epistemic identities) principles, encourages students to develop their own identity for the manner in which they apply the acquired knowledge within their cultural or communal setting. The S1 and S2 principles also suggest that a program design allow students to become confident learners and formulate and evaluate questions and problems in a social interactive forum.
The second category of formulating curricula involves the S3 (Development of disciplinary practices of discourse and representation) and S4 (Practices of formulating and solving realistic problems). These two principles show that a situative program should encourage students to “progress in a variety of practices of learning, reasoning, cooperation, and communication, as well as to the subject matter contents that should be covered.” This is to say that teacher should go beyond the classroom textbooks to reference and utilize real-world experiences that are relevant for the students.
The third category of constructing assessments is composed of the S5 (Assessing participation in inquiry and social practices of learning), S6 (Student participation in assessment), and S7 (Design of assessment systems) principles. These three principles interact to form a method of systematic assessment and progress tracking based upon the student’s individual increase in judgment, general observations of the extent of a student’s proactive participation within the group, and the amount of learning applied by a student in solving problems.
With regards to motivating students to learn Algebra, a learning program design and or methodology would embody all of the aforementioned precepts to stimulate motivation. The effect would be a learning environment that associates certain mathematical theories or concepts to practical applications by leveraging group dynamics to enhance individual understanding, assessment, and social benefit from the origination of related conclusions of the solved problems. By adopting this teaching approach, a student and a group would gain the ability to apply algebra to daily situations, as well as teach and assess each other’s progress as knowledge is transferred by a question and answer mechanism of solving present and related problems.
Proposed Study
Early research on incorporating situative principles into algebra education has shown signs of promise. One graduate of the Algebra Project, a situative curriculum, stated “these models enabled me to be confident in myself as a mathematics student and know that I really do have an inner mathematician.”
While our proposal firmly advocates the redesign of current algebra curricula to follow proven situative design principles in order to increase the real-world applicability of algebra skills, we need more information on exactly how such curricula would affect learning. We believe that a situative learning environment will motivate children to better understand algebra and give them the skills and interest to use algebra outside of the classroom. We propose a study to investigate what skills learners gain and which ages of students benefit the most from a socially-based algebra curriculum.
Design
Experimental Conditions
This study will compare measured changes and gains in algebra applicability made by students in a traditional algebra class compared to those made by students in a situative algebra class. Each curriculum will be administered by a randomly selected, regular mathematics instructor to one classroom in each of grades 4 through 8.
Situative Condition
The assigned curriculum in the situative condition will adhere to the situative design principles previously discussed. Prior to the start of the school year, teachers in the situative classrooms will be given materials explaining the situative perspective on learning and will go through 3 credit-bearing one-hour training sessions. These training sessions will concentrate on training the teacher how to properly implement developmentally and educationally appropriate situative principles into their algebra classrooms. These training sessions will emphasize students’ development of algebra skills in a inquiry-based social environment. For further explanation of the situative training, see Appendix N/A.
Traditional Condition
The assigned curriculum in the traditional algebra classroom condition will be one adhering to classic behaviorist method of teaching algebra. The teachers in the traditional condition will continue using textbooks and workbooks in the same manner they have instructed in the past. We expect that almost all of the algebra lessons and practice in the traditional condition will come directly from these textbooks and workbooks with the possible inclusion of a few side projects.
While we expect that the teachers’ effectiveness may be a factor in our results, we keep in mind that our findings are the result of “the curriculum as implemented by a teacher”. At various points throughout the school year our staff will monitor the classroom practice to confirm that the experimental conditions were being met and these findings will be reported in the final publication.
Participants
We are interested in the way a situative algebra curriculum may change education for the average student in a normal school. Thus, we will select a school in a suburb in the California bay area with a median income of approximately the region’s average. We will also confirm that percentage of low-income students in the school is approximately the same as the national average (by similar percentage of subsidized lunches in the school). We expect that half of the participants will be girls and half will be boys.
We will select two mainstream algebra classes from each of 4th, 5th, 6th, 7th, and 8th grades. Each class will be comprised of 20 to 25 students so our expected N will be 23 in each of the grade*treatment cells.
Duration
The treatments will be administered from pretest at the beginning of the school year in September until posttest at the end of the academic year in June. Since mathematics instruction takes place every day of the week for all students, we expect a consistent influence of the assigned curriculum.
Assessment
We expect students’ algebra abilities and gains over the year to vary depending on what condition the students are in, what grade the students are in, and the month during which they are assessed. For this reason, we will be assessing the students in a variety of manners.
In addition to the pretest at the start of the school year and the posttest at the end of the school year, we plan to administer three embedded assessments throughout the school year and another assessment at the beginning of the next school year. The students will thus be assessed in September, November, January, March, and June. The goal of these embedded assessments is to monitor each student’s growth curve to see “where the action is”, or when he or she benefited the most from the instruction.
Each of the five assessments over the course of the year will be made up of 4 separate tests with different problems for each test and at each assessment date. The first two tests will be administered by an unbiased outside tester who is blind to the conditions and to the goals of the study. The first test will evaluate a student’s ability to solve real-world algebra problems. This test will measure situative students’ abilities to perform near transfer and traditional students’ abilities to perform real-world algebra problems. The second test will evaluate all students’ abilities to solve real-world algebra problems that involve similar algebra concepts as worked on in class but on problems that involve different subjects than what the student is familiar with. This second test will measure the situative student’s ability to perform far transfer. The test administrator will carefully note the students’ methods of reasoning about the problem as well as the accuracy of their answers. These notes will be converted to a Likert scale ranking the student’s ability to apply algebraic concepts to real-world problems. This method of scoring places more emphasis on ability to use algebra rather than the ability to get a correct answer.
The third and fourth tests for each of the assessments will be administered by the classroom teacher to the entire class. Unbiased measurers will observe and record the classroom interactions and each student’s interactions in the classroom environment. Each student’s work and interactions will be converted into a Likert scale for interaction and another scale for application of algebraic concepts to a real-world problem. Also, all observations will be used as qualitative data to characterize the classrooms’ methods.
At the beginning of the next school year, we will administer the individual tests once more to each individual participant in order to determine how well the student retained algebraic concepts. We will also obtain qualitative data on how frequently they used algebra throughout the summer to determine which students were confident using algebra as a tool.
Results/Discussion
The results of this study will help us determine ways in which we can increase students’ motivation to learn and use algebra. Since the situative perspective suggests that more interactive and real-world problems will benefit students’ interest, understanding, and retention, we will analyze the ways in which children learn in a traditional algebra class and in a situative algebra class. We will pay attention to the curves of the algebraic reasoning scale from the individual tests and will try to pinpoint which participant groups benefited the most from each style of instruction and when. Since we are particularly interested in determining how we can help students learn to use algebra in their daily lives, we will also pay special attention to which students reported using algebra over the summer.
References
Bruning, R. H., Schraw, G. J., & Ronning, R. R. (1995). Cognitive psychology and instruction. Englewood Cliffs, N.J.: Prentice Hall.
Greeno, J. G., Collins, A. & Resnick, L. B. (1996). “Cognition and learning” (Chap. 2). In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology. New York: Macmillan.
Mathematics Education in the Middle Grades (2000). Center for Mathematics, Science and Engineering Education – National Research Council. National Academy Press.
Moses, R. “The algebra project.” http://www.algebra.org.