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Investigation of Conceptual and Procedural Based Curricula among
7th Grade Students at a Predominantly Hispanic Populated Middle School
MSP Teacher Research Award Application |
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Michael Garcia
migarcia@utep.edu |
Vision
Our vision is for all children, regardless of ethnicity and socioeconomic status to have the opportunity to participate and succeed in higher level mathematics programs.
Rationale The controversy has long reined concerning the “best” approach to teaching mathematics to all students and particularly to “high risk” populations. Mathematics pedagogy grounded in Vygotskian theory approaches mathematics as a conceptual system rather than a collection of discrete procedures, and provides intense coverage of advanced topics that in the United States are reserved for students in higher socioeconomic level schools. The Vygotskian idea that learning leads development is a fundamental principle of conceptual learning. Vygotsky noted that the possibilities of genuine education depend both on the already existing student’s knowledge and experience (level of actual development – LAD) as well as on the characteristics (student’s potential to learn) that are in the student’s zone of proximal development (ZPD). “Students come to the classroom with preconceptions about how the world works. If their initial understanding is not engaged, they may fail to grasp new concepts…” (How People Learn, 1999, p. 5).
While a conceptual base to lead development is important, the communication system for algebra lies in the procedural, or more traditional approach to teaching mathematics. A balanced approach to algebra teaching/learning may be the answer to this complex problem. A combination of conceptual and procedural teaching, or balanced approach to teaching algebra seems like a logical approach.
Hypothesis
A balanced approach, conceptual and procedural together, to teaching mathematics to a lower socioeconomic predominantly Hispanic population will increase the passing rate on the standardized Algebra end of course exam.
GoalsThe Wiggs 7th Grade team will develop a strong research foundation for the investigation of a balanced conceptual and procedural curriculum for teaching mathematics.
| • To develop baseline data concerning teaching conceptual and procedural mathematics 7th grade curriculum to a more wide spread population by integrating high quality research findings into mathematical educational practice. |
• To improve students' standardized mathematics achievement by transition to increasingly complex mathematics learning
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Treatment and Sample
The Connected Mathematics Project (CMP) developed through an NSF funded project at Michigan State University is considered a tool for conceptual development of algebraic thinking. Selected modules from this program will be combined with a more traditional approach to determine if the balanced curriculum will increase the percentage of students passing the state mandated end of course exam. The following concepts will be emphasized through the use of the CMP modules.
Pythagorean Theorem and Irrational Numbers
Quadratic Equations
Algebraic Reasoning
Exponential Relationships
Data and Statistics
The state mandated curriculum requirements will be integrated into the project design.
The curriculum project will run throughout the academic year 2004-2005. The Glenco curriculum is a more traditional procedural algebra curriculum. It focuses on procedural teaching of Algebraic Concepts rather than deep conceptual understanding of “big ideas.”
Two eighth grade classrooms at Wiggs Middle School will be used to for the experiment.
Classroom I:
Glenco Curriculum. Students enrolled in classroom I will be taught through the Glenco Text, a procedurally based program.
Classroom II:
CMP. Students enrolled in Classroom II will be taught through the CMP (dual language added) program.
Classroom III:
A combination of the two curricula will be implemented for a balanced approach.
The following table represents the research objectives, outcomes, and other important information concerning the project.
Table 1. Outcomes matrix of the Wiggs Algebra research program effectiveness
| Research Objectives |
Output/ Outcome |
Evaluation Deliverable |
Quantitative Indicators |
Method/ Measure |
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To identify and categorize learning contexts of a balanced mathematics curriculum |
Student understanding of Mathematics concepts
Knowledge of and skills in mathematics |
Pre and post test on conceptual knowledge
Pre and post content test from the state mandated skills for 7th grade students |
# of students successful on post tests
# of students able to communicate “big ideas” in interviews
# of students able to successfully complete formal 7th grade instruction |
Adaptation of concept development activities
Adaptation of pilot instruction
Analysis of Pre and Post exams
Assessment interviews |
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To develop baseline data concerning teaching a balanced conceptual and procedural mathematics curriculum to a more wide spread population by integrating high quality research findings into mathematical educational practice. |
# of students who complete algebra courses
Data comparing conceptual and procedural teaching of 7th grade mathematics |
Program structure designed to meet the needs of minority and lower socioeconomic students in mathematics |
# of students successful in each class/comparative data
curriculum series adaptation to teach “big ideas” based on results of study |
Comparison of project scores after conceptual and procedural curriculum implementation |
Wiggs Middle School in the EPISD has 709 students in the sixth, seventh, and eighth grades. These include 82.1% of which are considered qualifying as lower socio-economic status. The sample will come from Wiggs Middle School seventh grade population. The students involved in this project will be those in the classes of teachers involved with the PETE/Noyce project. (n=90)
Confidentiality Participants will be assigned a code number in order to preserve their anonymity, and data will remain confidential. There will be no personally identifying information used about participants in any presentation or paper resulting from this research. The obtained data will be kept in a locked room at UTEP, accessed only by members of the research team and destroyed when they are no longer needed for the purposes of the MSP grant or at the end of the grant at the latest. There are no direct benefits for participating, although the information provided may be used to review the MSP grant’s activities, or to understand and/or improve teacher preparation at UTEP and the surrounding El Paso County. Participation is completely voluntary, and may be withdrawn at any time with no penalty or loss of benefit to the participants. There are no apparent physical or psychological risks associated with participation in the present study.
| January 2004 |
Feb. 2004 |
March 2004 |
April 2004 |
May 2004 |
June 2004 |
July 2004 |
| Develop combined activities and align with State standards. |
Pre-test students. Begin activities at Wiggs Middle School |
Continue activities at Wiggs Middle School |
TAKS Month
Interview Students |
Finish activities at Wiggs Middle School and post-test students. |
Analyze data results from pre- and post-tests |
Write final report and prepare article for publication |
BudgetThe stipends for teachers will cover all copying and other incurred expenses during the time of the grant.
Stipends for Participants: 3 teacher participants ($1000 / teacher) $3,000. TOTAL $3,000.00