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The Influence of Developmental Levels of Thinking on Understanding of Advanced Mathematical Concepts in Middle School Students |
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P.I. Sue Spotts 845 CSusanSpotts@netscape.net
Co-P.I. Alex Bustillos ZE629@msn.com Wiggs Middle School 6,7,8th grades |
Purpose:
Data from placement of University of Texas at El Paso declared mathematics, science, and engineering majors shows that 36% of high school graduates and first year students were placed in Pre-Calculus and only 15% of students were placed in Calculus courses. One of the main causes of this is that few high school students take a Calculus course in high school. NAEP (2000) data indicates that only 10-12% of high school students take Calculus courses. This percentage drops significantly for minority students: only 3-4% of Hispanic high school students take Calculus courses in high school. This proposal will explore the influence of developmental levels of middle school students in regards to understanding calculus concepts.
Research Question:
Do Developmental Levels among 6th, 7th, and 8th grade students influence the capability to learn and understand “big ideas” in calculus conceptual learning?
Rationale:
In order to increase the number of minority and lower socioeconomic status high school students taking Calculus courses and help them to be successful in Calculus the role and placement of these courses need to be rethought. This project is focused on exploration of possibilities of early development of big Calculus ideas in middle grades.
It is generally accepted that Calculus is a subject for older students, the “elite” and is often considered a “gatekeeper” course, a course that keeps students from progressing towards degrees that require upper level mathematics. It is well documented that minority and lower socioeconomic status students are underrepresented in mathematics related careers. These same students continually score lower on national and international tests and course-taking patterns reveal that they have limited access to upper level mathematics courses. The problem is two pronged as these students work with teachers who may not be qualified to teach upper level mathematics courses and the lack of participation from minority and lower socioeconomic students in mathematics programs prevent them from success in mathematical related careers.
Mathematics standards, along with a shortage among qualified teachers, have brought forth increased interest in the preparation teachers receive in their fields. The teachers’ educational background is the most widely accepted standard of teachers’ understanding of and expertise in their field. Educational backgrounds of mathematics teachers are not consistent. While no one would argue the need for teachers to know their content, many middle school mathematics teachers fall short in meeting recommendations for coursework preparation made by national associations of teachers. Only 7 percent of middle school mathematics teachers have taken courses in all recommended areas and about one-third have completed none of the coursework recommendations (NSF, 1998). Often state certification requirements do not maintain high expectations in mathematics background for teachers. One study found that most secondary students pursuing a minor in education were not required to take courses in pedagogy and that most elementary teachers did not have adequate subject matter preparation (Luft, Buss, Ebert-Mat, & Eslamieh, 1997). 40 per cent of high-school mathematics teachers in high-poverty schools have no training in mathematics (The Education Trust, 1996).
Teacher shortages often force school districts to place teachers in mathematics classrooms with little or no background in this important curriculum area. There is evidence that shows a correlation between out-of-field teaching (lack of strong formal preparation in the content area being taught) and lower student performance (ECS, 1999). It is content area preparation, then, and not certification per se, that may be a relevant consideration. These factors, along with the sociological background of minorities and lower socioeconomic environments influences keep a large percentage of students from participating and succeeding in mathematics courses like Calculus.
Research Sample, Design and Analysis:
A pilot study was conducted with a small sample of middle school students with above average GPAs. The pilot sample consisted of two sixth graders, four seventh graders, and six eighth graders from Wiggs middle school. Pre and post content tests were administered and a ten day treatment program was administered using a hands-on visualization approach to learning “big ideas” in calculus. Results of the pilot study indicated that while the more mature eighth graders brought more prior knowledge to the project but after the treatment all students had gained understanding of advanced mathematical concepts. The maturity level did not enter into the results of the research.
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. A series of activities to teach Calculus Concepts, based on the pilot study will be developed and aligned with State curriculum standards. These activities will be introduced to students in 6th through 8th grade. Pre- and Post-tests will be administered to determine if these activities increase conceptual understanding and if there is an age/development obstacle to calculus learning.
TIMELINE
| Jan. |
Feb |
March |
April |
May |
June |
July |
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Develop Calculus activities and align with State standards |
Pre-test students
Begin activities at Wiggs Middle School |
Continue activities at Wiggs Middle School |
TAKS Month |
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 |
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. All participants will be informed of the details of the project. All participants will sign or have their parents sign consent forms.
Budget
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Equipment |
TI83 graphing calculators, overhead calculator screen, and CBRs |
$1500.00 |
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Stipends for Participants |
4 teacher participants
$200 @ |
$800.00 |
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Materials |
Paper for activity data sheets 10 reams |
$340.00 |
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Food for Student Participants |
Pizza for Wiggs Students |
$360.00 |