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1 1 The Effect of an Overarching Topic on Student Performance in Algebra II Christine Consoletti and David Collins J.E.B. Stuart High School Fairfax County (VA) Public Schools June 2003 Question Does an overarching topic help contextualize the math to increase student interest and comprehension? The basic hypothesis was that by giving the context of how math is used, students would understand the purpose. By understanding the purpose, students interest level would increase, which in turn would improve participation and comprehension. This is viewed as cyclic process, where students who are interested learn more and students who learn are more interested. A positive cycle of learning was created. As the research progressed, two other questions emerged: Do hands-on activities help to increase student interest and comprehension? and Does peer pressure associated with oral presentations motivate students to learn more in preparing them? Study and Implementation The research project was designed to investigate how an overarching topic could increase student interest and comprehension. The project was conducted over two math chapters (Conic Sections and Polynomial Functions). In the control chapter on Conic Sections, an overarching topic was not used. In the Polynomial Chapter, polynomial functions were introduced by building a 4-ft high roller coaster in the classroom. During the entire chapter, the overarching topic was used extensively to model concepts being taught: Students watched a movie on roller coasters. Students were able to play with the roller coaster, and observe the shape, velocity, and acceleration. Students drew a roller coaster with a specific polynomial shape (example, a negative quartic roller coaster). Students answered questions on tests and quizzes about roller coasters. To answer the secondary question, if hands-on activities would increase student interest and comprehension, several hands-on activities were used: Students measured a cardboard semi-circular tunnel and determined an equation to calculate the height at any location Students measured a map of the White House grounds to determine the foci of the Ellipse.

2 2 In the Polynomial Chapter, hands-on activities included: Students playing with the roller coaster, and observing the shape, velocity, and acceleration. Students drawing a roller coaster with a specific polynomial shape (example, a negative quartic roller coaster). Students creating polynomials that met different criteria during a game using wikki-sticks and white boards. Students investigating acceleration and velocity using CBRs. The third question about how oral presentations can increase student motivation came up after the project started. Oral presentations were used as a method to measure student comprehension. However, once the presentations began, it was impressive to see how motivated the students were to appear knowledgeable in front of their peers. Student interest and comprehension served as dependent variables. Students interest was measured using observation and questionnaire. During both chapters, the researchers kept a log about each day s activities and how the students reacted. At the end of each chapter, students completed a questionnaire on which activities they enjoyed and which activities helped them learn. Student comprehension was also measured by responses on the questionnaire, test scores, and videotapes of oral presentations. The questionnaire asked students to rate their understanding of each topic in the chapter (Nothing, Some, Most, All). In both video taped chapters, students gave oral presentations in which they were required to complete a problem, describe how they solved it using key words, and respond verbally to higher-level questions. Some data is difficult to compare because it was collected over two different topics. Both chapters were taught differently than previous chapters: More class days were spent More hands-on activities were used Each student did an oral presentation. Literature Review After selecting the research questions, the researchers pursued other articles and papers that would guide the study. The focus of an overarching topic was to contextualize academic concepts (Hamayan, 1990). The roller coaster model was intended to draw on students prior experiences and help them categorize the major concepts. For instance, sharing everything they knew about roller coasters with their other classmates. In an attempt to familiarize students with the new concept of polynomial functions by linking the overarching topic (Mohan, 1986). Many of the hands-on demonstrations used were designed to integrate different learning styles and incorporate other content areas. The introduction to the roller coaster and CBR activity included many aspects of physics (a course many students were enrolled in during the study). The theory of Spatial Intelligence was used when the students were asked to draw the polynomial function (Ormrod, 2000) The wikki-stick game and tunnel activity used the spiral fashion of learning. Manipulatives allow

3 3 students to develop conceptual understanding of concepts, making better connections between abstract symbols and the concept (Kelly, 2002). The initial purpose of the oral presentations component of the project was to further document research findings. It was not until after the first set of presentations that the social and peer-relation implications of the presentations was realized. Lev Vygotsky proposes that learning is primarily a social and cultural process (Pransky, 2002). All communities do not think, believe or learn in identical ways and even students in a multicultural classroom can be confused and misunderstood due to language, culture and socioeconomic differences (Delpit, 1996). The usage of keywords during oral presentations create rich language experiences that foster higherlevel thinking and make connections between language and the academic concepts (Kelly, 2002). Constructivism is a theory of knowledge and learning where children construct their own understanding of the world. (Brooks & Brooks, 1999). Teachers can create appropriate learning contexts so students can construct or scaffold their own understanding of academic concepts. The clues provided during the tunnel activity and questions asked during the oral presentations were designed to have students construct meaning for themselves. Finally, the use of games, such as the wikki-stick activity, was designed to create a positive learning environment. The game was designed to encourage students to participate in their own learning. Though competitive, the team component of the game created a low stress, safe, fun environment yet still allowed for learning to occur. This type of activity helps students cope with mathematics anxiety. Small amounts of anxiety, facilitating anxiety, often improve performance and comprehension. Students approach their classwork carefully and think about their responses in a thoughtful and reflective fashion when asked to complete tasks with low levels of anxiety (Shipman & Shipman, 1985). Before students were asked to give their oral presentation, the researchers modeled a typical presentation, gave the students sample questions, and reduced the class size observing the presentation all in hopes of keeping the anxiety levels below the debilitating, destructive level. Results Student Comprehension Student comprehension was measured using three methods: student questionnaires, test scores, and qualitative differences in oral presentations. Although the student questionnaires showed no significant difference in student comprehension, both the test scores and the oral presentations showed a significant improvement in our experimental chapter. The questionnaire gave each student an opportunity to rate their knowledge on different concepts in each chapter. Below is a sample questionnaire used to evaluate Chapter 8:

6 6 presentations were employed. Student questionnaires indicate that a majority of students agreed they learned from giving oral presentations. References Brooks, J., & Brooks, M. (1999), In Search of Understanding: The Case for Constructivist Classrooms. Alexandria, VA: Association for Supervision & Curriculum Development. Delpit, L. (1996), Other People s Children: Cultural Conflict in the Classroom. New York: The New Press. Hamayan, E. V., Perlman, R. (1990), Helping Language Minority Students After They Exit from Bilingual/ESL Programs: A handbook For Teachers. NCBE Program Information Guide Series, Spring (1). Kelly, G. N. et al. (2002), Learning Spanish While Practicing Mathematics Concepts and Skills: A Winning Combination. Teaching Children Mathematics, 9(3), Mohan, B. (1986), Language and Content. Reading, MA: Addison-Wesley. Ormrod, J. E. (2000), Educational Psychology: Developing Learners. Upper Saddle River, NJ: Merrill. Pransky, K., Bailey F. (2002), To Meet Your Students. The Reading Teacher, 56(4): Shipman, S., & Shipman V. C. (1985), Cognitive Styles: Some Conceptual, Methodological and Applied Issues. Review of Research in Education, Vol. 12. Vygotsky, l. (1986), Thought and Language. Cambridge, MA: MIT Press.

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Ohio Standards Connection Data Analysis and Probability Benchmark F Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data. Indicator