Integration of Physical Education with Mathematical Concepts: Broaden Horizons and Deepen Understandings (Abstract of the research proposal)

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Theoretical Perspectives

Learning theorists posit that learning occurs best when students make connections between previous knowledge and current learning and when students understand relationships among concepts (Dewey, 1938; Bruner, 1987; Piaget, 1970; Vygotsky, 1978). Brain researcher, Cromwell (1989) reports that the brain uses previous experiences to organize new information and searches for meaning from those experiences. The brain perceives and processes information in an interconnected and holistic manner. To foster students to gain an in-depth understanding of concepts, it is crucial for teachers to provide them with meaningful and integrated learning experiences. Interdisciplinary teaching is viewed as one of the effective approaches to meet this educational aim (Lancaster & Rikard, 2002; Lipson, Walencia, Wixson, & Peters, 1993). Interdisciplinary teaching integrates two to more subject areas into meaningful association to enhance and enrich students learning in each subject area (Cone, Werner, Cone, & Woods, 1998). Interdisciplinary teaching through physical education has received a great deal of attention by K-12 educators, as well as teacher preparation programs. Proponents view movement as an effective vehicle for providing integrative, concrete and authentic contexts to strengthen students' learning (Christie, 2000; Cone et al., 1998). They argue that through interdisciplinary teaching in physical education, the primary focus of learning movement concepts and skills would be extended and complemented. A supplementary focus of helping students make meaning of abstract concepts in another subject area also would be augmented and reinforced. However, how teachers apply interdisciplinary teaching practices to support this theoretical hypothesis still remains an untapped research area.

Research Purposes

The primary purpose of this study is to investigate how interdisciplinary teaching impacts students' learning of movement concepts and skills and students' conceptual understanding of math concepts. The secondary aim of this study is to investigate the strategies the teacher applies to facilitate the integrated learning experiences.

Research Methods

Participants and research setting. The second author, an accomplished elementary physical education teacher, and students from a second grade class will be selected as participants following receipt of parental permission. The teacher has taught elementary physical education for more than thirty years and has expertise in interdisciplinary teaching. She is the lead author for Interdisciplinary Teaching Through Physical Education (Cone, Werner, Cone, and Woods, 1998). She has published several articles on interdisciplinary teaching and made numerous presentations related to using the interdisciplinary teaching approach at national, regional and state conventions. The rational for choosing second grade children is: (a) these students primarily function in Piaget's concrete operational stage, (b) the primary focus of the physical education curriculum for second grade is fundamental movement and (c) second grade children are learning basic mathematical concepts and problems. This school was selected as the research setting because the student population represents a diversity of cultural, ethnic and socioeconomic backgrounds.

Data sources. The data sources will consist of videotaping lessons, coding taped lessons, descriptive anecdotal records, interviews, and students' concept maps. First, the teacher will teach a five-lesson unit on fundamental movement while integrating math concepts learned in coordination with the second grade classroom teacher. All lessons will be videotaped. Second, a rubric for assessing children's movement responses (RACMR) will be developed and validated for this study prior to official data collection. The RACMR will be used to code the 5 taped lessons to obtain quantitative data in terms of children's movement variety and movement quality. Third, using protocols for descriptive anecdotal records, we will describe the children's movement responses to the teacher's teaching while watching each of the 5 taped lessons to obtain descriptive data. Fourth, the teacher and 10 randomly selected students will be formally interviewed at the beginning and at the conclusion of the unit. The interviews will focus on gathering qualitative data on the teaching strategies and her perspectives of students' movement content learning and conceptual understanding of math. In addition, the interviews will reveal students' perceptions of what they learned and understood in terms of movement content and mathematical concepts throughout the unit. Finally, students will also construct a concept map of movement concepts and math concepts at the beginning and again at the end of the unit. Concept maps are tools for organizing and representing knowledge (Trochim, 2000). So, we use concept maps to gather students' knowledge of movement and math concepts and understanding of relationships among them.

Data analysis. With regards to the quantitative data coded from the 5 taped lessons by using RACMR, descriptive statistics will be used to analyze students' demonstration of movement variety and quality in each of the 5 lessons because of small sample size (5 lessons). The qualitative data gathered from the descriptive anecdotal records and the transcribed interviews will be analyzed by using constant comparison technique (Glaser and Strauss, 1967). This includes reading and reading the descriptions and transcripts, identifying similar instances and labeling them with tentative assertions, grouping similar ideas into categories, and organizing categories into themes. To confirm the categories and themes emerged from data analysis, the qualitative data will be further analyzed using ATLAS qualitative data software. The concept maps constructed by students will be analyzed by using The Concept System software designed by Trochim (2000) to conduct the analysis including construction of the similarity matrix, multidimensional scaling, cluster analysis, and averaging of ratings. The mean scores of the links and the nodes on the concept maps will be analyzed by using dependent t test to examine a statistical difference between the pre- and post-test (at the beginning and the end of the unit).

Educational significance

The significance of this research project lies in (a) providing researchers with the validated instrument for assessing students' movement responses in authentic settings, (b) providing both researchers and practioners with descriptive information about how students apply mathematical concepts learned in classroom to enrich their movement content learning and how they make meanings of abstracted math concepts through engaging in concrete and applied movement experiences, (c) providing practioners with insightful information about students' views of the interdisciplinary learning experiences, and (d) providing both researchers and practioners with insights about how the teacher works with a classroom teacher to design sequential integrated learning tasks and uses appropriate teaching strategies to expand students learning movement content and to deepen students' understanding of math concepts.

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