UBC Theses and Dissertations
An evaluation of an alternative organization for curriculum emphasizing the interconnectedness of mathematics Millar, Duncan Stuart
This study was initiated as a response to the call of the National Council of Teachers of Mathematics (NCTM) and British Columbia Ministry of Education for a mathematics curriculum which would enable students to formulate connections among key mathematical ideas. As well, the study addresses the problem of students' errors in selecting appropriate strategies to complete a given algebraic task. Authorities such as Fey, Barbeau, Cooney, McKnight, and Manhard believe that a traditional curriculum organized around isolated mathematical objects (i.e., Real Numbers, Exponents, Radicals, Polynomials, etc.) tends to produce fragmented teaching and learning. The study investigated an alternative organization of the curriculum which emphasizes the main processes of mathematics (i.e., Factor, Simplify, and Solve). The research questions focused on the effects this reorganization would have on: students' understanding about the interconnectedness of mathematics, students' abilities in selecting appropriate strategies, students' achievement scores on standard tests, and amount of class time needed to cover the learning outcomes in the curriculum. Two Mathematics 11 classes were selected to participate in the study. One was taught using the traditional organization of curriculum emphasizing mathematical objects, while the other was taught using an alternative organization of curriculum emphasizing mathematical processes. The various research questions required both quantitative and qualitative methods in the acquisition and analysis of data. The teacher's journal was used to record classroom observations for the duration of the study. Tests containing open-ended items were given at the beginning and the end of the study to determine students' abilities in selecting appropriate strategies and to evaluate students’ understanding of the interconnectedness of mathematics. These tests were followed by interviews with five students from each class to clarify their responses on the written tests and to provide further information with regard to the research questions. Students' achievement on standard tests was determined through an analysis of covariance. From observations recorded in the teacher's journal it was noted that the process-organized class dealt with general ideas and concepts during introductory lessons rather than at the end of the unit as in the object-organized class. As well, the process class had numerous discussions about the main ideas of mathematics which occurred on a regular basis from the beginning of a unit till the end. From the journal and the acetate rolls used during instruction, it was determined that the process class required fewer class periods than the object class to cover the same portion of the curriculum. Although there was no statistically significant difference between the classes in terms of achievement scores on the standard tests, the process class was better able to identify the inappropriate use of strategies in a given solution and was better able to provide an appropriate strategy of their own in responding to algebraic tasks. Findings from this study suggest that teachers should rely less on the traditional mathematical object organization as shown in curriculum guides and textbooks to structure their units and lessons, and more on their own organization of curriculum emphasizing what they believe to be most important mathematical ideas. An organization of the curriculum should not only highlight the main mathematical concepts and ideas, but it should also indicate how these ideas and concepts are related and connected. This study provides some evidence that when students experience a curriculum that is organized so as to emphasize processes which are used with different mathematical objects, their understanding of the interconnectedness of mathematics is improved.
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