Browsing by Subject "algebra"
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Item Preservice teachers' knowledge of linear functions within multiple representation modes(2009-05-15) You, ZhixiaThis study examines preservice teachers? knowledge in the case of linear functions. Teachers? knowledge in general consists of their subject matter knowledge and their pedagogical content knowledge. In this study, teachers? subject matter knowledge is examined by looking at their ability to adapt to different representation modes. The framework for subject matter content knowledge consists of five components: (1) flexibility across formal mathematical symbolisms; (2) flexibility between visual and algebraic representations; (3) flexibility within visual representations; (4) flexibility with real-life situations, and (5) procedural skills. In terms of pedagogical content knowledge, two aspects were examined across five corresponding components. These two aspects were knowledge of students? conceptions and misconceptions, and teachers? teaching strategies. The primary source of data for the study was from two tests and six interviews. The results showed preservice teachers performed poorly in terms of representation flexibility. Furthermore, most of the preservice teachers had limited knowledge of the nature and sources of students? mistakes as well as effective teaching strategies to help students with their misconceptions. In terms of knowledge structure, representation flexibility was found to be significant in both CK and PCK compared to procedural skills. Moreover, the representational flexibility in terms of CK seemed to strongly predict the overall PCK performance. Representational flexibility seemed to be related to the use of instructional representations. Overall, there was a strong relationship between various components of CK and PCK.Item Preservice Teachers? Content Knowledge of Function Concept within a Contextual Environment(2012-10-19) Brown, IrvingThe overarching goal of this dissertation research was to develop and measure the psychometric properties of an instrument to assess preservice teachers? content knowledge of the function concept embedded in contextual problems. This goal was accomplished through two research projects described in two central chapters. Chapter II reports on the collective case study that was used to pilot test the instrument and Chapter III details the rationale used in item selection and the psychometric properties of the new instrument. Unlike existing research studies that examine a broad range of function related topics using various forms of symbolic, tabular, and graphical representations as the basis for questions and problems, this study focused solely on function problems immersed in various real world contexts. Since this is not a common approach to measuring content knowledge of the function concept, the existing instruments in published studies were not found to be suitable for this specialized purpose. The psychometric measurements of the instrument did not suggest that the instrument was valid or reliable so more research will be required to validate the instrument. However, based on the preliminary results from testing, several potential suggestions can be made to teacher educations programs. Inferences drawn from the mathematical problem-solving cognition will aid in the development and validation of future instruments to assess preservice mathematics teachers? knowledge of how to connect their knowledge mathematical concept of function to a contextual setting.Item Solving single variable equations in the algebra classroom(2009-08) Goodson, Renee Nicole; Armendariz, Efraim P.; Daniels, Mark L.This report recognizes the common mistakes students make solving single variable equations and attempts to connect these errors to varying levels of developmental readiness. Striving to meet the needs of all students, this report offers an alternative to lecture based mathematics lessons by exploring the benefits of a unit based curriculum. The unit poses an overarching problem for the students to investigate and answer, while the students still receive the instruction on solving algebraic equations. The goal is to move beyond traditional procedures when solving equations to help students become more familiar with symbol manipulation involved in solving real world story problems.