Browsing by Subject "Algebra--Study and teaching (Secondary)--Texas--Case studies"
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Item An investigation of secondary school algebra teachers' mathematical knowledge for teaching algebraic equation solving(2007) Li, Xuhui, 1969-; Treisman, Uri; Ferrini-Mundy, JoanThis study characterizes the mathematical knowledge upon which secondary school algebra teachers draw when pondering problem situations that could arise in the teaching and learning of solving algebraic equations, as well as examines the potential connections between teachers' knowledge and their academic backgrounds and teaching experiences. Seventy-two middle school and high school algebra teachers in Texas participated in the study by completing an academic background questionnaire and a written-response assessment instrument. Eight participants were then invited for followup semi-structured interviews. The results revealed three topic areas in equation solving in which teachers' mathematical subject matter understanding should be strengthened: (a) the balancing method, (b) the concept of equivalent equations, and (c) the properties of linear equations in their general forms. The participants provided a wide range of instances of student misconceptions and difficulties in learning how to solve linear and quadratic equations, as well as a variety of strategies for helping students to improve their understanding. Teachers' subject matter knowledge played a central or prerequisite role in their reasoning and decision-making in specific contexts. When the problem contexts became broader or more general, teachers drew from across the three basic domains of mathematical knowledge for teaching (knowledge of the mathematical subject matter, knowledge of learners' conceptions, and knowledge of didactic representations) and showed individual preferences. Overall, teachers tended to rely more heavily upon their knowledge of students' specific or general learning characteristics. Statistical analyses suggest that teachers who majored in mathematics and who had the most experience in teaching first-year or more advanced algebra courses performed significantly higher on the assessment than their counterparts, and there is a linear relationship between teachers' performance and the number of advanced mathematics course they have taken. Neither course-taking in mathematics education nor number of years of algebra teaching made a significant difference in their performance. Results are either unclear or inconsistent about the role of teachers' (a) use of algebra textbooks, (b) prior experience with a method or a manipulative, and (c) participation in professional development activities. Teachers also rated (a) collaborating with and learning from colleagues and (b) dealing with student conceptions and questions as highly influential on their professional knowledge growth.Item A study of changes in students' understanding of three algebraic concepts: variables, expressions, and equality(2006) Cushman, Jane Ries; Smith, Jennifer ChristianThis study of ASK ME-Algebra, an online high school algebra curriculum, focuses on students acquiring knowledge about the concepts of variables, expressions, and equality. The Online Mathematics Initiative (OMI) of the Distance Education Center (DEC) of the University of Texas researched and developed the algebra curriculum to address and encompass both Texas’s and national standards for high school algebra. Twelve school districts in Texas used ASK ME-Algebra in classrooms and with independent learners for credit recovery1. Designed by researchers as a functions-based and problem-based instructional approach to algebra, ASK ME-Algebra assists students 1 Credit recovery is for students who have failed a course. The students take the course again but in a shorter time-period (i.e. one semester instead of a whole school year or two semesters). to gain an understanding of algebra concepts (i.e. functions, linear functions, linear equations and systems of equations). The methodology chosen for this study was a design experiment since it aligns with the constructivist viewpoint of the researcher. This design experiment will show that ASK ME-Algebra increases students’ understanding of the concepts of variables, expressions, and equality without structured instruction. The teacher of the classroom negatively affected the implementation of the curriculum by using structured instruction during the last two-thirds of the course. The data for this study includes responses to pre- and post-algebra tests, comparative data from ninth grade Algebra I students, observations, all of the treatment groups’ saved online work, and periodic interviews of the treatment group from a central Texas alternative high school using the online curriculum as independent learners.