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This 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.

published_or_final_version / Education / Master / Master of Education

<p>This thesis investigates grade seven learners perceived experiences in learning algebra.Things that learners do and say during algebra lessons and about algebra were investigated. The study was done at one of the previously disadvantaged schools in Cape Town, South Africa.The data were collected through observations, a questionnaire and interviews. Observations were made from the day the topic was started in two grade seven classes. Two different teachers taught the two classes. Focus group interviews were conducted, two group of learners, ten learners from each of the two classes were interviewed. Learners devised a number of strategies for solving problems related to sums and differences. The principal learning difficulties experienced by learners in algebra related to the transition from arithmetic conventions to those of algebra, the meaning of literal symbols and the recoginition of structures. It became obvious then that developing algebraic thinking is not necessarily dependent upon algebraic notation and that the presence of algebraic notation says little about the level of problem solving.</p>

The purpose of this study was to determine whether students taught by certified teachers and those taught by uncertified teachers had significantly different achievement on a state Algebra I End of Course examination. The specific research questions were: (1) Does type of teacher certification impact Algebra I End of Course (EOC) Exam scores for high school freshman when controlling for students' past mathematics success as measured by 8th grade TAAS mathematics test scores and teachers' years of experience? (2) Does type of teacher certification impact Algebra I End of Course (EOC) Exam passage rates for high school freshman when controlling for students' past mathematics success as measured by 8th grade TAAS mathematics test scores, socio-economic status, ethnicity, gender, and teachers' years of experience? This research was conducted in a large north Texas suburban school district. The entire population (N=1,433) of freshman students enrolled in year-long Algebra I was included for this study. Three statistical tests were used in data analysis for the first question. Analysis of covariance using student as well as teacher as the unit of analysis and hierarchical multiple regression were used to analyze students' specific scores. Logistic regression was used for the second research question. This study found that students in classes with non-certified teachers scored eight points lower on the Algebra I EOC Exam than those in classes with certified teachers. However, when controlling for students' prior mathematics achievement and other variables, the difference was of no practical significance. There was no practical significance in a student's odds of passing the examination between students in certified teachers' classrooms and those in uncertified teachers' classrooms. The results of this study offer further understanding of the debate over type of certification.

The purpose of this study was to investigate the effectiveness of the graphing calculator on the achievement, attitude toward mathematics, and confidence in learning mathematics of Algebra II students.

The purpose of this study was to survey Algebra II teachers in the State of Texas to determine the extent to which they use technology for the delivery of instruction. Additionally, the study attempted to determine reasons why teachers do or do not use technology when they have a choice.

This study investigated the use of computer-based instruction as a means of teaching Algebra I, compared to the teaching of the same topics using traditional methodologies. The achievement level of the two groups, and three aspects of attitude toward mathematics were considered. Achievement and attitude differences by gender were also analyzed.

The purpose of this study was to evaluate the influence of block scheduling and instructional strategies on student achievement in Algebra I. The study was conducted during the 1997-98 school year. This study was comprised of two components, a quantitative study and a qualitative study. The quantitative study focused on block and traditional scheduling and the influence identified through scores on the Texas End-of-Course exam for Algebra I. The sample for this study consisted of 59 school districts from five counties in the north Texas area. The qualitative portion of this study focused on 10 classrooms, 5 block and 5 traditional, taken from the sample of 59 districts. Data for the qualitative study included questionnaires, interviews, and observations. The End-of-Course scores were analyzed using an ANOVA at the .05 level of significance, no significant difference was identified in the achievement levels of the two groups. The qualitative data was organized by categories derived from the NCTM teaching standards. Data from this portion of the study indicated that teachers in both block and traditionally scheduled classes spend their class time in a similar manner, using similar materials, and using more traditional strategies. Additional analyses of data based upon usage of the graphing calculator and manipulatives also resulted in no significant difference. Although all comparisons between block and traditional scheduling and usage or non-usage of technology and/or manipulatives resulted in no significant difference, the block groups and those using technology and/or manipulatives had higher mean scores. This indicates that allowing teachers more time to use alternative instructional strategies would benefit the student, but this will not take place without the teacher receiving training and support.

The purpose of this study was to examine the effectiveness of a technology-enhanced unit on slope in algebra. The technology used in the study was the Topological Panorama Camera (Topocam). The research questions explored the learning and transfer of knowledge about slope and the engagement level of students during Topocam learning activities. The Topocam is a computer-controlled camera that moves on a modular track while it scans a scene through a vertical slit. Students can program the speed of the camera and frequency of pictures. They then witness the results of time and motion in the image created by the camera. Data for this study were collected from a pretest/posttest, as well as from observations of indicators of engaged learning. The research population consisted of 46 students from three classes of Algebra I students. Three classroom teachers each taught a unit on slope, while a fourth teacher conducted the activities with the Topocam for all the classes. The classroom activities focused on the concept of slope as a rate of change utilizing coordinate grids. The Topocam activities involved students in collaboratively making and testing predictions about slope. The findings of the study indicate that student learning did occur with this technology-enhanced unit on slope in algebra. Students showed statistically significant improvement in understanding slope and in transferring that concept to other situations. Since technology was only part of the unit presentation, the amount of learning attributed to the Topocam activities cannot be determined. However, students demonstrated a high degree of engagement in learning while working with the Topocam which suggests that the activities were a factor. A low correlation between students’ slope unit test scores and previous algebra performance may indicate that students who have not been successful in algebra were more successful in the technology-enhanced unit. Some variation was found between classes that could be attributed to other factors than the Topocam.