The program includes targeted opportunities for candidates to develop skills, knowledge, and practices specific to teaching and learning mathematics and science, mathematics and science teacher preparation, and research in both of these areas. Students admitted after should use the myProgress system for program details. Enter your keywords. Section menu.
Integrated Studies. Although other projects have effectively used hands-on learning, problem-based learning, authentic assessment, and technology, to my knowledge, none have used them simultaneously with at-risk students. Utilizing knowledge gained from the literature review, I wrote a unit of instruction that ties together other successful models, while also integrating innovative lessons to teach mathematics to at-risk students.
To achieve the objectives stated in the previous paragraph, I began by writing a unit of instruction entitled the Architect Unit. The unit consists of 11 lessons that employ methods such as CAI Computer Assisted Instruction , hands-on learning, thematic teaching, and authentic assessment. Teamed in groups of two, students designed their own floor plans, built their own quarter-inch scale model homes, and presented their work at a public exhibition.
The exhibition was three fold with an oral component, a career component, and a rubric scoring component. Scoring was completed by outside community members, one of which was a professional architect.
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The most significant result of this study appears to be that the Architect Unit of instruction can be used to help at-risk students successfully learn mathematics. This is verified by the rubric scores given by the community judges involved in the project. Nine out of ten teams of students achieved successful scores.
In addition, the overall class mean on the pre-test improved from It should be noted that the post-test was not given directly after instruction, but four weeks after CAI.
The overall success of the students in this study shows a major change in their performance, especially considering that the students were selected because of their record of academic failure and inability to complete junior high school. With less money being allocated for at-risk programs, like continuation schools, researchers need to continue the development of curriculum for secondary at-risk students. Computer-Assisted Instruction CAI uses state-of-the-art technology to allow a more complete understanding of basic concepts for the aspiring mathematician.
This project applies findings of current educational research to the introduction of the basic elements of trigonometry. The computer gives the student the freedom to explore interesting areas without the tedium of calculating and graphing by hand. This will enable more thorough learning of elemental trigonometry than has been evident using traditional modes of instruction in a basic course.
This original computer program is a creative introduction to trigonometry. Each screen interactive and allows students to manipulate graphics and calculations. Dynamic graphics animate each lesson. Prerequisite algebra and geometry skills are reviewed. The unit circle is employed in the definitions of degree, radian, sine, cosine, and tangent. The original arc-based definitions are used to link geometric concepts to the trigonometric basics. Cartesian graphs are thoroughly explored. Three test screens provide a means of assessment for the user.
Several screens offer discovery environments which allow the investigation of key ideas. It is recommended that this program be used by students interested in an alternative approach to independent learning and by teachers as an enhancement to classroom instruction. Many efforts have been made to develop programs and curriculums that are successful in helping at risk and low achieving students increase their knowledge and understanding of mathematics. Pre-existing data acquired from normal practice in education was used to measure student achievement.
A control group of 96 students having similar characteristics gender, ethnicity, socioeconomic status and comparable Procedures Scale Score and Total Math Scale Score on their sixth grade Stanford Achievement Test-9 was chosen from all ten middle schools in the same school district. The two groups were then compared for the next five academic years using state and national standardized testing scores, California High School Exit Exam Scores, and class schedules to determine when the students successfully completed an Algebra 1 course. Results of the study showed no overall significant difference between the study groups.
However, two other findings of interest were exhibited. First of all, the experimental group demonstrated less proficiency on the California Standards Test for General Math, but slightly more knowledge and understanding on the California Standards Test for Algebra, and significantly more knowledge and understanding on the California Standards Test for Geometry compared to the control group. A study was undertaken to evaluate whether the use of computer-assisted instruction utilizing the Accelerated Math AM program would improve student achievement in mathematics.
The study compared student achievement gains in math between those students who used AM material and those who used teacher-prepared materials. The Math Lab classroom instruction for both groups was a combination method of direct instruction and individualized instruction based on the progress and pace of the student learning ability.
The contrast group students were from the Math Lab classes in a high school in northern California during the school year of , and the experimental group students were from the Math Lab classes in the same high school during the school year.
The teacher for both groups was the author. Students in both groups took the same test three times during the course. However, there was no statistically significant difference in achievement mean gains between the two groups. The Accelerated Math program was no better than the teacher developed curriculum as measured by student gains in mathematics achievement according to this limited study. Responses were categorized and tallied for each topic. Data were then analyzed a collectively and b by sorting the data according to the type of department where the program is housed.
There is a shortage of qualified individuals prepared to work in the field of mathematics education. Future research in the area is recommended. The intent of this project was to develop a set of lessons designed to integrate literature into the middle school mathematics classroom. Five different lessons were field tested with students in grades six through eight. Six different teachers tested the lessons.
Each lesson was introduced by the teacher reading a book out loud to a class. After completing the lessons, students and teachers completed an opinion survey. The purposes for the survey were to study the appeal of the literature book, and to study the interest of the students in integrating literature into the mathematics classroom. The outcome of this project, for the most part, found each literature book appealing. The most important conclusion of this study appeared to be that integrating literature into the middle grades mathematics classroom is a positive experience for students.
The objective of this project was to develop and evaluate a series of prompts that would improve both student problem solving skills and attitude towards mathematics. Each prompt consisted of a series of several problems, ranging from rudimentary to challenging, and also included a writing component where students needed to communicate their mathematical reasoning.
The first prompt, together with the attitude survey, was administered at the beginning and end of the year for comparison. The study was conducted in a sixth grade classroom over the course of one academic year. The pre- and post- of the first prompt showed significant improvement, particularly in communication, with the number of students showing at least substantial understanding doubling.
In conclusion, problem solving abilities may not be transferable across content areas, or may take longer than one academic year to show significant improvement, but rich problem solving experiences can improve attitude towards mathematics. The purpose of this project was to develop and evaluate a three-week unit on statistics for a high school algebra course.
The unit would be a supplement to an existing algebra course that did not already include statistics as a content objective. The unit was field tested in junior high and high school classrooms during the spring of The unit was evaluated to determine appropriateness for a beginning algebra course and to determine if the statistics content was relevant. There is a challenge from national and state California standards to teach statistics to all high school students. Most high schools teach a traditional mathematics sequence that ignores statistics.
There are also nationwide and statewide emphases on establishing algebraic thinking throughout all grade levels. Proportional reasoning is an essential skill that is part of every algebra curriculum. A review of the research on proportional reasoning is included to show both the complexity of this area of mathematics and the need to develop this kind of thinking throughout the middle grades and into high school. The unit of curriculum developed for this project, entitled Two-Way Tables , is included as an appendix.
It is a unit that combines statistical ideas with proportional reasoning activities yet still has students engaged in algebraic thinking. This material consists of directions for the teacher as well as student worksheets, quizzes, and a test. This study was designed primarily to develop and field test a set of supplementary activities integrating graphing calculators into the Intermediate Algebra curriculum at the community college level.
Graphing calculators first became economically feasible in The advantages of this new technology over computers were realized immediately. An entire class set of calculators could be purchased for less that the cost of a desktop computer, placing the power of technology and visualization into the hands of every student.
Initial research and curriculum material was directed towards precalculus and calculus course. This includes prealgebra and algebra as well as precalculus and calculus. At the time this study was begun in , little or no research had been conducted in community college algebra classrooms. This project was designed to develop curriculum material for use at that level. The author began writing a series of activities to supplement the existing traditional course material. A set of TI81 graphing calculators was made available by the mathematics department for classroom use only.
Student reactions were determined by overall performance and an optional daily journal. The results of the field study were mixed. With only limited access, some students were frustrated because they did not have time to become acquainted completely with the calculator.
There did not appear to be enough classroom time for the students to become comfortable with the calculator as well as learn the algebra. The results of the study suggest that supplementing the existing curriculum is not the best method for integrating graphing calculators into the curriculum; more research is needed to determine better methods. The entire course content needs major changes in order to realize fully the potential of this new technology. With the new California State high school graduation requirements, it has become increasing important that students attain mastery of basic computational skills while continuing on in an Algebra 1 course, our Fundamental Testing Program, the FTP, was designed.
The purpose of this study was to evaluate the FTP. The FTP is a series of short low-stakes tests designed to review and reinforce basic math skills that have been identified as necessary to successfully complete Algebra 1. Three contrast groups were used to test the effectiveness of the FTP.
A pretest and posttest given to all three groups measured the growth of each student. The mean gain score of each class was calculated. The mean gain score of the group doing the standard FTP was 6. The mean gain score of the group doing the modified FTP using calculators was 4. The control group not participating in the FTP had a mean gain score of 1. The group doing the standard FTP had a significantly higher mean gain score than those of the FTP class using calculators.
The results of this study provide evidence that the FTP is a worthwhile intervention for use in high school math classes to assist students in mastering and maintaining basic computational skills while continuing on in a college preparatory program. It primarily consists of commands to move forward and turn right, in the same prescribed amounts. Investigating the figures drawn by this process is rich in mathematics, primarily geometry.
Altering the POLY procedure to encompass compounded angles re-affirms the mathematics of POLY for all such variations, as well as leading to further mathematical investigations. This investigation is a qualitative case study designed to examine whether and when the Latino population in elementary school develops negative attitudes toward mathematics. Thirty eight randomly selected Latino students in two California elementary schools, on urban and one rural, were interviewed to collect information about their perception of what mathematics is, their attitude towards mathematics, their perception of their own performance in this discipline, and their perception of the utilization of mathematics outside of school.
Subjects in this study tended to conceptualize mathematics almost exclusively as arithmetic. The provided few examples of how mathematics is used outside of school. The research found that the Latino population studied tends to like mathematics until about grade four; by grades five and six, negative attitudes emerge with a sense of inadequacy especially evident in the female subjects. Rational numbers represented in decimal form present various difficulties for middle school children. The purpose of this study was to examine how fifth grade students made sense of decimals in order to provide teachers with a lens through which they may view their own classroom and make informed decisions regarding instruction of decimals.
Research shows that symbol manipulation without understanding is ineffective. The review of research focused on how students understand mathematical concepts in general and then looked specifically at the complexity of learning decimal notation. The research review suggested that knowledge of quantity determined understanding of decimal numerals. This investigation then, focused on how ten fifth grade students determined quantity of a decimal numeral. The results revealed: 1 The underachieving students interpreted decimal numerals using whole number rules and 2 The higher achieving students who revealed knowledge of quantity appeared to interpret decimal quantity by connecting them with their fraction equivalent.
The purpose of this project was to develop a middle school curricular unit which utilized integration of conceptual content and constructive teaching strategies to significantly improve student comprehension of identified mathematics and scientific concepts and subconcepts. The unit developed for this purpose focused on the concept of density. The project utilized 12 hands-on laboratory investigations which maximized student involvement. The unit introduced mathematical and scientific concepts and subconcepts progressively, spiraling previous data to aid in the sense making of new and more challenging information.
The integration of a mathematical strand of measurement and calculation, necessary for the interpretation of the scientific data generated by the laboratory experiments, also led students to realize the essential role mathematics plays in conceptual understanding. Embedded, often informal, daily assessment allowed early identification of misconceptions, giving rise in turn to extensions and opportunities to remediation.
A field test of the unit was conducted with three eighth grade classes and one seventh grade class. Prior to, and immediately following, the field test, pretests and posttests of mathematical and scientific concepts and subconcepts, were administered. Of the two science tests administered, one was an informal evaluation which consisted of group definitions and illustrations of density and its subconcepts, as well as volume, mass, and measurement.
The second science test consisted of a question essay evaluation which required students to define and explain terms and concepts. A question math test, based upon measurement and the utilization of scientific measurement tools, density calculations, and the interpretation of graphic data, was administered and evaluated. The data generated by the pretests and posttests were analyzed statistically.
Academic growth and understanding, as evidenced in the analysis, were significant. This information supports the efficacy of constructive methods of education coupled with integrated, conceptual, curriculum. All students showed increased knowledge of the limit of the difference quotient definition of the derivative that could be attributed to the multiple choice problems.
All students showed their strongest understanding of the derivative in a graphical sense in terms of the slope of a tangent line.
Master's Thesis in Mathematics Education
Those students who took a more active role in the free-response problems showed a greater knowledge of the derivative than those who did not. Among those who took an active role, students who recognized the value of these problems showed even greater knowledge. The focus of this project was to develop a series of concrete lessons and to evaluate the impact of these materials on student performance in preparing them for their first year algebra course. The project materials consisted of a problem-solving unit taught at the beginning of the school year, several Problems of the Week to assess algebraic thinking, and six focused lessons to develop understanding of variables, expressions and equations.
Two pretests and posttests were administered to evaluate the effectiveness of the materials. The data analysis showed these materials were effective in the setting of this project, thus they will be made available to other middle school teachers. This study was designed to develop and field test a set of lessons in 1s, 10s, and s place-value for third, fourth and fifth grade students for use by classroom teachers.
Most lessons at the elementary concept level in place-value are part of second and third grade curriculum. Yet research has shown that a high percentage of fourth and fifth grade students do not understand the basic concepts of place-value Ross, ; U. Department of Education, Five problems with imbedded assessment and a pre-post assessment task were developed and field tested in five classrooms in the spring of The field testing was a collaborative action research model with the field test teachers contributing to the development of the lessons.
The teaching model used small group work with minimal teacher intervention followed by presentations to the class by each group. Teachers guided but did not direct the instructions. Included in the appendix are the lessons, a set of field test teacher beliefs, sample teacher dialogue, and the results of a field test teacher questionnaire.
The results of the field test were positive based on the responses of the participating teachers. However, limitations of the study include lack of a control group, homogeneous cultural make-up of the classrooms, high dependence of the lessons on language, the length of the study, and the narrow focus of the place-value topics. The research team consisted of the author and Sharon H. Ross, Associate Professor of Mathematics.
Ross is preparing a research paper to report the student outcomes in understanding place-value. According to California mathematics standards, the use of history in mathematics classes has been de-emphasized. At the same time, however, research shows that student interest in mathematics is an indicator of student achievement. Internationally, the use of history to enhance mathematics instruction has gained in popularity.
The challenge to have all students successfully comprehend Algebra I has placed an increased value on raising student interest in this subject. A review of literature has been included to show that algebra has evolved through an interesting, interconnected history of people and ideas. Some researchers maintain that the stages of this history correlate with the way students learn. Other educators who have implemented history in the classroom found positive influences on student attitude.
The purpose of this research was to assess the effect that four lessons involving the history of mathematics would have on motivating Algebra I students. Data from this project could be used to support math instruction that integrates math history into the standard curriculum.
Master's Theses | Department of Mathematics
The tested lessons provide direction or ideas for how to add math history to the curriculum. The four lessons, which included personal stories and ideas about four famous mathematicians were tested in three high school Algebra I classrooms during the school year. Statistical analyses indicate that the students who were exposed to the history had a more positive opinion of mathematics than those who were not given the history lessons. Our Office Location Icon.
Arata Summer This study was designed to develop and field test a set of materials integrating chaos theory and fractal analysis into the precalculus curriculum.