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The purpose of this grounded theory study was to discover the factors that contribute to the success or failure of college algebra for students taking college algebra by distance education Internet, and then generate a theory of success or failure of the group of College Algebra Internet students at one Utah college. Qualitative data were collected and analyzed on students’ perceptions and perspectives of a College Algebra Internet course that they took during the spring or summer 2006 semesters at a bachelor’s degree-granting college in Utah. The participants were chosen from any of the six sections, and purposeful sampling was applied. Interviews played a major role in data collection. Each interview took place in person and was taped and later transcribed for analysis. The outcomes showed that one theme emerged as the catalyst for success for a College Algebra Internet student, that of self-responsibility. Four other themes found in the data helped, but were not necessary for success. Many enrolled based upon past experiences with personal environmental factors. It also helped to have a solid mathematical background, a good attitude, and a strong structural support network. However, those participants who prioritized and devoted their time to enriching their mathematical skills and staying focused on the goal had the most success in the course regardless of any other factor. By setting aside time and staying completely devoted to the course from the very beginning established, above all else, a successful outcome. Motivation to continue in this path occurred either from an outside influence or by an innate drive to be successful in the course.

There has been much attention about improving the skills and abilities of students in Science. One critical factor is the quality of teacher education programs for preparing science teachers. There has been little research and much debate about what constitutes an effective science teacher education program. Teacher beliefs are thought to be important factors which influence how science teachers teach. This is a three year longitudinal study which explores changes in twelve teachers using a mixed method design. Semi-structured interviews were used to explore the beliefs about teaching, learning, and the Nature of Science. Four cohorts of teachers represented the different critical stages of the teaching continuum. Two cohorts of teachers represented entry and exit stages of preservice education. The other two cohorts represented teachers who taught less than four years and more than four years in the classroom. Classroom observations and self-reported surveys were gathered. The major outcomes of this research include: 1) Teacher beliefs about teaching and learning shift towards being more student-centered during their preservice education; 2) Despite previous reports that most graduates revert to teacher-centered beliefs in the first years of teaching, the beliefs of Iowa preservice teacher beliefs, remained similar to their previous student-centered beliefs 3) Teacher beliefs about the Nature of Science, which were initially represented as a socially constructed entity, became less frequent as teachers progress through the teaching continuum from preservice to inservice teachers; 4) Student-centered beliefs about teaching and learning, derived from teacher interviews, are correlated with classroom observations and self-reported surveys of instructional strategies. The findings from this study shed light on understandings concerning the evolution of teacher beliefs. Factors effecting teacher beliefs include college preparatory education programs, school communities, and the individual teachers themselves. There is a need to continue explorations of how these factors are interrelated, as well as how to influence and sustain the development of reformed-based beliefs about teaching and learning in order to influence instructional practices.

The purpose of this study was to investigate the relationship between addition and subtraction as inverse operations, to determine how drill in addition facts will affect knowledge of subtraction facts; to infer, if possible, when addition is conceptualized as an operation with reversibility; and to determine at which grade levels a particular method of drill is effective. The sample was drawn from Logan, Utah , small, city school district of 3700 students. The experimental groups consisted of 12 elementary and eight secondary existing classrooms of students. The control groups consisted of 10 elementary and five secondary existing classroom groups. A total of 1007 elementary and secondary students were involved in the study. The sample included treatment and control groups from first through the ninth grades. The treatment consisted of administering drill on the addition facts, to classroom groups using the overhead projector. All students were tested three times, at the beginning of the study, after one week and after two weeks; using two tests, an Addition Facts Test, which contained the 100 basic addition facts, and a Subtraction Facts Test which contained the 100 basic subtraction facts. Four scores were considered for each test; "time'', the "number left out", the "number missed", and the "total error". Gain scores showing loss or progress from the pretest to each of the two posttests were computed for each of these four scores. All groups corrected their own test papers immediately after taking the tests . The statistical analysis included the following: Correlation coefficients were computed between addition and subtraction scores for each of the four scores mentioned. Correlation coefficients were computed between the addition and subtraction scores for each gain score. Two-way analyses of variance were computed for grade level effect and treatment effect for each of the 16 gain scores. The results included: The correlation coefficients for addition and subtraction "time" scores were positive and significant at every grade level. The correlation of the first grade, .30, was significantly lower than that of the second grade, .72. The correlations showed an increasing trend to .87 at the seventh grade, then a falling off in the eighth and ninth grades. The correlation coefficients for addition and subtraction error scores were positive and significant for the "number left out" and "total missed" scores for grades one through seven. For the two posttests, the correlation coefficients for the "time" gain scores from the first grade were negative. They were positive and significant for grades two, four, five, seven, and eight. The results for the correlation of error gain scores were mixed. Of the 16 two-way analyses of variance for gain scores, five showed significant F ratios, two were concerned with addition and three with subtraction; four analyses showed significant grade level effect, three analyses showed significant treatment effect, and two showed significant interaction. On nine scores there were large differences between fir s t and second grade grou ps . The results are consistent with what one would expect if first grade students had not formed the concept of addition as an operation with reversibility. The results are consistent with what one would expect if: at the second grade level, addition were conceptualized as an operation with reversibility for a good portion of the students, yet the r e were a good number for whom this reversibility were limited or inoperative; the concept of addition as an operation continued to develop with a more pronounced reversibility during grades three and four. It was concluded that: First grade children do not possess the requisite understanding to profit from drill of the type used in this study. Second grade students have a good start on understanding and can profit from practice experiences in addition and subtraction. Maximum gains were made in third and fourth grade gr oups with the type of drill used in the study.

This study investigated the learning of middle school mathematics teachers as they worked in a student-sensitive lesson study group. Three mathematics teachers collaborated to develop and teach student-sensitive math lessons. The original Japanese lesson study model was extended to involve a diversity consultant with experience and expertise in providing student-sensitive instruction. Collaboratively, the members of the lesson study group tailored their mathematics lessons to provide enhanced mathematics instruction to the diverse groups of students in their classrooms. The lesson study team held weekly meetings to develop three student-sensitive lessons over a six-month period. A case study design was used to allow an in-depth examination of teachers’ participation in the student-sensitive lesson study, with the researcher being the tool of investigation. Data were collected from observations, interviews, and group-produced documents. The findings of the study indicate that the student-sensitive lesson study stimulated in-depth mathematical discussions among participants and prompted a re-evaluation of the teachers’ own mathematical knowledge. While in collaboration with the diversity consultant, the teachers worked to include student-sensitive context in mathematics lessons, and considered the critical role of high student expectations as part of student-sensitive mathematics teaching. The group engaged in reflection on their participation in student-sensitive lesson study, and they further considered factors that affected their knowledge and practice of improved mathematics teaching.

This study examined six novice pre-service secondary science teachers’ lesson planning processes when designing instruction while enrolled in a spring education course prior to their student teaching. Six novice pre-service secondary science teachers enrolled in an education course during the spring semester prior to their student teaching. During the course, participants were introduced to the lesson planning software, Tennessee’s Next Generation Tools for Teaching Standards-Based Science, version 1.4 (Jordan & Audet, 2007). This software provides resources, sample lesson plans, and links lesson planning with four science reform documents, Benchmarks for Science Literacy (American Association for the Advancement of Science, 1993, p. 4), Science for All Americans (American Association for the Advancement of Science, 1990), National Science Education Standards (NSES) (National Research Council, 1996), and Tennessee Curriculum Standards (Tennessee Department of Education, 2007). Participants used this software to write their first science lesson plans. The focus of this research was to examine the processes novice pre-service teachers pursue as they engage in lesson planning and the sources that influence their planning decisions. Findings are as follows: 1) novice pre-service secondary science teachers acknowledged the importance of Standards but planned in a sequence that found lesson activities before objectives; 2) despite similar experiences with a science lesson plan template, students used two different approaches to lesson planning; 3) science education reform documents were consulted by all participants when writing lesson plans, however participants did not find all of the science education reform documents to be beneficial.

This quantitative study explored whether or not the mathematics curriculum and instruction of the schools in the TennGaLina cluster were impacted by the place-based educational reform promoted by the Annenberg Rural Challenge. The study focused on the programs of five small rural Southern Appalachian schools. Qualitative methods of grounded theory were used to analyze data from interviews, surveys, and school artifacts.