This study focused on the evaluative listening practices of four teachers who participated in an algebra professional development involving lesson study. This instrumental case study operationalizes the enactment of teacher listening followed by teacher questions and responses to define listening-to-question. Also, questioning-to-listen is operationalized as the enactment of purposefully posing questions to posture oneself to listen to students' mathematical thinking. Because of the tacit aspect of teacher listening and the visibility of teacher questioning, interrelating listening and questioning affords teachers an accessible point of entry into developing listening practices. In response to participants wondering as to when evaluative listening is appropriate in the mathematics classroom, this study discusses six instances of teaching excerpts along a continuum of listening orientations from directive to observational to responsive. The results indicate positive aspects of evaluative listening towards an observational and responsive listening stance. Results of the study also confirm a reliance on low-order gathering information questions as the predominant type of teacher question posed in mathematics teaching. This study reveals the necessity of contextualizing teacher questions to inform appropriate uses of evaluative listening. Future professional development should consider emphasizing positive aspects of evaluative listening in mathematics teaching.

This study examined success rates and end-of-semester grades for three instructional methods used in developmental algebra and college algebra. The methods investigated were traditional lecture, laboratory, and computer mediated learning. The population included the 10,095 students who had enrolled in developmental algebra and college algebra at Richland College in Dallas, Texas, for five semesters. Success was defined as earning a grade of A, B, C, or D in a course.

"The problem of this study was to test the hypothesis that the use of certain visual aids will improve instruction in algebra. Two experiments were devised. In the first simple balance scales were used and in the second models were used. The experimenter also wished to learn through the testing of this hypothesis how to conduct such a study"--Introduction. / Typescript. / "August, 1950." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements of the degree of Master of Arts." / Advisor: H. A. Curtis, Professor Directing Paper. / Includes bibliographical references.

In this study, a community of high school Common Core Algebra I teachers in a socio-economically and racially diverse suburban high school participated in a lesson study process facilitated by an instructional coach to design curriculum for an algebra lab model. The model was intended to address issues of equity and access in mathematics education, which incorporated skills support, social-emotional learning, and authentic tasks to help students needing additional support succeed in a de-tracked Common Core Algebra I course. Pedagogical strategies were examined through the lens of “Danielson’s Framework for Teaching,” an instrument used to promote highly effective instructional strategies and evaluate the quality of teaching; this framework was used as a lens to construct authentic task lessons and assess teacher practice. A major finding was that an emphasis on skills support and social-emotional learning promoted increased participation and student achievement in the Common Core Algebra I course; an overemphasis on authentic tasks in the lab course was found to be counterproductive. Peer observations, collaboration, and instructional coaching were also found to be highly impactful and vital to the curriculum development process and enhancement of teacher practice. To ensure a productive lesson study process, the researcher advises school leaders to consider tenets of adult learning theory and teachers’ capacity for transformational learning when selecting teachers to develop and implement innovative curricular and instructional approaches.

Standardized aptitude and achievement tests are often accompanied by directions which recommend skipping items perceived as difficult and returning to answer them if time permits. Prior to the present study, the only empirical research in this area was a single study concerning the effects of examinee decisions to follow or disregard these instructions. It was the conclusion of this research that it was to the advantage of high ability examinees to follow the instructions to skip but that conformity to the instructions was disadvantageous to middle and low ability examinees. The present study, in contrast, was concerned with the effects of differing instructions concerning skipping and was quasi-experimental in design. The sample consisted of 423 eighth through twelfth grade students of algebra and biology. Intact classes representing three ability levels were assigned at random to treatment conditions consisting of instructions to skip, not to skip, and with no advice concerning skipping (only “skip” and “do not skip” instructions for the algebra classes.) Schoolwide tests were administered using special answer sheets designed to identify skipped items even when examinees later returned and answered some or all previously skipped. The scores from these tests were used in determination of end-of-course grades. The primary dependent variables were number-right test scores and the number of items skipped. For each subject area, two, two-way factorial analyses of variance evaluated the effect of the differing instructions across ability levels, one for the number-right scores and one for the number of items skipped. For the algebra test, there was no significant treatment effect for number-right scores. However, there was a significant interaction (p≤.01) between ability level and treatment, with high ability examinees receiving “do not skip” instructions performing significantly worse than their counterparts who received “skip” instructions. For the biology test scores, the main effect for treatment and its interaction with ability were not significant (p>.05). For the number of skips in both algebra and biology, the main effect for treatment was significant (p<.01), with the fewest skips in the “do not skip” groups. In addition, for the number of skips in algebra, the main effect for ability was significant (p<.05) with the fewest skips in the middle ability group. While the instructions apparently had their intended effect, and while the treatment-ability interaction in algebra was consistent with the findings of prior research, the number of items skipped by groups instructed to do so were not large, and groups instructed not to skip had meaningful number of skips nevertheless. Thus it was not surprising that neither the biology scores nor the algebra scores differed significantly according to treatment. Extensive secondary analyses of item and other statistics provided no basis for explaining the interaction between ability and treatment for the algebra scores. It was concluded that instructions to skip items had relatively little effect for tests of the type employed in this study. / Ph. D.

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The purpose of this study was to compare the effects of Web-based learning (WBL) versus those of traditional instructor-based learning (IBL) on student knowledge and satisfaction based on student learning styles. Other goals were to determine if WBL is more effective for those with a particular learning style. The study examined a sample of undergraduate students who were enrolled in the college algebra offered as both oncampus instructor-based (traditional) and Web-based at the university of North Texas (UNT). A total of 36 Web-based students and 58 instructor-based students participated in this study. This study utilized a posttest-only intact group. The Kolb Learning Style Inventory (LSI) measured the learning styles of students. This study used learning methods (Web-based learning (WBL), instructor-based learning (IBL)), and learning styles (Diverger, Converger, Assimilator, and Accommodator) as independent variables. Student knowledge and student satisfaction was measured at the end of the course as independent variables. Based upon the results of the LSI, post-learning exam, and satisfaction a series of two-way analysis of variance (ANOVA 4x2) techniques and independent variable tests was used for each of the dependent variables, knowledge and satisfaction, based on a student's learning styles. The results revealed that students' learning styles were statistically significant for knowledge when learning on the Web versus instructor-led. In addition, the learning style was important factor for Web-based learning. The results indicated students with Assimilator and Converger as learning styles received better result with the Web-based learning method. Furthermore, this study found there is significant difference in student satisfaction based on learning on the Web versus instructor-led. The outcome of the study could be of particular interest in educational institutions; especially those that want to transfer some of their traditional courses onto the Web. The finding also has implications for training organizations as they seek efficient and effective ways to satisfy their training needs.

The problem of this study was to determine the extent to which certain characteristics of teachers of first-year algebra were related to a) their pupils' attitudes toward algebra and b) their pupils' achievements in algebra. An additional aspect of the study was to ascertain and study the differences between Anglo- and Latin-American pupils' attitudes and achievements in algebra.