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 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.

The problem of this study was to determine if the teachers of Algebra I rated highest and lowest according to the Texas Teacher Appraisal System differed significantly in a measure of achievement. The analyses indicated that there were significant differences in achievement between the classes taught by the highest and lowest ranked teachers.

The purpose of this study was to investigate the nature of mathematical connections used by selected teachers when teaching the topic of algebra and to investigate their perceptions of their use of connections. The participants were selected on the basis of teaching experience as well as their willingness to share their ideas. An interpretive paradigm was used to collect and analyse data. The data was collected from three participating teachers. These participants were selected from the three secondary schools in the town of Tsumeb in Namibia. I used video recordings of two lessons per teacher as well as semi-structured interviews as my tools to gather data. After the two lessons were video recorded, I conducted a workshop with the teachers to introduce them to the 5 types of mathematical connections pertinent to this study. We analysed the videos together using Businskas' framework as a basis for analysis. This then formed part of the stimulated recall interviews. It was found that, even though teachers were not aware of the concept of mathematical connections before our interactions, there was strong evidence of connections being made and used in their lessons. The two types of connections that were used most frequently (24.1 percent each) were procedural and instruction-oriented connections respectively. Part-whole relationships connections were used the least with a frequency of 12 percent. All three teachers agreed that they needed to make more connections when teaching and that they would think more about connections in future, particularly when preparing their lessons. The study makes recommendations to encourage the continuous use of connections in teaching mathematics.

The purpose of this study was to investigate the effectiveness of carefully designed teacher training in the use of the computer to teach graphing skills associated with Algebra II conic sections. Three areas were studied: the teachers' attitude toward mathematics, and the effect on students' achievement in the area of graphing skills.

Thesis (MEd)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: According to Prins(1995), readability factors in Mathematics text do not only influence the comprehension of questions, but also have a marked influence on learner achievement levels. Extending on Prins (op cit), this study sought to investigate whether there are any differences in the quality of interpretation and choice of algo-heuristic methods when isiXhosa-speaking learners respond to mathematical word problems set in English and isiXhosa. The study was located within an ethnographic framework, with all of the 109 participants speaking isiXhosa as LI. The participants were in grades 8 (44), Grade 9 (29) and grade 10(36) and all took Mathematics as one of their school subjects. Learners were divided into four groups based on achievement levels in English in June examinations. The study was cross-sectional, with each of the four groups comprising learners who were good achievers, average achievers and under achievers in English second language. A unique methodological and data collection design was undertaken in such a way that each of the participants responded to word problems set in both English and isiXhosa. Two questions were administered to all learners (one in each of the two languages). The two questions were written in two sessions. If a learner responded in English during the first session, s/he will respond in isiXhosa during the second session and vice versa. There was a 5-minute break in between the sessions. Data was analysed both quantitatively and qualitatively. The broad focus of the analyses was on learners' quality of interpretation of the given word problems and the choice of computational methods they employed when they responded to the word problems. Three categories were investigated under each of the focus areas. Categories investigated under the quality of interpretation were: [J Totally false interpretation [J Partially correct interpretation and [J Totally correct interpretation Categories investigated under the choice of computational methods were: [J Standard methods [J Non-standard methods [J Unidentifiable methods The evidence gathered suggested that isiXhosa-speaking learners interpret word problems better when they are set in isiXhosa rather than English. Another important finding was that isiXhosa-speaking learners prefer to use standard methods when they respond to word problems set in English and also prefer to use non-standard methods when they respond to word problems set in siXhosa. / AFRIKAANSE OPSOMMING: Volgens Prins (1995) beïnvloed leesbaarheidfaktore in Wiskundetekste nie net die verstaan van vrae nie, maar het dit ook 'n merkbare invloed op leerders se prestasievlakke. Ter uitbreiding op Prins (op cit) het hierdie studie gepoog om ondersoek in te stelof daar enige verskille in die kwaliteit van interpretasie en keuse van algo-heuristiese metodes is wanneer isiXhosasprekende leerders op wiskundige woordprobleme reageer wat in Engels en isiXhosa gestel is. Die studie is binne 'n etnografiese raamwerk geplaas. Al 109 deelnemers het isiXhosa as eerste taal gepraat. Die deelnemers was in Graad 8 (44), Graad 9 (29) en Graad 10 (36) en het Wiskunde as een van hul skoolvakke geneem. Leerders is in vier groepe verdeel, en die indeling is op prestasievlakke in Engels in die Junieeksamen gebaseer. In hierdie deursneestudie het elk van die vier groepe uit leerders bestaan wat goeie presteerders, gemiddelde presteerders en onderpresteerders in Engels tweede taal was. 'n Unieke metodologiese en data-insamelingsontwerp is op so 'n wyse toegepas dat elkeen van die deelnemers op woordprobleme gereageer het wat in beide Engels en isiXhosa gestel is. Twee vrae is aan elke leerder gestel, een in elk van die twee tale. Die twee vrae is in twee sessies beantwoord. As 'n leerder tydens die eerste sessie in Engels reageer het, sou sy/hy tydens die tweede sessie in isiXhosa beantwoord, en omgekeerd. Daar was 'n pouse van vyf minute tussen die sessies. Data is beide kwantitatief en kwalitatief ontleed. Die breë fokus van die analises was op die kwaliteit van die leerders se interpretasie van die woordprobleme en die keuse van bewerkingsmetodes wat hulle aangewend het wanneer hulle op die woordprobleme reageer het. Drie kategorieë is in elk van die fokusareas ondersoek. Die kategorieë wat onder die kwaliteit van interpretasie ondersoek is, was: Cl 'n Algeheel verkeerde interpretasie Cl 'n Gedeeltelik korrekte interpretasie en Cl 'n Algeheel korrekte interpretasie Kategorieë wat onder die keuse van bewerkingsmetodes ondersoek is, was: u Standaardmetodes u Nie-standaardmetodes en o Onidentifiseerbare metodes Die gegewens wat ingewin is, het daarop gedui dat isiXhosasprekende leerders woordprobleme beter interpreteer wanneer die probleme in isiXhosa eerder as in Engels gestel is. 'n Ander belangrike bevinding was dat isiXhosasprekende leerders verkies om standaardmetodes aan te wend wanneer hulle op woordprobleme wat in Engels gestel is, reageer, en dat hulle ook verkies om nie-standaardmetodes te gebruik wanneer hulle op woordprobleme reageer wat in isiXhosa gestel is.

One purpose of this study was to determine whether any differences in immediate achievement or retention existed between students using manipulatives and students not using manipulatives. Also addressed in this study is whether or not the use of manipulatives is more beneficial for girls than boys and whether the use of manipulatives is more beneficial for low-ability students than for high-ability students. Students selected for this study were from a large suburban school district in Texas. The students were from eight intact classes, four of which were designated as the experimental group and the other four as the control group. The sample consisted of one hundred eighty-seven students. All students were tested with a test developed by the researcher. This same test was administered as a pretest, posttest, and retention test. The following supplemental data were also gathered on the students: mathematics scores from the California Test of Basic Skills and scores from the mathematics section of the Texas Educational Assessment of Minimum Skills test. Analysis of the data revealed no statistical difference in the mean scores of students instructed with or without manipulatives when the test was administered immediately after instruction. Nor was there any statistical difference in the mean scores when the test was administered two months after instruction. There was no statistical difference in the mean gain scores from the pretest to the posttest between boys and girls or between high- and low-achieving students. Nor was there any statistical difference between the mean gain scores from the pretest to the retention test between boys and girls or between high- and low-achieving students. It is recommended that further studies be conducted to investigate achievement and retention of students using manipulatives at the secondary level. It is also recommended that variables other than achievement be studied to determine the effects of manipulatives on secondary students.

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