The purpose of this study was to examine how second graders use writing and language when they are learning to add multidigit numbers in mathematics class. Second grade students were taught addition conceptually with a focus on sharing their strategies and thought processes with each other during the mathematics lesson. Two social norms were established with students so that sharing information and asking for clarity when they did not understand would be natural and expected. Students kept a daily mathematics journal to answer the class's Problems of the Day. Patterns found in student journals indicated three stages of multidigit learning. In Stage One, students used little or no words to explain their solution, illustrations show students using counting by ones strategies. Stage Two represents students using appropriate mathematics strategies and vocabulary to explain their solutions in detail. Lastly, Stage Three consists of students solving multidigit problems with little or no word explaining their solution process and illustrations are few. Results of the study indicated that students' oral explanations of solutions to addition problems included more detail compared to students' written justification of similar problems.

Teacher preparation programs invest significant resources to influence the beliefs of preservice teachers, including clinical faculty who mentor preservice teachers during practicum experiences. Despite the work of university personnel to guide preservice teachers' beliefs, their influence wanes once preservice teachers cross the threshold into inservice teaching. New mentors, including mentor teachers, instructional coaches, and administrators take the place of university personnel. This quantitative study examined how the beliefs of 77 novice inservice teachers changed toward reform-based mathematics instruction during their first year of teaching. Of the 77 subjects, 50 were interns and 27 had completed student teaching. Near the end of their first year of teaching, subjects were surveyed for their current beliefs at the time of completing the survey. Their beliefs from the time immediately preceding the beginning of their first year of teaching were measured retrospectively. During their first year, school-based personnel served as their "˜transitional faculty' as they supported the novice teachers' teaching experiences. The novice inservice teachers' perceptions of the transitional faculty's beliefs and support, as well as the alignment of their curriculum materials, were also surveyed. Relationships between changes in the beliefs of the novice inservice teachers and their perceptions of their transitional faculty and curriculum were examined. The overall belief means for novice inservice teachers decreased, the extent of which is statistically significant. Analyses of covariance revealed that the perceived beliefs and support of transitional faculty played a statistically significant role in the belief change of novice inservice teachers, as did their curriculum materials. This study highlights the importance of creating systems to improve mentor selection and training so the work of university personnel is not undone during the novice's first year of teaching.

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The problem with which this study is concerned is that of comparing the results of teaching community college students enrolled in a transferable mathematics sequence for business and economics majors by a computer-aided instructional program and by the traditional lecture method. In order to effectively resolve this problem, an A Programming Language System 360 (APL/360)-aided instructional program was developed and an experimental study was conducted. The APL/360-aided instructional program consisted of three sets of materials.: a manuscript on APL/360, a list of APL programs defining operators relevant to a computer-aided study of calculus, and a collection of problems based on these programs and calculus concepts. The subjects for the experiment were forty-four students enrolled in three sections of Mathematics 112 at Mountain View College of the Dallas County Community College District. The control group, students taught by the traditional lecture method, consisted of twenty-one students. The experimental group, students taught by the APL/360-aided instructional program, consisted of twenty-three students. The same instructor taught all students. The essential difference in the two teaching methods was the use of the computer as a teaching-learning aid in the computer-aided instructional program. The computer was a course supplement to classroom instruction and aided students in obtaining insight into the nature of mathematical concepts as well as serving as a computational aid.

Made available in DSpace on 2016-04-04T18:33:01Z (GMT). No. of bitstreams: 1 Romildo Alonso.pdf: 470624 bytes, checksum: 99056acabaecbe6f54e0370d7004c4d6 (MD5) Previous issue date: 2003-12-16 / This paper is part of a research project called University, Teaching and Teacher Education, the reason for having chosen this subject being the fact that the Educational Projects usually are very well written, but not transferred into practice. This may be due to the lack of (1) a supporting team, (2) teachers knowledge about the Project and (3) participation of students in creating the Project. The aim of this investigation at the graduation course in Mathematics at Funda??o de Ensino Oct?vio Bastos is to discover the educational and teaching concepts professed by the teachers of future mathematics teachers, based on the Educational Project, of the legal requirements and research in the area. A survey questionnaire with objective questions was used for collecting initial information; later on, interviews were held with the same teachers. Analysis of the data revealed distances and closeness of their concepts and praxis to the Educational Project and to the latest research on teacher education. It was suggested that collectively at FEOB, and especially at the Mathematics graduate course, efforts be made to modernize the course according to requirements of this new century. This research contributed to direct the same reflections and proceedings used here to similar graduate institutions for teacher training. / Este trabalho est? vinculado ? linha de pesquisa Universidade, Doc?ncia e Forma??o de Professores, e justifica-se pelo fato de os Projetos Pedag?gicos das institui??es de ensino superior serem, de uma maneira geral, bem elaborados, mas n?o seguidos dentro das propostas que os caracterizam. A falta de um grupo de apoio, o seu pleno conhecimento por parte dos professores e a n?o participa??o do corpo discente na sua elabora??o t?m sido os motivos pelos quais as atividades escolares n?o contemplam as diretrizes propostas para a consolida??o do aprendizado. O objetivo desta pesquisa, que tem por locus a Funda??o de Ensino Oct?vio Bastos FEOB Curso de Licenciatura em Matem?tica, ? investigar as concep??es de educa??o e de ensino dos professores formadores de professores, considerando o Projeto Pedag?gico da Institui??o, especialmente o do Curso de Matem?tica, as exig?ncias legais e as pesquisas na ?rea. Para coleta dos dados, utilizou-se primeiramente de um question?rio composto por quest?es objetivas e, posteriormente, de entrevistas, ambos aplicados aos professores. A an?lise dos dados permitiu verificar distanciamentos e aproxima??es de suas concep??es e pr?ticas com o Projeto Pedag?gico e com a literatura atual sobre forma??o de professores, assim como foi poss?vel sugerir direcionamentos para a organiza??o de um trabalho coletivo na FEOB, e particularmente no Curso de Licenciatura em Matem?tica, visando a moderniza??o do curso dentro das exig?ncias da sociedade considerando os desafios do s?culo XXI. As contribui??es desta pesquisa est?o no fato de que as reflex?es sobre os resultados obtidos possam nortear reflex?es e procedimentos de mesma natureza em Institui??es Superiores de forma??o de professores e similares.

This qualitative study explored a mathematics workshop for parents and the impact on a parent’s mathematical content knowledge in rational numbers, perceptions of current instructional practices, and parental beliefs in supporting their children in learning mathematics. A 6-week parent workshop on rational numbers was offered in a rural middle school. Data sources included interviews and workshop audio transcriptions. This study concluded that a mathematics workshop supports parents in developing a conceptual understanding of rational numbers and rational number operations. Furthermore, parents recognized the importance of discourse, representation, and justification for building conceptual understanding in mathematics. Parents, who participated in the workshops, were more open to the use of standards based instructional practices for developing conceptual understanding. Parental engagement in mathematics should include discourse at home to help students justify and explain their thinking. Questions related to the teaching of non-standard procedures without building a conceptual understanding hindered many parents from completely accepting new instructional practices.

ABSTRACT The main purpose of this study was to investigate whether conducting a short-term online review of college algebra prerequisite skills at the start of a college algebra course concurrently with the normal course instruction and assignments would have a significant influence on student success. When failure rates in an entry-level college course such as college algebra can range from 20% to 60% or higher, it could present problems for the student and the institution (Burd & Boser, 2009). Research indicates that students who cannot pass entry-level college math courses have decreased chances of obtaining a college degree and it can limit the students' course of study (Adelman, 1999; Thiel, Peterman, & Brown, 2008). While several factors have been found to influence college algebra success, such as instructional practices, students' attitudes toward mathematics, and level of math anxiety, a secondary purpose of this study investigated whether students' gender and number of prior attempts at taking a college algebra course were factors that might interact with student performance. A quantitative study was conducted in the researcher's college algebra class at the University of South Florida in the fall semester 2010. The design included a treatment group and control group; participants in both were given a pretest and posttest before and after the 4-week treatment period, and all participants took the required departmental final exam. Of the original 187 participants in the study, the final statistical analyses were computed using data from the 165 students who completed the pretest, posttest, and final exam. Participants who were randomly assigned to the treatment group received an online review of college algebra prerequisite skills using the program, MyMathTest (Pearson Education, n.d.b), which included interactive instruction and practice with a minimum requirement of 3 hours per week for the 4-week treatment period; participants who were randomly assigned to the control group received an alternative assignment based upon their college algebra coursework using the online program, MyLabsPlus (Pearson Education, n.d.a) that accompanied the class textbook, with a comparable weekly time requirement. After the four-week treatment period, the remaining 11 weeks consisted of the normal course of study and concluded with a comprehensive departmental final exam not prepared by the course instructor. No significant differences in achievement on the final exam were found between the two groups. Also, there were no interaction effects and no main effects for gender and performance on the final exam. Number of prior attempts at college algebra similarly had no impact upon final exam. However, student achievement in the researcher's class was observed to be higher than that found in the other college algebra classes in the department (i.e. the researcher's students performed higher on the departmental final exam and had a lower failure rate than the overall departmental failure rate). The fact the researcher's college algebra students had greater success when compared to the other college algebra students would suggest other possibilities for future regard. For example, studies comparing use of alternative instructional strategies and/or grading practices may reveal factors that influence college algebra performance. Investigations comparing alternative placement procedures and/or advising strategies might also contribute findings helpful to promoting student success in college algebra.

In the realm of academic engagement research, students are valuable sources of information to learn how and why students often engage unproductively in mathematics group work. However, although secondary mathematics students are often expected to engage in meaningful mathematical discourse in a small group setting, little research has been conducted to better understand student engagement in this setting from the perspective of the students themselves. This thesis attempts to understand how one junior high student described his own engagement in mathematics small group work as well as what factors influenced this engagement. By conducting several cycles of observations and interviews followed by qualitative analysis, we learned how this student engaged in a variety of ways in group work; on different occasions (and sometimes within the same class period), he talked with his peers about mathematics, remained silent, played on his phone, connected with peers across the room, and pursued off-topic conversation with his group mates. We also discovered that the student participant as well as his peers often ceased to engage productively when they encountered mathematics that they deemed too difficult. Several other factors impacted his engagement in complex ways, including his familiarity with group mates, fear of being singled out, and access to adequate help from a teacher. These results may inform researchers of new data collection and analysis methods to gain insights into student engagement and teachers of ways in which they may adapt instruction to better encourage students to engage productively.

While the use of student thinking to help build mathematical understandings in a classroom has been emphasized in best teaching practices, teachers still struggle with this practice and research still lacks a full understanding of how such learning can and should occur. To help understand this complex practice, I analyzed every instance of student thinking and every teacher response to that thinking during a high school geometry teacher's whole class discussion and used these codes as evidence of alignment or misalignment with principles of effective use of student mathematical thinking. I explored the teacher's practice both in small and large grains by considering each of her responses to student thinking, and then considered the larger practice through multiple teacher responses unified under a single topic or theme in the class discussion. From these codes, I moved to an even larger grain to consider how the teacher's practice in general aligned with the principles. These combined coding schemes proved effective in providing a lens to both view and make sense of the complex practice of teachers responding to student thinking. I found that when responding to student thinking the teacher tended to not allow student thinking to be at the forefront of classroom discussion because of misinterpretation of the student thinking or only using the student thinking in a local sense to help advance the discussion as framed by the teacher's thinking. The results showed that allowing student thinking to be at the forefront of classroom discussion is one way to position students as legitimate mathematical thinkers, though this position can be weakened if the teacher makes a move to correct inaccurate or incorrect student thinking. Furthermore, when teachers respond to student thinking students are only able to be involved in sense making if the teacher turns the ideas back to the students in such a way that positions them to make sense of the mathematics. Finally, in order to allow students to collaborate a teacher must turn the mathematics to the students with time and space for them to meaningfully discuss the mathematics. I conclude that the teacher's practice that I analyzed is somewhat aligned with honoring student mathematical thinking and allowing student thinking to be at the forefront of class discussion. On the other hand, the teacher's practice was strongly misaligned with collaboration and sense making. In this teacher's class, then, students were rarely engaged in sense making or collaborating in their mathematical work.

During the last several decades, mathematics reform has emphasized the goal of ensuring that students develop both conceptual and procedural understanding in mathematics. The current mathematics reform, Common Core State Standards for Mathematics (National Governors Association and the Council of Chief State School Officers [NGA Center & CCSSO], 2010), promotes this goal, with procedural knowledge building upon a strong conceptual base. This study uses content analysis to investigate the extent and ways in which Houghton Mifflin Harcourts Go Math! K-8 (HMH, 2016) supports teachers in building procedural fluency from conceptual understanding when teaching equivalence of fractions.Krippendorfs (1980) framework for content analysis guided this study. I identified a priori codes, and allowed for emergent codes, that characterize quality mathematical instruction. Careful analysis of the teacher editions of the textbook series revealed that, if the teacher instructions are to be followed with fidelity, students are not given opportunities to create and share their own strategies for solving tasks designed to help them learn equivalence of fractions. Neither are they given opportunities to make connections among strategies. All connections are introduced by the teacher. Although the teacher editions promote transitions from visual models to algorithms, they provide inconsistent use of problem-solving practice tasks and equal-sharing problems, two methods that are strongly supported by the research literature for developing procedural fluency from conceptual understanding in equivalence of fractions. Finally, the teacher materials include multiple instances in which the same or similar language and terms are used for mathematical and pedagogical practices found in mainstream research and professional literature, yet the practices were to be implemented in ways contrary to mainstream interpretations.Overall, Go Math! K-8 (HMH, 2016) provided little support to teachers in helping students build procedural fluency from conceptual understanding. A teacher-driven, rather than student-driven, approach to instruction was emphasized, thus minimizing opportunities for students to engage in the kinds of tasks and discourse recommended in the literature. The ways in which mathematical language and terms were implemented contrary to mainstream research interpretations can easily cause confusion among educators. The dearth of authentic problem-solving practice was inconsistent with quality mathematics instruction that supports students conceptual and procedural understanding.