The purpose of this study was to investigate the effect of teachers attending Cognitively Guided Instruction (CGI) professional development on students' problem solving strategies and the effect of students' use of strategies on their mathematics achievement as measured by a standardized test. First, the study analyzed the differences in students' use of strategies between treatment and control groups. The treatment was CGI professional development, and the teachers in the treatment group attended CGI workshops whereas the teachers in the control group did not. Next, the study analyzed the differences in the mathematics achievement of students between different strategy groups. A student posttest, which was ITBS (Math Problems and Math Computation), was used to compare students' mathematics achievement. A student pretest was used as a covariate. The results of this study showed that there were statistically significant differences in the students' use of strategies between the treatment and control groups at the second grade level. A greater percentage of treatment students used derived facts / recall strategies (the most advanced strategy for single-digit addition and subtraction) than control students did. The results related to the effect of students' use of strategies on their mathematics achievement showed that the students who used derived facst/recall strategies for single-digit problems had significantly higher mathematics achievement than students who used counting or concrete modeling strategies. Furthermore, the students who used invented algorithms for multi-digit problems had significantly higher mathematics achievement than the students who used standard algorithms.

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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This dissertation explores elementary mathematics teachers' understanding and implementation of effective questioning techniques within the instructional context. A qualitative, multiple case study design was employed for this dissertation in practice. This study was conducted in a K-5 school in Florida, focusing on four elementary school teachers in grades 3-5. Data collected included semi-structured interviews and live observations. Analysis of transcripts from interviews and observational notes provided an insider look into teachers’ planning and implementation of questioning. The research was driven by two research questions: How do teachers implement questioning in mathematics instruction? and What factors influence teachers' planning and implementation of questioning in mathematics instruction? Through the examination of these questions, the study sought to unveil critical insights into the planning processes, the types of questions incorporated during instruction, and teachers' conceptualization of what constitutes effective questioning. The findings of this dissertation revealed three themes which were 1) factors influencing questioning, 2) teachers’ understanding of effective questioning and professional development, and 3) alignment with learning objectives and student diversity. By identifying areas that warrant further examination, the study contributes ideas tailored to enhance the effectiveness of questioning in mathematics instruction. This dissertation in practice research aspires to guide instructional practices and make significant contributions to the broader landscape of mathematics education. In conclusion, this dissertation offers a nuanced exploration of the multifaceted dimensions of questioning in mathematics instruction, with the intention of providing practical recommendations for educators and contributing to the ongoing discourse in the field of mathematics education.

Syftet med föreliggande studie är att kartlägga mellanstadielärares användning av digitala spel i matematikundervisningen. För att uppnå studiens syfte har följande frågeställningar använts: Hur använder mellanstadielärare i olika åldrar digitala spel i matematikundervisningen? I vilket syfte använder mellanstadielärare i olika åldrar digitala spel i matematikundervisningen? För att besvara studiens syfte och frågeställningar genomfördes en analys av en kvantitativ webbenkät besvarad av lärare som uppfyllde studiens urvalskriterier. Det empiriska materialet samlades in från 117 respondenter och analyserades både deskriptivt och med hjälp av formell statistisk hypotesprövning för att undersöka om olika aspekter kring användningen av digitala spel är beroende av lärarens ålder. Studiens teoretiska ramverk var RAT-modellen som står för ”Replacement, Amplification, Transformation”. Modellen fokuserar på hur teknologi kan användas med syfte att ersätta, förstärka eller transformera undervisnings- och lärandeprocesser. Resultaten visar att digitala matematikspel används mest inom taluppfattning och algebra, och majoriteten av lärarna använder digitala spel regelbundet i matematikundervisningen. Resultaten indikerar att användandet minskar ju äldre läraren är och att det finns en statistisk signifikant skillnad i användningsfrekvensen mellan åldersgrupperna. Vidare framgår det att en majoritet av lärare mellan 21 och 60 år använder digitala spel för att förstärka lärandet, medan det är mer vanligt att lärare som är 61 år eller äldre använder spelen för att ersätta traditionella metoder. Resultaten visar att de två vanligaste syftena med att använda digitala matematikspel är för att variera undervisningen och för att eleverna ska få repetera och befästa kunskaper. / The purpose of the present study is to map the use of digital games in mathematics instruction by teachers of grades 4-6. To achieve the study's purpose, the following research questions were used: How do teachers of grades 4-6 of different ages use digital games in mathematics instruction? For what purpose do teachers of grades 4-6 of different ages use digital games in mathematics instruction? To address the study's purpose and research questions, an analysis of a quantitative web survey was conducted with teachers who met the study’s selection criteria. The empirical data was collected from 117 respondents and analyzed both descriptively and through formal statistical hypothesis testing to examine whether different aspects of the use of digital games are dependent on the teachers’ age. The theoretical framework of the study was the RAT model, which stands for "Replacement, Amplification, Transformation." The model focuses on how technology can be used to replace, amplify, or transform teaching and learning processes. The results show that digital mathematics games are used most frequently in number sense and algebra, and the majority of teachers use digital games regularly in mathematics instruction. The results indicate that the usage decreases with the age of the teacher, and that there is a statistically significant difference in usage frequency among different age groups. Furthermore, it appears that the majority of teachers aged 21 to 60 use digital games to amplify learning, while it is more common for teachers aged 61 and older to use the games to replace traditional methods. The results show that the two most common purposes for using digital mathematics games are to vary instruction and to allow students to practice and reinforce their knowledge.

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.