The purpose of this study was to develop a model to predict the college mathematics courses a freshman could expect to pass by considering their high school mathematics preparation. The high school information that was used consisted of the student's sex, the student's grade point average in mathematics, the highest level of high school mathematics courses taken, and the number of mathematics courses taken in high school. The high school sample was drawn from graduated Seniors in the State of Utah for 1979. The college sample was drawn from the fall semester 1980 at Utah State University, Weber State College, University of Utah, Westminster College, and Brigham Young University. The model was developed using ACT Scores as the dependent variable with the high school data in one equation and the college data in another equation and then predicting from high school to college using the ACT Scores as the bridge. The results showed that those students that had courses in the higher levels of mathematics in high school, were significantly more successful! in college mathematics. The level of mathematics was more significant than the grades received in mathematics. Females who had had higher levels of mathematics in high school were as successful! as males on that level.

The purpose of this narrative inquiry study was to investigate the influence of curricular mandates on the teaching practices of high school mathematics teachers. Narrative inquiry, philosophically based on John Dewey’s theory of experience (Dewey, 1938), provides the intimate study of an individual's experience over time and in context(s) (Clandinin & Connelly, 2000). This study focused on the experiences of three high school mathematics teachers’ stories of educational change with data collected through interviews and personal documents. Socio-cultural narrative analysis was used to interpret the participants’ stories of adaptation. The data, presented as an ethnodrama, is composed of scenes taken from the interviews and interweaves the participants’ stories of evolution as they tackled the struggles of change on multiple levels: curriculum, student assessment, and teacher evaluation. Results indicated teachers adopt both traditional and reform strategies when deciding on appropriate teaching practices. Collaboration and professional development were two important aspects used by the participants to enlarge their toolbox of teaching practices when forced to challenge their existing beliefs. This study contributes to the scarce research on the impact of curricular mandates on teaching practices. It also highlights the experiences of high school mathematics teachers as they embrace the paradigm shift associated with the mandates and implement changes to their practices to promote a more student-centered, collaborative environment.

It is the purpose of this study to review in brief the changes that have taken place since the turn of the century in content of mathematical studies in the high school and to examine theoretically the significance of such changes.

Hierarchical Linear Models were used to analyze data from one Texas school and identify effective and ineffective mathematics teachers using their students’ scores on two consecutive years of the state test (TAKS) over a three-year period. A model was developed which attempted to control for student grade level, as well as whether a class was an honors course. Special attention was paid to requiring statistically significant results. Results were minimal and may lack validity. The barriers to getting better results include missing data, the small sample size of students for an individual teacher, the non-random assignment of teachers to courses, and the extent of variability in the data. Most of these are beyond the control of educators. A better way of measuring student growth could reduce variability and improve the prospects of using a data driven approach to evaluate teachers. / text

Research shows that students who take advanced mathematics courses perform better on measures of college readiness than students who take less rigorous courses. However, no clear effect has been shown on requiring all students to take more advanced courses. This study examined whether increases in the number and level of mathematics courses required for high school graduation have resulted in increased levels of college aspirations and preparedness. Specifically, twenty years of data from a rural school district in Texas were analyzed to determine whether the impact on college entrance exam-taking and performance differed by the mathematics requirements in effect for each class. Logistic and linear regression modeling revealed no statistically significant effect of higher requirements. And while overall results by gender and race mirrored previous research, with males tending to have higher scores than females and White students tending to score higher than African-American and Latinx students, the increased requirements were not associated with any mitigation in these inequities.

Den här studien är en systematisk litteraturstudie som går ut på att presentera och analysera vad forskning visar beträffande svårigheter som elever möter inom området ”derivata” samt hur undervisningen kan utformas för att stötta eleverna i sitt lärande inom ”derivata”. Via systematiska sökningar som skedde både i databaser och manuellt valdes artiklar som passade in på urvalskriterier. Artiklarna analyserades utifrån frågeställningarna. Elevens svårigheter i sin förståelse för begreppet ”derivata” delades upp i tre huvudsakliga kategorier: tangentens ekvation och dess lutning i förhållande till ”derivata”, gränsvärde i förhållande till ”derivata” och förändringshastighet i förhållande till ”derivata”. Studien fann att eleverna uppvisade svårigheter när de gäller tangenten, tangentens lutning, förändringshastighet och gränsvärde. Att eleverna hade svårt med att förstå begreppet ”derivata” gjorde att de fick även svårare att se sambandet mellan alla andra begrepp. Gällande undervisningens utformning fann studien att användandet av olika representationer och digitala verktyg förebygger elevens svårigheter för begreppet ”derivata”. / This study is a systematic literature study aiming at presenting and analyzing what research shows regarding difficulties students encounter in the field of derivatives and how teaching can be designed to support students in their learning in derivatives. Through systematic searches which were done both in databases and manually, articles that matched given criteria were selected. The articles were analyzed based on the research questions. The students' difficulties in understanding the concept of derivatives were divided into three main categories: the tangent equation and its slope in relation to derivatives, the limit value in relation to derivatives and the rate of change in relation to derivatives. The study found that students experienced difficulties in the concept of the derivative, such as the tangent, the slope of the tangent, the rate of change and the limit. The fact that the students had difficulty with the concepts made them even more difficult to understand the connection between these concepts. Regarding the teaching, the study found that different representations and the using of digital tools prevent the students' difficulties in the concept of derivatives.

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The second semester of the high school senior year has been associated with a lack of motivation among students and increased frustrations among parents and teachers. This qualitative study examines the achievement goals and engagement outcomes of second semester high school seniors in their mathematics classes. Data were collected from eight high school seniors, three of their parents, and two teachers enrolled at an all male college preparatory school in Pennsylvania. In-depth interviews were used to gather participants’ definitions of success prior to their senior year and during the second semester of their senior year. Student participants’ behavioral, emotional and cognitive engagements were assessed through directed interview questions and observations. Data were analyzed using a three goal framework of task-involvement, ego-involvement, and work-avoidance (Nicholls, Patashnick, & Nolen, 1985). The participants’ definitions of success suggested four themes. First, student participants defined success in mathematics consistently as they recalled their four years of high school and transition into the second semester of their senior year. Second, the phenomenon of senioritis was found to be more perceived than real for most of the participants. The work-avoidant participants described feeling the effects of senioritis for most of the second semester whereas the task-involved and ego-involved students reported brief effects before regaining focus. Third, students’ achievement goals in mathematics were found to be more closely aligned to their parents’ goals and less aligned to their teachers’ goals. Lastly, students described different achievement goals from one class to another during the same semester, at times even within the same discipline. Implications for practice and suggestions for future research were also discussed. / Math & Science Education

Made available in DSpace on 2016-04-27T16:57:17Z (GMT). No. of bitstreams: 1 Marcia Maioli.pdf: 1743976 bytes, checksum: 9544533ab3da7d2f0ca7533934544bf2 (MD5) Previous issue date: 2012-06-11 / This is a theoretical research that studies the contextualization established on national curricular documents as one of the pedagogic principles that structure the curricula on High School. The study stands for the contextualization as a potentially rich pedagogic principle to improve mathematic learning by the students, but it needs to be understood in its purposes and uses by different actors. For such, the investigation was developed based on bibliographic sources that involve studies about learning, comparison of meanings and language; curricular documents for High School; researches about contextualization on mathematical teaching and, aiming at investigating how are developed activities inspired on the contextualization of curricula that are practiced in class; it is also considered the set of dissertations involving Hypothetical Learning Paths developed on the research project in which this work is inserted. It could be verified that the contextualization implementation was not a simple action - nor even for professionals that are in touch with researches or theories that concern Mathematical Education. The National Curricular Parameters for High School outline that contextualizing the content that is aimed to be learned means, primarily, to assume that all knowledge involves a relation between subject and object. The idea of knowledge as a network of meanings defended by Machado and Pires; the process by which more relevant and inclusive concepts are presented is one in which the learner´s cognitive structure interacts with a new material presented to them as defended by Ausubel; the role of instruments and signs as mediators on the conversion of social relations according to higher mental functions considered by the studies of Vygotsky; the different language conceptions explored by Koch provide important clues about the relation processing between learning subject and study object. The contextualization is strongly related to the assignment of meanings to what is learned, and therefore, it embraces a cognitive aspect that cannot be neglected. Besides that, for the perspective established of learning, 10 knowledge is the product of activity context and culture in which it is developed and used, so the scholar culture influence cannot be ignored concerning what is learned in it / Esta é uma pesquisa teórica que estuda a contextualização estabelecida em documentos curriculares nacionais como um dos princípios pedagógicos estruturadores dos currículos do Ensino Médio. O estudo defende que a contextualização é um princípio pedagógico potencialmente rico para melhorar a aprendizagem matemática dos alunos, mas precisa ser compreendida em seus propósitos e usos pelos diferentes atores do processo de ensino e aprendizagem. Partindo desse ponto, delinearam-se os objetivos: investigar a contextualização como princípio pedagógico e construir conhecimentos que permitam a compreensão de seus propósitos e usos. Para tanto, a investigação foi desenvolvida com base em fontes bibliográficas envolvendo estudos sobre aprendizagem, aferição de significados e linguagem; documentos curriculares voltados ao Ensino Médio; pesquisas sobre contextualização no ensino de matemática e, visando investigar como se desenvolvem atividades inspiradas na contextualização nos currículos praticados em sala de aula, considerou-se também o conjunto de dissertações envolvendo Trajetórias Hipotéticas de Aprendizagem desenvolvidas no projeto de pesquisa em que este trabalho se insere. Constata-se que a implementação da contextualização não é uma ação simples, nem mesmo para profissionais que estão em contato com pesquisas ou teorias sobre Educação Matemática. Os Parâmetros Curriculares Nacionais - Ensino Médio destacam que contextualizar o conteúdo que se quer aprendido significa, em primeiro lugar, assumir que todo conhecimento envolve uma relação entre sujeito e objeto. A ideia de conhecimento como rede de significações defendidas por Machado e Pires; o processo por meio do qual conceitos mais relevantes e inclusivos, presentes na estrutura cognitiva do aprendiz, interagem com um novo material apresentado a ele, conforme defende Ausubel; o papel dos instrumentos e signos como mediadores na conversão de relações sociais em funções mentais superiores, considerados pelos estudos de Vygotsky; as 8 diferentes concepções de linguagem exploradas por Koch, fornecem pistas importantes sobre a forma como se processa a relação entre sujeito que aprende e objeto de estudo. A contextualização está fortemente relacionada à atribuição de significados ao que se aprende, portanto, abrange um aspecto cognitivo que não pode ser negligenciado. Além disso, para a perspectiva situada da aprendizagem o conhecimento é produto da atividade, contexto e cultura na qual ele é desenvolvido e usado, assim, não se pode ignorar a influência da cultura escolar sobre o que nela se aprende

This thesis deals with visual teaching aids that are used in the educational proces. It describes aids that are used in teaching mathematical functions at secondary schools. The aim is to describe briefly their historical development and by a questionnaire find changes in their use in teaching of mathematical functions in the past 10 years.