Academic literature on the topic 'Secondary Mathematics'

The aim of this thesis is to investigate and enhance our understanding of the notions of mathematical models and modelling at the Swedish upper secondary school level. Focus is on how mathematical models and modelling are viewed by the different actors in the school system, and what characterises the collaborative process of a didactician and a group of teachers engaged in designing and developing, implementing and evaluating teaching modules (so called modelling modules) exposing students to mathematical modelling in line with the present mathematics curriculum. The thesis consists of five papers and reports, along with a summary introduction, addressing both theoretical and empirical aspects of mathematical modelling. The thesis uses both qualitative and quantitative methods and draws partly on design-based research methodology and cultural-historical activity theory (CHAT). The results of the thesis are presented using the structure of the three curriculum levels of the intended, potentially implemented, and attained curriculum respectively. The results show that since 1965 and to the present day, gradually more and more explicit emphasis has been put on mathematical models and modelling in the syllabuses at this school level. However, no explicit definitions of these notions are provided but described only implicitly, opening up for a diversity of interpretations. From the collaborative work case study it is concluded that the participating teachers could not express a clear conception of the notions mathematical models or modelling, that the designing process often was restrained by constraints originating from the local school context, and that working with modelling highlights many systemic tensions in the established school practice. In addition, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported. In a questionnaire study with 381 participating students it is concluded that only one out of four students stated that they had heard about or used mathematical models or modelling in their education before, and the expressed overall attitudes towards working with mathematical modelling as represented in the test items were negative. Students’ modelling proficiency was positively affected by the students’ grade, last taken mathematics course, and if they thought the problems in the tests were easy or interesting. In addition empirical findings indicate that so-called realistic Fermi problems given to students working in groups inherently evoke modelling activities.

Much research supports that student mindset influences how well students do in school and that teacher actions influence student mindset. Research has also shown that just because a teacher has a growth mindset, it does not imply that their students will also have a growth mindset. This research looks closer as to why a teacher's mindset does not correlate with their students' mindset by further examining teacher mindset and the connection between teacher mindset and teacher actions. In summary, teachers' mindsets do not directly influence student mindset for a few reasons: secondary mathematics teachers have different mindsets towards honors and regular students, while they have heard about mindset, they do not understand mindset deeply, and mathematics teachers do not know how to help their students develop a growth mindset.

In addition to the memorization, algorithmic skills and vocabulary which is the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher level skills through Laboratory Experiences in Mathematical Biology (LEMBs) which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. LEMBs are constructed so they require no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. In this work examine how LEMBs are designed with the student as the primary focus. We explain how well-designed LEMBs lead students to interact with mathematics at higher levels of cognition while building mathematical skills sought after in both academia and industry. Additionally, we describe the online repository created to assist in the teaching and further development of LEMBs. Since student-centered teaching is foreign to many post-secondary instructors, we provide research-based, pedagogical strategies to ensure student success while maintaining high levels of cognition.

The main purpose of the study was to understand preservice secondary mathematics teachers&rsquo<br>pedagogical content knowledge of composite and inverse functions. The study was conducted with three preservice secondary mathematics teachers in Graduate School of Education at Bilkent University. The instruments of the study were qualitative in nature and in four different types of data forms: observations, interviews, documents, and audiovisual materials. Observation data came from fieldnotes by conducting an observation of lessons participants taught at Private Bilkent High School. Interview data came from the transcriptions of semi-structured interviews. Document data came from survey of function knowledge, journal writings, vignettes, and lesson plans. Audiovisual data came from the examination of the videotape of the lessons participants taught. The findings reveal that preservice secondary mathematics teachers&rsquo<br>knowledge levels in components of pedagogical content knowledge were not at the desired levels and also they experienced difficulty while integrating that knowledge. The results of the study indicate that teacher education should provide courses that cover the content relevant to students in order to assure both depth and breadth in subject matter knowledge of the preservice teachers. Moreover, the activities which mimics the classroom cases and assures the integration of knowledge components like vignettes would be used in teacher education programs. Results can inform educational practices, and reforms in Turkey, and provide a basis for further research, with increased pedagogical content knowledge as the ultimate goal.

A systemic functional analysis of the oral pedagogical discourse and board texts of secondary school mathematics lessons differentiated on the basis of school sector, gender and social class is completed through the development of a computer program to handle the linguistic analysis and the construction of a Hallidayan systemic framework for mathematical symbolism and visual depiction. The new frameworks allow for investigation of the unique contributions of language, mathematical symbolism and visual display in the construction of meaning in mathematical texts and the process of semiotic metaphor which occurs in movements between these codes. The systemic analysis of the classroom discourse is situated within a Foucauldian perspective of power, knowledge and truth in mathematics, mathematics education and wider discursive practices involving the private and state school sectors. The analysis of linguistic patterns, register selections and genres of four Year Ten secondary school mathematics lessons reveals that in private elite single sex schools the male students demonstrate the greatest participation and access to the discourse of mathematics while the female students participate in interpersonal patterns of deference which do not resonate with the tenor dimensions of mathematics. The monofunctional tendency orientated towards interpersonal meaning in the lesson of the working class students at a government school indicates that the social goal of the lesson is primarily directed towards maintaining tenor relations through covert manipulation as opposed to learning mathematics. The limited functionality of practical lessons in mathematics is also demonstrated as a shift from everyday discourse to mathematical discourse does not occur. Mathematical pedagogical discourse is characterised by a dense texture which arises in part from the strategies by which meaning is encoded in mathematical symbolism. As opposed to the lexical density and grammatical intricacy of written and spoken language respectively, mathematical symbolism realises grammatical density whereby multiple levels of clausal rankshift preserve the nuclear configurations of Operative processes and participants which describe relations of parts to the whole and continuous patterns of variation. In addition, inherent difficulties in mathematical pedagogical discourse arise from long implication chains of reasoning and dependence on multiple semiotic resources with the latter resulting in referential complexity and iii multisemiotic intertwining of lexical and participant chains and strings. The results of the analysis, interpreted through Bernstein's theory of pedagogical practices and coding orientations and Halliday's formulations of spoken and written language, reveal that the semantic orientation of working class students does not accord with that realised in mathematics.

Researchers have found that teachers' decisions affect students' opportunity to learn. Prior researchers have investigated teachers' decisions while planning, implementing, or reflecting on lessons, but few researchers have studied teachers' decisions and their reasoning throughout the teaching process. It is important to study teachers' reasoning for why they make the decisions they do throughout the teaching process. Furthermore, because inservice and preservice teachers differ in experience and available resources that they draw on while making decisions, it is helpful to consider the resources PSTs' draw on while reasoning. Curricular reasoning is a framework that describes teachers' thinking processes when making decisions during the teaching process. This study investigated secondary preservice teachers' decisions and curricular reasoning throughout the teaching process. Data were collected from two groups of secondary preservice teachers in a mathematics methods course focused on student thinking and mathematics. Results revealed that the preservice teachers used all seven curricular reasoning strands, especially drawing on mathematical meanings, mapping learning trajectories, and considering learners' perspectives. Specifically, this study demonstrates ways in which preservice teachers reason about their decisions and the intertwined nature of their curricular reasoning. The results from this study also imply that it may be helpful to consider the resources PSTs have access to, including their instructor, and that the order of their lesson planning may allow support for the mathematical learning trajectories within individual lessons. This study also provides validation for the curricular reasoning framework described by Dingman, Teuscher, Olson, and Kasmer (in press), provides subcategories of curricular reasoning strands, and has implications for teacher education.

Thesis (Ph. D.)--Illinois State University, 2000.<br>Title from title page screen, viewed May 4, 2006. Dissertation Committee: Beverly S. Rich (chair), Michael Marsalli, Edward S. Mooney. Includes bibliographical references (leaves 89-124) and abstract. Also available in print.