Update NPS / July 2008

SECNAV Speaks at Graduation; Message from NPS President Daniel Oliver; Charity Golf Tournamen

The Impact of the Utilization of Connected Mathematics Project with Direct instruction on Grade 8 Mathematics MAP Scores

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Examining Virtual Mathematics Instruction: A Comparative Case Study of In-Service Elementary Teachers with Mathematics Anxiety and Mathematics Teaching Self-Efficacy

Mathematics Anxiety (MA) and Mathematics Teaching Self-Efficacy (MTSE) have been reported as factors related to teachers’ mathematics instruction. This study investigated MA and MTSE in in-service elementary teachers’ virtual mathematics instruction. A comparative case study design was used to understand the relationship between MA, MTSE, and their virtual mathematics instructional practices. Two in-service elementary teachers from an urban public charter school district in a large metropolitan city in the Midwest participated. I employed qualitative methods to examine the results from the Abbreviated Mathematics Anxiety Rating Scale (AMAS), an adapted version of a researcher-developed instrument called the Mathematics Teaching and Mathematics Self-Efficacy Scale (MTMSE), interviews, teacher classroom observations, post-observation interviews, and a fraction simulation task to learn how teachers approached virtual mathematics instruction. Results indicated the in-service elementary teachers had low to moderate MA and high MTSE when teaching elementary mathematics concepts. However, if they were to have taught higher-level mathematics concepts, then they would have high MA and low MTSE. The in-service elementary teachers who had low to moderate MA and high MTSE heavily relied on direct instructional practices with a focus on procedural strategies. Also, these teachers experienced many challenges teaching mathematics in a virtual environment. Findings from this comparative case study have implications for teacher preparation programs, mathematics teaching professional development for in-service elementary teachers transitioning virtual mathematics pedagogy, improving mathematics performance for students, and assisting educational stakeholders in improving mathematics instruction

Active Methodologies for the Promotion of Mathematical Learning

In recent years, the methodologies of teaching have been in a process of transition. Multiple active methodologies have proliferated, with the aim of changing the concept we have had of teaching so far. These advocate for a student who plays a leading role in the process of building learning, while the teacher acts as a figure who facilitates and glimpses the paths to learning. In order to be able to carry out this type of teaching in an optimal way, it is necessary for the teaching and research community to be correctly trained in its pedagogical principles and in the tools that boost its implementation. Among these principles and tools, it is of vital importance that information and communication technologies (ICT) be adequately handled. The use of active methodologies (project-based learning, problem-based learning, service learning, flipped classroom, mobile learning, etc.) or innovative pedagogical approaches (simulation, role-playing, gamification, etc.) promotes an improvement in the motivation of students as well as their skills. This aspect is especially important in the area of mathematics, whose contents are characterized by their abstraction, thus highlighting the need for its dynamization in classrooms of different educational stages

Development of junior intermediate preservice teachers' mathematical knowledge and values / by Carlos Zerpa.

This research thesis is composed of two studies. The first study examined the validity and reliability of a locally developed instrument called the Perceptions of Mathematics (POM) questionnaire (Kajander, 2005). The POM questionnaire was used to measure mathematical knowledge and values on junior intermediate preservice teachers in the second study of this research thesis. The second study investigated preservice teachers’ change in mathematical knowledge and values via a mathematics methods course in education. This study included pretests and post-tests to examine preservice teachers’ preliminary mathematical knowledge, beliefs, and changes, in these factors, after taking the mathematics methods course at the junior intermediate level. The results in the first study show evidence that the POM questionnaire is a valid and reliable instrument. The results in the second study suggest that it is possible to change preservice teachers’ conceptual and procedural mathematics knowledge via a mathematics methods course in education. In addition, the results o f the second study suggest that preservice teachers’ academic background does not appear to influence their change in conceptual mathematical knowledge and values via a mathematics methods course. On the other hand, preservice teachers’ conceptual and procedural mathematical knowledge at the pretest, plus preservice teachers’ courses taken in high school, appear to influence their change in conceptual mathematical knowledge the most. These findings have implications for mathematics educators of teachers, as well as school boards, to help them better assess professional development needs

An industry oriented math teaching strategy for the Metro Group BEngTech program

BACKGROUND With traditional mathematical teaching methodologies in tertiary education, the conventional pathway is to build student understanding through mathematical content alone. Applications which utilise the mathematics then possibly follow in later courses. The problem with this traditional methodology of learning is that there is no close relationship with industry requirements for mathematical preparation. Industry oriented education is an approach to learning from an industry perspective. PURPOSE Taking into account the Bachelor of Engineering Technology student profile of vocationally orientated students this research is to trial the implementation of industry oriented math teaching and learning within the BEngTech program at Christchurch Polytechnic Institute of Technology, Otago Polytechnic, Waikato Institute of Technology and Wellington Institute of Technology as an alternative to the current method used of theoretical based teaching. DESIGN/METHOD In this research, a formative test within the BEngTech program at Christchurch Polytechnic Institute of Technology, Otago Polytechnic, Waikato Institute of Technology and Wellington Institute of Technology has been designed in the existing teaching plan for the MG5004 Engineering Maths 1. We have not modified any teaching content and learning outcomes in this class. The formative test comprised two questions relating to matrices: the first was generic (theoretical) and the second industry-oriented. RESULTS Since the first question was generic and the second question industry-oriented and major specific, we separated the results of students who are studying the majors of mechanical, civil, or electrical engineering into 3 groups. For each group we summarized the marks from the first question and second questions. These results show that the students did well in the first question which is theoretical based. However, most of the students were not confident in applying their theoretical knowledge to solve an industry-oriented question. CONCLUSIONS This study proved that the students lack knowledge of the industry application in the engineering math class and also there is a “disconnect” in students minds between a mathematics problem and an industry problem i.e. this study has clearly shown the need to close gaps in the BEngTech curriculum. A major outcome of this study is to have identified the nature of the gaps and hence point the way for further research to investigate how to include these in the BEngTech with appropriate integration of mathematics and engineering courses

Mathematical arguments from a critical perspective: an analysis of didactic practices in Elementary School

Os documentos oficiais brasileiros enfatizam que a finalidade maior da Educação Básica é a formação integral do educando, com ênfase em: pleno desenvolvimento da pessoa, preparo para o exercício da cidadania e qualificação para o trabalho. Nesta dissertação, discutimos o significado da formação integral do educando do ponto de vista da literatura existente e dos documentos normativos oficiais da Educação Básica brasileira. Buscamos entender e identificar metodologias sobre como o ensino de Matemática pode contribuir para a formação do educando. Entendemos que o senso crítico é uma modalidade de pensamento a ser desenvolvida na escola por contribuir para a consecução daquelas finalidades. Nesse sentido, defendemos que atividades com argumentações precisam ser trabalhadas em sala de aula de Matemática, não apenas as que objetivam validar resultados puramente matemáticos, como também as que, utilizando ferramental matemático, validam afirmações em contextos extrínsecos a esta ciência. Por meio delas é que se manifesta o pensamento crítico. Com o objetivo de favorecer o desenvolvimento dessa modalidade de pensamento em sala de aula de 6º e 7º anos do Ensino Fundamental, desenvolvemos atividades didáticas envolvendo argumentações em e com Matemática. Para tanto, apoiamo-nos principalmente nas contribuições de Nicolas Balacheff, sobre processos de prova e situações de validação, e de Ole Skovsmose e seus trabalhos sobre Educação Matemática Crítica, particularmente sua defesa da importância da proposição de cenários para investigação no trabalho escolar.The official Brazilian documents emphasize that the main purpose of Basic Education is the integral formation of the student, with emphasis on: full development of the person, preparation for the exercise of citizenship and qualification for work. In this dissertation, we discuss the meaning of the Integral Formation of the student from the point of view of the existing literature and of the official normative documents on Brazilian Basic Education. We seek to understand and identify how mathematical teaching methodologies may contribute to the education of the student. We understand that critical sense, as a thinking modality, should be developed in school to contribute to the accomplishment of those aims. We argue that activities with arguments need to be worked out in the Mathematics classroom. Not only those that validate purely mathematical results but also the ones that, using mathematical tools, validate statements extrinsic to this science. Critical thinking manifests through them. To favorize development of this kind of thinking in scholars of 6th and 7th grade, we applied didactic experiments involving arguments in and with Mathematics, based on contributions of Nicolas Balacheff and Ole Skovsmose. With respect to the first author, mainly on proof processes and validation situations and to the second, on his Critical Mathematical Education, specially about the importance of landscapes of investigations

Jogos no ensino de matemática: uma análise na perspectiva da mediação

The present research had as main objective to analyze the use of games in the teaching of Mathematics, in the initial years of Elementary School, considering the perspective of pedagogical mediation. In the theoretical scope we deal with the conceptions of mediation in Vygotsky, inserting the discussion about the game as mediating instrument; We bring a historical clipping about the development of the game concept; And we briefly discuss the processes of teacher formation to teach Mathematics, as well as some considerations about the textbook. We traced the path of qualitative research and the observation environment were classrooms in grades 3 and 5 of Elementary School. They participated in the investigation, besides teachers of these years of schooling, teachers of a course of Pedagogy, with the perspective of discussing the formation for the use of pedagogical games in the classes of Mathematics. For analysis of the interviews we take as reference the analysis of content of Bardin. In our argumentation about the results of the interviews, we articulated with the results of the analysis of the collection of textbooks of Mathematics adopted by the teachers of the highlighted years, understanding them as an important resource to support the planning of teaching activities. We evaluated in the textbooks the authors' proposal for the use of games in relation to the mathematical contents associated with them. The analysis of the interviews and textbooks, as well as the observations of the classrooms, strengthened the defense arguments of our thesis, that the game is only a mathematical learning mediation tool if there is an effective conjunction of guidelines, considering Teacher training, initial and / or continuing, and the proposals of the Mathematics textbooks. We identified gaps in initial and continuing teacher education in the early years, regarding the use of games in Mathematics teaching, and weaknesses related to such use in the classroom, insofar as the game is not generally used as Instrument of mediation of learning. In the observed practice there were no research or problem solving activities related to the games that would potentiate the knowledge formation by the participants and, in addition, the way games are proposed in the textbooks analyzed is, in general, inadequate, constituting an activity Little relevant to the teacher's practice, if not complemented or resized. Our study did not aim to make generalizations based on the conclusions we reached, from the selected clipping, but alert about the risk of recommending the use of mathematical teaching methodologies without the theoretical and formative input that needs to precede this use in the classroom of class.A presente pesquisa teve como objetivo central analisar o uso de jogos no ensino de Matemática, nos anos iniciais do Ensino Fundamental, considerando a perspectiva da mediação pedagógica. No âmbito teórico tratamos das concepções de mediação em Vigotski, inserindo a discussão sobre o jogo como instrumento mediador; trazemos um recorte histórico acerca do desenvolvimento do conceito de jogo; e abordamos, de modo breve, os processos de formação de professores para ensinar Matemática, além de algumas considerações sobre o livro didático. Trilhamos o caminho da pesquisa qualitativa e o ambiente de observação foram salas de aula de 3º e 5º anos do Ensino Fundamental. Participaram da investigação, além de professoras destes anos de escolaridade, professoras de um curso de Pedagogia, na perspectiva de discutirmos sobre a formação para o uso de jogos pedagógicos nas aulas de Matemática. Para análise das entrevistas tomamos como referência a análise de conteúdo de Bardin. Em nossa argumentação sobre os resultados das entrevistas, fizemos a articulação com os resultados da análise da coleção de livros didáticos de Matemática adotada pelas professoras dos anos destacados, entendendo-os como importante recurso de apoio ao planejamento das atividades docentes. Avaliamos, nos livros didáticos, a proposta dos autores para o uso de jogos, em relação aos conteúdos matemáticos a eles associados. A análise das entrevistas e dos livros didáticos, bem como das observações das salas de aula, fortaleceram os argumentos de defesa de nossa tese, de que o jogo só constitui ferramenta de mediação de aprendizagem matemática se houver uma conjunção efetiva de orientações, considerando-se a formação do professor, inicial e/ou continuada, e as propostas dos livros didáticos de Matemática. Identificamos lacunas na formação inicial e continuada das professoras dos anos iniciais, relativas ao uso de jogos no ensino de Matemática, e fragilidades relativas a esse uso, em sala de aula, na medida em que o jogo não é, de modo geral, utilizado como instrumento de mediação da aprendizagem. Na prática observada não foram propostas atividades investigativas ou de resolução de problemas relacionados aos jogos que potencializassem a formação de conhecimento pelos participantes e, além disso, a forma como os jogos são propostos nos livros didáticos analisados é, em geral, inadequada, constituindo uma atividade pouco relevante para a prática do professor, se não for complementada ou redimensionada. Nosso estudo não teve como objetivo fazer generalizações com base nas conclusões a que chegamos, a partir do recorte selecionado, mas alerta sobre o risco da recomendação do uso de metodologias de ensino de Matemática sem o aporte teórico e formativo que precisa preceder essa utilização em sala de aula