Thesis advisor: Lillie R. Albert / In mathematics education, there is an imperative for more just and equitable experiences in mathematics spaces, as well as ongoing efforts to move classroom instruction toward mathematical inquiry. While Mathematics Teacher Educators (MTEs) are expected to support multiple initiatives in mathematics education, they are particularly responsible for the professional learning of teachers and teacher candidates. MTEs must therefore prepare and support the professional learning of teachers to achieve twin goals. This study was designed to understand how MTEs envision their roles in supporting development of teachers across MTEs’ many professional functions in their work toward the twin goals of equity and inquiry. The findings suggest that identifying the forms mathematical knowledge takes is important for mathematical inquiry and that interrogating these forms can be used to counter pervasive social myths about who can do mathematics. Further, MTEs articulated three interrelated values for application of mathematics inquiry teaching for justice and equity: creating space, supporting sense-making, and naming how power and privilege have operated and continue to operate in mathematics spaces. Finally, MTEs described how mathematics inquiry practices are a mode for understanding the world and can be used to promote equity by uncovering biases and assumptions. These findings suggest a promising avenue for leveraging mathematical inquiry to increase equitable outcomes in mathematics spaces. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Lynch School of Education. / Discipline: Teacher Education, Special Education, Curriculum and Instruction.

In this workshop we present an innovative teaching, learning and research setting that engages beginning teachers in mathematical inquiry as they investigate, represent and connect mathematical ideas through mathematical conversation, reasoning and argument. This workshop connects to the themes of teacher preparation and teaching through problem solving. Drawing on new paradigms to think about teaching and learning, we orient our work within complexity theory (Davis & Sumara, 2006; Holland, 1998; Johnson, 2001; Maturana & Varela, 1987; Varela, Thompson & Rosch, 1991) to understand teaching|learning as a complex iterative process through which opportunities for learning arise out of dynamic interactions. Varela, Thompson and Rosch, (1991) use the term co-emergence to understand how the individual and the environment inform each other and are “bound together in reciprocal specification and selection” (p.174). In particular we are interested in the conditions that enable the co-emergence of teaching|learning collectives that support the generation of new mathematical and pedagogical ideas and understandings. The setting is a one-week summer math program designed for prospective elementary teachers to deepen particular mathematical concepts taught in elementary school. The program is facilitated by recently graduated secondary mathematics teachers to provide them an opportunity to experience mathematics teaching|learning through rich problems. The data collected include questionnaires, interviews, and video recordings. Our analyses show that many a-ha moments of mathematical and pedagogical insight are experienced by both groups as they work together throughout the week. In this workshop we will actively engage the audience in an exploration of the mathematics problems that we pose in this unique teaching|learning environment. We will present our data on the participants’ mathematical and pedagogical responses and open a discussion of the implications of our work.

No description available.

This design experiment research introduces a mathematical inquiry titled Pattern Math. The Pattern Math activities create an atmosphere where students can think mathematically, communicate mathematically and make connections between different mathematical concepts. Based on simple patterns with complex explanations, the Pattern Math activities provide students with the opportunity to develop their conceptual understanding of mathematics. Through reflections on the activities, students are able to reexamine their views of learning mathematics. This design experiment research has a narrative approach and incorporates the teaching and research technique of interactive writing. The research highlights the power of inquiry. By providing students with the opportunity to work within their zone of proximal development, the Pattern Math activities provide students with the opportunity to make mathematical discoveries and come to understand algebra and arithmetic with conceptual understanding.

This design experiment research introduces a mathematical inquiry titled Pattern Math. The Pattern Math activities create an atmosphere where students can think mathematically, communicate mathematically and make connections between different mathematical concepts. Based on simple patterns with complex explanations, the Pattern Math activities provide students with the opportunity to develop their conceptual understanding of mathematics. Through reflections on the activities, students are able to reexamine their views of learning mathematics. This design experiment research has a narrative approach and incorporates the teaching and research technique of interactive writing. The research highlights the power of inquiry. By providing students with the opportunity to work within their zone of proximal development, the Pattern Math activities provide students with the opportunity to make mathematical discoveries and come to understand algebra and arithmetic with conceptual understanding.

Made available in DSpace on 2018-06-27T19:13:29Z (GMT). No. of bitstreams: 3 Maria Gorete Nascimento Brum.pdf: 8802552 bytes, checksum: fccee26b2259d4d64d9915baa90c7e42 (MD5) Maria Gorete Nascimento Brum.pdf.txt: 190259 bytes, checksum: 3a9bb078358c2a811eb9324e17c92f95 (MD5) Maria Gorete Nascimento Brum.pdf.jpg: 3778 bytes, checksum: 39dbeec2321b4010477b95c2a3be9c4a (MD5) Previous issue date: 2012-08-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present research investigated the contributions of the use of investigative activities in the exploration of standards and regularities in numerical and geometric sequences as elements that become easy the learning of the pupils of 5º series of Basic Education. This work was carried through with a group of 5º degree with 30 pupils of the State school of Basic Education Marechal Rondon in the periphery of the city of Santa Maria, RS. The date of the research, qualitative matrix, had been gotten of the direct action teacher s in the classroom with the pupils by means of the observation and the registers in its diary beyond the analysis of the pupils, work and the presentations to the great group. It can be inferred that the objectives considered in the sessions as explore the standard concept, to recognize, to describe standards, to continue the drawing of the sequence was reached. The objectives to generalize, to explore the notion and properties of the numbers pairs, uneven and multiple, as well as the involution of natural numbers and to work the concept of area and perimeter of plain figures, partially had been reached. The results presented for the pupils it can be concluded that the investigative activities worked with the pupils of 5ª degree, had propitiated the increase of interest, the motivation in the accomplishment of the activities proposals in classroom and as consequence had an improvement in the learning. / A presente pesquisa investigou as contribuições da utilização de atividades investigativas na exploração de padrões e regularidades em sequências numéricas e geométricas como elementos facilitadores da aprendizagem dos alunos de 5º série do Ensino Fundamental. Este trabalho foi realizado com uma turma de 5º série com 30 alunos da escola Estadual de Ensino Fundamental Marechal Rondon na periferia de Santa Maria R.S. Os dados da pesquisa, de cunho qualitativo, foram obtidos da ação direta do professor na sala de aula com os alunos por meio da observação e dos registros no seu diário de campo, além da análise dos trabalhos dos alunos e de suas apresentações ao grande grupo. Pode-se inferir que os objetivos propostos nas sessões como explorar o conceito de padrões, reconhecer, descrever padrões, continuar o desenho da sequência foram plenamente atingidos. Os objetivos de generalizar, explorar a noção e propriedade dos números pares, ímpares e múltiplos, bem como a potenciação de números naturais e trabalhar o conceito de área e perímetro de figuras planas, foram parcialmente atingidos. Dos resultados apresentados pelos alunos pode-se concluir que as atividades investigativas trabalhadas com os alunos de 5º série, propiciaram o aumento de interesse, a motivação na realização das atividades propostas em sala de aula e como consequência houve uma melhoria na aprendizagem.

In this workshop we present an innovative teaching, learning and research setting that engages beginning teachers in mathematical inquiry as they investigate, represent and connect mathematical ideas through mathematical conversation, reasoning and argument. This workshop connects to the themes of teacher preparation and teaching through problem solving. Drawing on new paradigms to think about teaching and learning, we orient our work within complexity theory (Davis & Sumara, 2006; Holland, 1998; Johnson, 2001; Maturana & Varela, 1987; Varela, Thompson & Rosch, 1991) to understand teaching|learning as a complex iterative process through which opportunities for learning arise out of dynamic interactions. Varela, Thompson and Rosch, (1991) use the term co-emergence to understand how the individual and the environment inform each other and are “bound together in reciprocal specification and selection” (p.174). In particular we are interested in the conditions that enable the co-emergence of teaching|learning collectives that support the generation of new mathematical and pedagogical ideas and understandings. The setting is a one-week summer math program designed for prospective elementary teachers to deepen particular mathematical concepts taught in elementary school. The program is facilitated by recently graduated secondary mathematics teachers to provide them an opportunity to experience mathematics teaching|learning through rich problems. The data collected include questionnaires, interviews, and video recordings. Our analyses show that many a-ha moments of mathematical and pedagogical insight are experienced by both groups as they work together throughout the week. In this workshop we will actively engage the audience in an exploration of the mathematics problems that we pose in this unique teaching|learning environment. We will present our data on the participants’ mathematical and pedagogical responses and open a discussion of the implications of our work.

Using elements of design experiment research and autoethnography, this action research project investigated how viewing learning as complex participation in a community of practice characterized by mathematical inquiry impacted my teaching practice in a grade 10 Applied Mathematics class in a rural Manitoba high school. This report of the research project describes and analyzes both my attempts to change my teaching practice by drawing on theories of learning mathematics as complex participation in a community of practice and the changes that resulted from these attempts. The analysis focuses on the characteristics of a community of practice characterized by mathematical inquiry, how I attempted to foster such a community, what challenges I faced when I changed my teaching practice in this way, and how insights from this practitioner research project can inform the teaching of mathematics as well as theorizing about the learning of mathematics.

Using elements of design experiment research and autoethnography, this action research project investigated how viewing learning as complex participation in a community of practice characterized by mathematical inquiry impacted my teaching practice in a grade 10 Applied Mathematics class in a rural Manitoba high school. This report of the research project describes and analyzes both my attempts to change my teaching practice by drawing on theories of learning mathematics as complex participation in a community of practice and the changes that resulted from these attempts. The analysis focuses on the characteristics of a community of practice characterized by mathematical inquiry, how I attempted to foster such a community, what challenges I faced when I changed my teaching practice in this way, and how insights from this practitioner research project can inform the teaching of mathematics as well as theorizing about the learning of mathematics.