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Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment InterjectionsLemon, Travis L. 16 July 2010 (has links) (PDF)
In order to investigate ways pre-service student teachers (PSTs) might learn to teach with high-level tasks and effectively incorporate student thinking into their lessons a teaching experiment was designed and carried out by the cooperating teacher/researcher (CT). The intervention was for the CT to interject into the lessons of the PSTs during moments of opportunity. By interjecting a small question or comment during the lesson the CT hoped to support the learning of both the students of mathematics in the class and the PSTs. This in-the-moment interjecting was meant to enhance and underscore the situated learning of the PSTs within the context of actual practice. Essentially the PSTs learned how to manage and improve the discourse of the classroom in the moment of the discourse. This study utilized both an ongoing analysis of the data during collection in order to inform the instruction provided by the CT and a retrospective analysis of the data in order to develop an understanding of the developmental sequence through which PSTs progressed. The results suggest the interjections provided to the PSTs served multiple roles within the domains of mathematical development for the students of mathematics and pedagogical development for the PSTs. A classification of the interjections that occurred and the stages of development through which PSTs passed will be discussed. Implications from this work include increased attention to the groundwork leading up to the student teaching experience as well as an adjustment to the role of cooperating teacher to be more that of a teacher educator.
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Specialdidaktiska perspektiv på grundläggande antals- och taluppfattningWästerlid, Catarina Anna January 2022 (has links)
Syftet med föreliggande licentiatavhandling är att, utifrån ett specialdidaktiskt perspektiv, bidra med kunskap om lågpresterande elevers grundläggande antals- och taluppfattning, och hur utvecklingen av denna kan stödjas. Den övergripande forskningsfråga som besvaras är vilka aspekter, som ur ett specialdidaktiskt perspektiv, är särskilt betydelsefulla att beakta vad gäller lågpresterande elevers kunskapsutveckling inom grundläggande antals- och taluppfattning. Avhandlingen består av två delstudier. I delstudie 1, som är en systematisk litteraturöversikt, studeras vad som är kännetecknande för lågpresterande årskurs F-3-elever och hur de definieras i forskningslitteraturen. I den andra studien, delstudie 2, undersöks vilket kunnande gällande tals del-helhetsrelationer som förskoleklasselever utvecklar i en undervisningsinsats där konceptuella subitiseringsaktiviteter fokuseras. Specialdidaktikens förebyggande och stödjande roll utgör studiens övergripande förståelseram där de lågpresterande elevernas kunskapsutveckling förstås i förhållande till vilket lärande som möjliggörs i undervisningen. Det matematiska innehållet är grundläggande antals- och taluppfattning med fokus på konceptuell subitisering. Teorier om barns antals- och taluppfattningsutveckling (Baroody m.fl., 2009; Nunes &Bryant, 2007; Sayer m.fl. 2016), inbegripet teorier om subitisering (Clements m.fl., 2019; Kaufman m.fl., 1949) och groupitizing (Starkey &McCandliss, 2014), har utgjort den innehållsliga utgångspunkten. För att tolka specialdidaktikens specifika bidrag och krafter i relation till allmän matematikdidaktisk kompetens har ramverket Mathematical Knowledgefor Teaching (MKT) (Ball m.fl., 2008) använts, mer specifikt de tre delarna specialized content knowledge, knowledge of content and students och knowledge of content and teaching. Resultatet av syntesen visar att den specifika kompetens som krävs i relation till innehållet (specialized content knowledge), är fördjupad kunskap om centrala aspekter och vanliga trösklar i elevers kunskapsutveckling inom grundläggande antals- och taluppfattning för att motverka framtida matematiksvårigheter. Även fördjupad kunskap om elevers individuella variationer vad gäller att förstå och hantera antal och tal (knowledge of content and students) för att tidigt kunna identifiera elever i svårigheter är centralt och slutligen fördjupad kunskap om hur lågpresterande elevers antals-och taluppfattning kan stödjas och svårigheter förebyggas och överbryggas i undervisningen (knowledge of content and teaching). Specialdidaktikens bidrag förstås som krafter som hjälper till att balansera relationen mellan den svagpresterande eleven, läraren och matematikinnehållet i undervisningen, så att lärande möjliggörs. Specialdidaktisk kompetens kan därmed sägas komplettera den allmänna ämnesdidaktiska kompetensen (MKT) genom sitt bidrag med fördjupad kunskap om hur elever som inte utvecklas som förväntat i matematik kan stödjas, i grundläggande antals- och taluppfattning, vilket bildar Specialdidactic Mathematical Knowledge for Teaching eller SMKT.
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A Case Study on the Impact of Intermediate Elementary Teachers’ Pedagogical Content Knowledge and Expectancy Beliefs of Students on Scaffolding Practices in Mathematics InterventionBlakeslee, Deborah 01 January 2024 (has links) (PDF)
This study investigated the impact expectancy beliefs had on third through fifth-grade teachers’ instructional teaching practices. These instructional teaching practices included how teachers used their pedagogical content knowledge, specifically their content knowledge for teaching mathematics and formative assessment, to make scaffolding decisions while supporting students in mathematics intervention. The investigation included the analysis of stratified sampling procedures, expectancy beliefs, observations, and self-reported scaffolding ratings. A multiple case study was conducted to understand how four participants, the teachers in the study, expected students to perform in mathematics intervention along with the participants’ pedagogical content knowledge and the impact those beliefs and knowledge had on scaffolding practices. Scaffolding practices highlighted in this study were the teachers’ use of cognitive activation, mathematical discourse, and handling errors productively. Findings suggested that even though teachers demonstrated having content knowledge for teaching mathematics and effective use of formative assessment the teachers still scaffolded just-in-case students might need it during mathematics intervention. The results also suggested that teachers relied upon their expectancy beliefs of students to make scaffolding decisions more than the teachers relied upon their own pedagogical content knowledge. Additionally, this study found that a scaffolding workshop focused on teacher actions may impact the teachers’ self-reported ratings and in turn the teachers’ scaffolding practices. Discussion of the findings in relation to the current literature and their implications was provided. Continued research was suggested to examine how teachers self-rate their scaffolding practices pre- and post-scaffolding workshops and the impact that may have on teachers’ scaffolding practices. These findings add to the research in the field of mathematics education in equitable teaching practices, mathematics intervention, and scaffolding practices.
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Analisando a mobilização de conhecimentos algébricos de professores de educação básica : o momento de preparação de aulas sobre equaçõesOliveira, Felipe Augusto Pereira Vasconcelos Santos e January 2014 (has links)
Orientador: Prof. Dr. Alessandro Jacques Ribeiro / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Ensino, História, Filosofia das Ciências e Matemática, 2014. / Essa é uma pesquisa a qual fora desenvolvida no programa de pós-graduação em Ensino, História e Filosofia das Ciências e Matemática na Universidade Federal do ABC, em Santo André, cujo título é: "Analisando a mobilização de conhecimentos algébricos de professores de educação básica: O momento de preparação de aulas sobre equações.". Os objetivos dessa pesquisa consistem em mapear, investigar e compreender quais os conhecimentos algébricos que são mobilizados por professores quando estão elaborando suas aulas sobre equações para a Educação Básica. Adotou-se uma abordagem qualitativa como metodologia de pesquisa e os dados foram obtidos através de questionários e da análise documental das aulas preparadas pelos professores dessa pesquisa; gravações em áudio dos encontros os quais os professores preparam suas aulas em duplas. Os seis sujeitos de pesquisa são pessoas que preparam aulas para a Educação Básica nos conteúdos matemáticos tanto para seu ofício como professor(a) efetivo ou contratado, quanto para o desenvolvimento de pesquisa associado aos projetos de formação inicial ou continuada. Com isso, para fundamentar essa pesquisa inclusive nas análises dos dados, foram utilizados os trabalhos de Shulman (1986 e 1987) e Ball e equipe (2008). Estes últimos autores sugerem o quadro teórico do "Conhecimento Matemático para o Ensino", que é o "conhecimento matemático necessário para realizar o trabalho de ensinar matemática", além da existência de dois subdomínios, a partir dos trabalhos de Shulman: (i) Conhecimento Comum do Conteúdo e Conhecimento Especializado do Conteúdo; e (ii) Conhecimento do Conteúdo e os Estudantes e Conhecimento do Conteúdo e o Ensino. Após analisarmos os dados, baseados na perspectiva do conhecimento matemático para o ensino, pudemos identificar, entre outros, os seguintes conhecimentos algébricos: Reconhecimento de que uma sentença matemática não é equação (Conhecimento Comum do Conteúdo); Compreensão dos multisignificados do símbolo "=" (Conhecimento Especializado do Conteúdo); Reconhecimento dos conteúdos prévios para que os alunos possam compreender e participar de uma aula sobre equações (Conhecimento do Conteúdo e os Estudantes); Utilização de uma abordagem etimológica das palavras "equação" e "igualdade", com o objetivo de promover uma discussão destes conteúdos em sala de aula (Conhecimento do Conteúdo e o Ensino) e, por fim, Reconhecer que o conteúdo de equação, em especial a equação polinomial de 1º grau, tem forte relação e importância para o conteúdo de inequações, funções e outros conteúdos mais avançados (Conhecimento Curricular). / This is a research which had been developed in Master¿s program in Teaching, History and Philosophy of Sciences and Mathematical at the Federal University of ABC, in Santo André, whose title is "Analyzing the mobilizations of algebraic knowledge from basic education teachers: The moment to prepare lessons about equations". The objectives of this research are to map, investigate and understand which algebraic knowledge that was mobilized by teachers when working out their classes about equations for Basic Education. We adopted a qualitative approach to research methodology and data were collected through questionnaires and documentary analysis of the lessons had been prepared by the teachers of this research; audio recorded in meetings when teachers had planned their lessons in pairs. Those six teachers are people who prepare lessons for Basic Education in mathematical content to their craft both as a teacher actual or engaged, and for the development of research projects associated with initial or continuing training. Thus, to support this research including data analysis, the work of Shulman (1986 and 1987) and Ball et al. (2008) were used. Ball et al. suggest the theoretical framework of "Mathematical Knowledge for Teaching" which is the "Mathematical Knowledge needed to perform the job of teaching math" beyond the existence of two subdomains, from the works of Shulman: (i) Common Content Knowledge and Specialized Content Knowledge; also (ii) Knowledge of Content and Students, and Knowledge of content and Teaching. After analyzing the data, based on the perspective of mathematical knowledge for teaching, we identified, among others, the following algebraic knowledge: Recognition of a mathematical sentence is not an equation (Common Content Knowledge); Multimeaning understanding of the "=" symbol (Specialized Content Knowledge); Recognition of prior knowledge, so that students can understand and participate in an equations class (Content Knowledge and Students); Use an etymological approach of the words "equation" and "equality" with the aim of promoting a discussion of such content in the classroom (Content Knowledge and Teaching) and, finally, recognize that the contents of the equation, especially linear polynomial equation, has a strong relationship and importance to the content of inequalities, functions and other more advanced contents (Curricular Knowledge).
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The Effects Of A Mathematics Teaching Methods Course On Pre-service Elementary Mathematics TeachersSevis, Serife 01 July 2008 (has links) (PDF)
The purpose of this study is to examine the effects of a mathematics teaching methods course on pre-service elementary mathematics teachers&rsquo / content knowledge for teaching mathematics (CKTM). In order to accomplish this purpose, pre-service mathematics teachers&rsquo / understanding of basic concepts and procedures in school mathematics, use of mathematical definitions, presentation of mathematical content to students, identification of common errors, misconceptions and solution strategies and evaluation of unusual solution methods were examined with the help of a multiple choice test.
The data were collected from 43 senior pre-service mathematics teachers from a teacher education program at a large public university in Ankara. The participants were given an 83-item test to measure their content knowledge for mathematics teaching at the beginning and after the methods course. The purpose of the pre- and post-test assessment was to measure the amount of change in the participants' / knowledge for mathematics teaching. The test was developed and piloted at the University of Michigan in the USA for Learning Mathematics for Teaching (LMT) Project. Quantitative data analysis techniques were used to answer the research questions.
The results indicated that there was a significant effect of the mathematics teaching methods course on pre-service teachers&rsquo / content knowledge for teaching mathematics. Moreover, the findings showed that there is no significant mean difference between male and female pre-service teachers, and between the pre-service teachers who have taken at least one mathematics teaching elective course and the ones who have not taken any elective course related to mathematics teaching in terms of their CKTM. Also, the study showed that there is a significant positive relationship between pre-service teachers&rsquo / CKTM and their academic achievement on undergraduate mathematics content courses.
The study is expected to make important contributions to the literature by providing information about whether the methods courses significantly contribute to pre-service teachers&rsquo / understanding of knowledge for mathematics teaching. Moreover, the findings of the study is hoped to inform teacher educators and policy makers about the needs and improvements in teacher preparation programs.
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Investigating Elementary Teachers’ Mathematical Knowledge for Teaching Geometry: The Case of Classification of QuadrilateralsNg, Dicky 07 May 2012 (has links) (PDF)
This paper examines the mathematical knowledge for teaching (MKT) in Indonesia, specifically in school geometry content. A translated and adapted version of the MKT measures developed by the Learning Mathematics for Teaching (LMT) project was administered to 210 Indonesian primary and junior high teachers. Psychometric analyses revealed that items related to classification of quadrilaterals were difficult for these teachers. Further interactions with teachers in a professional development setting confirmed that teachers held a set of exclusive definitions of quadrilaterals.
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Conhecimento matemático para o ensino de polinômios na educação básicaLautenschlager, Etienne January 2017 (has links)
Orientador: Dr. Alessandro Jacques Ribeiro / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Neurociência e Cognição, 2017. / O presente estudo preocupou-se em investigar se e como o conceito anel de polinomios e (re)construido por professores de Matematica que lecionam na Educacao Basica. Neste estudo, discutiu-se a importancia da construcao de conceitos matematicos, tendo por um lado a contribuicao do campo da ciencia cognitiva, principalmente os trabalhos Anna Sfard, e as recentes pesquisas sobre conhecimento matematico para o ensino, na area de Educacao Matematica, utilizando, essencialmente os trabalhos de Debora Ball, Jose Carrillo e seus colaboradores. Adotou-se a metodologia de pesquisa de natureza quantiqualitativa e o processo de coleta de dados se desenvolveu por meio de encontros do Curso de Extensao \O Ensino de Algebra para a Educacao Basica., ministrado na Universidade Federal do ABC, no estado de Sao Paulo, e conduzido por professores universitarios integrantes do programa Observatorio da Educacao. Para a producao de dados da pesquisa, utilizou-se como instrumentos metodologicos os questionarios e os registros escritos, elaborados/produzidos pelos professores-participantes da pesquisa durante os encontros do referido curso. A partir da analise dos dados, os resultados da investigacao apontam para a necessidade de promover acoes que possam ampliar e aprofundar o conhecimento especifico matematico desses professores, dado que ninguem pode ensinar o que nao sabe. Tambem evidenciamos a necessidade de um (re)pensar sobre o ensino de polinomios, uma vez que tal a analise dos dados realizados revelou que os professores desconhecem procedimentos para se operar com polinomios. Espera-se com este estudo chamar a atencao das politicas publicas para a necessidade de investimento na formacao continuada dos professores de matematica e, por conseguinte, na valorizacao da carreira docente. / This study intended to investigate mathematical knowledge building for teaching the concept of polynomial with Math teachers in Basic Education. In this study, the importance of building mathematical concepts was discussed, considering contributions from the cognitive sciences field, particularly Anna Sfard`s works, and recent research on mathematical knowledge for Algebra teaching from the Math Education field, using essentially works by Ball, Carrillo and their collaborators. A qualitative-quantitative approach for our research design was adopted, and the data gathering process was developed from meetings of a Extracurricular Course on Algebra Teaching for Basic Education, offered at the Federal University of ABC, in São Paulo State, conducted by university professors from the Education Observatory program. In producing the research data, questionnaires and written registers were used, elaborated by research participants themselves during the Course`s meetings. From the analysis of the data, the research results point to the need to promote actions that can broaden and deepen the specific mathematical knowledge of these teachers, given that no one can teach what they do not know. We also show the need for a new thinking about the teaching of polynomials, once such analysis of the data revealed that teachers are not aware of procedures to operate with polynomials. It is hoped that this study will draw the attention of public policies to the need for investment in the continuing education of mathematics teachers and, consequently, in the valorization of the teaching career.
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A geometria no curso de Pedagogia a distância do acordo Brasil-Japão : conhecimentos para a docência mobilizados na formação inicialMoreno, Heliete Martins Castilho 09 April 2014 (has links)
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Previous issue date: 2014-04-09 / O trabalho intitulado “A Geometria no Curso de Pedagogia a distância do acordo Brasil-Japão: conhecimentos para a docência mobilizados na formação inicial” resultou da pesquisa realizada no Programa de Pós Graduação em Educação, na linha de Educação em Ciências e Educação Matemática da Universidade Federal de Mato Grosso (UFMT), junto ao Grupo de Estudos e Pesquisas em Educação Matemática (GRUEPEM). O interesse em saber quais as contribuições que a realização da área de Matemática oferece aos acadêmicos para o exercício de suas funções docentes nos anos iniciais do ensino fundamental surge desde a primeira participação como professora formadora do Curso de Pedagogia a distância da UFMT nas oito ofertas realizadas. Tendo como objetivo geral “Investigar os conhecimentos para docência em Geometria, mobilizados pelos acadêmicos do Curso de Pedagogia na modalidade a distância do acordo Brasil-Japão”, elegeu-se a abordagem qualitativa, com base em Bogdan e Biklen (1994) e a análise interpretativa com método da análise de conteúdo de acordo com Bardin (2011) e Laville (1999) para responder o problema de pesquisa: Quais conhecimentos para a docência foram mobilizados com a Geometria apresentada no curso de formação inicial de Pedagogia a distância do acordo Brasil-Japão? Para a produção de informações utilizou-se os registros das acadêmicas nos fóruns que discutiram assuntos de geometria no decorrer da área, nos relatórios do estágio realizado em Geometria depois de concluída a área de Matemática e nos Trabalhos de Conclusão de Curso. Os dados foram analisados utilizando a teoria de García (1999) sobre a formação de professores, com apoio de Tardif (2002) e Shulman (1986). Freitas e Bittar (2004), Nacarato (2001), Nacarato e Passos (2003) e Lorenzato (2006) contribuíram com os temas sobre ensino de Matemática. Foram utilizadas como categorias de análise, os componentes do conhecimento profissional propostos por García (1999): psicopedagógico, do conteúdo, didático do conteúdo e do contexto. Os sujeitos foram selecionados a partir da classificação dos relatórios de estágio, que resultou em cinco acadêmicas que realizaram o estágio em Geometria, em Escolas Brasileiras no Japão, no Ensino Fundamental I, que têm a Pedagogia como primeira formação superior e que contribuíram pelo menos uma vez em cada um dos fóruns analisados. A análise realizada aponta a mobilização, pelas acadêmicas, durante o desenvolvimento da área de matemática no Curso de Pedagogia a distância do acordo Brasil-Japão, dos quatro componentes do conhecimento para a docência apontados por García (1999). Acreditamos que pela natureza dos próprios documentos analisados, a categoria mais presente nos fóruns foi o Conhecimento de Conteúdo, enquanto que nos relatórios de estágio foi o Conhecimento Didático do Conteúdo e nos Trabalhos de Conclusão de Curso foi o Conhecimento Psicopedagógico. O Conhecimento do Contexto aparece muito pouco nos TCC, não aparece nos fóruns, mas é mobilizado nos relatórios de estágio de uma forma considerável. / The paper entitled "The Geometry in Pedagogy Course of distance the Agreement Brazil - Japan: knowledge for teaching mobilized in the initial training" resulted from research conducted in the post-Graduation Program in Education, in line de Science Education and Mathematics Education of University Federal de Mato Grosso (UFMT) with the Group of Studies and Research in Mathematics Education (GRUEPEM). The interest in knowing what are the contributions that holding the area of Mathematics offers academics to carry out their teaching duties in the early years of elementary school arises from the first participation as a trainer currently teaching pedagogy of distance at UFMT the eight offerings made. Having the general objective "to investigate the knowledge in teaching Geometry, mobilized by academics of the Education Course of distance the Agreement Brazil-Japan", chose a qualitative approach, based on Bogdan and Biklen (1994) and interpretive analysis method with content analysis according to Bardin (2011) and Laville (1999) to answer the research problem: What skills for teaching were mobilized with the geometry shown in the initial course of Pedagogy distance of the agreement Brazil-Japan? To produce information were used remarks from the academic foruns boards that discussed matters of geometry throughout the area, on the reports of internship in geometry after the completion in Mathematics area and Course Conclusion Paper (CCP). Data were analyzed using the theory of Garcia (1999) on teacher training, supported by Tardif (2003) and Shulman (1986). Freitas and Bittar (2004), Nacarato (2001), Nacarato and Passos (2003) and Lorenzato (2006) contributed to the topics on teaching mathematics. Psycho pedagogic, content, didactic content and context: the components of professional knowledge proposed by García (1999) were used as categories of analysis. The subjects were selected from the classification of internship reports, which resulted in five academics who were trainee in Geometry in Brazilian Schools in Japan, in elementary school, who have Pedagogy as superior first training and who contributed at least once in each of the analyzed forums. The analysis points to the mobilization by academics, during the development of the area of mathematics at the Pedagogy Course of distance of Brazil-Japan agreement, the four components of knowledge for teaching pointed out by García (1999). We believe that by the nature of the documents themselves analyzed, the most current category on the forums was the Knowledge Content, while the reports of internship was Didactic Content Knowledge and on course conclusion paper was the Psycho pedagogic Knowledge. The Knowledge Context appears very little in the CCP, doesn’t appear on the forums, but it is mobilized in internship reports with an appreciable extent.
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Att få syn på avgörande skillnader : Lärares kunskap om lärandeobjektet / Learning to see distinctions : Teachers' gaining knowledge of the object of learningMårtensson, Pernilla January 2015 (has links)
Lärare som undervisar i matematik förväntas kunna mer avancerad matematik än vad de undervisar om. Men formell matematikkunskap anses inte vara tillräckligt för att lärare ska kunna undervisa så att ämnesinnehållet blir begripligt för eleverna, de behöver även pedagogical content knowledge (PCK). Begreppet belyser en speciell form av ämneskunskap för undervisning och skiljer sig från den matematikkunskap som används av andra välutbildade vuxna. Det har föreslagits att olika arrangemang av kollegialt och praktikbaserat lärande kan utveckla lärares PCK. Ett exempel på ett sådant arrangemang är learning study. Den här avhandlingen handlar om den kunskap om lärande och undervisning i matematik som studiens lärare utvecklar då de deltar i learning studies och utforskar sin praktik utifrån ett variationsteoretiskt perspektiv. Det yttersta syftet med en learning study är att utveckla elevernas lärande om specifika lärandeobjekt, genom att undersöka vad som kan vara kritiskt för elevernas lärande. I ett samarbetsprojekt med fyra högstadielärare genomfördes två learning studies i matematik, under ett år. Lärargruppen undersökte vad eleverna behöver lära för att de ska förstå i) varför en kvot kan vara större än talet i täljaren och ii) olika representationer av konstanterna k och m i räta linjens ekvation. Under learning study-arrangemangets olika steg samlades studiens empiri in och denna består av filmade lektioner, inspelade möten där lärargruppen planerade och analyserade undervisning och elevers lärande, skriftliga elevtest samt elevintervjuer. Studien har en variationsteoretisk utgångspunkt, vilket innebär att lärande förklaras ske när en person ser något på ett nytt och mer kvalitativt sätt, genom att personen urskiljer aspekter som han/hon inte tidigare har urskilt. Studien visar de två lärandeobjektens kritiska aspekter samt hur de kritiska aspekterna gradvis förändrades och specificerades. Förändringen var ett resultat av att lärargruppen fick syn på avgörande detaljer om på vilket sätt eleverna förstod ämnesinnehållet samt hur skilda sätt att förstå kunde användas i undervisningen för att utveckla elevernas lärande. Där av titeln att få syn på avgörande skillnader. Denna form av utvecklad kunskap om lärandeobjektet kan ses som ett bidrag om PCK och vad det kan vara. / It is a common view that teachers need more than formal content knowledge to teach and to make the content comprehensible to others. They also need pedagogical content knowledge, or PCK (Shulman, 1986). It has been suggested that different teacher collaboration approaches may support teachers’ development of PCK (Chapman, 2013, Davis & Renert, 2014; Steele & Rogers, 2012). This thesis aims to provide insights into the kind of knowledge about teaching and learning mathematics that teachers develop through their participation in a specific collaboration approach called learning study. Four teachers of mathematics and their 74 students (aged 15−16 years) participated in two learning studies over the course of one year. The foremost aim of a learning study is to enhance student learning about specific objects of learning and to identify what is critical for the students’ learning (Marton & Tsui, 2004). The objects of learningin the two learning studies were to understand that dividing with a denominator between 0 and 1 gives a quotient larger than the numerator and to understand different representations of the constants b and m in the equation of the straight line. During the two learning studies data were collected from 8 video-recorded lessons, 2 written student tests, student interviews, and 14 audio-recorded sessions in which the teachers and I (PhD student) planned, analysed and revised teaching and student learning. The analysis was based on variation theory (Marton & Tsui, 2004) and focused on what participants considered to be critical aspects of the objects of learning and on the components embedded in that knowledge. The result shows the identified critical aspects of the two objects of learning and, furthermore, how the teachers’ knowledge about those critical aspects gradually changed and became more refined and specified in relation to their students’ understanding. The thesis provides an insight into the value of the teachers’ enhanced knowledge of the object of learning, in relation to how PCK can be understood.
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Investigating Elementary Teachers’ Mathematical Knowledge for TeachingGeometry: The Case of Classification of QuadrilateralsNg, Dicky 07 May 2012 (has links)
This paper examines the mathematical knowledge for teaching (MKT) in Indonesia, specifically in school geometry content. A translated and adapted version of the MKT measures developed by the Learning Mathematics for Teaching (LMT) project was administered to 210 Indonesian primary and junior high teachers. Psychometric analyses revealed that items related to classification of quadrilaterals were difficult for these teachers. Further interactions with teachers in a professional development setting confirmed that teachers held a set of exclusive definitions of quadrilaterals.
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