scholarly journals Characteristics of teacher knowledge produced by pre-service mathematics teachers: the case of open-ended problem-based learning

Author(s):  
Jani Hannula

One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper, I present a case study, conducted within the education course, in which I analyse the characteristics of teacher knowledge produced by five small groups of pre-service teachers in an open-ended problem-based learning task. The results indicate the problem-based learning approach has the potential for enhancing specialised content knowledge such as knowledge of different representations of and applications of mathematical concepts. The results also highlight the challenges in using this approach for enhancing horizon content knowledge such as knowledge about the relationships between mathematical concepts. The findings in this case study suggest that problem-based learning can be used to develop mathematics teacher education, although further research is needed to design instructional practices that enhance pre-service teachers’ horizon content knowledge.

2021 ◽  
Vol 10 (1) ◽  
pp. 68-83 ◽  
Author(s):  
Crystal Kalinec-Craig ◽  
Emily P. Bonner ◽  
Traci Kelley

This article describes an innovation in an elementary mathematics education course called SEE Math (Support and Enrichment Experiences in Mathematics), which aims to support teacher candidates (TCs) as they learn to teach mathematics through problem solving while promoting equity during multiple experiences with a child. During this 8-week program, TCs craft and implement tasks that promote problem solving in the context of a case study of a child’s thinking while collecting and analyzing student data to support future instructional decisions. The program culminates in a mock parent–teacher conference. Data samples show how SEE Math offers TCs an opportunity to focus on the nuances of children’s strengths rather than traditional measures of achievement and skill.


Author(s):  
Juliane Colling ◽  
Adriana Richit

O artigo, que se baseia nos resultados de uma pesquisa de mestrado sobre as perspectivas de utilização das tecnologias digitais na formação inicial docente em matemática, evidencia e discute aspectos transversais da articulação das tecnologias digitais ao processo de desenvolvimento de conhecimentos profissionais na formação de professores. Tomando por referencial o conceito de conhecimento profissional de Lee Shulman e o construto sobre os conhecimentos pedagógico, tecnológico e do conteúdo – TPACK, a pesquisa buscou evidenciar as perspectivas de articulação dos conhecimentos tecnológico, pedagógico e do conteúdo (matemático) nas diversas atividades formativas de um Curso de Licenciatura em Matemática de uma universidade pública federal do Sul do Brasil. O material empírico da investigação, de natureza qualitativa e baseada em uma análise de conteúdo bardiniana, constituiu-se mediante a aplicação de questionários e realização de entrevistas com docentes e discentes do referido Curso, bem como análise dos Planos de Ensino das diversas componentes curriculares e demais atividades promovidas ao longo do processo formativo. Como resultado, identificamos quatro categorias de análise, sendo: perspectiva voltada à prática docente na Educação Básica; perspectiva voltada ao desenvolvimento de conhecimentos da Matemática; perspectiva voltada ao desenvolvimento de conhecimentos sobre as tecnologias e suas possibilidades pedagógicas; e perspectiva associada a aspectos transversais da formação e profissão docente, sendo esta última apresentada e discutida neste artigo. A análise dessa perspectiva mostrou que a articulação entre os conhecimentos pedagógicos, tecnológicos e do conteúdo é intrínseca ao próprio processo formativo no respectivo Curso, que relaciona estes conhecimentos de forma transversal nas distintas atividades no decorrer do percurso formativo. Os professores do Curso compreendem e evidenciam a importância de promover a formação dos futuros professores de matemática contemplando diferentes aspectos do conhecimento profissional, e o fazem numa perspectiva de transversalidade na medida em que promovem o uso de diferentes tecnologias também nas atividades de planejamento e gestão do ensino. Os acadêmicos do Curso, por sua vez, percebem as possibilidades de uso dos recursos digitais de forma articulada à prática docente, tendo uma percepção crítica e reflexiva de uso destes recursos nas suas práticas sociais, em sua organização profissional e nas práticas profissionais cotidianas. Os documentos analisados, igualmente, apontam para a importância e as possibilidades da articulação das tecnologias no desenvolvimento de diferentes conhecimentos profissionais subjacentes à formação docente em matemática, bem como à futura prática de sala aula na educação básica dos acadêmicos do Curso.   Palavras-chave: Conhecimento Pedagógico, Tecnológico e do Conteúdo. TPACK. Formação Inicial de Professores de Matemática. Tecnologias Digitais.   Abstract This paper, which is based on master research results concerning the perspectives of using digital technologies in mathematics teacher education, evidences and discusses transversal aspects of the articulation of digital technologies to the process of developing professional knowledge in teacher education. Based on the professional knowledge concept of Lee Shulman and on the theoretical construct related to pedagogical, technological and content knowledge – TPACK, the investigation aimed highlight perspectives to articulate technological, pedagogical and content (of math) knowledge in the distinct formative activities of a Mathematic Degree Course in a Brazil South’ federal public university. The empirical material of the research, which pursues a qualitative nature and bases on Bardin’ content analysis, was constituted from questionnaires and interviews realized with teachers and students of the Course, as well as analyses on teaching plans of all curricular components and distinct activities promoted during the Course. As result, we identified four categories: a perspective on teaching practice in Basic Education; perspective focused on the development of mathematical knowledge; perspective aimed at developing knowledge about technologies and their pedagogical possibilities; and perspective associated with transversal aspects to the teacher education and professional practice. In this article, we will discuss the last category. The analysis on this perspective highlighted that the articulation among pedagogical, technological, and content knowledge is inherent to the teacher education process of the Course, which relates this knowledge in a transversal way within the course’ disciplines. Teachers of the Course comprehend and evidence the importance to promote the education of prospective mathematics teachers taking into account the distinct professional knowledge aspects, and they do this on a perspective of transversally insofar as they also use technologies to plan and manage the teaching. Furthermore, students perceive the possibilities to use digital technologies in an integrated way to the teaching practice, developing a critical and reflexive perception related to the use of these resources in their social practices, professional organization, and everyday professional practices. Also, the documents analyzed point to the importance and possibilities arising from the articulation of digital technologies in the development of professional knowledge underlying to mathematics teacher education and future classroom practice in basic education of the Course’ students.   Keywords: Pedagogical, technological and content knowledge. TPACK. Prospective Teacher Education. Digital Technologies.


2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Hans-Georg Weigand

Advantages and disadvantages of the use of digital technologies (DT) in mathematics lessons are worldwidedissussed controversially. Many empirical studies show the benefitof the use of DT in classrooms. However, despite of inspiringresults, classroom suggestions, lesson plans and research reports,the use of DT has not succeeded, as many had expected during thelast decades. One reason is or might be that we have not been ableto convince teachers and lecturers at universities of the benefit ofDT in the classrooms in a sufficient way. However, to show thisbenefit has to be a crucial goal in teacher education because it willbe a condition for preparing teachers for industrial revolution 4.0.In the following we suggest a competence model, which classifies– for a special content (like function, equation or derivative) –the relation between levels of understanding (of the concept),representations of DT and different kind of classroom activities.The flesxible use of digital technologies will be seen in relationto this competence model, results of empirical investigations willbe intergrated and examples of the use of technologies in the upcoming digital age will be given.


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