Preservice Teachers’ Mathematical Knowledge about Repeating Patterns and their Ability to Notice Preschoolers Algebraic Thinking

Background: Several studies have shown that many preservice teachers (PTs) who teach in the early years have a superficial knowledge about repeating patterns (RPs), which affects their knowledge about children’s algebraic thinking. Objective: This article aims to understand PTs’ algebraic thinking and their ability to notice preschoolers algebraic thinking and how these two domains articulate within a teacher education experiment. Design: The study follows a qualitative methodology based on participant observation, complemented by document collection. Setting and participants: The study stems from a teaching experiment carried out in a school module focused on patterns and algebra of a degree in basic education, with two pairs of PTs as participants. Data collection and analysis: The data come from the written productions and discussions between the elements of each pair of PTs within the scope of the tasks proposed in the teacher education course, adopting an original analysis framework. Results: The results reveal that the PTs successfully identify the structure of the RPs and the general position of each term; however, one of the pairs still find difficulties in fully understanding that mathematical object. The pairs attend to relevant aspects of children’s algebraic thinking, although sometimes with limited interpretation. Conclusions: This study highlights the importance of creating opportunities in initial teacher education for PTs to develop their algebraic thinking from an early algebra perspective and to analyse, in this context, the preschoolers’ work.

Download Full-text

O que dizem as pesquisas sobre a Resolução de Problemas na formação inicial de professores de Matemática: um olhar sobre as fragilidades metodológicasWhat research on problem solving in the initial teacher education of mathematics says: a look into the methodological weaknesses

Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática ◽

10.23925/1983-3156.2020v22i2p721-750 ◽

2020 ◽

Vol 22 (2) ◽

pp. 721-750

Author(s):

Luiz Otavio Rodrigues Mendes ◽

Ana Lucia Pereira ◽

Marcelo Carlos de Proença

Keyword(s):

Teacher Education ◽

Problem Solving ◽

Teaching And Learning ◽

Basic Education ◽

Initial Teacher Education ◽

Future Research ◽

Point Problem ◽

Mathematical Content ◽

Revisión Sistemática ◽

Starting Point

ResumoA resolução de problemas, quando trabalhada com o problema como ponto de partida, tem apresentado profícuas possibilidades no ensino superior. No entanto, quais as possíveis fragilidades quando se trabalha com esta abordagem nesta perspectiva? À vista disso, este artigo apresenta o resultado de uma pesquisa que tem como objetivo desvelar as fragilidades que se evidenciam a partir do desenvolvimento da abordagem de resolução de problemas, em que se tem o problema como ponto de partida na formação inicial de professores de Matemática, apresentadas em teses e dissertações. A partir de uma revisão sistemática da literatura, encontramos 12 pesquisas que constituíram o corpus de dados, para serem analisadas seguindo as técnicas de Análise de Conteúdo, de onde foi possível identificarmos quatro categorias. Os principais resultados revelam que as fragilidades se relacionam com: I) dificuldades quanto à falta de conhecimento sobre o conteúdo matemático da educação básica pelos licenciandos; II) dificuldades apresentadas pelos licenciandos em comunicar suas ideias a respeito do conteúdo matemático trabalhado; III) dificuldade no entendimento dos problemas pelos estudantes; e, IV) dificuldades relativas ao tempo, referentes à realização das atividades pelos licenciandos e ao desenvolvimento da abordagem de ensino. Tais apontamentos podem contribuir com pesquisas futuras que desejem traçar este caminho, aprimorando-as e contribuindo com o processo de ensino e aprendizagem da Matemática.Palavras-chave: Solução de problemas, Formação inicial de professores, Matemática.AbstractWhen working with the problem as a starting point, problem-solving has presented fruitful possibilities in Higher Education. However, what are the possible weaknesses when working with this approach from this perspective? In view of this, this article presents the result of research that aims to unveil the fragilities that are evident from the development of the problem-solving approach, in which the problem is taken as a starting point in the initial training of mathematics teachers, presented in theses and dissertations. From a systematic review of the literature, we found 12 surveys that constituted the corpus of data, to be analyzed following the Content Analysis techniques, from which it was possible to identify four categories. The main results reveal that the weaknesses are related to I) difficulties related to the students’ lack of knowledge about the mathematical content of basic education; II) students’ difficulties to communicate their ideas about the mathematical content worked; III) students’ difficulty in understanding the problems; and, IV) difficulties related to time, concerning the students’ activity performance and the development of the teaching approach. Such notes can contribute to future research that wishes to follow this path, improving them and contributing to the process of teaching and learning Mathematics.Keywords: Problem-solving, Initial teacher education, Mathematics.ResumenLa resolución de problemas cuando se trabaja con el problema como punto de partida, ha presentado posibilidades fructíferas en la educación superior. Sin embargo, ¿cuáles son las posibles debilidades de entender y trabajar con este enfoque en esta perspectiva? En vista de esto, este artículo presenta el resultado de una investigación que tiene como objetivo develar las debilidades que se evidencian a partir del desarrollo del enfoque de resolución de problemas, en el que el problema se toma como punto de partida en la formación inicial de docentes de Matemáticas, presentadas en tesis y disertaciones. A partir de una revisión sistemática de la literatura, se encontraron 12 investigaciones que constituían el corpus de datos, para ser analizadas siguiendo las técnicas de Análisis de Contenido de manera cualitativa. Los principales resultados revelan que las debilidades están relacionadas con I) dificultades relacionadas con la falta de conocimiento sobre el contenido matemático de la Educación Básica por parte de los estudiantes de docencia, II) dificultades presentadas por los estudiantes de docencia para comunicar sus ideas sobre el contenido matemático trabajado, III) dificultad presentada por los alumnos para comprender problemas y IV) dificultad relacionada con el tiempo para desarrollar actividades y aplicar el enfoque. Tales notas pueden contribuir a futuras investigaciones que deseen trazar este camino, mejorarlas y contribuir al proceso de enseñanza y aprendizaje de las Matemáticas.Palabras clave: Resolución de problemas, Formación inicial de profesores, Matemáticas

Download Full-text

Informing Teaching Through Community Engagement

Handbook of Research on Service-Learning Initiatives in Teacher Education Programs - Advances in Educational Marketing, Administration, and Leadership ◽

10.4018/978-1-5225-4041-0.ch015 ◽

2018 ◽

pp. 278-298

Author(s):

Trish Lewis ◽

Letitia Hochstrasser Fickel ◽

Glynne Mackey ◽

Des Breeze

Keyword(s):

Teacher Education ◽

Preservice Teachers ◽

Community Engagement ◽

Initial Teacher Education ◽

Teacher Education Programs ◽

Learning Needs ◽

Diverse Range ◽

White Middle Class ◽

Lower Socioeconomic

Preservice teacher education programs prepare teachers for a variety of educational settings that serve a diverse range of children. Research suggests that many graduates lack confidence and the capability to teach those from backgrounds different from their own, including children from different cultural and linguistic backgrounds, those from lower socioeconomic backgrounds, and children with additional learning needs. In the bicultural, and increasingly multicultural, New Zealand context, preservice teachers are overwhelmingly from White, middle-class, monolingual backgrounds. This chapter offers a case study of the development of a community engagement course within an initial teacher education degree program. Based on Kolb's model of experiential learning and Moll's notions of funds of knowledge and identity, the course aims to enhance preservice teachers' knowledge of the lives of children they teach, and their dispositions and cultural competence for teaching, through personal and professional interaction with the community.

Download Full-text

Scoping the meaning of ‘critical’ in mathematical thinking for Initial Teacher Education

Policy Futures in Education ◽

10.1177/1478210317719778 ◽

2017 ◽

Vol 15 (6) ◽

pp. 713-728 ◽

Cited By ~ 4

Author(s):

Jane Furness ◽

Bronwen Cowie ◽

Beverley Cooper

Keyword(s):

Teacher Education ◽

Preservice Teachers ◽

New Zealand ◽

Adult Learners ◽

Mathematical Thinking ◽

Initial Teacher Education ◽

Adult Participation ◽

Achievement Data ◽

Key Policy ◽

Administrative Tasks

Current strong emphasis on literacy and numeracy in New Zealand educational policy, as elsewhere, reverberates in different ways in institutions charged with children’s and adults’ learning. A common response is to locate literacy and numeracy centrally in programmes aimed at preparing children for and enhancing adult participation in 21st century life and work. These agendas overlap in preservice teacher education. Preservice teachers enter Initial Teacher Education (ITE) programmes as adult learners engaged in building literacy and numeracy capability for teaching across the curriculum, working with student achievement data and administrative tasks, aspects of which may also be useful in their wider lives. These activities involve making judgements that require critical thinking, another key policy focus in New Zealand and internationally for children’s and adults’ learning. This article explores meanings of ‘critical’ in the context of mathematical thinking in ITE programmes. Given that mathematically based arguments can have both helpful and harmful consequences for humanity, we propose that development in preservice teachers’ capacity for critical mathematical thinking is crucial. In these times of significant global change we advocate for development of the kind of critical mathematical thinking that facilitates teachers working actively in pursuit of a socially just and sustainable world.

Download Full-text

Gaining insight into teaching profession by using film: a preservice teachers’ experience

MATEC Web of Conferences ◽

10.1051/matecconf/201929013003 ◽

2019 ◽

Vol 290 ◽

pp. 13003

Author(s):

Daniela-Maria Creţu

Keyword(s):

Teacher Education ◽

Preservice Teachers ◽

Teacher Education Program ◽

Research Question ◽

Teaching Profession ◽

Initial Teacher Education ◽

Instructional Tools ◽

Analysis Technique ◽

Second Year ◽

Insight Into

Films can be used as instructional tools in higher education in different disciplines. In the context of teacher education, films with and about teachers and pupils are valuable resources for learning about the teaching profession. The purpose of this study is to examine the pre-service teachers’ reflections on a film with an educational content and message - The Triumph (The Ron Clark Story, 2006). One research question guided the investigation: What are the students’ cognitive and emotional gains for the teaching profession as a result of watching this film? The participants consisted of eighty-two second year students, enrolled in an initial teacher education program at a Romanian university. At the end of a one-semester course, named Pedagogy (Instruction and Students’ Assessment) pre-service teachers were invited to watch a film and then to reflect about it, by completing an open-ended questionnaire. The responses were analyzed through the content analysis technique. Examples of comments made by preservice teachers are presented and analyzed. The results show a range of understandings gained by future teachers through the use of the film.

Download Full-text

The Initial Algebraic Knowledge of Preservice Teachers

Mathematics ◽

10.3390/math9172117 ◽

2021 ◽

Vol 9 (17) ◽

pp. 2117

Author(s):

Alberto Zapatera ◽

Eduardo Quevedo

Keyword(s):

Preservice Teachers ◽

Primary School ◽

Student Teachers ◽

Algebraic Thinking ◽

Early Algebra ◽

Primary School Students ◽

Training Process ◽

School Students ◽

Starting Point ◽

Single Solution

Early algebra proposes to incorporate algebra in primary school from the first years of schooling. The success of this incorporation depends, to a large extent, on the training of teachers, so the objective of this article is to study whether the degree of algebraic knowledge of student teachers at the beginning of their training. To conduct this, 106 preservice teachers were given a questionnaire. This survey is based on two daily life situations. They had to propose tasks to develop algebraic reasoning in primary school students. Most of the participants designed tasks in which they assigned specific values to the indeterminate ones and solved them arithmetically. In this way, they transformed open situations and numerous opportunities to promote algebraic thinking in students through the generalization and representation of relationships and functions into closed single-solution problems that do not promote algebraic thinking. We can see from the results that the participants’ algebraic knowledge is insufficient. Therefore, it is necessary to include in their training process the programs and experiences that will allow them to design tasks in order to detect and promote algebraic thinking in their future students. Sequences of tasks are presented to develop both situations by generalizing and representing relationships and functions, which can serve as a starting point for future training programs and experiences.

Download Full-text

Contribuições da Theory-Driven Evaluation para avaliação do Pibid

Estudos em Avaliação Educacional ◽

10.18222/eae.v30i73.5852 ◽

2019 ◽

Vol 30 (73) ◽

pp. 70

Author(s):

Fernanda Litvin Villas Bôas ◽

Leila Chalub Martins ◽

Joaquim José Soares Neto

Keyword(s):

Teacher Education ◽

Public Schools ◽

Qualitative Methodology ◽

Initial Teacher Education ◽

Font Size ◽

Change Models ◽

Education Theory ◽

La Red ◽

The Right ◽

Education Process

O presente artigo tem como objetivo discutir o processo de formulação e implementação do Programa Institucional de Bolsas de Iniciação à Docência (Pibid), a partir do arcabouço teórico-metodológico da Theory-Driven Evaluation (TDE). O Pibid tem como propósito qualificar a formação inicial de professores a partir da inserção do licenciando no cotidiano das escolas da rede pública. Para a construção do modelo de ação e de mudança sugeridos por essa abordagem, foi utilizada metodologia qualitativa e os dados foram discutidos com base na análise de conteúdo. O seu modelo de ação evidencia a articulação entre as instituições parceiras e os atores, mobilizados por instrumentos de incentivo e valorização, que resulta em um modelo de mudança eficaz. Verificou-se que o Pibid atua sobre os determinantes corretos, resultando em mudanças significativas no processo de formação inicial de professores. A análise do modelo mostra que o Pibid interfere positivamente no processo de formação inicial docente.Palavras-chave: Avaliação de Programas, Formação Inicial de Professores, Theory-Driven Evaluation, Pibid. Contribuciones de La Theory-Driven Evaluation para la evaluación del Programa PibidEl presente artículo tiene el objetivo de discutir el proceso de formulación e implementación del Programa Institucional de Becas de Iniciación a la Docencia (Pibid), a partir del marco teórico-metodológico de la Theory-Driven Evaluation (TDE). El Pibid tiene el propósito de calificar la formación inicial de profesores desde su inserción en el cotidiano de las escuelas de la red pública. Para construir el modelo de acción y de cambio sugerido por este enfoque se utilizó metodología cualitativa y los datos se discutieron en base al análisis de contenido. Este modelo de acción evidencia la articulación entre las instituciones asociadas y los actores, movilizados por instrumentos de incentivo y valorización, que resulta en un modelo eficaz de cambio. Se verificó que el Pibid actúa sobre los determinantes correctos, resultando en cambios significativos en el proceso de formación inicial de profesores. El análisis del modelo muestra que el Pibid interfiere positivamente en el proceso de formación inicial docente.Palabras clave: Evaluación de Programas, Formación Inicial de Profesores, Theory-Driven Evaluation, Pibid. Contributions from Theory-Driven Evaluation to the evaluation of PibidThe present article aims to discuss the process of formulation and implementation of the Programa Institucional de Bolsas de Iniciação à Docência [Institutional Teacher Initiation Scholarship Program] (Pibid) using the theoretical-methodological framework of Theory-Driven Evaluation (TDE), which proposes to evaluate a program based on its defining theory. The PIBID is a Federal Government program that aims to improve initial teacher education by introducing teacher licensure students into public schools’ daily activities since their early stages in college. In order to outline the program’s action and change models as suggested by TDE, we used qualitative methodology and conducted a discussion of data based on content analysis. The action model demonstrates the articulation between partner institutions and the program’s actors, who are mobilized by incentive instruments, which resulted in an effective change model. We found that PIBID acts on the right determinants, thus causing significant change in the initial teacher education process. Our analysis of the program’s model shows that PIBID affects positively the initial teacher education process.Keywords: Program Evaluation, Initial Teacher Education, Theory-Driven Evaluation, Pibid.

Download Full-text

A importância do Pibid na formação de professores: narrativas sobre as primeiras experiências de licenciandos em ciências biológicas

Revista Brasileira de Educação em Ciências e Educação Matemática ◽

10.33238/rebecem.2021.v.5.n.2.27086 ◽

2021 ◽

Vol 5 (2) ◽

pp. 294-312

Author(s):

Carolina Buso Dornfeld ◽

Andressa Oliveira Cipriano ◽

Ângela Coletto Morales Escolano

Keyword(s):

Biological Sciences ◽

Teacher Education ◽

Basic Education ◽

Dimensional Space ◽

Three Dimensional ◽

Initial Teacher Education ◽

School Life ◽

Social Growth ◽

Time Space ◽

Three Dimensional Space

Resumo: Buscamos analisar experiências de licenciandos em Ciências Biológicas de duas IES para compreender como a experiência na participação no Pibid contribui para a formação inicial de professores, considerando as dimensões do Espaço Tridimensional, tais como o tempo, espaço, pessoal e social. Realizamos a Análise de Conteúdo das narrativas elaboradas por 18 pibidianos em dois períodos de participação (10 e 18 meses). Observamos: os pibidianos adentram a escola, com sentimentos que perpassam o medo, mas também, com o sentimento de querer contribuir com a aprendizagem dos alunos; apresentaram momentos de superação das inseguranças iniciais do ser professor e demonstraram crescimento pessoal e social. Consideramos que o Pibid oportunizou o contato com a complexidade escolar, permitindo o desenvolvimento de dimensões importantes para o trabalho docente.Palavras-chave: Espaço Tridimensional; Cotidiano Escolar; Educação Básica. The importance of Pibid in teacher's education: narratives about the first experiences of students in the education program with a science specializationAbstract: We seek to analyze experiences of Biological Sciences undergraduates from two Universities to understand how participating in Pibid contributes to their initial teacher education, considering the dimensions of the Three-dimensional Space such as time, space, personal and social. We executed the Content Analysis of the narratives elaborated by 18 pibidians in two participation periods (10 and 18 months). We observed: Pibidians enter the school with feelings that permeate fear, in addition to wanting to contribute to the students' learning; They presented moments of overcoming insecurities and demonstrated personal and social growth. We consider that Pibid provided the opportunity for contact with school complexity, allowing development of important dimensions for the teaching work.Keywords: Three-dimensional Space; School Life; Basic Education.

Download Full-text

Informing Teaching Through Community Engagement

Early Childhood Development ◽

10.4018/978-1-5225-7507-8.ch061 ◽

2019 ◽

pp. 1225-1245

Author(s):

Trish Lewis ◽

Letitia Hochstrasser Fickel ◽

Glynne Mackey ◽

Des Breeze

Keyword(s):

Teacher Education ◽

Preservice Teachers ◽

Community Engagement ◽

Initial Teacher Education ◽

Teacher Education Programs ◽

Learning Needs ◽

Diverse Range ◽

White Middle Class ◽

Lower Socioeconomic

Download Full-text

A COVID-19 Re-envisioned Teaching Practicum Curriculum

Research in Social Sciences and Technology ◽

10.46303/ressat.2021.29 ◽

2021 ◽

Vol 6 (2) ◽

pp. 249-266

Author(s):

Carisma Nel ◽

Carolina Botha ◽

Elma Marais

Keyword(s):

Teacher Education ◽

Preservice Teachers ◽

Student Teachers ◽

Initial Teacher Education ◽

Teacher Education Programs ◽

School Partnerships ◽

Teaching Practicum ◽

Alternative Placement ◽

University School Partnerships ◽

Faculties Of Education

The changes taking place in the schooling landscape because of the coronavirus are real and meaningful and have implications for the training of preservice teachers, especially the teaching practicum component of their initial teacher education programs. The havoc caused by COVID-19 forced many faculties of education into a state of ‘panic-gogy’ to ensure that student teachers could complete their teaching practicums. In this paper we argue that consideration should be given to core teaching practices and practice-based teacher education pedagogies (i.e., representations and approximations) that can be used in alternative “placement contexts” that will supplement and harness the authenticity of school-based experiences. We provide two conceptual tools, collaboratively developed by teaching practicum educators and mentor teachers, that can be used as heuristic by other university-school partnerships when considering teaching practicum redesign efforts.

Download Full-text

Sistemas de avaliação da educação superior em Portugal e Brasil

Estudos em Avaliação Educacional ◽

10.18222/eae.v29i72.5200 ◽

2018 ◽

Vol 29 (72) ◽

pp. 596

Author(s):

Edilene Rocha Guimarães ◽

Manuela Esteves

Keyword(s):

Higher Education ◽

Teacher Education ◽

Qualitative Methodology ◽

Initial Teacher Education ◽

Educación Superior ◽

Education Evaluation ◽

Higher Education Curriculum ◽

Evaluation Systems ◽

Educacion Superior ◽

Curricular Practices

O artigo apresenta um estudo comparado entre Portugal e Brasil sobre os sistemas de avaliação da educação superior e suas influências nos currículos de formação inicial de professores. Utilizou-se a metodologia qualitativa para analisar como os sistemas de avaliação constituem referencial básico para os processos de regulação e supervisão da educação superior, a fim de promover a melhoria da qualidade e valorização das identidades institucionais. Os resultados indicam que o processo de avaliação externa tem influenciado os currículos, pois destacam os aspectos positivos e os pontos fortes dos cursos, reforçando concepções e práticas curriculares atuais. Conclui-se que os processos de regulação e supervisão, ao referenciarem os resultados da avaliação externa que valorizam as identidades institucionais, criam estratégias políticas para que a gestão institucional assuma a responsabilização e prestação de contas pela melhoria da qualidade da formação inicial de professores.Sistemas de Avaliação, Educação Superior, Currículo, Formação Inicial do Professor. Sistemas de evaluación de la educación superior en Portugal y BrasilEl artículo presenta un estudio comparado entre Portugal y Brasil sobre los sistemas de evaluación de la educación superior y sus influencias en los currículos de formación inicial de profesores. Se utilizó la metodología cualitativa para analizar cómo los sistemas de evaluación constituyen un referente básico para los procesos de regulación y supervisión de la educación superior, a fin de promover la mejora de la calidad y la valorización de las identidades institucionales. Los resultados indican que el proceso de evaluación externa ha influido en los currículos, ya que destacan los aspectos positivos y los puntos fuertes de los cursos, reforzando conceptos y prácticas curriculares actuales. Se concluye que los procesos de regulación y supervisión, al referenciar los resultados de la evaluación externa que valoran las identidades, crean estrategias políticas para que la gestión institucional asuma la responsabilidad y la rendición de cuentas por la mejora de la calidad de la formación inicial de profesores.Sistemas de Evaluación, Educación Superior, Currículo, Formación Inicial del Profesor. Higher education evaluation systems in Portugal and BrazilThe article presents a study comparing Portugal and Brazil's higher education evaluation systems and their influences on initial teacher education curricula. We used a qualitative methodology to analyze how the evaluation systems provide a basis for higher education and supervision processes in order to promote improvement in education quality and the valuing of institutional identities. Results indicate that external evaluation processes have influenced the curricula as they underline the positive aspects and strengths of teacher education programs, thus reinforcing current curricular practices and concepts. We conclude that as regulation and supervision processes build on evaluation results that promote institutional identities, they create political strategies that foster institutional management’s accountability for improving the quality of initial teacher education.Evaluation Systems, Higher Education, Curriculum, Initial Teacher Education.

Download Full-text