Conhecimentos Evidenciados Por Futuras Professoras de Matemática Sobre os Números Racionais e Sobre seu Ensino

ResumoEste artigo objetiva identificar os conhecimentos evidenciados por um grupo de licenciandas ao ensinar noções e procedimentos concernentes ao conceito de fração e à resolução de operações em Q na Educação Básica. Considera-se as categorias refinadas por Ball, Thames e Phelps a partir de trabalhos de Shulman, no que diz respeito aos conhecimentos necessários ao professor que ensinará Matemática. Opta-se por discutir neste trabalho os resultados de dois questionários aplicados a quatro estudantes de um curso de Licenciatura em Matemática ao iniciar uma formação sobre números racionais e seu ensino, vinculada ao projeto de pesquisa “Um estudo sobre os conhecimentos necessários ao professor de matemática para ensinar frações”. As respostas das participantes a esses questionários indicaram dificuldades como: localizar frações na reta numérica; fixar uma unidade comum a todas as frações para ser o inteiro e compará-las; e representar uma fração em que o denominador seja maior que o numerador. Esses desafios, muito presentes em alunos da Educação Básica, persistem mesmo após essas licenciandas terem integralizado mais de 50% do curso. Diante disso, considera-se que o formador de professores precisaria incluir em suas aulas situações que lhe permita discutir com os futuros professores aspectos relacionados ao conteúdo, às causas dos erros cometidos pelos alunos e maneiras de superá-las. Palavras-chave: Formação de Professores. Ensino de Fração. Conhecimento Comum do Conteúdo. Conhecimento do Conteúdo Especializado. AbstractThe goal of this article is to identify the knowledge that a group of student-teachers has for teaching notions and procedures regarding the concept of fractions and solving equations in Q in Basic Education. We consider the categories refined by Ball, Thames and Phelps, based on the works of Shulman, with respect to the knowledge necessary for a teacher to teach Mathematics. In this paper, we have chosen to discuss the results of two questionnaires applied to four students in a Mathematics Teaching Degree program at the start of the training program on Rational Numbers and how to teach them, linked to the research project “A study on the knowledge necessary for a Mathematics teacher to teach fractions” (Um estudo sobre os conhecimentos necessários ao professor de matemática para ensinar frações). The participants’ answers to these questionnaires indicated difficulties, such as: locating fractions on a number line; finding a common unit for all fractions to be a whole number and, thus, be able to compare them; and representing a fraction in which the denominator is greater than the numerator. These challenges are frequently present among students in Basic Education and they persisted even after the student-teachers completed 50% of the program. As such, we believe that teacher trainers need to include situations in their classes to discuss with future teachers aspects related to the content, to the causes of mistakes made by students and ways to fix them. Keywords: Teacher Trainer. Teaching Fractions. Common Content Knowledge. Specialized Content Knowledge.

An Analysis of Pre-service Teachers’ Understanding of the Knowledge Needed for Teaching Mathematics

In contexts of adversity, there is a need to educate pre-service teachers with specialized content knowledge so they can carry out the work of teaching effectively. This article draws upon a study with three pre-service teachers in Malawi that examines the understanding they develop of the knowledge needed to carry out mathematics teaching tasks, in particular, the knowledge needed sequence instructional tasks sequence and use mathematical representations in classrooms. The research was conducted in one teacher education college where the curriculum is under development and has an emergent demand for qualifying teachers in mathematics. The research methodology was based on a questionnaire, interviews, teaching observations, and group discussions. The data were thematically analyzed through two themes reflecting the knowledge pre-service teachers considered necessary for teaching mathematics. While the first theme reveals how pre-service teachers understand this knowledge as a reference for meeting curricular standards and students’ needs, the second captures a form of understanding that attempts to go beyond conceptual knowledge. The findings can help better understand the pre-service teachers’ learning and experience during teacher education and how theoretical constructs are conceived in challenging contexts of teacher education.

Matematikklæreres refleksjoner om egne undervisningsutfordringer

Matematikkundervisning stiller krav til matematikkfaglig og matematikkdidaktisk kunnskap. Mens mange forskere har studert kunnskapen lærere har, eller den kunn­skapen de bruker i undervisningen, retter denne studien fokuset mot hvilke matematiske undervisningsutfordringer som er i fokus når lærere reflekterer over egen matematikk­undervisning, og hvilke deler av den profesjonelle kunnskapsbasen de trekker inn i refleksjonene. Andretrinnslærerne i denne studien reflekterer omkring mange sentrale matematiske undervisningsutfordringer, men det matematiske fokuset i refleksjonene er ofte uklart – selv når de reflekterer over undervisningsutfordringer som stiller krav til spesialisert matematisk kunnskap. Resultatene fra studien indikerer også at lærerne ofte bruker et upresist og hverdagslig språk når de reflekterer over egen matematikk­undervisning. Nøkkelord: matematiske undervisningsutfordringer, undervisningskunnskap, tallforståelse Mathematics teachers’ reflections about experienced tasks of teaching Abstract Teaching requires a special content knowledge as well as pedagogical content knowledge. Whereas many studies have investigated the knowledge teachers have or use in teaching, this study investigates what mathematical tasks of teaching that are in focus when teachers reflect on their own mathematics teaching, and what aspects of the professional knowledge base they draw upon. The second grade teachers in this study reflect on several core tasks of teaching mathematics, but their reflections tend to have an unclear mathematical focus — even when they reflect upon tasks of teaching that require specialized content knowledge. The results from this study also indicate that the language teachers use to reflect on their own mathematics teaching tends to lack precision and rigor. Keywords: mathematical tasks of teaching, mathematical knowledge for teaching, number sense

Teacher's Specialized Content Knowledge on the Concept of Square: A Vignette Approach

In learning geometry, the discussion about the definition of quadrilateral is a material that is difficult and not easily taught by the teacher. This study aims to explore the teacher's specialized content knowledge about square. This is a descriptive-qualitative research. The process of selecting subjects begins with searching prospective subject data according to the level of the teacher through a portfolio of 82 teachers in South East of Sulawesi: (33 First Teachers, 33 Young Teachers, and 16 Intermediate Teachers). The research subjects consisted of three teachers, namely: First Teacher, Young Teacher dan Intermediate Teacher with score > 50. Data were taken using vignette. The results show that there is a difference when the teacher is asked to define a square with when given a definition of a square. First Teacher is accurate when given a square definition with the symmetry and diagonal axis attributes; the side attribute is not accurate in giving arguments to the square definition. Young Teacher is inaccurate when given the definition of a square with side and angle attributes; accurate with symmetry and diagonal axis attributes; but it is not accurate when given a square definition. Regarding attributes of side; Intermediate Teacher revealed that the side and angle attributes are inaccurate but accurate with the symmetry and diagonal axis attributes but do not appear / are not used when asked to define a square. Specialized content knowledge First Teacher is better because it has been able to reconstruct concepts from a square, but Young Teacher and Intermediate Teacher are still influenced by concept images and figural concepts.

The Effects of Play Practice Instruction on the Badminton Content Knowledge of a Cohort of Chinese Physical Education Majors

Purpose: The purpose of this study was to examine the effects of Play Practice instruction on the badminton content knowledge and skill of a cohort of Chinese physical education majors. Method: Seventy-two second-year students participated in semester-long courses following either the principles of Play Practice or skill-focused instruction. A control/comparison group experimental design with pre- and postmeasures was used in this study. Separate analyses of variance with repeated measures (Time × Group) were conducted to examine the effects of Play Practice and skill-focused instruction for each of four dependent variables: (a) forehand clear, (b) tactical understanding, (c) game performance, and (d) specialized content knowledge. Results: Students from both conditions made significant improvements in all four variables across the semester. However, students in the Play Practice condition showed significantly greater gains in tactical understanding, game performance, and specialized content knowledge. In particular, while 75% of students who experienced Play Practice reached the 3.0 benchmark score for adequate specialized content knowledge, only 8% of students in skill-focused instruction reached this standard.