Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers

2020 ◽  
Vol 9 (1) ◽  
pp. 63-87
Author(s):  
Mervenur Belin ◽  
Gülseren Karagöz Akar
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Rational Number ◽  
Teacher Educators ◽  
Instructional Sequence ◽  
Real Numbers ◽  
Mathematics Teacher Educators ◽  
Number Sequences ◽  
Prospective Mathematics Teachers ◽  
Long Division

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students’ understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers’ understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers.

scholarly journals Comparison of prospective mathematics teachers’ problem posing abilities in paper-pencil test and on dynamic geometry environment in terms of creativity

2020 ◽  
Vol 9 (3) ◽  
pp. 243
Author(s):  
MEHMET FATIH ÖÇAL ◽  
TUĞRUL KAR ◽  
GÜRSEL GÜLER ◽  
ALI SABRI İPEK
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Creative Thinking ◽  
Dynamic Geometry ◽  
Thinking Skills ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Mathematical Concepts ◽  
Prospective Mathematics Teachers

This study aims to investigate the similarities and differences between prospective mathematics teachers’ creative thinking skills in paper-pencil test and on a Geogebra-supported environment in terms of problem-posing. This case study used purposive sampling method for determining the participants. Findings revealed that the activities carried out in the GeoGebra-supported environment were insufficient to produce creative problems, and GeoGebra’s main utility to prospective teachers was in identifying their mistakes related to mathematical concepts and discrepancies among numerical values of the problems posed. The reasons for the low achievement in posing problem were discussed: These were; (i) lack of problem-posing experience, (ii) the structure of problem-posing activity, and (iii) prospective teachers’ mathematical content knowledge.

scholarly journals Japanese and Swedish Mathematics Teacher Educators’ Pedagogical Content Knowledge – An Institutional Perspective

2019 ◽  
Vol 21 ◽  
Author(s):  
Yukiko Asami-Johansson ◽  
Iiris Attorps
Keyword(s):  
Problem Solving ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Prospective Teachers ◽  
Teacher Educators ◽  
Institutional Perspective ◽  
Pedagogical Content ◽  
Mathematics Teacher Educators ◽  
Structured Problem Solving ◽  
Area Determination

The aim of this paper is to investigate which kind of conditions and constraints affect Japanese and Swedish teacher educators’ pedagogical content knowledge (PCK). We analyse the praxeologies of the lessons in which the educators teach area determination. Our study shows that the Japanese teacher educators’ PCK are more explicitly shared by the community of the teacher educators compared to the Swedish counterpart. Also, the detailed Japanese curriculum and the structured problem solving approach promote to illustrate how to construct rich mathematical and didactical organisations for prospective teachers.

scholarly journals TIPE PEMBUKTIAN MAHASISWA CALON GURU MATEMATIKA

2021 ◽  
Vol 10 (1) ◽  
pp. 351
Author(s):  
Mu'jizatin Fadiana ◽  
Yulaikah Yulaikah ◽  
Lajianto Lajianto
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Deductive Reasoning ◽  
Mathematical Proof ◽  
Inductive Reasoning ◽  
Tertiary Institution ◽  
Simple Task ◽  
Descriptive Research ◽  
Prospective Mathematics Teachers ◽  
Quantitative Descriptive

The ability to prove formal mathematics is an important ability that must be mastered by undergraduate prospective mathematics teachers. However, students who are prospective mathematics teachers have difficulty in constructing proof in mathematics courses. Therefore, this study aims to explore the tendency of mathematical proof methods for prospective mathematics teachers in second year lectures. The method used in this research is quantitative descriptive research. Participants in this study were 30 prospective mathematics teachers at a tertiary institution in Tuban, East Java. The research instrument is a simple task of compiling mathematical evidence. The results of the study were analyzed using the classification of types of proof by Miyazaki, namely classifying the types of deductive and inductive reasoning. The results showed that prospective mathematics teachers had a greater tendency to use deductive reasoning than using inductive reasoning. Type A proof is the most common type of proof. In addition, around 70% of prospective teachers still experience difficulties in compiling evidentiary tasks.

The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views

2016 ◽  
Vol 6 (1) ◽  
pp. 145 ◽  
Author(s):  
Gürsel Güler
Keyword(s):  
Content Analysis ◽  
Mathematics Education ◽  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Professional Lives ◽  
Analysis Method ◽  
Structured Interviews ◽  
Content Analysis Method ◽  
Prospective Mathematics Teachers ◽  
Experience Difficulty

<p>The aim of this study is to examine the difficulties prospective mathematics teachers experience in mathematical proving, the courses in which they have difficulties in proving, the importance of proof in mathematics education and its functions in their professional lives. The data of the study was collected via semi-structured interviews with fifteen academicians who volunteered to take part in the study. Content analysis method was used to analyze the data obtained. As a result of the study, based the views of the academicians, it was seen that prospective mathematics teachers experience four different difficulties in proving. Besides, in line with the views of the academicians the following categories were formed: the courses that prospective teachers experience difficulty, the importance of proof in mathematics education and its functions in prospective teachers’ professional lives and these categories were presented with their subcategories.</p>

Arithmetic for Majors?

1953 ◽  
Vol 46 (8) ◽  
pp. 560-564
Author(s):  
Jack D. Wilson
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
School Administrators ◽  
School Officials ◽  
Prospective Mathematics Teachers

School administrators are now asking that prospective mathematics teachers be given a better preparation for teaching arithmetic and general mathematics. This paper outlines certain trends related to these requests and describes a course in arithmetic to give prospective teachers the kind of training now being demanded by school officials.

Use of Video Analysis to Support Prospective K-8 Teachers' Noticing of Equitable Practices

2014 ◽  
Vol 2 (2) ◽  
pp. 108-140 ◽  
Author(s):  
Amy Roth McDuffie ◽  
Mary Q. Foote ◽  
Corey Drake ◽  
Erin Turner ◽  
Julia Aguirre ◽  
...  
Keyword(s):  
Instructional Practices ◽  
Video Analysis ◽  
Prospective Teachers ◽  
Mathematics Teacher ◽  
Teaching And Learning ◽  
Teacher Educators ◽  
Mathematics Teacher Educators

Mathematics teacher educators (MTEs) designed and studied a video analysis activity intended to support prospective teachers (PSTs) in learning to notice equitable instructional practices. PSTs from 4 sites (N = 73) engaged in the activity 4 to 5 times during the semester, using a set of 4 “lenses” to analyze teaching and learning as shown in videos. In an earlier analysis of this activity, we found that PSTs increased their depth and expanded their foci in noticing equitable instructional practices (Roth McDuf_ e et al., 2013). In this analysis, we shift the focus to our work as MTEs: We examine our decisions and moves in facilitating the video analysis activity with a focus on equity, and we discuss implications for other MTEs.

scholarly journals Acessar ou Interagir? Uma Análise em Disciplinas da Licenciatura em Matemática no Cederj

EAD em FOCO ◽  
2016 ◽  
Vol 6 (3) ◽  
Author(s):  
Robson Marques De Souza ◽  
Marcelo Almeida Bairral
Keyword(s):  
Distance Education ◽  
Virtual Environment ◽  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Rio De Janeiro ◽  
Master's Degree ◽  
Discrete Mathematics ◽  
Undergraduate Mathematics ◽  
Mathematics Courses ◽  
Prospective Mathematics Teachers

Este artigo é recorte de uma pesquisa de mestrado que analisou aspectos da formação inicial em Matemática no Polo do Centro de Educação Superior a Distância do Estado do Rio de Janeiro (Cederj) em Paracambi-RJ. Exemplifica sucintamente diferentes ferramentas disponibilizadas na plataforma e reflete sobre possíveis formas de promover interação entre licenciandos em Matemática. Ilustra acessos em três disciplinas (Matemática Discreta, Pré-Cálculo e Instrumentação no Ensino de Geometria (IEG)) obtidos por meio do histórico de entradas no ambiente no período de julho a dezembro de 2013. Identifica momentos específicos nos quais os licenciandos utilizam as ferramentas comunicativas para estabelecer contato com professores, tutores e colegas de curso, seja para sanar dúvidas, realizar ou postar atividades. Esses momentos estão concentrados nos períodos de avaliação, sendo uma exceção a disciplina IEG, na qual se detectou um acesso mais regular e indícios que sugerem maior interação no ambiente virtual da disciplina.Palavras-chave: Educação a Distância, Plataforma Cederj, Licenciatura em Matemática, interação.  Access or Interact? An Analysis of Undergraduate Courses of the Prospective Mathematics Teachers at CEDERJAbstract This article is part from a master's degree research that analyzed aspects of prospective mathematics teachers at the Polo Cederj in Paracambi-RJ. It briefly describes various tools available on the platform and reflects on ways to promote interaction among undergraduates students in Mathematics. It illustrates the access in three subjects (Discrete Mathematics, Pre-Calculus and Didactic of Geometry (DG)) obtained through the log access in the virtual environment in the period from July to December, 2013. It identifies specific times in which prospective teachers seek the tools and use them to make contact with teachers, tutors and fellow course, is to clarify doubt, perform or post activities. These moments are concentrated in the periods of assessment, as an exception to DG subject, in which were found more regular access and evidence to suggest more interaction within virtual environment of course.Keywords: Distance Education, Cederj platform, Undergraduate Mathematics Courses, interaction.

scholarly journals Prospective Mathematics Teachers Understanding of Classical and Frequentist Probability

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2526
Author(s):  
Carmen Batanero ◽  
Nuria Begué ◽  
Rocío Álvarez-Arroyo ◽  
Silvia M. Valenzuela-Ruiz
Keyword(s):  
Content Analysis ◽  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Frequency Data ◽  
Urn Model ◽  
Frequentist Probability ◽  
Prospective Mathematics Teachers

Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist approaches to probability. To achieve this goal, content analysis was used to categorize the prospective teachers’ answers to a questionnaire with open-ended tasks in which they had to estimate and justify the composition of an urn, basing their answers on the results of 1000 extractions from the urn. Most of the sample proposed an urn model consistent with the data provided; however, the percentage that adequately justified the construction was lower. Although the majority of the sample correctly calculated the probability of an event in a new extraction and chose the urn giving the highest probability, a large proportion of the sample forgot the previously constructed urn model, using only the frequency data. Difficulties, such as equiprobability bias or not perceiving independence of trials in replacement sampling, were also observed for a small part of the sample. These results should be considered in the organisation of probabilistic training for prospective teachers.

scholarly journals Exploring the Prospective Mathematics Teachers Computational Thinking in Solving Pattern Geometry Problem

2021 ◽  
Vol 13 (3) ◽  
pp. 1756-1767
Author(s):  
Swasti Maharani ◽  
Zeni Fadlila Agustina ◽  
Muhammad Noor Kholid
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Computational Thinking ◽  
Future Research ◽  
Mathematics Model ◽  
Geometric Pattern ◽  
Prospective Mathematics Teachers ◽  
Pattern Problem

This research aims to describe the characteristic of mathematics prospective teacher's computational thinking (CT) in solving the geometric pattern problem. The subject consists of 65 preservice mathematics teachers in Universitas in Madiun. The instrument was used in this research are geometric pattern problem tests and interview guidelines. The result shows that are three types of mathematics prospective teachers in solving the problem. First, CT substantial, i.e. prospective mathematics teachers use the conceptual knowledge who collaborated with procedural knowledge exactly. They use mathematics iteration to find the pattern and express them to the general form easily. Second, CT Nominal, i.e. prospective mathematics teachers, use manual ways to solve the pattern problem. They count using numeric, not symbolic, of solving the pattern formed. They can understand the design but can't express it to the mathematics model. Third, CT procedural, i.e. mathematics prospective teacher using the procedural knowledge only, not an expert in concept, and following the steps who teaches from experience before. The recommendation for future research is to develop the research to find the other characters in other mathematics subjects, in other students, to develop the learning models who can embody CT.

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