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.

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>

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 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.

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.

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 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.

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 Knowledge evidenced by prospective mathematics teachers when performing a task involving geometry, teaching and the use of technology

2019 ◽  
Vol 21 (2) ◽  
Author(s):  
Yuri Morales-López
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Pedagogical Content ◽  
Trainee Teachers ◽  
Types Of Knowledge ◽  
Use Of Technology ◽  
Prospective Mathematics Teachers ◽  
Almost All ◽  
Use Of Knowledge ◽  
Do So

The types of knowledge that prospective mathematics teachers use when faced with tasks involving technology are interesting because this knowledge can be used as a basis for analyzing the relevance of these types of activities when teaching mathematics. This investigation is intended to identify the knowledge evidenced by these prospective teachers when they carry out an activity involving geometry, technology and pedagogy. To do so, a task was designed which was used with 65 trainee teachers, and the Technological Pedagogical Content Knowledge model was used to analyze the information gathered. The results show that prospective teachers make use of knowledge in all of the domains and almost all of the subdomains of the model, confirming that this type of activity triggers these types of knowledge.

scholarly journals Developing prospective mathematics teachers’ knowledge of the modelling approach

2018 ◽  
Vol 9 (2) ◽  
pp. 146-158
Author(s):  
Juhaina Awawdeh Shahbari ◽  
Michal Tabach
Keyword(s):  
Mathematical Model ◽  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Linear Process ◽  
Pedagogical Knowledge ◽  
Modelling Activity ◽  
Important Approach ◽  
Modelling Competencies ◽  
Prospective Mathematics Teachers ◽  
Modelling Approach

Modelling is considered an important approach that requires prospective teachers to be qualified both in modelling competencies and in pedagogical knowledge. In order to investigate the development of these competencies, we examined 49 prospective mathematics teachers studying in a course that included a sequence of modelling activities. During the course, groups of 5–6 participants engaged in these modelling activities as learners. The data include two sets of reports by the prospective teachers on their observations of a recorded modelling activity carried out by a group of five 6th grade students. The first set of reports was collected before the prospective teachers worked on any modelling activities, while the second set was collected after they had engaged in the modelling activities. The findings indicate that, prior to working on modelling activities, most of the prospective teachers described the students’ modelling activity as a linear process and focused on the final mathematical model and the mathematical results. After the prospectiveteachers engaged in the activities, most of their reports identified cyclical processes as the mathematical models progressed.

scholarly journals PENGEMBANGAN MODEL PEMBINAAN KOMPETENSI CALON GURU MATEMATIKA MELALUI LESSON STUDY

2014 ◽  
Vol 3 (1) ◽  
Author(s):  
Rahmad Bustanul Anwar ◽  
Dwi Rahmawati
Keyword(s):  
Social Competence ◽  
Human Resources ◽  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Lesson Study ◽  
Professional Competence ◽  
Personal Competence ◽  
Research Activities ◽  
Prospective Mathematics Teachers

Education has a very important role in improving the quality of human resources. Therefore, education is expected to be one of the ways to prepare generations of qualified human resources and has the ability to deal with the progress of time and technology development . In order to enhance the quality of student mastery of competencies in the development of prospective teachers in this study will be applied to the activities in the process of lesson study in lecture . Lesson study is a model of coaching to people who work as both teacher educators and lecturers through collaborative learning and assessment in building sustainable learning communities. The purpose of this research is to improve the competence of prospective mathematics teachers through lesson study . More specifically , this study aims to describe the efforts made to improve the pedagogical, professional competence , social competence and personal competence prospective mathematics teachers through lesson study . Subjects in this study were students who took the micro teaching courses totaling 15 students , divided into 3 group . This type of research is a qualitative descriptive study is to develop the competence of prospective mathematics teachers through lesson study . Lesson study conducted collaborated with Action Research activities ( Action Reseach). The results of this research activity is the implementation of lesson study to greater competence to prospective teachers teaching mathematics through the micro subjects namely: pedagogical competence categories were 80 % and 20 % lower, professional competence categories were 46.7 % and 53.3 % lower, personal competence 100 % category being and social competence categories were 86.7 % and 13.3 % lower .

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