Characterizing Students’ Understandings of Mathematical Proof

1998 ◽  
Vol 91 (8) ◽  
pp. 714-717 ◽  
Author(s):  
Eric J. Knuth ◽  
Rebekah L. Elliott
Keyword(s):  
Mathematics Teachers ◽  
Mathematical Proof ◽  
Secondary Level ◽  
Secondary Curriculum ◽  
Mathematics Educators ◽  
Teachers And Students

For many secondary-level mathematics teachers and students, the notion of mathematical proof often conjures up images of mathematical rigor in the form of two-column proofs. Yet in recent years, many mathematics educators have been reexamining the nature of mathematical proof in the secondary curriculum.

scholarly journals Role of Educational Technology in Public and Private Institutes at Secondary School Level in District Karak (Khyber Pukhtunkhwa) Pakistan

2012 ◽  
Vol 2 (5) ◽  
pp. 39
Author(s):  
Qaiser Suleman ◽  
Ishtiaq Hussain ◽  
Zaitoon Akhtar
Keyword(s):  
Educational Technology ◽  
Secondary Schools ◽  
Secondary Level ◽  
School Level ◽  
Private Institutions ◽  
Chi Square ◽  
Public And Private ◽  
Secondary School Level ◽  
Teachers And Students

Educational technology plays a fundamental role in enhancing teaching learning process. It has facilitated instructional process and made it more productive, dynamic and effective. Therefore the study was conducted to explore the role of educational technology in public and private institutes in district Karak (Khyber Pukhtunkhwa) Pakistan in comparative perspectives. The main objectives of the study were: to compare the availability of educational technology in public and private institutions at secondary level; to compare the usability of educational technology in public and private institutions at secondary level and to know the usefulness of educational technology in public and private institutions at secondary level. All the heads, teachers and students in public and private secondary schools in district Karak constituted the population of the study. In order to ensure adequate sample, 60 heads, 180 teachers and 600 students serving and studying in public and private sectors at secondary school level in District Karak were selected randomly. The study was delimited to the selected male public and private secondary schools. The study was also delimited to those technologies which are commonly used. The study was descriptive in nature therefore, the researchers decided to develop questionnaire for the collection of data. A single questionnaire was developed for the whole sample. Pilot testing was conducted to know the weakness, misconceptions and ambiguities of the questions. After conduction of pilot testing, the questionnaire was revised and then its final version was prepared in the light of valuable suggestions of the heads, teachers and students. The researchers personally visited to the respective sample and distributed the questionnaires among the heads, teachers and students in public and private secondary schools. In this way data was collected. After the collection of data, the data was organized, tabulated and analyzed. The researchers decided to apply chi-square for the statistical treatment of the data. Therefore, chi square was applied to compare the responses of the sample. After analysis of the data, it was concluded that educational technologies are not available in both sectors. Some technologies are available in minor amount but these technologies are not used in both public and private sectors. Key Words:Educational Technology, Availability of Educational Technology, Usability of Educational Technology, Importance of Educational Technology

scholarly journals FLAWS IN PROOF CONSTRUCTIONS OF POSTGRADUATE MATHEMATICS EDUCATION STUDENT TEACHERS

2019 ◽  
Vol 10 (3) ◽  
pp. 379-396
Author(s):  
Zakaria Ndemo
Keyword(s):  
Mathematics Education ◽  
Student Teachers ◽  
Mathematics Teachers ◽  
Teaching And Learning ◽  
Mathematical Proof ◽  
Education Student ◽  
Written Responses ◽  
Induction Strategy ◽  
Proof Comprehension ◽  
Analytic Induction

Intending to improve the teaching and learning of the notion of mathematical proof this study seeks to uncover the kinds of flaws in postgraduate mathematics education student teachers. Twenty-three student teachers responded to a proof task involving the concepts of transposition and multiplication of matrices. Analytic induction strategy that drew ideas from the literature on evaluating students’ proof understanding and Yang and Lin’s model of proof comprehension applied to informants’ written responses to detect the kinds of flaws in postgraduates’ proof attempts. The study revealed that the use of empirical verifications was dominant and in situations. Whereby participants attempted to argue using arbitrary mathematical objects, the cases considered did not represent the most general case. Flawed conceptualizations uncovered by this study can contribute to efforts directed towards fostering strong subject content command among school mathematics 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.

Analisis kemampuan pembuktian matematis parabola menggunakan guided learning berdasarkan tingkat resiliensi

2020 ◽  
Vol 2 (2) ◽  
pp. 121-130
Author(s):  
Destia Wahyu Hidayati ◽  
Arie Wahyuni
Keyword(s):  
Fixed Point ◽  
Mathematics Teachers ◽  
Mathematical Proof ◽  
Research Data ◽  
School Level ◽  
High School Level ◽  
Guided Learning ◽  
Analysis Technique ◽  
Addition And Subtraction ◽  
High Level

One of the geometry materials at the high school level is a parabolic. The ability to prove parabolic formulas is needed by students majoring in Mathematics Education who will become mathematics teachers after graduating. Having an understanding of proof of the formula will make learning more meaningful. The purpose of this research is to find out a description of the proof of parabolic formula based on high, medium, and low resilience levels, so that various obstacles can be overcome early. This research is qualitative research. Data collection techniques used resilience questionnaires, test questions to prove the parabola formula, and interviews. The data analysis technique used data triangulation. The results showed that (1) there are three indicators in mathematical proof of parabolic mastered by students at high, medium, and low resilience levels, namely drawing the vertex, fixed point, and directrix line, determining the length of the two points, determining the results of the equation squared, (2) determining the coordinates of the vertex, fixed point, and the equations of the directrix mastered by students with a high level of resilience, but not yet mastered by students at moderate and low resilience levels, (3) determining two lines of the same length in the image according to the definition parabolic and determining the results of the multiplication distribution on addition and subtraction have been mastered by students at high and medium resilience levels, but not yet mastered by students at low resilience levels,

scholarly journals Creative Education System at Secondary Level in Bangladesh: Teachers’ and Students’ Perspectives

2020 ◽  
Vol 10 (2) ◽  
pp. 350
Author(s):  
Sabina Yasmin ◽  
Tahmina Ferdous Tanny ◽  
Md. Rahmat Ullah
Keyword(s):  
High School ◽  
Education System ◽  
Secondary Level ◽  
Primary Data ◽  
Survey Method ◽  
Research Approach ◽  
Sources Of Information ◽  
Secondary Sources ◽  
Creative Education ◽  
Teachers And Students

The creative education system is introduced in different stream of Bangladesh education towards developing the ingenious capability of students. The study is an endeavour that tries to know the possibilities and difficulties in the creative education system at the secondary level in Bangladesh from the teachers’ and students’ perceptions. It is an exploratory type of research that used primary and secondary sources of information to look for the problems, underlying the system. To collect primary data, Ambarkhana Girls’ High School & College; and Osmani Medical High School of Sylhet Sadar have been chosen as the study area. From the second tier of the chosen institutions; 60 students and 20 teachers are selected using a systematic random sampling method. The social survey method has been implied in this research and data collected through face to face interview method; along with a few well responded and informed respondents’ in-depth interview. Collected data from the respondents are then analyzed through a mixed research approach. The study findings reveal that most of the students signify the system enjoyable to study, memorizing reduced for textbooks learning, and appearance in examination turned easier. While others find the system confusing, difficult to understand questions and answer in examination hall within limited time. Besides, the system reciprocally encourages students to enrol in coaching centres for a vague idea about question pattern; lack of linkage between book and exam questions; and also, to get good marks. Findings from teachers' evaluation depict that though they welcome the system they are not well prepared to assimilate the system because of inadequate training facilities, absence of inquisitive seeking awareness program, dependence on the readymade question paper, challenges exerted on them to give students attention and proper guidance. The study recommends introducing well-researched textbooks avoiding mistakes, improving integrative classroom learning, controlling coaching business, increasing training facilities for teachers, providing awareness programs to make effective the creative education system in a competitive world of education.

scholarly journals When and Why of Mother Tongue Use in English Classrooms

1970 ◽  
Vol 16 (1-2) ◽  
pp. 42-51 ◽  
Author(s):  
Ashok Raj Khati
Keyword(s):  
Foreign Language ◽  
English Language ◽  
Language Use ◽  
Mother Tongue ◽  
Secondary Level ◽  
Final Part ◽  
Classroom Observations ◽  
Group Discussions ◽  
English Classrooms ◽  
Teachers And Students

It is often felt that teachers and students overuse their mother tongue, in this case, most probably the Nepali in English as a foreign language (EFL) classroom particularly in government-aided (Nepali medium) schools of Nepal. This, in result, minimizes the students' exposure to English. This article starts with defining mother tongue. Then, it presents the use of mother tongue in EFL classroom in the global and Nepalese contexts followed by summary of three classroom observations and two focused group discussions among teachers and students studying at the secondary level. The final part of the paper presents some simple and applicable strategies and ways of enhancing English language use in the classroom on the part of students provided by three teachers' trainers based on their experience. DOI: http://dx.doi.org/10.3126/nelta.v16i1-2.6128 NELTA 2011; 16(1-2): 42-51

scholarly journals Combining Tier 2 and Tier 3 Supports for Students with Disabilities in General Education Settings

2016 ◽  
Vol 2 (2) ◽  
pp. 331 ◽  
Author(s):  
K. Sandra MacLeod ◽  
Leanne S. Hawken ◽  
Robert E. O'Neill ◽  
Kaitlin Bundock
Keyword(s):  
General Education ◽  
Problem Behavior ◽  
Students With Disabilities ◽  
Problem Behaviors ◽  
Secondary Level ◽  
Tier 2 ◽  
Research And Practice ◽  
Tier 2 Interventions ◽  
Teachers And Students ◽  
Tier 3

<p>Secondary level or Tier 2 interventions such as the Check-in Check-out (CICO) intervention effectively reduce problem behaviors of students who are non-responsive to school-wide interventions. However, some students will not be successful with Tier 2 interventions. This study investigated the effects of adding individualized function-based support for four students with disabilities who were not successful in general education settings while receiving only a secondary level intervention. Results indicated that the combination of secondary and individualized function-based interventions effectively decreased problem behavior for all participants. Teachers and students rated the interventions as acceptable and effective. Research and practice implications are discussed.</p>

Reviews: Fear of the Unknowns

1983 ◽  
Vol 14 (2) ◽  
pp. 126-129
Author(s):  
Joanne Rossi Becker
Keyword(s):  
Qualitative Study ◽  
Mathematics Teachers ◽  
Mathematics Anxiety ◽  
Theoretical Framework ◽  
Target Audience ◽  
Mathematics Educators ◽  
And Mathematics ◽  
Depth Interviews ◽  
Three Components

Although the title of this book implies a target audience of math-anxious people, it is equally, if not more, suitable for teachers of mathematics and mathematics educators. Do You Panic about Maths? Coping with Maths Anxiety attempts to build a model of the interaction between reason and emotion to explain the behavior of adults anxious about mathematics. The model was derived from a qualitative study of adults that had three components: hour-long interviews with two dozen people; 36 2-hour sessions with a group of four women and three men; and individual in-depth interviews, consisting of 12 or 24 sessions, with three women. Buxton relates his model to the work of Skemp, with whom he has collaborated. Indeed, he has extended Skemp's (1979) model of intelligence in this book. In addition to the theoretical framework he discusses, Buxton provides some ideas for coping with one's mathematics anxiety and gives suggestions for mathematics teachers about how to teach to avoid or combat students' anxiety.

Thanks from the Editorial Panel

2018 ◽  
Vol 111 (7) ◽  
pp. 558-559
Keyword(s):  
High School ◽  
Mathematics Teachers ◽  
Mathematics Teacher ◽  
Teacher Educators ◽  
School Mathematics ◽  
High School Mathematics ◽  
College And University ◽  
Mathematics Educators ◽  
High School Mathematics Teachers

The success of Mathematics Teacher is very much dependent on the volunteer efforts of many mathematics educators. Those who serve as department editors, manuscript referees, and publications and courseware reviewers include high school mathematics teachers, curriculum designers, college and university mathematicians, and teacher educators. Their contributions are deeply appreciated.

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