Connecting Research to Teaching: Learning and Teaching Indirect Proof

1996 ◽  
Vol 89 (6) ◽  
pp. 474-482 ◽  
Author(s):  
Denisse R. Thompson
Keyword(s):  
Mathematics Education ◽  
Formal Proof ◽  
Learning And Teaching ◽  
Indirect Proof ◽  
Content Domain ◽  
Teaching Learning ◽  
Mathematical Behavior

Proof! It is the heart of mathematics as individuals explore, make conjectures, and try to convince themselves and others about the truth or falsity of their conjecture. In fact, proving is one of the main aspects of mathematical behavior and “most clearly distinguishes mathematical behavior from scientific behavior in other disciplines” (Dreyfus et al. 1990, 126). By its nature, proof should promote understanding and thus should be an important part of the curriculum (Hanna 1995). Yet students and teachers often find the study of proof difficult, and a debate within mathematics education is currently underway about the extent to which formal proof should play a role in geometry, the content domain in which reasoning is typically studied at an intensive level (Battista and Clements 1995).

scholarly journals 9th International Conference on University Teaching and Innovation (CIDUI): Learning and teaching innovation impacts

2017 ◽  
Vol 7 (2) ◽  
pp. 115
Author(s):  
CIDUI Organising Comittee ◽  
Beatriz Amante ◽  
María Martínez
Keyword(s):  
Science Education ◽  
University Teaching ◽  
Teaching Innovation ◽  
Learning And Teaching ◽  
International Conference ◽  
Points Of View ◽  
Teaching Learning ◽  
Year 2000 ◽  
The Impact

The Organising Committee of the 9th International Conference on University Teaching and Innovation (CIDUI) wishes to thank the Editorial Board of the Journal of Technology and Science Education (JOTSE) for publishing this special issue.Since the year 2000, a new CIDUI conference has been held every two years. Today, it is a well-established event that provides an opportunity to share advances and innovation in the field of higher education.Like the previous editions, this one was also committed to fostering an especially participatory working dynamic and to promoting different points of view. The programmed debates were complemented by contributions from recognised specialists regarding the main topic of the conference: Learning and teaching innovation impacts. In relation to this general subject, papers were specifically focused on one of the four thematic axes proposed for this edition:Analysis of the impact on university teaching and learningNew training scenesProfessional DevelopmentInnovative methodologies in teaching – learning processesThe present special issue of the Journal of Technology and Science Education - JOTSE consists of eleven papers. 

scholarly journals Riding Out the Storm: Out-of-Field Teaching Practice in Indonesia

Humaniora ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 161
Author(s):  
Esti Rahayu ◽  
Shuki Osman
Keyword(s):  
Professional Learning ◽  
Teaching Practice ◽  
Qualitative Case Study ◽  
School Leaders ◽  
Document Analysis ◽  
Classroom Observations ◽  
Extended Time ◽  
Learning And Teaching ◽  
Teaching Learning

As out-of-field teachers existence led to change in teachers, this research aimed to explore their commitment to learning and teaching, and how their schools supported them. Five Indonesian teachers who started teaching as out-of-field teachers and their school leaders were interviewed for this research. The qualitative case study was employed to explore the problem through interviews, classroom observations, and document analysis. The findings reveal that the initial commitment to teaching, learning, and growing is an investment for further actions throughout the teaching practice. The schools provide necessary assistance through the induction and during their in-service in the provided and requested professional learning, being trusted and acknowledged by school leaders, and having resourceful colleagues. From their schools’ support, the out-of-field teachers become more knowledgeable and remain as teachers for an extended time.

scholarly journals COMPLEMENTARY EDUCATION SPACES OF VENEZUELAN MATHEMATICS EDUCATORS. CASE: VENEZUELAN SCHOOL FOR THE TEACHING OF MATHEMATICS - EVEM

2020 ◽  
Vol 24 ◽  
Author(s):  
Cinthia del Carmen Humbría Burgos ◽  
Fredy Enrique González
Keyword(s):  
Mathematics Education ◽  
Qualitative Study ◽  
Social History ◽  
Mathematics Teaching ◽  
Scientific Field ◽  
Epistemology Of Science ◽  
Complementary Education ◽  
Mathematics Educators ◽  
Teaching Of Mathematics ◽  
Teaching Learning

ABSTRACT Qualitative study on mathematical educators complementary education spaces, considering the Venezuelan School for Mathematics Teaching. Referents: Social history (Bernal); Epistemology of Science (Toulmin); Scientific Field (Bourdieu); Systemic vision of Mathematics Education in Venezuela (Beyer). Finding: EFC-EMVs are dialogic, interdisciplinary, generate knowledge about teaching-learning of mathematics, for the Venezuelan educational reality.

scholarly journals Negocjowanie programu nauczania języka obcego z uczniami w Polsce

Neofilolog ◽  
1970 ◽  
pp. 143-156
Author(s):  
Paweł Sobkowiak
Keyword(s):  
Decision Making ◽  
Foreign Language ◽  
Language Learning ◽  
Learning Process ◽  
Foreign Language Learning ◽  
Learning And Teaching ◽  
Teaching Learning ◽  
Different Levels

This paper aims to explore the rationale of classroom negotiation - understood as a discussion between all participants in the teaching/learning process to decide on the organization of foreign language learning and teaching. It outlines relevant issues connected with the process syllabus and the benefits that can be expected from involving students in classroom decision making. The article presents results of research conducted in Polish schools among both students and teachers at different levels of education in order to see to what extent the foreign language syllabus is negotiated there.

Exploring My Images of Mathematics and Its Influence on Learning

2020 ◽  
Vol 11 ◽  
pp. 23-48
Author(s):  
Basanta Raj Lamichhane
Keyword(s):  
Mathematics Education ◽  
Transformative Learning ◽  
Learning Strategies ◽  
Lived Experiences ◽  
Quality Standards ◽  
Ethnographic Research ◽  
Transformative Learning Theory ◽  
Pedagogical Approach ◽  
Negative Images ◽  
Teaching Learning

The major aim of this paper is to explore my images of mathematics and its influences on my teaching-learning strategies. I have employed an auto/ethnographic research design to excavate my lived experiences largely informed by interpretive and critical paradigms. To generate field texts dialectical and historical-hermeneutic approaches have been used. The Habermas’ knowledge constitutive interest and Mezorows’ transformative learning theory were used as theoretical referents. The writing as a process of inquiry has been used to create layered texts through thick descriptions of the contexts, critical self-reflexivity, transparent and believable writing aiming to ensure the quality standards of the research. The research illuminates that most of the negative images of mathematics have been emerged by the conventional transmissionist ‘one-size-fits-all’ pedagogical approach. Likewise, it has indicated that to transform mathematics education practices towards more empowering, authentic, and inclusive ones, it must be necessary to shift in paradigms of teaching and practitioners’ convictions, beliefs, values, and perspectives as well.

Teaching and Learning With Artificial Intelligence

2021 ◽  
pp. 73-98
Author(s):  
Libi Shen ◽  
Irene Chen ◽  
Anne Grey ◽  
Anchi Su
Keyword(s):  
Artificial Intelligence ◽  
Teaching And Learning ◽  
Learning Assessment ◽  
Modern World ◽  
Learning And Teaching ◽  
Curriculum Assessment ◽  
Education Major ◽  
Fast Speed ◽  
Artificial Intelligence In Education ◽  
Teaching Learning

Artificial intelligence (AI) is developing at a fast speed and has incessantly impacted the modern world for decades. AI technologies are beneficial for all kinds of industries, including businesses, economics, transportation, hospitals, schools, universities, and so forth. Many researchers have investigated the development of artificial intelligence in education (AIEd), specifically on how AI assists teaching, learning, assessment, references, and collaboration. Several questions arise. What impact do AI technologies have on education? How do AI technologies assist teaching (e.g., curriculum, assessment, student learning, and teaching practices)? How do teachers cope with AI Technologies in education? What are the ethical concerns of AI technologies? What are the barriers of AI-based learning in education? The purpose of this chapter is to explore the evolution and the challenges of AI technologies in education. Major research on AI from 1999 to 2019 will be reviewed. Problems with AI in education will be raised and solutions for solving the issues will be recommended.

Computer-Based Mathematics Education

2021 ◽  
pp. 28-51
Keyword(s):  
Mathematics Education ◽  
Programming Languages ◽  
Technological Diffusion ◽  
Electronic Technology ◽  
Chronological Order ◽  
Computer Based ◽  
Teaching Learning ◽  
The Impact ◽  
Modern Technologies

In this chapter, the authors mention, briefly, the attempts made from the 1970s to today to insert modern technologies in the teaching/learning of mathematics. They start with the first pocket calculators in the 1970s, which had a rapid technological diffusion that still exists. They focus on the impact that digital electronic technology has had on teaching/learning math. They will not follow a strictly chronological order, preferring to dwell on what, in their opinion, are the fundamental stages. So, the advent of the PC and programming languages—Logo, Basic, Pascal—CAI programs, DGS software, CAS. They conclude with their MatCos Project, after mentioning the new coding languages, including Scratch.

A New Way of Teaching

1996 ◽  
Vol 178 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Fernand J. Prevost
Keyword(s):  
Mathematics Education ◽  
Education Reform ◽  
Classroom Discourse ◽  
Teaching And Learning ◽  
National Curriculum ◽  
And Mathematics ◽  
Teaching Learning ◽  
Change Task ◽  
Analysis Of Teaching ◽  
Present Understanding

A new view of teaching is emerging from the work of the constructivists and mathematics education reform leaders. In particular, we examine here four aspects of teaching that must change: task selection, guidance of classroom discourse, setting the learning environment, and the analysis of teaching and learning. Several national curriculum projects are working to effect these changes and examples of their work are provided. This work has motivated individual teachers to similarly design investigations that engage students in the study of significant mathematics, and two examples are included. Assessment must also change and students must learn to become less dependent on “authority” for the correctness of answers. Finally, our present understanding of constructivism and its implications for teaching/learning must not be static; though that view now may be at the center, we must listen to those who are on the edges and expect to be changed again and again in the years ahead.

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