scholarly journals Exploration of Student Thinking Process in Proving Mathematical Statements

2020 ◽  
Vol 8 (2) ◽  
pp. 150
Author(s):  
Deni Hamdani ◽  
Ketut Sarjana ◽  
Ratna Yulis Tyaningsih ◽  
Ulfa Lu’luilmaknun ◽  
J. Junaidi
Keyword(s):  
Mathematical Thinking ◽  
Routine Activities ◽  
Student Thinking ◽  
Thought Process ◽  
Mathematical Statement ◽  
Complete Proof ◽  
Proof Scheme ◽  
Fundamental Part ◽  
Thinking Process ◽  
The Way

A mathematical statement is not a theorem until it has been carefully derived from previously proven axioms, definitions and theorems. The proof of a theorem is a logical argument that is given deductively and is often interpreted as a justification for statements as well as a fundamental part of the mathematical thinking process. Studying the proof can help decide if and why our answers are logical, develop the habit of arguing, and make investigating an integral part of any problem solving. However, not a few students have difficulty learning it. So it is necessary to explore the student's thought process in proving a statement through questions, answer sheets, and interviews. The ability to prove is explored through 4 (four) proof schemes, namely Scheme of Complete Proof, Scheme of Incomplete Proof, Scheme of unrelated proof, and Scheme of Proof is immature. The results obtained indicate that the ability to prove is influenced by understanding and the ability to see that new theorems are built on previous definitions, properties and theorems; and how to present proof and how students engage with proof. Suggestions in this research are to change the way proof is presented, and to change the way students are involved in proof; improve understanding through routine proving new mathematical statements; and developing course designs that can turn proving activities into routine activities.

KARAKTERISTIK PENCAPAIAN KEMAMPUAN PEMBUKTIAN DAN KEPERCAYAAN DIRI MAHASISWA MELALUI METODE MOORE

2018 ◽  
Vol 4 (2) ◽  
pp. 72-82
Author(s):  
Iyon Maryono ◽  
Siska Amanda Lucita Dewi ◽  
Agus Hikmat Syaf
Keyword(s):  
Learning Outcomes ◽  
Mixed Method ◽  
Student Learning Outcomes ◽  
Student Thinking ◽  
Student Responses ◽  
Self Confidence ◽  
Teacher Students ◽  
Thinking Process ◽  
Better Than ◽  
Important Activity

Pembuktian dalam matematika adalah suatu aktivitas yang penting, tetapi aktivitas ini tergolong sulit bagi mahasiswa calon guru matematika. Masalah ini salah satunya dipengaruhi oleh kepercayaan-diri. Tujuan penelitian ini adalah untuk menganalisis karakteristik pencapaian kemampuan pembuktian matematis dan kepercayaan-diri mahasiswa melalui metode Moore. Penelitian ini menggunakan metode campuran bertahap yaitu tahap kuantitatif dan tahap kualitatif. Pada tahap kuantitatif disimpulkan bahwa kemampuan pembuktian pada kelas yang menggunakan metode Moore lebih baik daripada kelas yang menggunakan model pembelajaran langsung. Metode Moore dapat mengungkap proses perkembangan capaian pembelajaran mahasiswa dalam pembuktian, sehingga dosen dapat memberikan umpan balik untuk mengembangkannya. Pada tahap kualitatif, dihasilkan karakteristik kemampuan pembuktian beberapa mahasiswa. Karakteristik ini ditinjau berdasarkan respon mahasiswa terhadap masalah pembuktian. Pada pembelajaran dengan metode Moore, mahasiswa tidak diperbolehkan membuka bahan ajar, sehingga dosen harus mengikuti alur berpikir mahasiswa dan mengarahkan proses berpikirnya. Sebagai implikasi, metode Moore baik digunakan dengan catatan mahasiswa harus belajar terlebih dahulu sebelum pembelajaran di kelas.Proving in mathematics is an important activity, but this activity is classified as difficult for prospective mathematics teacher students. This problem is influenced by self-confidence. The purpose of this study was to analyze the characteristics of achievement of students' mathematical proving ability and self-confidence  through the Moore method. This study uses a phased mixed method, namely quantitative and qualitative stages. In the quantitative stage, it was produced: "Based on the overall and PAM categories, the ability to prove the class using the Moore method is better than the class that uses the direct learning model". Moore's method can reveal the process of developing student learning outcomes in proof, so that lecturers can provide feedback to develop it. In the qualitative stage, the characteristics of the ability of several students are produced. these characteristics are reviewed based on student responses to the problem of proof. In the Moore method of learning, students are not allowed to open teaching materials, so the lecturer must follow the flow of student thinking and direct the thinking process. As an implication of the results of this study, the Moore method is well used with the notes that students must study before learning in class.

scholarly journals Mathematical Thinking Process of Autistic Students in Terms of Representational Gesture

2016 ◽  
Vol 9 (6) ◽  
pp. 93 ◽  
Author(s):  
Sriyanti Mustafa ◽  
Toto Nusantara ◽  
Subanji Subanji ◽  
Santi Irawati
Keyword(s):  
Facial Expressions ◽  
Learning Process ◽  
Mathematical Thinking ◽  
Digital Camera ◽  
Qualitative Approach ◽  
Recording Process ◽  
Data Collecting ◽  
Students With Autism ◽  
Thinking Process

<p class="apa">The aim of this study is to describe the mathematical thinking process of autistic students in terms of gesture, using a qualitative approach. Data collecting is conducted by using 3 (three) audio-visual cameras. During the learning process, both teacher and students’ activity are recorded using handy cam and digital camera (full HD capacity). Once the data is collected (the recording process is complete), it will be analyzed exploratively until data triangulation is carried out. Results of this study describes the process of mathematical thinking in terms of a gesture of students with autism in three categories, namely correctly processed, partially processed, and contradictory processed. Correctly processed is a series of actions to solve the problems that are processed properly marked with a matching gesture, partially processed is a series of actions to resolve problems with partially processed properly marked with discrepancy gesture, while contradictory processed is a series of actions to solve the problems that are processed incorrectly marked with the dominance of discrepancy gesture. Matching gesture demonstrate the suitability of movement or facial expressions when observing, pointing, and uncover/calling the object being observed, while the discrepancy gesture indicates a mismatch movements or facial expressions when observing, pointing, and uncover/calling the object being observed.</p>

Collaborative Solution Discovery: A Problem Solving Process

2019 ◽  
pp. 100-103
Author(s):  
Katharine Clemmer
Keyword(s):  
Problem Solving ◽  
Learning Environment ◽  
Real Time ◽  
School System ◽  
Mathematical Thinking ◽  
Self Regulation ◽  
Math Learning ◽  
New Approach ◽  
Problem Solving Process ◽  
The Way

Loyola Marymount University (LMU) has developed a new approach to problem solving, Collaborative Solution Discovery (CSD), to help practitioners in a school system leverage their individual passions in a way that grows students’ positive math identity through mathematical thinking, problem solving, and self-regulation. By focusing on how students and teachers interact with each other in real-time in an ideal classroom, practitioners take ownership of a process to guide their students in growing their positive math identity and thus taking ownership of their own math learning. Practitioners measure progress along the way through metrics that are created, defined, used, and continually refined by themselves to attain their ideal math learning environment. The entire CSD process results in a system that owns ist improvement efforts—improvement efforts that are flexible, adaptable, and sustainable.

scholarly journals Students’ cognitive style in mathematical thinking process

2020 ◽  
Vol 1613 ◽  
pp. 012055
Author(s):  
M Izzatin ◽  
S B Waluyo ◽  
Rochmad ◽  
Wardono
Keyword(s):  
Cognitive Style ◽  
Mathematical Thinking ◽  
Thinking Process

‘The Serried Maze’: Terrain, Consciousness and Textuality in Machen'sThe Hill of Dreams

2013 ◽  
Vol 3 (1) ◽  
pp. 46-63 ◽  
Author(s):  
Kostas Boyiopoulos
Keyword(s):  
Pattern Recognition ◽  
Subject Matter ◽  
Thought Process ◽  
The Subject ◽  
The Hill ◽  
The Way

This essay looks at Arthur Machen's underexplored experimental masterpiece The Hill of Dreams (1897/1907), his personal novel rooted in the Decadent nineties. Its daringness does not just lie in the subject matter but also in the manner its stylistic techniques evoke. The present investigation is interested in Machen's multifarious use of the image of the maze/labyrinth – or Welsh caerdroia – an apt symbol for the presentation of London. Machen's labyrinth is a motif, a metaphor for the thought process, and a metafictional device. In the story of Lucian Taylor, the troubled self-destructive litterateur, the labyrinthine characterises not only setting, terrain, self-movement, mind, and textual tissue, but also the way these components, or modalities, come together. Aside from showcasing the various ways the labyrinth materialises in The Hill of Dreams, the essay argues that Machen's achievement consists of a discursive meta-labyrinth that cuts across, or combines, the different spheres of consciousness, terrain, and textuality. The concepts of pattern recognition, liminal thresholds, and ‘infolding’ are employed in support of the claims made.

scholarly journals Cognitive linguistics and metaphor research: past successes, skeptical questions, future challenges

2006 ◽  
Vol 22 (spe) ◽  
pp. 1-20 ◽  
Author(s):  
Raymond W. Gibbs, Jr
Keyword(s):  
Cognitive Linguistics ◽  
Empirical Studies ◽  
The Past ◽  
Linguistic Research ◽  
Fundamental Part ◽  
Cognitive Linguistic ◽  
Future Challenges ◽  
Future Work ◽  
The Way

An important reason for the tremendous interest in metaphor over the past 20 years stems from cognitive linguistic research. Cognitive linguists embrace the idea that metaphor is not merely a part of language, but reflects a fundamental part of the way people think, reason, and imagine. A large number of empirical studies in cognitive linguistics have, in different ways, supported this claim. My aim in this paper is to describe the empirical foundations for cognitive linguistic work on metaphor, acknowledge various skeptical reactions to this work, and respond to some of these questions/criticisms. I also outline several challenges that cognitive linguists should try to address in future work on metaphor in language, thought, and culture.

The Empire Strikes Back: How Right-Wing Nationalists Tried to Recapture Russian Literature

1996 ◽  
Vol 24 (4) ◽  
pp. 601-624 ◽  
Author(s):  
Kathleen Parthe
Keyword(s):  
Russian Literature ◽  
The Political ◽  
Right Wing ◽  
Thought Process ◽  
The World ◽  
Political Spectrum ◽  
The Way

This article attempts to reconstruct the khod myshleniia (thought process) of the ultra-nationalist, ultra-conservative camp, not just because it is interesting in and of itself but also because of the way that some of their ideas, concerns, and ways of seeing Russia and the world are shared by a growing number of people in the middle of the political spectrum. The extremists' ideas about russifikatsiia may not spread very far, but russkost' is a powerful and attractive concept.

Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking

2015 ◽  
Vol 46 (1) ◽  
pp. 88-124 ◽  
Author(s):  
Keith R. Leatham ◽  
Blake E. Peterson ◽  
Shari L. Stockero ◽  
Laura R. Van Zoest
Keyword(s):  
Professional Development ◽  
Classroom Discourse ◽  
Classroom Practice ◽  
Mathematical Thinking ◽  
Student Thinking ◽  
Common Language ◽  
Mathematical Concepts ◽  
Community Values ◽  
Important Group ◽  
Education Community

The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. We conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical opportunities—what we call Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. We analyze dialogue to illustrate a process for determining whether a classroom instance offers such an opportunity and to demonstrate the usefulness of the construct in examining classroom discourse. This construct contributes to research and professional development related to teachers' mathematically productive use of student thinking by providing a lens and generating a common language for recognizing and agreeing on a critical core of student mathematical thinking that researchers can attend to as they study classroom practice and that teachers can aspire to notice and build upon when it occurs in their classrooms.

scholarly journals أفكار جديدة وطرق متعددة في دراسة علم اللغة

لارك ◽  
2019 ◽  
Vol 1 (24) ◽  
pp. 15-22
Author(s):  
علي اسماعيل الجاف
Keyword(s):  
Language Use ◽  
Fundamental Part ◽  
New Ideas ◽  
The Way

Linguistics is the study of Languages.  This goes all the way from identifying the sounds of a language to making policies about language use.  Because language is such a fundamental part of who we are, understanding how it works and all the information that it contains can help us understand a whole of other things too.  Languages are the basis of all of our interactions and thoughts.  Worldwide, we speak over 6000 distinct languages, with many more dialects and regional varieties.  The paper concentrates on understanding how languages work, who uses them, why they can be useful to us and what we can do with them in a big task, but there is a discipline and an approach with new ideas about linguistics as a science.

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