Introducing Mathematical Language as We Record Student Thinking

This review essay introduces the work of the Egyptian scientific historian and philosopher Roshdi Rashed, a pioneer in the field of the history of Arab sciences. The article is based on the five volumes he originally wrote in French and later translated into Arabic, which were published by the Centre for Arab Unity Studies and which are now widely acclaimed as a unique effort to unveil the achievements of Arab scientists. The essay reviews this major work, which seems, like Plato’s Republic to have “No Entry for Those Who Have No Knowledge of Mathematics” written on its gate. If you force your way in, even with elementary knowledge of computation, a philosophy will unfold before your eyes, described by the Italian astronomer Galileo Galilei as “written in that great book which ever lies before our eyes—I mean the universe—but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.” The essay is a journey through this labyrinth where the history of world mathematics got lost and was chronicled by Rashed in five volumes translated from the French into Arabic. It took him fifteen years to complete.

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KARAKTERISTIK PENCAPAIAN KEMAMPUAN PEMBUKTIAN DAN KEPERCAYAAN DIRI MAHASISWA MELALUI METODE MOORE

Jurnal Analisa ◽

10.15575/ja.v4i2.3681 ◽

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.

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Proof Theory of the Cut Rule

10.1093/oso/9780198748991.003.0010 ◽

2018 ◽

Author(s):

J. R. B. Cockett ◽

R. A. G. Seely

Keyword(s):

Proof Theory ◽

Graphical Representation ◽

Basic Component ◽

Graphical Representations ◽

Mathematical Language ◽

Basic Logic ◽

Cut Rule ◽

Structural Rules ◽

The One ◽

Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

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The importance of specific mathematical language for early proportional reasoning

Early Childhood Research Quarterly ◽

10.1016/j.ecresq.2020.12.003 ◽

2021 ◽

Vol 55 ◽

pp. 193-200

Author(s):

Elien Vanluydt ◽

Anne-Sophie Supply ◽

Lieven Verschaffel ◽

Wim Van Dooren

Keyword(s):

Proportional Reasoning ◽

Mathematical Language

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Mathematical Language and the Changing Concept of Physical Reality

New Approaches to Scientific Realism ◽

10.1515/9783110664737-010 ◽

2020 ◽

pp. 206-228

Keyword(s):

Physical Reality ◽

Mathematical Language

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Implications of Lesson Study for Tertiary-Level EFL Teachers’ Professional Development: A Case Study From Turkey

SAGE Open ◽

10.1177/21582440211023771 ◽

2021 ◽

Vol 11 (2) ◽

pp. 215824402110237

Author(s):

İlknur Bayram ◽

Fatma Bıkmaz

Keyword(s):

Professional Development ◽

Lesson Study ◽

English Language ◽

Research Question ◽

Teaching Style ◽

Language Teachers ◽

Student Thinking ◽

Pedagogical Content ◽

Starting Point

This qualitative case study carried out at a Turkish university with four English language teachers aims to explore what teachers experience in the planning, implementation, analysis, and reporting phases of the lessons study process and what the implications of lesson study for teacher professional development can be. Data in this four-month study were gathered through observations, interviews, whole group discussions, and reflective reports. Findings revealed that lesson study had potential challenges and benefits for the professional development of teachers. The model poses challenges in finding a topic and research question, determining the lesson design and teaching style, making student thinking observable and analyzing qualitative data. On the other hand, it benefited teachers in terms of increasing their pedagogical content knowledge, reflectivity, research skills, collaboration, and collegiality. This study suggests that lesson study might be a good starting point for institutions wishing to adopt a more teacher-led, inquiry-driven and collaborative perspective for professional development.

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