scholarly journals Development of a Mathematical Language Scale in Fraction Teaching (MLSFT)

2022 ◽  
Vol 9 (2) ◽  
pp. 71-87
Author(s):  
Belgin BAL İNCEBACAK ◽  
Esen ERSOY
2017 ◽  
Vol 53 (9) ◽  
pp. 1633-1642 ◽  
Author(s):  
David J. Purpura ◽  
Jessica A. R. Logan ◽  
Brenna Hassinger-Das ◽  
Amy R. Napoli

2018 ◽  
Vol 11 (1-2) ◽  
pp. 279-295
Author(s):  
Mohammed Aref

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.


Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely

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.


2021 ◽  
Vol 55 ◽  
pp. 193-200
Author(s):  
Elien Vanluydt ◽  
Anne-Sophie Supply ◽  
Lieven Verschaffel ◽  
Wim Van Dooren

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1966
Author(s):  
Melania Bernabeu ◽  
Salvador Llinares ◽  
Mar Moreno

This paper reports sophistication levels in third grade children’s understanding of polygon concept and polygon classes. We consider how children endow mathematical meaning to parts of figures and reason to identify relationships between polygons. We describe four levels of sophistication in children’s thinking as they consider a figure as an example of a polygon class through spatial structuring (the mental operation of building an organization for a set of figures). These levels are: (i) partial structuring of polygon concept; (ii) global structuring of polygon concept; (iii) partial structuring of polygon classes; and (iv) global structuring of polygon classes. These levels detail how cognitive apprehensions, dimensional deconstruction, and the use of mathematical language intervene in the mental process of spatial structuring in the understanding of the classes of polygons.


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