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Overlap Algebras: a Constructive Look at Complete Boolean Algebras [PDF]

open access: yesLogical Methods in Computer Science, 2020
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set.
Francesco Ciraulo, Michele Contente
doaj   +5 more sources

Teaching in the Montessori Classroom [PDF]

open access: yesJournal of Montessori Research, 2020
The theory of Montessori education has been interpreted by some researchers to be vaguely formulated. However, as shown in previous research, Maria Montessori’s didactic approach to teaching and learning mathematics is fully consistent with variation ...
Eva-Maria Tebano Ahlquist   +1 more
doaj   +3 more sources

Variations on Noetherianness [PDF]

open access: yesElectronic Proceedings in Theoretical Computer Science, 2016
In constructive mathematics, several nonequivalent notions of finiteness exist. In this paper, we continue the study of Noetherian sets in the dependently typed setting of the Agda programming language.
Denis Firsov   +2 more
doaj   +4 more sources

Quotient completion for the foundation of constructive mathematics [PDF]

open access: yesLogica Universalis, 2013
We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory.
Maietti, Maria Emilia   +1 more
core   +4 more sources

Microteaching and Peer Assessment in Mathematics Teaching Practice

open access: yesBrock Education: a Journal of Educational Research and Practice, 2023
Considering the characteristics that teachers should have, concepts such as critical thinking, active learning, taking responsibility, evaluation, analysis, self-evaluation and reflective thinking are important.
Aziz İlhan   +2 more
doaj   +2 more sources

Instance reducibility and Weihrauch degrees [PDF]

open access: yesLogical Methods in Computer Science, 2022
We identify a notion of reducibility between predicates, called instance reducibility, which commonly appears in reverse constructive mathematics. The notion can be generally used to compare and classify various principles studied in reverse constructive
Andrej Bauer
doaj   +1 more source

Foundations of Mathematics and Mathematical Practice. The Case of Polish Mathematical School

open access: yesStudia Historiae Scientiarum, 2022
The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed.
Jan Woleński
doaj   +1 more source

The Effect of Constructive and Independence Play on Prior Knowledge of Mathematics

open access: yesJMKSP (Jurnal Manajemen Kepemimpinan dan Supervisi Pendidikan), 2023
This study aims to investigate the impact of constructive play and the level of independence on prior knowledge of mathematics. The research method used is experimental.
Resti Elma Sari, Hendri Budi Utama Budi
semanticscholar   +1 more source

Constructive Problems in Discrete Mathematics: a Comparative Analysis of the Exam with and without a Computer

open access: yesComputer tools in education, 2022
The paper analyzes an experiment on the use of manipulators for solving constructive tasks related to the different concepts in teaching discrete mathematics students of a technical university. These concepts include a logical circuit, a finite automaton,
A. Chukhnov, S. Pozdnyakov
semanticscholar   +1 more source

Kant, Gödel, and the problem of synthetic a priori judgements [PDF]

open access: yesКантовский сборник, 2017
Debates over Kant’s famous postulate about the existence of synthetic a priori judgements in mathematics, formulated in the Critique of Pure Reason, have been raging for over two centuries.
Pushkarsky A. G.
doaj   +1 more source

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