FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W25649963> ?p ?o ?g. }

• W25649963 endingPage "13" @default.
• W25649963 startingPage "7" @default.
• W25649963 abstract "Philosophical positions and epistemological . theoties related to mathematics, such as logicism, formalism, constructivism, structmalism, empiiicism, have always had a significant influence on the guiding ideas and leading piinciples in mathematics education.. This not only holds for cuniculum development and teaching methodology but also for theoretical work and empirical researCh related to the mathematical learning process. As Seymour PAPERT has pointed out in Mindstorms: BOURBAKI's theory of motheT-structure is learning theory Whether it is a good or bad one is another question. a similar way PLATO's and PROCL US' of EUCLID's elements with its idealistic ontology and its emphasis on the dialectic between analysis and synthesis being the capstone of the mathematical sciences comprises the elements of a mathematical pedagogy and of a theory of learning. [42], [50], [66] This phenomenon can be pursued thwugh the history of mathematics and its concomitant philosophy. Of course, the observation not only holds for global mathematical but also for epistemological views of particular parts or concepts of mathematics, such as the set-theoretical foundation of the function concept, the logical interpretation ofvatiables as place holders, the interpretation of geometry in terms of Felix KLEIN's Erlanger Program etc On the other hand, considering the inverse relation, what was said by Rene THOM in his 1972 Exeter speech is also true: In fact, whCther one wishes it or not, all mathematical pedagogy, even if scarcely coherent, rests on a of mathematics. Such philosophies may consist in a teacher's 'private opinion on the natw·e of mathematics and mathematical knowledge (often indirectly acquired in his own academic studies), and in his thoughts about how this is related to his teaching and to the learning of his students .. They are also inherent in didactical principles such as the spiral approach (BRUNER), the deep-end principle (DIENES: [16]), the operative principle (AEBLI), etc They underlie theories of stages in the learning process (PIA GET, VAN HIELE) or theories of transfer, and they also stand behind hypotheses of empirical studies on how children learn or faiL As Wi'S pointed out by Thomas S.. KUHN, each research paradigm has philosophical and ontological assumptions among its different components, an4 these are parts of the paradigm's bias, its strength and weakness .. Often they are a source of profound discrepancies between competing approaches and of controversies between research grtmps or individual researchers. , Recent developments in mathematics education show a new dynamics in the field. New and epistemological theories have entered the scene: the theory of epistemological obstacles (BACHELARD, BROUSSEAU( !OJ, CORNU, SIERPINSKA), a synthesis of Kuhnian theory dynamics and Piagetian genetic epistemology (v,GLASERSFELD, CAWTHRON & ROWELL) a new quasiempiricist of mathematics (LAKATOS [43], SNEED, JAHNKE), a complementarist view of mathematics (KUYK, OTTE [51]), the epistemology of microworlds and of the society of based on cggnitive studies within research on artificial intelligence (PAPER T, MINSKY} They claim to provide a better backgrnund for an investigation of pupils' real learning behaviour both from a cognitive and a social point of view. They also claim to give a more adequate foundation for the theory and practice of mathematics teaching .. Based on these developments, and supported by new empirical data, strong criticisms have been put forward especially against positions elaborated in close connection with the new-math philosophy DefiCiencies of this reform are being characterized by terms like HJourdain effect, Topaze effect, metacognitive shift, etc (BROUSSEAU [91]), and by exhibiting its one-sided mentalistic orientation guided by the assumption of the autonomous, universal, coherent, and homogeneous natures of both mathematical structures and the human mind Other failures are related to a purist or static view that neglects the applications which belong to mathematical theories and concepts as they do to physical theories, and neglects the representational, the social, the procedural and the processual dimensions of mathematics This criticism says that the stmctural concepts of mathe-" @default.
• W25649963 created "2016-06-24" @default.
• W25649963 creator A5070417775 @default.
• W25649963 date "1987-01-01" @default.
• W25649963 modified "2023-09-23" @default.
• W25649963 title "Philosophical and Epistemological Aspects of Mathematics and Their Interaction with Theory and Practice in Mathematics Education." @default.
• W25649963 cites W1815090327 @default.
• W25649963 cites W1990474964 @default.
• W25649963 cites W1996471421 @default.
• W25649963 cites W2007072885 @default.
• W25649963 cites W2042720364 @default.
• W25649963 cites W2061587970 @default.
• W25649963 cites W2483494328 @default.
• W25649963 cites W2489100041 @default.
• W25649963 cites W2782194687 @default.
• W25649963 cites W3045066449 @default.
• W25649963 cites W768501250 @default.
• W25649963 hasPublicationYear "1987" @default.
• W25649963 type Work @default.
• W25649963 sameAs 25649963 @default.
• W25649963 citedByCount "22" @default.
• W25649963 countsByYear W256499632013 @default.
• W25649963 countsByYear W256499632014 @default.
• W25649963 countsByYear W256499632015 @default.
• W25649963 countsByYear W256499632017 @default.
• W25649963 countsByYear W256499632019 @default.
• W25649963 crossrefType "journal-article" @default.
• W25649963 hasAuthorship W25649963A5070417775 @default.
• W25649963 hasConcept C111472728 @default.
• W25649963 hasConcept C118840557 @default.
• W25649963 hasConcept C119754765 @default.
• W25649963 hasConcept C13184196 @default.
• W25649963 hasConcept C133281099 @default.
• W25649963 hasConcept C138885662 @default.
• W25649963 hasConcept C142362112 @default.
• W25649963 hasConcept C145420912 @default.
• W25649963 hasConcept C153349607 @default.
• W25649963 hasConcept C17744445 @default.
• W25649963 hasConcept C183140480 @default.
• W25649963 hasConcept C199539241 @default.
• W25649963 hasConcept C2780506305 @default.
• W25649963 hasConcept C30759668 @default.
• W25649963 hasConcept C33923547 @default.
• W25649963 hasConcept C34355311 @default.
• W25649963 hasConcept C40238689 @default.
• W25649963 hasConcept C41895202 @default.
• W25649963 hasConcept C527412718 @default.
• W25649963 hasConcept C558565934 @default.
• W25649963 hasConcept C73301696 @default.
• W25649963 hasConcept C94625758 @default.
• W25649963 hasConceptScore W25649963C111472728 @default.
• W25649963 hasConceptScore W25649963C118840557 @default.
• W25649963 hasConceptScore W25649963C119754765 @default.
• W25649963 hasConceptScore W25649963C13184196 @default.
• W25649963 hasConceptScore W25649963C133281099 @default.
• W25649963 hasConceptScore W25649963C138885662 @default.
• W25649963 hasConceptScore W25649963C142362112 @default.
• W25649963 hasConceptScore W25649963C145420912 @default.
• W25649963 hasConceptScore W25649963C153349607 @default.
• W25649963 hasConceptScore W25649963C17744445 @default.
• W25649963 hasConceptScore W25649963C183140480 @default.
• W25649963 hasConceptScore W25649963C199539241 @default.
• W25649963 hasConceptScore W25649963C2780506305 @default.
• W25649963 hasConceptScore W25649963C30759668 @default.
• W25649963 hasConceptScore W25649963C33923547 @default.
• W25649963 hasConceptScore W25649963C34355311 @default.
• W25649963 hasConceptScore W25649963C40238689 @default.
• W25649963 hasConceptScore W25649963C41895202 @default.
• W25649963 hasConceptScore W25649963C527412718 @default.
• W25649963 hasConceptScore W25649963C558565934 @default.
• W25649963 hasConceptScore W25649963C73301696 @default.
• W25649963 hasConceptScore W25649963C94625758 @default.
• W25649963 hasIssue "1" @default.
• W25649963 hasLocation W256499631 @default.
• W25649963 hasOpenAccess W25649963 @default.
• W25649963 hasPrimaryLocation W256499631 @default.
• W25649963 hasRelatedWork W117912344 @default.
• W25649963 hasRelatedWork W14712532 @default.
• W25649963 hasRelatedWork W1488090801 @default.
• W25649963 hasRelatedWork W1606328991 @default.
• W25649963 hasRelatedWork W1734280967 @default.
• W25649963 hasRelatedWork W1978701263 @default.
• W25649963 hasRelatedWork W1993565392 @default.
• W25649963 hasRelatedWork W2014126975 @default.
• W25649963 hasRelatedWork W2037612913 @default.
• W25649963 hasRelatedWork W2051251117 @default.
• W25649963 hasRelatedWork W2054893111 @default.
• W25649963 hasRelatedWork W2057277196 @default.
• W25649963 hasRelatedWork W2067822693 @default.
• W25649963 hasRelatedWork W2072405721 @default.
• W25649963 hasRelatedWork W2082005547 @default.
• W25649963 hasRelatedWork W2149355902 @default.
• W25649963 hasRelatedWork W2326972230 @default.
• W25649963 hasRelatedWork W2332128459 @default.
• W25649963 hasRelatedWork W2378758346 @default.
• W25649963 hasRelatedWork W2394136705 @default.
• W25649963 hasVolume "7" @default.
• W25649963 isParatext "false" @default.

• next