Математичко мишљење: општа или посебна правила закључивања?
Mathematical thinking: general or particular patterns of reasoning?
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Vygotsky proposes that the highest so called structural level of
knowledge comprises formal structure of knowledge (built-in
intelligence) along with patterns of reasoning establishing a
foundation for this structure. There is no doubt that structural
level of knowledge differs from area to area (compare, for
example, mathematics with history). On the other hand, some
patterns of reasoning such as modus ponens are general,
applicable to many (perhaps all) areas of school/scientific
knowledge. Being concerned with typical patterns of reasoning
applied in (school) mathematics, we examined in more detail
the following question: Are patterns of reasoning general or
nevertheless particular, distinctive to school/scientific area?
Our analysis evidences that some patterns of reasoning are
general (applicable to knowledge in general or to knowledge of
several school/scientific domains), whereas others are primarily
reserved for mathematical thinking (compare, for example,
reaso...ning by induction with reasoning by mathematical
induction). Along with that, patters of reasoning may be
context dependent even within a single domain. In case of
specialization, we can examine different mathematical objects
(particular numbers, factorable polynomials, regular polygons,
etc.). Having in mind research in artificial intelligence (from
general problem solver to expert systems), it is clear that, beside
general patterns of reasoning, competent problem solving also
requires those patterns that are specific to a particular domain
and probably sensitive to context of application.
Кључне речи:
patterns of reasoning / heuristics / mathematics / problem solving / artificial intelligenceИзвор:
Знање и постигнуће, 2004, 189-202Издавач:
- Београд : Институт за педагошка истраживања
Институција/група
IPITY - CHAP AU - Kadijević, Đorđe PY - 2004 UR - http://ipir.ipisr.org.rs/handle/123456789/1057 AB - Vygotsky proposes that the highest so called structural level of knowledge comprises formal structure of knowledge (built-in intelligence) along with patterns of reasoning establishing a foundation for this structure. There is no doubt that structural level of knowledge differs from area to area (compare, for example, mathematics with history). On the other hand, some patterns of reasoning such as modus ponens are general, applicable to many (perhaps all) areas of school/scientific knowledge. Being concerned with typical patterns of reasoning applied in (school) mathematics, we examined in more detail the following question: Are patterns of reasoning general or nevertheless particular, distinctive to school/scientific area? Our analysis evidences that some patterns of reasoning are general (applicable to knowledge in general or to knowledge of several school/scientific domains), whereas others are primarily reserved for mathematical thinking (compare, for example, reasoning by induction with reasoning by mathematical induction). Along with that, patters of reasoning may be context dependent even within a single domain. In case of specialization, we can examine different mathematical objects (particular numbers, factorable polynomials, regular polygons, etc.). Having in mind research in artificial intelligence (from general problem solver to expert systems), it is clear that, beside general patterns of reasoning, competent problem solving also requires those patterns that are specific to a particular domain and probably sensitive to context of application. PB - Београд : Институт за педагошка истраживања T2 - Знање и постигнуће T1 - Математичко мишљење: општа или посебна правила закључивања? T1 - Mathematical thinking: general or particular patterns of reasoning? EP - 202 SP - 189 UR - https://hdl.handle.net/21.15107/rcub_ipir_1057 ER -
@inbook{ author = "Kadijević, Đorđe", year = "2004", abstract = "Vygotsky proposes that the highest so called structural level of knowledge comprises formal structure of knowledge (built-in intelligence) along with patterns of reasoning establishing a foundation for this structure. There is no doubt that structural level of knowledge differs from area to area (compare, for example, mathematics with history). On the other hand, some patterns of reasoning such as modus ponens are general, applicable to many (perhaps all) areas of school/scientific knowledge. Being concerned with typical patterns of reasoning applied in (school) mathematics, we examined in more detail the following question: Are patterns of reasoning general or nevertheless particular, distinctive to school/scientific area? Our analysis evidences that some patterns of reasoning are general (applicable to knowledge in general or to knowledge of several school/scientific domains), whereas others are primarily reserved for mathematical thinking (compare, for example, reasoning by induction with reasoning by mathematical induction). Along with that, patters of reasoning may be context dependent even within a single domain. In case of specialization, we can examine different mathematical objects (particular numbers, factorable polynomials, regular polygons, etc.). Having in mind research in artificial intelligence (from general problem solver to expert systems), it is clear that, beside general patterns of reasoning, competent problem solving also requires those patterns that are specific to a particular domain and probably sensitive to context of application.", publisher = "Београд : Институт за педагошка истраживања", journal = "Знање и постигнуће", booktitle = "Математичко мишљење: општа или посебна правила закључивања?, Mathematical thinking: general or particular patterns of reasoning?", pages = "202-189", url = "https://hdl.handle.net/21.15107/rcub_ipir_1057" }
Kadijević, Đ.. (2004). Математичко мишљење: општа или посебна правила закључивања?. in Знање и постигнуће Београд : Институт за педагошка истраживања., 189-202. https://hdl.handle.net/21.15107/rcub_ipir_1057
Kadijević Đ. Математичко мишљење: општа или посебна правила закључивања?. in Знање и постигнуће. 2004;:189-202. https://hdl.handle.net/21.15107/rcub_ipir_1057 .
Kadijević, Đorđe, "Математичко мишљење: општа или посебна правила закључивања?" in Знање и постигнуће (2004):189-202, https://hdl.handle.net/21.15107/rcub_ipir_1057 .