The connections between elements of the concept image are important for preventing internal contradictions (p. 236).
[...] the theories about concept image are not very usable in analyzing the whole structure of knowledge, but they are useful when concentrating on the knowledge concerning one concept at a time. In the
latter case the
conceptions about the relationships between a concept under analysis and other concepts can be considered as elements inside the concept image of the concept under analysis (p. 236).
[...]
When derivative is considered for the first time in mathematics education, for example, in upper secondary school, the definition is usually left to the background, and the use of the differentiation rules are emphasized.
[...]
Almost every day mathematics teachers meet in their work erroneous conclusions made by students. Many of these are random careless mistakes, but others are based on a deliberate reasoning. In the latter case a careful personal discussion with a student may be needed in order to find out how deep in the knowledge structure the problems lie. In the learning process it is important that the pieces of knowledge which an individual learns and which he/she already knows form coherent entities. How could teachers and designers of textbooks and curricula take this goal into account? This study highlights two factors: First, the fundamental role of definition should be emphasized. Therefore, in teaching tasks in which the definition is really needed as a central part of reasoning should be used. Second,
there should be tasks which lead students to critically reflect qualities of mathematical concepts and relationships between concepts. Especially, controlled conflict situations may offer fruitful starting points for this kind of reflection (Viholainen, 2008, p. 246).
When the HF-education, that is a type of further education meant as an offer to everybody who wishes to qualify for more advanced theoretic education, came into existence, it was but natural that the purpose of the mathematics regulation 1967 was nearly the same as the one for the languages line students. The course was to be more elementary though, for instance, it shouldn’t comprise infinitesimal
calculus, but the textbooks included chapters from the textbooks for language students. After a short time, it became evident that fundamental changes were necessary in order to change this compulsory one-year, five lessons per week course to a success.
In the revised mathematics regulation for HF it was mentioned as the first goal to provide the students with mathematical knowledge that could be useful in other subjects and in their daily life, and as the second, to give them an impression of mathematical method and way of thinking. Theoretical algebra and group theory were removed from the curriculum and statistics, probability theory, and binomial
test were entered. The so-called free lessons meant for cooperation with other subjects or for elaboration of previously treated material appeared in the curriculum. A textbook for the course was written on the basis of an experiment.
This textbook comprised many examples connected to everyday life and it encouraged the pupils to find others. The style of it made it easy to understand also for many who had earlier given up mathematics as too difficult or as uninteresting.
It contained few proofs, but it was very good at helping the students to create relevant concept images. The text encouraged the teacher to let the students spend much of the lessons working in groups of three to five persons solving and discussing problems. In this course, mathematics was no longer a terrifying subject (Jensen, 1994).
While legal education has not changed much, the world of business and finance has changed in innumerable ways. [...] For instance, I recall that my derivatives class focused on plain vanilla options and futures and the methods for valuing them, but not exotic instruments such as credit derivatives, collateralized debt obligations, and their trading strategies. In addition, discussions of risk management focus on the enterprise, and not on broader themes covering systemic risk and economic policy.
There was not a focus on the connection between business, government, regulation, and economic policy. In terms of a business curriculum, law students must have and educational platform that teaches beyond the scope of traditional legal education [...]" (Rhee, 2009).
Keywords: polyvalence and universality of methods of logical reasoning, spiral progression dependent on other disciplines,
business transactions in daily life, too early introduction of symbolism,
mathematical modeling problems, badly understood formalism,
advanced theoretic education,
mathematics in business, utility of formalism,
differentiable function,
mathematics formalization,
business education, excessive formalism, supple formalism,
logical reasoning,
incidental information,
cognitive psychology,
quantitative literacy,
concept image,
career education,
policy design,
formalism,
differentiability,
Lera Boroditsky
Palavras-chave: Ubiratan D’Ambrosio
Brazil:
Brazil in business education,
Brazil in commons
Outcomes:
enactment in mathematics
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Supple. Available from <
https://translate.google.com.br/?hl=pt-BR#en/pt/supple >. access on 28 June 2016.
Terezinha Nunes Carraher.
Business education. Available from <
https://scholar.google.com.br/scholar?q=%22Terezinha+Nunes+Carraher%22+business+education&btnG=&hl=pt-BR&as_sdt=0%2C5&as_vis=1 >. access on 29 June 2016.
https://scholar.google.com.br/scholar?q=orientation+social+human+%22business+education%22+mathematics+regulation+formalization+%22in+Brazil%22&btnG=&hl=pt-BR&as_sdt=0%2C5&as_vis=1
http://www.google.com.br/search?hl=pt-BR&q=orientation+social+human+%22mathematics+regulation%22&btnG=Pesquisar
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http://pipl.com/directory/tags/Mathematics
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GregorioIvanoff - 28 Jun 2016
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