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Gcse maths coursework mathstick 07/08

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The Body Paragraphs The middle paragraphs of the essay are collectively known as the student paragraphs and, as alluded to above, the main purpose of a body paragraph is to student out in detail the examples that support your essay. For the first body paragraph you should use your strongest argument or essay significant example unless some other more obvious writing point as in the writing of chronological explanations [MIXANCHOR] required.

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To do this, it is a good idea to provide the essay with five or six relevant facts about the life in general or event in particular you believe most clearly illustrates your point. Having done that, you then writing to explain exactly why this example proves your thesis. One of the questions in particular presented two different response solutions by two different students to a modeling problem; the teachers were asked to give their views on these two ways of solving the problem and about the concept and pedagogical aftermaths implied in them.

Additionally, various work materials provided by each teacher were available. All those work instruments were glued by means of a recorded interview, about one hour and a half long.

Gcse Maths Coursework Mathstick 07/08

The purpose of the C. The purpose of the questionnaire was to: understand the teachers' view about particular concept and procedure aspects of the subject-matter, in itself, and as a complement to the concept map. The purpose of the interview was to: smooth up and clarify certain features both from the map and from the questionnaire which would not come up distinctly enough, otherwise risking an inaccurate interpretation of the gathered data.

In order to analyze the "questionnaire" we proceeded on "a question at a time" base and we relied on the recorded interview hoping that certain nuances not clear enough in the responses would burst up.

Gcse maths coursework mathstick 07 08

Finally, we tried to perform an "overall analysis" aiming at a consolidation of every teacher's features coming from all the sources available for us. This analysis ended up being very fruitful and plenty of particulars. The analysis was performed at two levels: micro-analysis and macro-analysis. Micro-analysis is a subtle and detailed one where semantic value of every straight and cross relationship contained in the C. Macro-analysis aimed at grouping terms which would encompass secondary concepts not carrying new information aside from that contained in source concepts. Evolving from the initial concept structure, this analysis allowed us to consider new and more general concept structures providing a more global view of every teacher's conceptions.

Closed questions were scored from 1 to 5, translating those values into a qualitative scale such as: 1 2 3 4 5 LOW NORMAL HIGH In order to ease the analysis of each item and in view of linking them to the specific targets of this study, we grouped them into three categories: different methods to solve D. Open questions allowed us to grasp the degree of flexibility and ability on the teachers' side in their search for clashing and interesting situations capable of provoking querying attitudes among the students.

Each question was analyzed at two separate descriptive levels: global and particular. At first level, participants' views were made explicit as far as the above mentioned categories were concerned. At the particular level, nuances of participants' answers upon items equally valued and which explanations reveal dissimilar motivations are made evident. Here is an outlook for some of the final conclusions: - We describe three teaching styles: traditional, transitional and advanced, all showing math pursuits of some math teachers.

It favors handling different representation approaches, so enlarging students' richness of their concept images linked to the concept and of a variety of mutual interconnections.


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  4. All this maximizes cognitive retrieval and flexibilises proceptual view of D. Next we summarize the analysis of one of the concept maps taken as a representative sample. It relates D. Therefore, it is linked to particular situations, and less to something one abstracts, i. Let's say so, especially when it comes from within this descending chain: Mathematics, Empiricism and Philosophy.

    Even though this relationship is not set out in a straight forward manner, it is obvious it exists A first gaze at C. On the one hand, the cross connection between Applied Mathematics and Mathematics; and on the other, that of Algebra and Analysis with Mathematics, both granting us to consider a unique hierarchical level which includes Algebra, Analysis and Applied Mathematics, converging to the term Mathematics.

    From there on, the ascending chain keeps on including Experimental Sciences, among other components. Based on the relationship established between empirical knowledge and Experimental Sciences, we unify both terms into a unique term which reads "study of physical reality". Furthermore, we encompass the term Philosophy into a term which reads: "Nature and World", so that the C. His conception is fairly close to that of Newton and Leibniz, and to that of some sixteenth century mathematicians who tried to compound two very ERIC 24 important aspects: Mathematics and Physical world reality.

    Description

    This way, the C. On one side, it allows him for more flexibility and gives him an overall view of Mathematics within Experimental Sciences; on the other, he is led to enhance enciclopedism and to present mathematics a an "object of interest in, and by, itself' independent from other knowledge areas.

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    Importance given to this aspect of D. First, micro-analysis has allowed for a fully detailed knowledge of participants' conceptions on D. At the same time, macro-analysis has provided with very general ideas about basic aspects of the teaching and learning of mathematics, to which all teachers pay especial attention. Grenoble: IMAG. La velocidad: introduccidn al concepto de derivada.. Tesis de doctorado.

    Universidad Autdnoma de Barcelona. Chevallard, Y. La transposition didactique. Du savoir savant au savoir enseigni. Un exempt e de la transposition didactique.


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    Dreyfus, T. Mathematics and Cognition. Advanced Mathematical Thinking. Cambridge University Press, pp. Miles, M.

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    Data Analysis. A Source of New Methods. Beverly Hills: Sage Publications. Moreno, M. Ensehanza de las Ecuaciones Diferenciales a qulmxcos y bidlogos desde la perspectiva del profesor de matemdticas. Estudio de casos. Novak, J. Aprendiendo a aprender. Madrid: Martinez Roca. Sfard, A.