Meanings |
Problems |
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A representative and an articulated sample of problem-situations that allows the contextualization, exercising, amplification, and application of mathematical knowledge, which comes from mathematics itself and from other contexts, is presented.
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Problem generation situations are proposed (problematization).
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Languages |
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A wide repertoire of representations (verbal, graphic, material, iconic, symbolic...) is used to model mathematical problems and ideas, analysing the relevance and potential of each type of representation and carrying out translation processes between them.
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The language level is made appropriate for the students to which it is addressed.
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The construction, improvement, and use of representations to organize, interpret, and record ideas are promoted.
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Concepts |
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The fundamental concepts of the subject are presented in a clear and correct way and are adapted to the educational level to which they are addressed.
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Situations are proposed where students have to generate or negotiate definitions.
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Propositions |
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The fundamental propositions of the subject are presented in a clear and correct way and are adapted to the educational level to which they are addressed.
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Situations are proposed where students have to generate or negotiate propositions.
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Procedures |
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The fundamental procedures of the subject are presented in a clear and correct way and are adapted to the educational level to which they are addressed.
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Situations are proposed where students have to generate or negotiate procedures.
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Arguments |
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Propositions and procedures are explained and argued (justified and demonstrated) in a manner appropriate to the educational level at which they are addressed.
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The justification of mathematical statements and propositions is favoured through various types of reasoning and proving methods.
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Relations |
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Mathematical objects (problems, definitions, propositions, etc.) are related and connected to each other.
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The diverse meanings of the objects that intervene in the mathematical practices are identified and articulated.
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Processes |
Communication, argumentation |
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Situations are promoted where the student has to argue (describe, explain, verify) and formulate conjectures about mathematical relations, investigate and justify them.
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Situations are proposed that allow the student to communicate using mathematical language to express his/her ideas with precision.
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Situations are proposed where the student can analyse and evaluate the mathematical thinking and strategies of others.
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Modelling |
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Situations are presented that allow the student to use mathematical models to represent and understand quantitative relationships (identify, select characteristics of a situation, represent them symbolically, analyse and reason the model, recognize the characteristics of the situation, the precision, and limitations of the model).
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The use of technology and the use of functions to model patterns of quantitative change are promoted.
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Generalisation |
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Situations, where students have the opportunity to describe, explain, and make generalizations and conjectures about geometric and numerical patterns, are promoted.
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Epistemic conflicts |
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The contents, problem-situations, and their solutions, concepts, propositions, language, etc. are presented correctly without errors, contradictions, ambiguities.
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