*Marcelo LellisLuiz Márcio Imenes*

This article aims to contribute to the discussion about the teaching of mathematics in high school, considering the recent National Curriculum Parameters for this level of education. The text comprises three cores:

notes on the changes that have been proposed about Brazilian education;

considerations about the current teaching of mathematics in high school (high school or high school, as it was called until recently);

a suggestion of priority contents and appropriate approaches for a new teaching of Mathematics.

In the first part, the authors sought to limit objective information; in the rest, more personal analyzes, evaluations and opinions predominated.

## About changes in teaching

### Panorama

With a certain amount of simplification, it can be said that the dominant educational paradigm during the seventies, in Brazil and worldwide, was essentially contentious, displaced from social contexts and based on training, without reflection on the part of the student. Certainly this model has always been challenged with proposals for changes in the teaching of the various subjects, but, at least in our country, the overall picture changed little until the nineties, when, to some extent, the contest gained official support embodied in the Curriculum Parameters. Nationals. These belong to a number of controversial initiatives by the Ministry of Education, which also include the evaluation of textbooks, the National High School Examination (ENEM), the National Course Examination (Provão), the Teaching Appreciation Fund. , etc. and aim to transform the various levels of education.

Outside the scope of the executive, the National Congress enacted in 1996 Law 9394 of the National Education Guidelines and Bases (LDB / 96), itself a factor of change. As a result, in 1998, the National Board of Education instituted the National Curriculum Guidelines for High School (DCNEM) and, in the second half of 1999, the Secretariat of Education released the National Curriculum Parameters for High School (PCNEM).

Governmental measures already have an impact on primary and university education, although not always in a positive way. In elementary school, however, progress seems clear to us. Groups of educators wishing to replace the purely informative educational paradigm find reasonable success. Particularly in the teaching of mathematics, the new parameters can be supported by a very active community of mathematical educators, consolidated since the 1980s, which is itself an unofficial transformative element. It was the practices, studies and research of this community that guided the Curriculum Parameters in the discipline.

PCNEMs, however, are still too recent for us to glimpse changes in high school, and in mathematics the debate among mathematical educators has barely begun. This, incidentally, is one of the motivations of this text.

### Elements of DCNEM and PCNEM

Let's start with the most general. DCNEM interpret and specify LDB / 96, being the reference for the rest of the document that presents the parameters for the three areas of high school. These should be taken as a continuation of the elementary school parameters.

High School is defined as the final stage of the basic education of the student, which is necessary for every educated citizen and aims to "introduce the youth into the world as a whole", because then comes a specialized stage (at work or at university, etc.). It is repeatedly stated that the primary education level should not have as its main objective the preparation for entrance exams. The proposed teaching has as philosophical foundations:

the aesthetics of sensitivity (which values the creative, the curious, and favors autonomous, nonstandard work);

equality policy (which seeks solidarity and respects diversity as the basis of citizenship);

the ethics of identity (which promotes the autonomy of the student, school, pedagogical proposals, etc.).

Sensitivity, equality and identity, characterized as we have seen, never harmonize with a teaching that was limited to transmitting information and training procedures, in which learning was reduced to the memorization of what was presented. Therefore, DCNEM conceives knowledge as a collective construction (which is much more than information) and learning as the construction of competences around knowledge (representation and communication, research and understanding, socio-cultural contextualization).

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These conceptions practically require a pedagogical action that favors "learning to learn" and the development of competences through strategies that mobilize reasoning rather than memory. In such a process, it is necessary condition that the contents are significant from the learner's point of view and, therefore, be contextualized and treated in an interdisciplinary manner. Often, the simple contextualization already entails interdisciplinarity, because understanding a real context and acting on it depends on the different points of view of different disciplines.

DCNEM considers High School composed of three areas of knowledge:

(i) Natural Sciences, Mathematics and its technologies,

(ii) Languages, Codes and their technologies,

(iii) Humanities and their technologies.

The realization of the ideas contained in the PCNEM should take place based on the pedagogical proposal of each school that, from a common base for every country (75% of the workload), will provide "a diversification of types of studies, from the most humanistic to the most scientific or artistic "

The part of the PCNEM related to mathematics presents the purposes of teaching the subject. It takes into account its formative character (develops specific skills), its instrumental aspect (applications in reality and science) and its status as a science (its own research and validation methods as well as its organization). We also point out the two-way relationships between mathematics and technology: the first as an instrument for entering the technological universe and the latter as a source of transformations in mathematical education.

The principles contained in DCNEM and the parameters related to mathematics relate harmonically, although the texts have different authors. The parameters are intended for students to understand the applications of mathematics in various situations, which echoes the idea of a contextualized teaching; The parameters propose that learners develop analysis and judgment, problem solving, communication and representation, which corresponds to a vision of learning as "competence building"; The parameters have as purpose of teaching the understanding of mathematics, the confidence in its use and some personal satisfaction with it, which reflects, among other ideas, the ethics of identity and the promotion of autonomy. For more examples we recommend reading the original texts.

Finally, we point out that the parameters do not present a program, a list of contents. They suggest that a common national core should be established in the future after reflection and debate. An appropriate selection of content would avoid over-specialization (because the intended training is general) and take into account social and cognitive factors.

**Appreciation**

In general, our opinion about DCNEM and PCNEM is very positive. Although the discourse in both documents contains a dose of dream and desire - or precisely because of this - we believe it indicates a considerable improvement in Brazilian education. We still believe that there are concrete possibilities to implement a teaching that comes close to the proposed objectives.