What is the importance of mathematics in business life

Ethnomathematics: A Reflection on the Mathematics of Masons

ORIGINAL ITEM

SWANTES, Vilson [1], XAVIER, Márcio Pizzete [2], SCHWANTES, Eloísa Bernardete Finkler [3], SCHWANTES, Daniel [4], JUNIOR, Affonso Celso Gonçalves [5], KRACKE, Elisa [6], JUNIOR, Élio Conradi [7]

SWANTES, Vilson. Et al. Ethnomathematics: A reflection on the mathematics used by masons. Revista Científica Multidisciplinar Núcleo do Conhecimento. 04 year, Ed. 07, Volume 13, pp. 46-66. July 2019. ISSN: 2448-0959

Contents

1. SUMMARY

This article is the result of reflections on ethnomathematics and analysis of study sessions conducted with Bricklayers in the community of Mercedes - PR. He finds motivation in the writings of Professor Ubiratan D ’Ambrosio, who recognizes the existence of mathematical knowledge in various cultural areas. The focus of the research explores dialogues with each professional, through problem situations, using math to budget the amount of ceramics necessary to coat walls and floors. In doing research with the masons, it was interesting to know whether they were formal or informal. The statements showed an understanding that mathematical knowledge is dynamic, a cultural product that emerges in various areas of human activity and that circulates in and through the world of life and becomes firmly established in school.

Keywords: mathematical education, ethnomathematics, problem situations, study sessions, ceramic budget.

2. INTRODUCTION

In all cultures, throughout history, we find records of evolved activities that indicate the existence and necessity of some type of mathematical knowledge. This is empirical knowledge used in the practice of several professions, passed down through generations, and often used without people noticing its presence.

When math sanders to solve a problem situation, it is sometimes possible to solve it without necessarily attending school. Mathematical knowledge can of course be developed through daily practice, for example, in the work of bricklayers, professionals who routinely use this knowledge.

For many decades in the history of education, knowledge from social practices was ignored and not discussed in school. Today the suggestion to examine the mathematical knowledge that exists in the life of students outside the school context is gaining more and more space. This knowledge that man has built up in space and time is a valuable legacy that must be taken into account in school curricula or in the methodology used. There are many educators who believe that system knowledge can be constructed from concepts that are present in the daily life of professions, of people.

For Professor Ubiratan D’ambrrésio, all children already have a knowledge of mathematics before they even enter school. For the researcher, this knowledge is ethnomathematics[8]. The author would like to tell us that knowledge is not only the result of years of study, but also the result of experiences lived among citizens of the same or different social groups.

According to the researcher, the main proposition of ethnomathematics is to try to understand the mathematical knowledge / doings of any group of interest, community, people or nation. In this sense, his writings consider ethnomathematics:

“… The math practiced by cultural groups, such as urban and rural communities, groups of workers, occupational classes, children of a certain age group, indigenous societies and so many other groups identified by goals and traditions together for groups”. (2001, p.9).

The author sees ethnomathematics like:

“… A strategy developed by the human species throughout its history to explain, understand, manage and live with the sensitive reality, perceptible and with its imaginary, of course, in a natural and cultural context. ”(D’AMBROSIUS, 1996, p. 7)

Bricklayers, sometimes illiterate and most of the time with little education, use mathematical knowledge to build houses, make ceramic nesting sites, build walls, buildings that are still considered today, solid and sturdy constructions. There certainly exists in this work, mainly used in the calculations and in the organization of mathematical reasoning, a knowledge that can be used in the school context, or in the integration of students with a tendency to this type of profession, either in one Approach More practical math discipline. For Carneiro,

[…] Mathematics teaching in this conception will enable the student to link the Indian concepts to their daily experience, according to their natural, social and cultural environment. The point is not to reject academic mathematics, but to take into account values ​​that are experienced in group experiences when one considers the historical-cultural ties (CARNEIRO, 2012, p. 3).

In recent decades, the number of educators studying ethnomathematics as a research program and / or as a proposal for educational work has grown. The goals of these teachers are, among other things, to know the processes of generation, organization and dissemination of knowledge and mathematical ideas in cultural groups, and how to develop measures in the field of mathematics teaching that contextualize the formal content dealt with in the classroom.

The ethnomathematics perspective allows us to work in the classroom an educational proposal that encourages students and teachers in the development of creativity that leads to both new and rich forms of learning. This socio-cultural wealth, which flows into the learning process of teaching, is, according to Professor Ubiratan D'Ambrosio, part of a “program that aims to improve the processes of generation, organization and transmission of knowledge in different cultural systems and the interactive forces, which act on and between the three processes. ”(D’AMBRÓSIO, 1993, p.7).

Another perspective on ethnomathematics was developed by the Brazilian researcher Gelsa Knijnik. For this author, ethnomathematics allows

To study the Eurocentric discourses that introduce academic and school mathematics; Analyze the effects of the truth generated by academic and scientific mathematics discourses; Discuss issues of differences in math education, taking into account the centrality of culture and the balance of power they establish; and examine the language games that make up each of the different math and analyze their family similarities. (KNIJNIK, 2006, p.120).

In Knijnik's studies, the author characterizes ethnomathematics as mathematical that is produced by social groups that use their knowledge to carry out their activities. Knijnik (2002, p. 33), who makes a counterpoint between formal and informal mathematics[9]t, think about it after [...] h that when you acquire the knowledge produced by academic mathematics when you are confronted with real situations, the one that seems more appropriate.

Giardinetto (1999): “The teacher can and should use the daily knowledge to support the teaching-learning process” (p. 68) by bringing the student into the realm of reasoning and the habit of critical reading, research , questions, creativity, indispensable for citizen education. In this way, they are valued and the previous knowledge of the students is proven, which is derived from this, other knowledge, always from what is known.

It is important to establish knowledge ties between the community and the knowledge of the school and the knowledge of the school with the knowledge of the community. Through this establishment and these relationships it is possible to be able to end both knowledge meaning.

The thesesis that the author defends is that the school, more than just reproducing daily knowledge, has to mediate between this and school knowledge, that is, it has to make the wisdom of humanity available to the new generations, which is a product turns out. Historically and socially. This knowledge must be socialized, because “it is not the individual individual to construct all knowledge, but to have constituted the right of access to this knowledge” (GIARDINETTO, 1999, p. 47).

For D’ambrsio (2001), knowledge in this context represents a dynamic character that is always open to new approaches. To do this, the teacher must stay up to date, constantly evaluate his or her practice, practice new teaching methods and improve previously experienced pedagogical measures so that they can be used pedagogically.

Breda, Lima and Guimarées (2011, p. 15), in their studies, say that:

I began to look at the ethnomathematics proposal as a way of distinguishing the work that the teacher develops in schools, that is, the conteudistic and meaningless practice can be replaced by a teacher who is oriented by a new look, the promotes the appreciation of the socio-cultural context of education, its thought processes and its ways of understanding, explaining and carrying out its practice in today's society, an invitation to reconsider its educational practices and its implications or even to consider its role as Lecturer who deals with different points of view in the school context.

Thus, in the school context, as a study course that seeks to know and understand the knowledge produced and used in different cultures, ethnomathematics can be researched to support teaching so that students can understand the various “mathematics” involved in other contexts appreciate the cultural diversity and intellectual and creative development of each people, culture or community.

We math teachers, according to D’ambrosius (2001), need to be clear and in perfect harmony with our role as educators before the mission of preparing our young people for a happy future. We have to teach math, yes, but also about humanity. In this context, the author emphasizes

The pedagogical proposal of ethnomathematics is to bring mathematics to life, to deal with real situations in time and [agora] space [aqui] n. And to question the here and now through criticism. We immerse ourselves in cultural roots and practice cultural dynamics. In education, we effectively recognize the importance of different cultures and traditions for the formation of a new civilization that is supra-cultural and transdisciplinary. (D’AMBRÓSIO, 2001, p. 46).

In order to make this a reality, the teacher has to review his teaching practice on a daily basis, develop an educational project that always values ​​the knowledge and history of each student and in this individuality a new and practical context for the art of teaching. It is important that the teacher in the classroom, in addition to enjoying and based on the knowledge that the student brings from the environment in which he lives, makes him believe that he also has an important role in the (re) construction of social and cultural knowledge as well as knowledge plays mathematician.

In the words of Rosa Neto, mathematics must be interpreted as a natural socio-cultural product of a people because,

Mathematics was created and developed by humans according to their needs. (…) Culture is a form of adaptation because it is a way of acting on the environment that was built with it. (ROSA NETO, 2002, p.7 e 19).

In this context, there is a significant relationship between mathematics and culture, both as a result of our adaptation to the needs of survival over time, which is the culture that past generations have left us, an empirical legacy, systematic and scientific.

3. JUSTIFICATION

Mathematics has always been viewed as the basic science of several areas of knowledge. Mastering his knowledge is fundamental to solving problematic situations in several areas. In view of this importance and relevance, it is necessary to look for new forms (methods) of teaching them, always looking for more efficiency for the teaching-learning process in the school context.

Much research in this area also points to the low incomes of students in relation to learning the discipline, saying that there is a need to contextualize the content more in order to enable better learning. His teaching, which is often viewed by students, parents and even teachers as abstract, unrealistic, i.e. from what is taught in the classroom, imagines them to be far removed from the daily needs outside of school.

This lack of connection with everyday life, as well as the excess of symbology taught in math in schools, sometimes encourages the spread of wrong ideas about this discipline in the school context. The thesis we defend finds theoretical foundations in the writings of Professor Ubiratan D'ambr'sio, from the perspective that the production of mathematical knowledge cannot be detached from the social movements and culture of those who produce this knowledge .

With this in mind, we can affirm that there is an interdependence between the mathematics produced, the society that produces it, and the culture that subsidizes that production. This interweaving is built on multiple hands through a cognitive process, mediated by the creative action of various actors, all motivated by the need to read, understand and explain the reality in which they live.

When we look at the history of mankind and the sciences, we realize that not only mathematics but also will build and rebuild other areas of knowledge that will recede at every historical moment and according to the demands of society. Pompey and Monteiro (2001), in the book The Mathematics and the Transversal Issues, emphasize that the teacher understands the current scope of his or her role in society because, according to the authors,

Current teachers face a major challenge: they are trained in a fragmented process to overcome the limits imposed by this formation and to extrapolate the limits of the content that is partially and a-historically seen (POMPEU and MONTEIRO, 2001 , P. 15).

Given the requirements of this magnitude, it is necessary that we try to understand the epistemological process of mathematics, that is, the generative process of this knowledge, the reason for its organization and systematization. Minimizing this framework has been a concern of several educators and researchers over the past few decades.

For Rolim,

Thinking about the historical-cultural context in the process of teaching maths, it is important to remember that “doing” involves more than rules and techniques; it must be recognized that mathematics as a science is itself a building of humanity (ROLIM, 2010, p. 43).

It is a fact that the educational proposition characterized by educational practices that promote socio-cultural education and enable learning relationships to be created in the classroom to meet the daily needs of students has increased. More and more as an educational alternative. According to D’ambrsio, this means creating conditions so that students can cope with different situations in their daily life in the classroom.

It is a perspective that makes math teaching more contextualized, with assessments and concerns of a socio-cultural nature. According to D’ambrsio (2001), ethnomathematics is the field of education that seeks to reflect on the mathematical knowledge that arises from interaction in a particular cultural group. For the author, the math classes in this perspective are based on the math knowledge from outside the class, and this knowledge should be developed from the student's experience.

D’ambrsio (2001, p. 22) In this context, he also makes the following statement:

Everyday life is impregnated with knowledge and the production of culture. At every moment they compare, classify, measure, explain, generalize, deduce and evaluate in a certain way the material and intellectual instruments that correspond to their culture (D’ambr’sio, 2001, p. 22).

In our study, the key question was: What kind of math (formal or informal) do bricklayers use to budget the amount of ceramics needed to coat walls and floors. It was evident that the professional Mason is practicing his work functions with math skills learned from daily practice. For Monteiro (2002, p. 102) “cultural know-how has different validation paths, a different logic for its configuration. The question is why one has become universal and legitimized and the other not. “In this perspective, the author refers us to situations similar to those in this investigation.

According to Gerdes:

For centuries, bricklayers, sometimes illiterate and mostly with very little schooling, built houses, walls and other buildings that are still considered solid and sturdy structures today. So it exists in their work, in the way they carry out their calculations and organize their mathematical reasoning, a wisdom that can be found in the school context or in the integration of certain students with a tendency towards this type of occupation or in a more " practical ”approach and closer to everyday life for students in general. This situation is mentioned in the work of this line of research, namely in Gerdes ‘terminology, as“ suppressed mathematics ”or“ hidden or frozen mathematics ”(GERDES, 1991, p. 29).

In the research we start from the assumption that the masons chosen to do this investigation constitute a group of workers who use a variety of mathematical knowledge in their daily life and without this knowledge not every activity would be in the daily life Develop or carry out civil engineering. Given that they tend to have little schooling, it was interesting to know how they acquired this math knowledge or whether it was provided through daily practice.

In this context, this investigative work can also help demystify the idea that mathematics is a science for the few, to understand that there is not a single mathematical language but several forms of thinking. Mathematically, each one is organized and structured in its social context.

For both, the school needs to develop educational projects that allow the exchange of experiences in activities in which math is used on a daily basis. In addition to exchanging experiences, this interaction also creates bonds and other educational relationships with the world that is lived outside of school, and this can be a facilitating way of learning the discipline.

Math lessons should be based on the math knowledge from outside the class, and that knowledge should be developed from the student's experience. Thus the author confirms that the ethnomathematical knowledge of the group / community has a lot of value because it serves, is efficient and suitable for many things that are peculiar to this culture, to this ethno, and there is no need to replace it. In a similar way, the mathematics of the dominant group serves him, it is useful and there is no way to ignore it (D’ambr’sio, 2001, p. 80).

For Carneiro,

[…] Mathematics teaching in this conception will enable the student to link the Indian concepts to their daily experience, according to their natural, social and cultural environment. The point is not to reject academic mathematics, but to take into account values ​​that are experienced in group experiences when one considers the historical-cultural ties (CARNEIRO, 2012, p. 3).

4. PROBLEMATING TO KNOW THE PATHS OF THE MATEMATIZAR OF THE MASON

In the research done with the group of masons, we worked out some problem situations to determine that math is used by these professionals to budget the amount of ceramics needed to coat walls and floors. This study was carried out from the perspective of D’ambrsio and ROSA, who view ethnomathematics as a research program in the history and philosophy of mathematics, with pedagogical implications when the authors consider:

So this research program represents a research methodology aimed at analyzing local mathematical practices as it seeks to uncover mathematical knowledge (ideas, concepts, procedures, procedures and practices) that originated in different cultural contexts throughout history (D'AMBR -SIO and ROSA 2016, p. 17).

Situation problem: To calculate the number of rectangular tiles of size cm b [20 por 30], necessary to coat the bathroom floor of an art gallery, dimensions 6, 00m x 4, 50m (Lezzi, 1996, p. 223), Oscar als “Starting point is the dimensions of the bathroom floor. For the size of the ceramic, we choose 6m, which can be divided by the ceramic side of the 20cm as well as the 30cm. Not even the 4, 50m.

This measure is only allowed by the 30 partba [medida do outro lado da cerâmica] r. So I decided on what would be easier, by ic [600cm] h dividing the 6m by 30cm, achieving the exact number of 20 ceramics in the direction of length. Well, with the pottery towards the 8 "side, I hit the number of 30 Lajotas.

Already in the 4, 50m, divisible by 30, I took the 4, [450cm] 50m and divided by 30cm, reaching the number of 15 tiles that fit into the width. So there are 15 tiles in the sense of 30cm. To do the calculation, I took the 30 tiles that go in length plus [600cm] the 15 that go in width, multiplied and got the number of tiles needed, which would be 450 tiles ”.

According to D’ambrosius (2001), Mason Sérgio's argument to have the same budget shows that “ethnomathematics is different in different environments” (p. 35). So the Mason begins his speech and emphasizes: “First you have to discover the square meters of the area, it would be times [operação de multiplicação]. I found 27m2, so i have to find out how many tiles fit in one square meter. Since the 30cm n [medida do comprimento da placa cerâmica] does not give exactly in one meter, I was raised and used 3m, then closed with 10 Lajotas. That result of 10 tiles multiplied by 5 tiles that fit in width. I found the number of 50 tiles in 3m2 ". One at a time, visualize the deductive thought the mason used to make the budget.

Sérgio reports that, having found that in 3m2 50 Piece fit, it just “... Take thise 27m2, divide by 3, which gives me 9 equal parts. Hence, 9 times 50, gives the result of the amount of ceramic that goes over the area. They are 450 ceramics and have yet to see the break. ”

The budget calculation carried out by the Mason Alberto, also on “450 ceramics. I have non-productive times ceramic side, 0, 20m times 0, 30m reach the number 0, 06m2. This result represents the area of ​​each ceramic. Now I have the side of the bathroom floor, 6m by 4.50m, and got a result of 27m2. Then, get the bathroom footage, 27m2eilt through the square meters of a part 0.06m2, gave 450 ceramics ”.

In the resolution of the unchecked: How many square tiles of 15 cm aside are required to internally coat a pool 15 m long, 6 m wide and 1.20 m deep (LEZZI, 1991, p. 195), Oscar reported: “I have myself decided to divide this 15m by 1,500cm by 15cm of the Lajota, resulting in 100 tiles the length of one side of the pool. So on the other hand it will give the same number i.e. that row multiplied by 2, gives 200 tiles that will fit on either side of the length.

The same process I used in width namely the 6m is 600cm and this 600cm divided by 15 gave me 40 tiles that would go in one width. Since we have two widths here, multiplying by 2, I found 80 tiles. Adding 200 tiles in length by 80 in width, I reached the number of 280 tiles that need to be multiplied by the depth, which is 1.20m, i.e. 120cm. Before that, however, I divided this 12 [medida da profundidade] 0cm by 15c [medida do azulejo] m and found 8 tiles that would go into the depth of the pool. Now, under the length and adding the width, I mean the 200 tiles plus the 80 tiles, times the 8 tiles of the depth, I reached the number of 2,240 tiles.

We still have to find the number of tiles from the bottom of the pool. This is easy to calculate as the length and width dimensions of the floor are the same as the sides, meaning 6m by 15m. So they go 100 ceramics in the length and 40 in the width of the bottom, a total of 4,000 ceramics removed from the bottom of the pool. Adding the number of tiles on the sides and the bottom, I got 6,240 ceramics ”. The Mason also stressed that "they will always need a reservation" to prevent possible failures, among other things.

The recognition of the existence of “other forms of thought”, as postulated by D’ambrsio (2001, p. 17), is evident in the mathematical reasoning that Sérgio uses to make the same budget. The bricklayer emphasizes that “first of all you have to know the square meters of wall and floor [laterais]. 15m plus 6m, over 15m and more 6m, the side would give [42m corridos] n. This time 1.20m [profundidade da piscina], gives 50, 4m2 area.

Then I find the footage from below [15m vezes 6m = 90m2] n. We are all. I did and gave 140, 4m2. Now I have to find out how many tiles fit in each square meter. Only that, since the tiles are 15cm x 15cm, does not read in one meter of the corrido. Then I added until I got 3m. In 3m [corridos] there are 20 Lajotas. Then I took 3 times [multiplicado por] 3, [cada face da piscina representa uma figura plana - duas dimensões] would be a total of 9m2, dhe gave 400 Lajotas ”. In the following illustration, visualize the mason's reasoning to clarify the problem situation.

Sérgio continues to explain his procedures: “I took the sum of M2 from dem Pool divided by 9 [9 partes]. Gave 15.6 equal parts of 9m2 each [140.4m2 : 9m2 = 15.6] r. These 15.6 parts correspond to the comparison of the ceramic quantity of 9m2, i.e. 400 ceramics. Then, in each part, 15.6 times 400 would be equal to 6,240 ceramics ”.

Even if the budget of 6,240 ceramics gave enough to coat the pool, Sérgio likes to emphasize: Would need about 5% more of that total value because of the breakage.

For Professor D’Ambrosio, human groups produce knowledge that, while not widespread in formal classrooms, is valid knowledge and that school and research in math education must recognize and deepen in order to enrich the act. educational.

D’ambrsio (2001, pp. 22-23) also states that

There are numerous studies on ethnomathematics in everyday life. It is an ethnomathematics that is not taken up in schools, but in the family environment, in the environment of toys and work, by friends and colleagues.

Solving this situational problem for Alberto revealed a knowledge identified with the procedure that would be used by a math teacher. Note his explanation: “The length of the swimming pool sides 15m + 15m, also adding the width 6m + 6m gives the circumference of the swimming pool, 42m. Now 42m times 1.20m from the depth of 50, 40m2 area on the sides of the pool. The bottom of the pool is 15m by 6m and gives 90m2. When I add the side width and the bottom, I mean the 50, 40m2 plus the 90m2 equals 140, 40m2. This divided by the size of the tile, which is 15cm x 15cm and which is in M2 ergibt 0, 0225m2, schanges to 6,240 tiles. Now just add a little to the pause buffer. ”

For Demo (1996) the building of knowledge begins from the knowledge that each individual allows to flow into his / her socio-cultural experiences. This has been shown in the forms of the matematizar used by every bricklayer. For the author, “There is no such thing as a flat board, absolute illiteracy; All speak, communicate, use basic vocabulary, manage common sense concepts, have references to the reality into which they are inserted ”(p. 32).

By entering the school everyone has already accumulated some knowledge, even if it is common sense. We shared with D’ambrosius (1993) when we postulated that we need to understand that by the time formal school begins, the child already has ethnomathematics that allows him to face the interpretations of the school's systematic mathematics.

According to Marques (2000), the bricklayer's matematizar forms indicate that “the learning processes are inevitably integrated into communicative and public communities in which people learn from and with one another” (p. 29). According to the understanding of Pompeius and Monteiro (2001), “a meaningful educational process begins with the interaction between school and community” (p. 55), the relationships of which define the role of the school as a privileged place for exchanging experiences with knowing what circulates in everyday life, understand better.

In the manifestations (verbalizations) expressed by the masons in the study sessions, especially from the mathematical preparation of these professionals, based on their work experience, in the exchange of knowledge that they have already participated all their lives, show that it is the formal education is able to appreciate and validate this prior knowledge, its culture and its social environment. We believe that an educational work that, dialogically of this knowledge, leaves Enrique and contextualizes the mathematical knowledge of the school.

In the words of Rolim

Thinking about the historical-cultural context in the process of teaching maths, it is important to remember that “doing” involves more than rules and techniques; It must be recognized that mathematics, as a natural science, is itself a building of humanity (ROLIM, 2010, p. 43).

From this perspective, from this perspective, a relationship is established that is prevalent in the business world where the term "win-win" is spoken and practiced. In a negotiation, this expression has one characteristic: nobody loses, everyone wins. An ideal relationship has been established between the company and the supplier.

For the Education Act, this relationship is pedagogically ideal, i.e. students, teachers, the whole context that is part of the educational process, to be happy, to be successful. It is then understood that, as in business, to achieve a pedagogical “win-win” relationship in the classroom, simply to make good and new planning in which this possibility is inserted.

An educational perspective in which entrepreneurs and suppliers, as in the business world, should adequately and timely disclose their perceptions, views and ideas, without judging each other's behavior in school in a way that respects and evaluates teachers the previous knowledge of his students.

And when the knowledge of everyday life comes into “confrontation” with formal knowledge in school, we can remember in a dialog that in the business world the supplier often thinks differently than the entrepreneur, but this relationship is or should never be conflict or cause some wear and tear. It must be a great learning opportunity in school and in business for everyone involved in this process.

The speeches of the masons, participants in the research, showed that the knowledge of mathematics they possess was acquired most of the time in the development and improvement of their profession, in day-to-day practice, or even seeing others lead the way Same activity.

The conversations we had with the masons during the study sessions showed that the knowledge produced outside the school scope is important and it is up to the teacher to save them and bring them closer to the classroom, which makes formal education meaningful and Articulates with the reality into which the student is inserted.

5. OBJECTIVES

5.1 Show that ethnomathematics is part of our daily life and reflect on the possibility of organized societal groups to produce mathematics in its various expressions in its field of action and discuss in school the way in which the meanings are produced Everyday; 5.2 Presenting ethnomathematics as one of the ways to a renewed education, within the larger movement called mathematics education, allows in this perspective, through reflection between teacher, student and community, try to modify the knowledge they both possess and transform the classroom into a democratic space for knowledge sharing; 5.3 To perceive ethnomathematics as an interesting educational alternative to working in the classroom, to demystify mathematics and to approach the real needs of the students' day.

6. METHODOLOGY

The investigative work was carried out through different moments, namely: bibliographical study of ethnomathematics, study sessions with masons in which situations were proposed-problem with the purpose of dialogical with each professional about the mathematical knowledge [formais ou informais] they use to solve the problem Budget the amount of ceramic needed to coat walls and floors. Reflection on possible connections between mathematics and reality in the possibility of establishing links between the mason's mathematical knowledge, constructed from their everyday needs, with the help of everyday and school mathematics practices.

7. EXPECTED CONTRIBUTION

If you consider that throughout the investigation, based on the masons' discourse, we find that these professionals, in order to solve the proposed problem situations, were not always supported in the knowledge of school mathematics.

While it was clear that the masons applied math knowledge in a practical and intuitive way, with specific strategies, not the math formulas taught in school.

We hope that teaching math in the classroom through the ethnomathematic[10]s approach enables teachers and students to learn about the cultural diversity of mathematics. That the results of this research will help develop a methodology that will contribute to the teaching of mathematics, bring opportunities for changes in classroom practice, approach school pedagogical practice with the knowledge produced in situations from the students' lives.

That from this reflection the pedagogical practice in the classroom can be transformed to the development of the full citizenship of the students. That, according to Pinheiro and Rosa (2016), who:

[...] Mathematics teachers immerse themselves in the cultural dynamics of the students and use teaching and learning strategies that value the cultural dimension in the classroom so that an inclusive mathematical education can be developed that effectively contributes to societal transformation (p. 79).

From the study sessions and the produced text, we want to provoke the readers to the possibility of an educational intervention that is based on the reality of the student and combines theory and practice in the development of systefined knowledge. It is also hoped that the reflections that result from reading the text will allow a fresh look at reality and math education, from the perspective of producing knowledge from daily practice.

The aim is to contribute to the constitution of the researcher professor of his practice by encouraging him to learn continuously, to be a teacher according to current educational needs and to transform the classroom into an environment for knowledge exchange. Saving the historical knowledge that has been socially built up by humanity.

8. BIBLIOGRAPHICAL NOTES

BREDA, Adriana LIMA, Valderez Marina do Rosário e GUIMARÃES, Gleny Terezinha Duro. A utilização da Etnomatemática nos cursos de formação continuada de professores: implicações das relações de poder saber na produção de subjetividades. Curitiba. November 2011. Available at: http://educere.bruc.com.br/CD2011/pdf/4668 _ 2898.pdf. Acessado em: 20/08/2017.

CARNEIRO, K. T. A. Cultura Surda na aprendizagem matemática da sala de recurso do Instituto Felipe Smaldone:uma abordagem etnomatemática. Anais do 4º Congresso Brasileiro de Etnomatemática. Belém, PA: ICEm4, 2012.

D’Ambrósio Ubiratan. Etnomatemática: Arte ou técnica de explicar e conhecer. Editora Ática, Série Fundamentos, 2nd edição, São Paulo, 1993.

——-. Educação matemática: da teoria à prática. 13ª ed. Campinas: Papirus, 1996. (Coleção Perspectivas em Educação Matemática).

————-. Etnomatemática - elo entre as tradições e a modernidade. Coleção Tendências em Educação Matemática, 1. Belo Horizonte: Autêntica, 2001, 112p.

D’AMBROSIO, U .; ROSA, M. To diálogo com Ubiratan D’Ambrosio: uma conversa brasileira sobre etnomatemática. In BANDEIRA, F. A .; GONÇALVES, P. G. F. (Orgs.). Etnomatemáticas pelo Brasil: aspectos teóricos, ticas de matema e práticas escolares. Curitiba, PR: Editora CRV. 2016. pp. 13-37.

DEMO, Pedro. Pesquisa e construção de conhecimento: Metodologia científica no caminho de Habermas. 3.ed. Rio de Janeiro: Tempo Brasileiro, 1996. 125p.

GERDES, Paul. Etnomatemática: Cultura, Matemática, Educação. Maputo. Instituto Superior Pedagógico, 1991.

GIARDINETTO, José Roberto Boettger. Matemática escolar e matemática da vida cotidiana. Coleção polêmicas do nosso tempo, autores associados, Campinas - São Paulo, 1999, 128p.

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8. Understood with an educational practice that values ​​the mathematics of different cultural groups, taking into account the informal concepts constructed by the subjects through their experiences outside the context of the school.

9. In this reflection we treat formal and informal mathematics in the idea that the first is viewed as a school, scientific, systematic, legitimized and connected to classroom contexts and the second as daily, spontaneous, knowledge of the everyday, connected to streets, experience and living in communities, social contexts.

10. In this work used to study the conceptions, traditions and mathematical practices of a social group and the p [pedreiros] educational work that can be developed in the perspective that the group interprets and codifies its knowledge; Acquire the knowledge that academic math produces by, when faced with contextualized situations, find the one that seems more appropriate.

[1]Master in Science Didactics - Mathematics, UNIJUI - RS. Degree and specialization in natural sciences and mathematics. Prof. Assistant of the CCA - Center for Agricultural Sciences, Campus of Marshal Cândido Rondon, UNIOESTE, PR - Brazil.

[2]Master in Sustainable Rural Development-UNIOESTE, Mathematics Specialist, Physics-UNIPAR, Personnel Management and Special Education with a Focus on Multiple Disabilities-UNIASSELVI, Degree in Mathematics with a Focus on Physics-UNIPAR.

[3]Specialization in science education - mathematics, physics and chemistry. UNIOESTE - State University of Western Paraná. Degree: natural sciences and mathematics. UNIJUI, RS. Professor of the State School of Paraná.

[4]He is Professor of Plant Protection and Human Health at the Pontifical Catholic University of Chile, Plant Science Department. His interdisciplinary position is shared by the Faculty of Agronomy and Ingeniería Forestal (FAIF), the Faculty of Medicine and the Faculty of Chemistry. Research professor in the working group Soil and Environment (GESOMA - UNIOESTE). Master in Agronomy from UNIOESTE, PhD in Agronomy from UNIOESTE (2013-2016) - Sandwich Period (CAPES grant) from the University of Lisbon, at the Instituto Superior de Agronomia (ULisboa).

[5]Research Productivity Level 1C from CNPq in the field of environmental sciences with three postdocs, UEM-PR (Brazil), University of Santiago de Compostela (Spain), UFG-GO (Brazil). He is currently Associate Professor at UNIOESTE-PR and Professor and Researcher at the Center for Agricultural Sciences, where he teaches chemistry. Lecturer in the master’s degree in agricultural sciences at the UEM. He is currently an ad hoc advisor to CNPq, CAPES and Fundação Araucária. Works as a voluntary environmental consultant at MP-SP and CONAMA-DF.

[6]Bachelor in Agronomy - UNIOESTE - State University of Western Paraná - Graduate in Administration - Unip - Universidade Paulista.

[7]Master's degree in Agronomy (Plant Production) at the State University of West Paraná (UNIOESTE). Agricultural engineer, graduate of UNIOESTE (2014-2018), works as a researcher in the working group for soil and the environment (GESOMA - UNIOESTE).

Submitted: June 2019.

Approved: July 2019.

Master in Sustainable Rural Development-UNIOESTE, Mathematics Specialist, Physics-UNIPAR, Personnel Management and Special Education with a Focus on Multiple Disabilities-UNIASSELVI, Degree in Mathematics with a Focus on Physics-UNIPAR.