SILVA, Angela Maria de Sousa e. The importance of educational games to teach math to Deaf and listeners. Multidisciplinary Core scientific journal of knowledge. 03 year, Ed. 06, vol. 07, pp. 13-33, June 2018. ISSN:2448-0959
- 1. Introduction
- 2. The importance of the educational games in math teaching
- 3. The difficulties in education for the deaf
- 4. The use of educational games in math teaching
- 4.1 A classroom experience
- 4.1.1 Golden Material – math alive
- 4.1.2 logical blocks-the simplicity of the instrument that helps to develop mathematical thinking
- 4.1.3. Cuisenaire sticks-introduction to construction of the facts
- 4.1.4 – seven Tangram pieces that cover the construction of geometric concepts
- 4.1.5 Geoboard-introduction to geometric figures
- Final considerations
This article aims to demonstrate how the use of educational games as the Golden Material, the logical blocks, the scale, the Tangran and the Cuisinaire Geoboard help in understanding the students ' mathematical knowledge, whether listeners or deaf. Is the result of bibliographical research. Also includes a classroom experience in the class of second year of elementary school, composed of fifteen students listeners and a deaf student.
Keywords: Deaf, pounds, Inclusion, Educational Games, math.
This work deals with the inclusion of deaf students in regular class of elementary school, in the teaching of mathematics. The inclusion of deaf students in public schools has been discussion among many teachers, because in General, they say they did not receive in their training curriculums, adequate preparation to work with these students.
Many teachers still don't know how to teach in regular classes with listeners and deaf. The story of the formation of the educator who works or will work with deaf learners throughout the fight the right to your own language. And is in 20th century Brazil in this battle is fought, resulting in a period of struggle for the right of the deaf to use Brazilian sign language (Libras, sign-spatial mode language whose origin goes back to the French Manual Alphabet which came to Brazil in 1856 brought by professor e. Huet). Only in the next century is that its claims were included with the law nº of 10,436 2002 recognising the Pounds as a means of expression, regulated by Decree No. 5,626, of 22 December 2005.
The inclusion of deaf students in regular classes is already a reality and reaffirming the right and the benefits of the education of the deaf students and listeners in regular classes, there are appropriate procedures and within the legal parameters regarding the inclusion of deaf students in the teaching of mathematics.
In this article, we seek to gather useful information and guidance to teachers of mathematics so that they can guide them in teaching students to be they deaf or listeners through educational games.
2. The importance of the educational games in math teaching
The Houaiss dictionary of the Portuguese Language defines the Word Game as follows: "1 – unrest: movement, oscillation; 2-bet: lance, hand, stop, departure; 3-ruse: cunning, 4-swing: swing; 5-joke: merriment, revelry, and games; 6-collection: set; 7-combat: competition, fight, battle, advocates; 8-fun: fun; 9-derision: grocejo, motejo, mockery, ridicule; 10-operating: moving; 11-fickleness: whim, instability, irregularity, variability, volubility, constancy, evariabilidade, regularity; 12-dupe: ludibrio; 13-management: maneuver, handling; 14-movement: dexterity, skill, mobility; 15-departure: competition, competition, show, battle, card game: card games ". (Houaiss, 2003). From this definition, and reaffirming the benefits that the game features, it can be said that your use in class helps in understanding the mathematical knowledge.
Learning math is a very difficult thing for most students. And as these difficulties in realizing new ideas and concepts will increase, the discipline will gradually become a "big deal". We need to understand the reasons for these difficulties in order to make mathematics a discipline like any other and allow students a more healthy and consistent learning through games. Anyway, it takes a lot of visual and concrete support to better teach and be understood by students.
Many educators say you shouldn't present the mathematics as a discipline difficult, abstract, or context of reality and many teachers are already using educational resources, such as games, to teach the content in the classroom. So, if both students listeners about the deaf students, promoting the school inclusion.
From a very early age children spend energy and part of your time playing and playing. To observe a child in game situations, how it develops your ability to formulate hypotheses and to solve problems.
Students present great ease of reasoning and ability to resolve problem situations, featuring objects and seeking a resolution based on line elucidações own. So, the games on regular classroom teaching resources assist used in all levels of education and are very important for social development, because it has students in class is afraid to ask your questions and the game does not feature This behavior.
The overall objective of this article is to demonstrate how the use of educational games as the Golden Material, the logical blocks, the Cuisinare Range, the Tangram and the Geoboard help in understanding the mathematical knowledge of children, whether listeners or deaf. And the specific objectives are: (I) describe what is a game and how to use it in class; (II) narrate how the Golden material, the logical blocks, Cuisenaire, the Tangran range and the Geoboard may be developed detailing the methodology to apply them in the classroom; (III) appropriate strategies of these games relate to deaf students.
This article is the result of bibliographical research carried out after the completion of the course of improvement in Educational Attendance specialized for deaf students-8th Edition, promoted by (the) Faculty of education (FACED), Federal University of Uberlandia, linked to the programme centre of teaching, research, extension and Education services.
As says Paulo Freire (1979):
(…) I now say to us as educators: Woe unto them, that stop your ability to dream, invent your courage to denounce (the possible dream). Woe unto them and those who, instead of visiting every now and then tomorrow, the future, for your deep engagement with today, with the here and the now, then woe to those who instead of this constant travel to tomorrow, if hitch up to a past of exploitation and routine.
So, this article is intended as a resource for teachers who want to know a little more about teaching mathematics, thinking about the inclusion of deaf students and awakening to the value of the educational games in the classroom.
3. The difficulties in education for the deaf
The difficulty in teaching to deaf students can be perceived from the sixteenth century, when the first deaf educators began to act. Prior to this, if you know great prejudice with the deaf, coming even from the Catholic Church, which regarded them as no immortal soul, and passing by Aristotle that regarded them as incapable of reason.
The education of the deaf does not come very success demonstrated throughout history, in addition to the teachers and listeners of the methods used in school (Skliar, 1998), and due to your disability, many deaf people have been blamed for this. However, without facing the linguistic issue, which is the main problem and the source of all the problems identified in the education of the deaf, can't make education of deaf people equal to the listener. This linguistic issue have evolved long after the creation of law nº 10,436, of 24 April 2002, which provides for on the Brazilian Sign Language-Pounds-and other matters, recognizing the Pounds as the mother tongue of deaf people.
Many deaf people are from families listeners and that hinders the process of language acquisition. The lack of a common language in the family makes these deaf stay segregated, separated from the conversations, feelings are shared, stories are told, anyway, environment where knowledge is informally built (Bernardino, 2000).
At school, this difficulty also exists, even in those where the Pound is already recognized as the first language of the deaf. But after the Decree of 2005 5626 this situation is changing, because the Pounds now is already in the curricula of teacher training. In Brazil, many deaf people already receive a bilingual education (pounds/Portuguese), with support in regular room with an interpreter, besides the teacher.
With the Decree No. 5,626, of 22 December 2005, which regulates law at 10,436, of 24 April 2002, which also features on the Brazilian Sign Language-Pounds, and art. 18 the law in 10,098, of 19 December 2000 it is expected that all deaf learn to your mother tongue Pounds and then the second that in the case of Brazil is Portuguese. But many students are not proficient in Portuguese language, causing difficulty in communication that can lead to a decontextualised education, mechanical, without meaning and understanding, not developing the autonomy.
The main difficulty, in addition to the communication with the deaf, is to adapt the language of mathematics. We believe that one of the possible solutions to resolve this issue would be the playful, whereas the education of the deaf is space – visual, which satisfies the mathematical games.
4. The use of educational games in math teaching
If you know that the math education offered in public schools presents itself, only in the so-called "spit and chalk" and "rote learning", where the student memorize, memorize and not learn in fact. The teachers use the same methodologies based on memorization of math teaching for the deaf and listeners. This makes the teaching of mathematics be scattered and inconsistent. We believe that many of these teachers do it for ignorance of the subject.
Many teachers transform mathematics in mechanical activities by reducing it to a simple resolution of addition and subtraction. Math lessons are very important activities and help in relation to school and reality, when it gives students live at the school experiences of your daily life.
The need for understanding of abstract situations is no easy task even for listeners and students or for students who are deaf. For the deaf so it's much more difficult to be achieved without a common language.
Working with games promotes all types of student, whether deaf or not. There needs to be a change in the pedagogical practices and it is necessary to develop strategies that help the process of teaching and learning of mathematics for children deaf and listeners, taking into account that bring math to reality and to the concrete is fundamental to learning of students and deaf even better, because it occurs primarily through visual perception.
With a view to the enhancement of the visuals for the deaf, it is understandable that the games that use Visual media can facilitate the learning of mathematics. On the assumption that this feature focuses on visual perception, becomes vitally important feature for learning deaf (Skliar, 1998).
Deaf students need a sensory and visual pedagogy and games and manipulable materials help in the development of autonomy. The interesting thing is that students meet the material and then make use of the rules of the game.
In this way, we believe that for students, in particular deaf, learn math more easily, it is necessary to use several strategies such as those mentioned previously, with greater emphasis on those activities that emphasize features visuals. So, in this article we will present some of the activities that have been developed in the classroom and who have contributed a lot to the learning of mathematics.
Note that the word game has an important relationship with education because it is not only connected to the entertainment, this is fun and pleasure, but also learning how reasoning, calculation, operation, among others. The use of playful activities in mathematics and concrete materials is entirely related to the cognitive development of the child. One has to reflect that some specific contents of mathematics have no relationship with the idea of being applied using games, but somehow promote a critical sense, investigator, which helps in understanding and understanding of particular topics related to teaching mathematics.
The math is present in our daily lives. When we use the money or measure something, we are using concepts that we learned in school. The author José Roberto Boettger Giardinetto contributes to the reflection on the relationship between the everyday and the school knowledge, where CITES that much of this knowledge is not used in real life in your book: "Mathematics and mathematics of everyday life".
As already mentioned, the games worked in the classroom must have rules, noting that these are efficient, showing positive interference in the construction of conservation concepts studied.
The deaf man perceives the world through the senses: smell, touch, taste and, above all, the vision. The seizure and the decoding of images to process, thus, more "natural". In the monograph titled "the image in the right environment while learning facilitator element with deaf children".
Teaching math is to reflect on the process of mathematics teaching and learning especially in the early years of elementary school teaching materials that strengthen the pedagogical practice, enabling the student to develop your intellectual autonomy, of your critical thinking and also the improvement of skills and competencies as previously quoted.
The games are an educational resource for the efficient construction of mathematical knowledge, but need to be planned. It is noticed that, when applied to a class pretty motivated, students present a better performance and better attitudes in front of their learning processes.
We should choose games that stimulate problem solving, especially when the content being studied is abstract, difficult and unlinked daily practice; We don't forget to respect the conditions of each class and the want of every student, always respecting the peculiarity of each. These activities should not be too easy or too difficult, as can also be tested before your application, in order to enrich the experiences through proposals for new activities, providing more of a learning situation.
In games with rules, students make deductions that develop logical thinking. They are most suitable for the development of the thinking skills to effectively work with a specific content. Procedures and rules should be presented to students before starting the game, establishing the possibilities and limits of action of each.
4.1 A classroom experience
4.1.1 Golden Material – math alive
We note, as mentioned above, a second year class of elementary school with fifteen students and listeners a deaf student who, in the classroom, the teacher used the games as educational resources in their math lessons, among them: the Golden Material, the logical blocks, Cuisenaire, the Tangran range and the Geoboard.
In this section, we will describe how they used these games in math class, in regular classroom class of second year of elementary school with hearers and the student deaf students which we will call ' Y '.
Golden Montessori Material is part of a set of those materials designed by the Italian educator Maria Montessori and medical. Montessorianos principles for the creation of any of its materials is the sensory education. It consists of cubes, rods, plates and large hub. This material is aimed at activities that help in the way of performing fundamental operations and in the teaching and learning of the decimal positional numeral system-.
The main objectives of the use of this material are: (I) assist in activities that support the teaching and learning of the decimal positional numeral system-; (II) Working methods to perform basic operations; (III) make the numerical relations to a more concrete image abstract; (IV) develop the logical mathematician.
There are other proposals to work with these materials which include: (I) stimulate the learner autonomy and independence and confidence in yourself; (II) develop concentration, coordination and order; (III) generate concrete experiences structured to lead, gradually increasing abstractions; (IV) cause the own student realizes the possible errors that commits to performing a certain action with the material; (V) working with the student's senses.
School practices as already said, it is still common, students "dominate" the algorithms from exhausting practice, but without being able to understand in fact very well. In class the teacher were the Golden Material facilitating the understanding of the content. It was obtained, so much more than a learning algorithms. There was a notable development of reasoning and learning so much nicer. He was worked in individual and group activities. Student's first contact with the material took place in order to make sure they play to explore freely. It was then that they realized the shape, the Constitution and the types of piece of material.
The use of Golden Material resulted in a pleasurable and meaningful learning through concrete and physical resources. As the deaf students use more spatial and visual aspects to form knowledge than students listeners, games like this with concrete parts are stimulants in teaching/learning and essential in math classes.
A very fruitful activity was the game called "Let's do a train" to understand that the successor is to have "one more" in numerical sequence. The teacher agreed with students to build a train. The first car was a little puppy. The next wagon had a cube more than the previous one, and so on. The last car was formed by two bars. When the class ended up riding the train, were given white sheets on which they wrote the code for each car. This activity led to the formation of the idea of successor and facilitated the idea of "one more" to students, following the numbers. She also contributed to the better understanding of the positional value of the digits in the numbers.
One of the individual activities carried out by Professor's name is "leaving the cubes". In it, each student received a number of cubes to exchange for bars and plates, thus developing the notion of unity, ten and hundred. Later, the student wrote in a white sheet numbers corresponding to the quantities of plates, bars and cubes obtained representing them with use of the table. This activity was very productive and it became interesting, as the numbers of cubes were increasing.
As individual activity, was proposed the holding of a saying. The teacher showed cards, one at a time, with numbers, and the students were showing him the corresponding parts, using the least amount of it. This game allowed the students relate to each group of pieces to your numeric value.
An activity that earned good advantage is called "exchanges", which occurred in Group and had his goal of trade was the understanding of the groups of ten in ten (ten units form a dozen, ten tens form a hundred etc.), characteristic of the system decimal. In this game, each group was given marked four to nine. In the group, each student in your time, threw the dice and withdrew the amount of cubes corresponding to the number that left in. In this way, that number gave right to withdraw only cubes. And to join ten of them made trading by a small bar. And every change of bar was entitled to play again. This occurred with the bars that by joining ten were exchanged for a plate and the right to play again.
This game has stimulated the students ' mental calculation and ended when the student "X" managed to form three plates. The understanding of the groups on the basis of ten is very important for the real understanding of operative techniques of fundamental operations. The right to play again developed the attention and concentration of students throughout the game.
When developing activities, the teacher asked the students themselves were registering the way they wanted the names of the different pieces of the material. And to the extent that they were playing, students were making the abstract concrete numerical relations, making it easier to understand and it was obtained, then, in addition to the understanding of algorithms, a great development of logical thinking, creativity and Motricity very pleasant.
4.1.2 logical blocks-the simplicity of the instrument that helps to develop mathematical thinking
Generally the logical blocks are quite used in the initial series, especially in early childhood education and the education of deaf students, because it enables to develop the first notions of logical operations and their relationships such as sorting and matching fundamental in the learning of mathematical concepts.
They form a set of geometric pieces small, distributed in triangles, squares, circles, and rectangles, which aims to assist in student learning and has 48 pieces distributed in three colors (blue, yellow and red), four shapes (rectangle, square, triangle, and circle), two different sizes (small and large) and two different thickness (thick and thin). Can be made of different types of materials (wood, rubber, plastic, paper).
In class when the teacher used the logical blocks, physical knowledge occurred when students took, observed and identified the attributes of each piece. The logical-mathematical occurred when the gang used these attributes without needing to have the material at hand (abstract reasoning).
At first students manipulated the level of recognition the material, then they made drawings with the forms of logical blocks, observing and comparing sizes, colors, and shapes. This work was done in small groups, where students enriched the knowledge of the physical characteristics of the blocks through the conversations.
To end this activity, parts of the logical blocks were distributed and scattered on top of the wallet, where each student individually picked up a piece and put it in the middle of the Pack, so that the pieces were stacked one by one. The student deaf did everything to the "tower". For the development of this activity, they had to reason what the right piece for the base, middle, or top of the Tower, leaving the "worse" for the next colleague. In this activity, students stimulated your ability to discern and reason, as well as stimulate motor skills. The student concerned was extremely upset when your "tower" fell. But the teacher knew how to circumvent the situation when taught to deal with your frustration.
The teacher presented a framework for classifying students the blocks and created together with the students the attributes that were given for the types of existing blocks. The blocks were separated according to the following categories: (I) the four shapes (circle, square, rectangle and triangle); (II) the two thicknesses (coarse and fine); (III) the two sizes (small and large); (IV) the colors (yellow, blue and red).
Soon after, the teacher made a painting on cardboard, chose some attributes and asked the students to split the blocks according to the selections made. First, chose only one attribute (square). Example: separate only the square pieces. Then it was adding attributes (red, thin, small). Students were completing the frame with square piece, small, thin and red.
All students participated with great enthusiasm of the proposed activities.
4.1.3. Cuisenaire sticks-introduction to construction of the facts
Created by Georges Cuisenaire (1891-1976) the scale is composed of Cuisenaire rods of ten colors, with each color of different size of the other, on a scale proportional to a centimeter of difference for each size. There are variations of this game and, therefore, the measures may change. But the proportions of a bar to another are always respected. In this way, all the bars of 1 cm are the same color, the same way with the two centimeters, and so on.
This game has several objectives: (I) work, comparison and inclusion numerical succession, the four operations, double, half of a quantity and fractions; (II) introduce the major/minor concepts, big/small, equal/different; (III) stimulate the curiosity and creativity; (IV) maintain the concentration and attention; (V) make concrete the basic concepts of the first mathematical operations; (VI) facilitate the understanding of the relation quantity/number and size comparison, between numbers; (VII) encourage the development of logic and thinking strategies; (VIII) working on the construction of the idea of number; (IX) work the motor coordination, analysis-synthesis, perceptual constancy of shape, sizes and colors; (X) regain self-confidence and confidence in the condition of learning; (XI) stimulate the question of error/hit, do/undo; (XII) promote the independence and autonomy; (XIII) show the numerical quantities, your composition and decomposition; (XIV) develop observation and visual perception, among others.
This last goal, to develop observation and visual perception, is of prime importance on student learning, as cited in deaf the previous paragraphs, the most important channel for the deaf is the vision. This way, the American Owen Wrigley, author of the book the politics of Deafness (1996), which serves as a theoretical basis for various jobs in Brazil, helped to dismantle the notion that deafness is something concrete, existence itself, independent of the senses that We give her. In other words, he disputes the deafness as a sensory impairment in body and that would bring some impediments to living in a world that is primarily made of sound. For him, the question needs to be moved from a problem of individual body to a social problem, with the consequent debate about the privilege of Visual channels at the expense of other possibilities: instead of the focus on the auditory canal, figure out a visual channel filled with possibilities.
In class when the teacher used the Cuisenaire scale, the student deaf played very well the activity, as well as the class in General. The purpose of use it was to make concretes the mathematical concepts, many of which are difficult to assimilate when focused so abstract and relate the different sizes with different amounts, facilitating the understanding of the operations basic mathematics. For example: four bars of two centimeters equals two bars of four centimeters. Soon, four + four = eight. After working the concrete material, the teacher took the class to work on the sheet, making the abstract.
The game favored the correspondence between the mental structures of the deaf student and the relationship he established with the parts, by means of activities. As an activity with this material, the teacher asked the students to create objects, separated by sizes and colors, using only the smaller bars or the greatest to do the mounts; or those that were the same color.
In proposing the development of each activity the teacher was watching the development of the group. How to: (I) delivered to groups of students cards with pictures that were the same size and same color of ten bars, asking them to put together the figures, putting the colored bars on the corresponding strips; (II) to deliver a different bar for each student. In a circle, they were showing your bar to another colleague, comparing them. The teacher asked questions such as: "Who has the biggest bar? Who has the smallest bar? To your PowerBar is higher or lower than the Student x? "; (III) ask students to put the bars in ascending order and exploit their position, asking why the purple bar was in this position or why the orange bar is the last.
4.1.4 – seven Tangram pieces that cover the construction of geometric concepts
The Tangram is a puzzle consisting of seven parts: five isosceles triangles of different sizes, a square and a parallelogram, to allow several different figures.
It is a tool that assists in the development of concentration, capacity of logical reasoning, spatial orientation and exercise creativity, and may also focus on cooperation, when assembling this jigsaw puzzle is made in group, making it less complex.
Using the Tangram, the teacher can address the following aspects of geometry: (I) identification of geometric figures; (II) comparison; (III) description; (IV) classification; (V) drawings and representations of Planar figures; (VI) notions of area and (VII) fractions.
It can be made of different types of materials (wood, plastic, EVA, paper).
In class when the teacher used the Tangram, physical knowledge occurred when the students observed different figures and reproduced. In addition, answered questions such as, for example: "what's the name of this picture?".
First, the students studied the legend of Tangram and your origin, then recognized and exploited the material mounting the square using the seven pieces with the help of the teacher.
After this activity, the teacher put on the table some figures formed with the Tangram as boat, House, cat and duck, challenging students to establish a figure like hers.
For which the activity was developed, students had to think about how to solve the challenge.
In this activity, students have developed the capacity of discernment, logical thinking and motor skills. The student concerned was extremely upset when he couldn't reproduce the figure of the teacher. But she knew how to drive the situation, when helped him play figure and taught him how to deal with your frustration.
All students participated with great enthusiasm and commitment of the proposed activities.
4.1.5 Geoboard-introduction to geometric figures
The Geoboard more used is the square made with wood and small nails set forming a lattice that can be used with a piece of rubber or elastic string.
Was used to work: (I) perimeter and area; (II) Diagonals and symmetry; (III) calculation of symmetrical figures, edges, vertices, construction of polygons between other situations involving plane geometry.
The main objective of the Geoboard is to have students explore the polygonal figures through visualization and construction, developing more easily the skills of space exploration.
The Geoboard was used by Professor in situations involving the calculation of symmetrical figures, edges, area, perimeter, vertices, construction of polygons between other situations involving plane geometry. It was very nice the way students have assimilated the geometric content, the result was really great and motivating.
As already mentioned, not to build the mathematical knowledge through mechanical methodologies. The best way to assimilate the geometric content is through handling, construction, exploration and representation of geometric shapes, and the Geoboard develops direct and simple way all these principles.
As we already know, the inclusion is guaranteed by law, but for it to really effect and for deaf students and listeners have a quality education it is necessary that the teacher have specialized training. A child is not born knowing, she passed the teachings. The role of the teacher in this sense is the mediator, for he shall produce the games for stimulants like activities that the student discover paths that lead to be subject end, creative and constructors of knowledge and transformation of a better world.
Starting from this principle, it is necessary that the teacher seeks to learn new pedagogical and methodological practices in pursuit of success in the learning of their students. It to look forward and fit the various forms of education to students, deaf or listeners, bringing knowledge to life.
However, what is observed in the context of educational teaching mathematics, is that there is a constant concern on the part of the teacher to make students "learn math" and with the use of the school games become more attractive and challenging abolishing the learning of mathematics as a mere exercise mechanization, rules and conventional signs devoid of any meaning to the students. In the specific case of Gold Material, abstract numerical relations are a concrete image, facilitating the understanding of the content. Gets, so, beyond the understanding of algorithms, a remarkable development of reasoning and learning so much nicer.
As for the deaf students it is necessary to respect and accept your difference is the language itself, in case the Pounds, of your form in the perception of the world and even in the construction of knowledge. Therefore, it is necessary to teachers who work with the inclusive education in order to meet these peculiarities of the deaf and the listeners, because each student is unique.
It constructs knowledge through vision. This difference needs to be understood, respected and all students both listeners as the deaf have their peculiarities valued and respected. You must strive for new pedagogical practices that help in the various areas of knowledge the knowledge-building, mainly through visual experience, the main route of access to knowledge for deaf students.
Considering the visual perception, the main route of access to knowledge for deaf and aspects that value the active role of the subject as constructor of your knowledge, and who value the kind of trigger of this construction, highlight the value of as pedagogical intervention Fireworks rules, by allowing students to both listeners about the deaf experience contradictions, to create strategies, do readings of observables, build coalitions that come awaken reflective and abstractions consciousness.
We believe that the motivation and improvement in the learning of mathematics in this class during these activities occurred due to the use of educational games. Don't propose recipes, but suggestions to be adapted to each reality and context. More than that, I hope with the article to draw attention to this matter, especially in relation to the need for more studies that help to deepen this important theme.
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 Master's degree in education from the USAL-Argentina, pedagogue by UNIPLI, an expert in learning disabilities from UERJ, Pedagogy for UNIPLI, school management by AVM, early childhood education by FACNEC.
 Master in applied mathematics to scientific computing from UERJ, degree in Mathematics from UERJ.