In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .

This project’s goal is to promote and improve the mathematical literacy of fourth-grade Hispanic/Latino and English learners through the use of a graphic mathematical mediated structure. Current California Common Core data finds fourth-grade Hispanic/Latino and English learners significantly behind White and Asian students in mathematics, especially in understanding written word problems. Research supports the assumption that as a tool, a graphic mathematical mediated structure could: 1) foster conceptual understanding; 2) build content terminology; 3) allow students opportunities to justify their solutions; 4) integrate writing in math; and 5) provide a platform for discourse. This innovative pedagogical project specifically focused on how fourth-grade Hispanic/Latino and English learners could navigate through a graphic math organizer in order to understand how to add and subtract fractions in word problems. The work presents six teacher models of graphic mathematical mediated structures. Each model provides a fourth-grade word problem related to fractions. Respectively, teacher and student templates, lists of content vocabulary, and suggestions to teach each problem-solving exercise using the graphic mathematical mediated structures that were created and developed are included. Struggling Hispanic/Latino and English learners’ need a pedagogical structure and process to succeed in solving math word problems. Hence, the need for a graphic mathematical mediated structure to diminish the groups’ prevalent mathematical achievement gap and to increase their achievement in mathematics.

<p>Thanks to I have got to explore different teaching ways around the problem solving in a year 3, in a multicultural school which is located south of Stockholm, I have been able to answer my question at issue in my degree work. My question at issue on this investigation and the purpose with my degree work was to explore different teaching ways that promotes pupils with another mother tongue than Swedish, to develop reading comprehension and to get a better understanding of mathematical concepts in problem solving tasks. On this investigation have I chosen to teach these pupils to explore, reach and gain a deeper understanding of what teaching about problem solving promotes these pupils. I have when it concerns choice of method and material collections assumed from a qualitative investigation and gathered the material with help from participation notices and interviews. </p><p>I have in my investigation reached the conclusion that those pupils with another mother tongue than Swedish developed reading comprehension and got a better understanding of mathematical concepts in problem solving tasks by being taught in a creative and varied teaching. A creative and varied teaching as I taught those pupils in contained:</p><ul><li>the pupils had to work with living-related problem tasks</li><li>the pupils had to work in pairs to resolve problem solving</li><li>the pupils had to work in larger groups to resolve problem solving</li><li>the pupils had to work in a creative way, by writing and drawing pictures and do their own mathematical fairy tale in problem solving</li><li>the pupils had to work with manipulatives to resolve problem solving in half classes.</li></ul> / <p>Tack vare att jag fick undersöka olika undervisningssätt runt problemlösning i en årskurs 3, i en mångkulturell skola som ligger söder om Stockholm, har jag kunnat besvara min frågeställning i mitt examensarbete. Syftet med examensarbetet var att undersöka vilken undervisning som gynnar elever med annat modersmål än svenska att utveckla läsförståelsen och få en ökad förståelse för matematiska begrepp i problemlösningsuppgifter. I undersökningen har jag valt att själv undervisa eleverna för att kunna undersöka, komma fram till och få en djupare förståelse om vilken undervisning runt problemlösning som gynnar dessa elever. När det gäller mitt val av metod och materialinsamling har jag valt att utgå från en kvalitativ undersökning, där jag har använt mig av deltagande observationer och intervjuer. </p><p>Jag har i min undersökning kommit fram till att dessa elever med annat modersmål än svenska utvecklade läsförståelsen och fick en ökad förståelse för matematiska begrepp i problemlösningsuppgifter genom att undervisas i en kreativ och varierad undervisning. En kreativ och varierad undervisning som jag undervisade eleverna i bestod av:</p><ul><li>att eleverna fick arbeta med elevnära problemuppgifter</li><li>eleverna fick arbeta med att lösa problemlösning i par</li><li>eleverna fick arbeta med att lösa problemlösning i större grupper</li><li>eleverna fick arbeta kreativt, genom att skriva och rita bilder och egna räknehändelser i problemlösning</li><li>eleverna fick arbeta med laborativt medel för att kunna lösa problemuppgifter i halvklasser.</li></ul>

Dins dels processos de recuperació de metalls de dissolucions diluïdes s'ha realitzat un estudi del procés d'extracció d'or i de zinc mitjançant resines amberlite XAD-2 impregnades amb sulfur de triisobutil fosfina (TIBPS) i àcid di-(2-etilhexil) fosfòric (DEHPA) respectivament.S'ha realitzat un estudi de l'equilibri de l'adsorció d'espècies metàl·liques d'aquests metalls amb les resines indicades anteriorment. Amb la metodologia emprada per a la determinació dels punts d'equilibri dels experiments en batch i en columna, s'ha vist que una única isoterma no podia descriure el fenomen global d'equilibri i que en funció de la metodologia emprada s'obtenien isotermes diferents.Es va introduir una nova variable per poder explicar el fenomen observat, i per tant, amb aquesta nova variable l'equació de la isoterma es converteix amb l'equació d'una supèrfície que s'ha definit com a Superfície d'Equilibri.S'han determinat les equacions de les Suprfícies d'Equilibri dels sistemes d'adsorció estudiats (Au(III) TIBPS/XAD-2 i Zn(II) DEHPA/XAD-2) observan una bona coincidència de tots els punts d'equilibri obtinguts sobre la superfície, així com, un bon ajust de totes les isotermes obtingudes en funció de les diferents metodologies emprades sobre les respectives superfícies d'equilibri. Aquest nou concepte generalitza el concepte d'isoterma d'un procés d'adsorció.Fimalment, s'ha plantejat un model matemàtic d'adsorció per a determinar el coeficient efectiu de difusió (De) i el coeficient de transferància de matèria (kf) per ambdós sistemes d'adsorció estudiats mitjançant l'aplicació del model de difusió de sòlid homogeni (HSDM), utilitzant com a condició de contorn en el model la isoterma de Langmuir obtinguda mitjançant els experiments en columna de llit fix i emprant també l'equació obtinguda mitjançant el nou concepte de Superfície d'Equilibri.Els resultats obtinguts són molt satisfactoris, per tant, es pot concloure que la Superfície d'Equilibri és una bona eina per a descriure l'equilibri en els processos d'adsorció d'or i zinc amb les resines amberlite XAD-2 impregnades amb TIBPS i DEHPA respectivament. / The study of the extraction process of gold and zinc with Amberlite XAD-2 resins impregnated with tri-isobutylphosphine sulfide(TIBPS) and di-(2-ethylhexyl) phosphoric acid (DEHPA), respectively, has been studied.The equilibria governing the metallic ions adsorption by the studied systems have been established. Taking into account the methodology used to get the equilibria points corresponding to batch and column experiments performed, it was noticed that a unique isotherm could not describe the global equilibrium and that different isotherms were obtained in function of the experimental methodology carried out.It was introduced a new variable for explaining the phenomenon observed. By doing this, the isotherm became a surface that it was called equilibrium isotherm.The equations corresponding the Equilibrium Surfaces of the adsorption systems studied (Au(III) / TIBPS-XAD-2 and Zn(II) / DEHPA-XAD-2) were determined. The equilibria points obtained by batch and column experiments as well as obtained isotherms were very well placed on the surface. Thus, this new concept generalises the concept of isotherm in an adsorption process. Finally, the homogeneous solid diffusion model (HSDM) was applied for performing an adsorption mathematical model for determining the effective diffusion coefficient (De) and the mass transfer coefficient (kf) of both studied systems. The obtained results were very successful, so, it can be concluded that the Equilibrium Surface is a very good tool for describing the equilibria of the studied adsorption processes.

Thanks to I have got to explore different teaching ways around the problem solving in a year 3, in a multicultural school which is located south of Stockholm, I have been able to answer my question at issue in my degree work. My question at issue on this investigation and the purpose with my degree work was to explore different teaching ways that promotes pupils with another mother tongue than Swedish, to develop reading comprehension and to get a better understanding of mathematical concepts in problem solving tasks. On this investigation have I chosen to teach these pupils to explore, reach and gain a deeper understanding of what teaching about problem solving promotes these pupils. I have when it concerns choice of method and material collections assumed from a qualitative investigation and gathered the material with help from participation notices and interviews.  I have in my investigation reached the conclusion that those pupils with another mother tongue than Swedish developed reading comprehension and got a better understanding of mathematical concepts in problem solving tasks by being taught in a creative and varied teaching. A creative and varied teaching as I taught those pupils in contained: the pupils had to work with living-related problem tasks the pupils had to work in pairs to resolve problem solving the pupils had to work in larger groups to resolve problem solving the pupils had to work in a creative way, by writing and drawing pictures and do their own mathematical fairy tale in problem solving the pupils had to work with manipulatives to resolve problem solving in half classes. / Tack vare att jag fick undersöka olika undervisningssätt runt problemlösning i en årskurs 3, i en mångkulturell skola som ligger söder om Stockholm, har jag kunnat besvara min frågeställning i mitt examensarbete. Syftet med examensarbetet var att undersöka vilken undervisning som gynnar elever med annat modersmål än svenska att utveckla läsförståelsen och få en ökad förståelse för matematiska begrepp i problemlösningsuppgifter. I undersökningen har jag valt att själv undervisa eleverna för att kunna undersöka, komma fram till och få en djupare förståelse om vilken undervisning runt problemlösning som gynnar dessa elever. När det gäller mitt val av metod och materialinsamling har jag valt att utgå från en kvalitativ undersökning, där jag har använt mig av deltagande observationer och intervjuer.  Jag har i min undersökning kommit fram till att dessa elever med annat modersmål än svenska utvecklade läsförståelsen och fick en ökad förståelse för matematiska begrepp i problemlösningsuppgifter genom att undervisas i en kreativ och varierad undervisning. En kreativ och varierad undervisning som jag undervisade eleverna i bestod av: att eleverna fick arbeta med elevnära problemuppgifter eleverna fick arbeta med att lösa problemlösning i par eleverna fick arbeta med att lösa problemlösning i större grupper eleverna fick arbeta kreativt, genom att skriva och rita bilder och egna räknehändelser i problemlösning eleverna fick arbeta med laborativt medel för att kunna lösa problemuppgifter i halvklasser.

Dans ce mémoire de thèse, nous développons d'abord des multiplications matricielles efficaces. Nous créons de nouveaux ordonnancements qui permettent de réduire la taille de la mémoire supplémentaire nécessaire lors d'une multiplication du type Winograd tout en gardant une bonne complexité, grâce au développement d'outils externes ad hoc (jeu de galets), à des calculs fins de complexité et à de nouveaux algorithmes hybrides. Nous utilisons ensuite des technologies parallèles (multicœurs et GPU) pour accélérer efficacement la multiplication entre matrice creuse et vecteur dense (SpMV), essentielles aux algorithmes dits /boîte noire/, et créons de nouveaux formats hybrides adéquats. Enfin, nous établissons des méthodes de /design/ générique orientées vers l'efficacité, notamment par conception par briques de base, et via des auto-optimisations. Nous proposons aussi des méthodes pour améliorer et standardiser la qualité du code de manière à pérenniser et rendre plus robuste le code produit. Cela permet de pérenniser de rendre plus robuste le code produit. Ces méthodes sont appliquées en particulier à la bibliothèque de calcul exact LinBox. / We first expose in this memoir efficient matrix multiplication techniques. We set up new schedules that allow us to minimize the extra memory requirements during a Winograd-style matrix multiplication, while keeping the complexity competitive. In order to get them, we develop external tools (pebble game), tight complexity computations and new hybrid algorithms. Then we use parallel technologies (multicore CPU and GPU) in order to accelerate efficiently the sparse matrix--dense vector multiplication (SpMV), crucial to /blackbox/ algorithms and we set up new hybrid formats to store them. Finally, we establish generic design methods focusing on efficiency, especially via building block conceptions or self-optimization. We also propose tools for improving and standardizing code quality in order to make it more sustainable and more robust. This is in particular applied to the LinBox computer algebra library.

O presente trabalho tem como objetivo investigar a compreensão dos conceitos de equação e função que serão aplicados na disciplina de Física-Química I do Curso de Química da UFPel. Para isso foram usados como fundamentação teórica o conceito de aprendizagem significativa de Ausubel, Mapas Conceituais e a Epistemologia do “Vê” de Gowin. Também foram utilizados os conceitos matemáticos de equação e função aplicados à Química, assim como a análise e o levantamento de ferramentas computacionais disponíveis na internet e as suas características em termos de aplicabilidade na área do ensino. Para a realização dessa pesquisa se fez uso de pré-testes com os alunos, visando identificar a existência dos subsunçores, assim como, a elaboração de mapas conceituais sobre os conhecimentos matemáticos exigidos na disciplina, particularmente, na Equação dos Gases Ideais. Os resultados foram analisados e permitiram o desenvolvimento de um objeto virtual de aprendizagem que privilegia o uso de equação e função matemática na Química. O objeto virtual de aprendizagem possibilita ao aluno o processo de interação, buscando desenvolver a sua aprendizagem, assim como elementos que promovam a interdisciplinaridade entre a Matemática e a Química. A interdisciplinaridade privilegiará a aplicabilidade de conceitos matemáticos na Equação dos Gases Ideais, especificamente na disciplina de Físico-Química I. / The present work has the objective of investigating the comprehension of the concepts of equation and function that will be applied in the Physics Chemistry subject I from the Chemistry Graduation Course at the UFPel. For that, Ausubel concept of meaningful learning, conceptual maps and the “V” epistemology were used as theoretical background. Besides, the mathematical concepts of equation and function applied to Chemistry were considered and also the analysis and the research of computational tools available on the internet and their characteristics related to the applicability in the teaching area. During the construction period of this research, some pre tests with the students were applied with the purpose of identifying the subsumers as well as the elaboration of the conceptual maps about the mathematical knowledge needed for the subject, mainly for the ideal gas equation. The results were analyzed and they allowed the development of a learning virtual object which privileges the use of mathematical equations and functions inside Chemistry The virtual object allows the student to get into the interaction process searching the development of his learning process as well as elements which promote the interdisciplinarity between Mathematics and Chemistry. Interdisciplinarity will privilege the applicability of mathematical concepts in the Ideal Gas Equation, mainly in the Physics Chemistry Subject I.

Text in Afrikaans / Die doel van hierdie navorsing is, om te bepaal of gesyferdheid by kleuters binne `n speelgroepsituasie ontwikkel kan word deur middel van `n program wat wiskundige konsepte aan kleuters oordra. Ten einde hierdie doel te bereik is `n wiskunde program waarin verskillende hulpmiddels gebruik word, vir die kleuters aangebied. Die wiskunde program wat gebruik is, is saamgestel aan die hand van Charner, Murphy en Clark (2007) se “The Giant Encyclopedia of Math Activities for Children 3 to 6”. Die aktiwiteite wat tydens die voortoets en natoets gebruik is, is uit verskillende bronne op die internet verkry. Die aktiwiteite is uit gemelde bronne geneem en aangepas om by kleuters se ontwikkelingsvermoë te pas. Aan die einde van die wiskunde program kon daar `n verbetering in al die leerders se wiskunde vaardighede waargeneem word. Die resultate van die studie dui dus daarop dat kleuters se begrip en vaardigheid met wiskundige konsepte op `n vroeë ouderdom in `n speelgroep ontwikkel kan word. / The aim of this study was to determine whether numeracy can be developed among preschoolers in `n playgroup situation by means of a numeracy programme which introduces them to mathematical concepts. To achieve this aim a numeracy programme was used to introduce the mathematical concepts. The numeracy programme that was used is a programme compiled from “The Giant Encyclopedia of Math Activities for Children 3 to 6” by Charner, Murphy and Clark (2007). The activities which were used during the pre-test and post-test were taken from different sources on the internet. The activities taken from these different sources were adapted to the appropriate developmental phase of the preschoolers. At the end of the programme the post-test indicated an improvement in the mathematical competence of all the learners. The results of the study prove that preschoolers in a playgroup can improve their numeracy skills in the early years. / Teacher Education / M. Ed. (Didaktiek)

TROMPIERE FILHO, Nicolino . Análise dos resultados da avaliação do SAEB/2003 via regressão linear múltipla. 2007. 99f. Tese (Doutorado em Educação) – Universidade Federal do Ceará, Faculdade de Educação, Programa de Pós-Graduação em Educação Brasileira, Fortaleza-CE, 2007. / Submitted by Maria Josineide Góis (josineide@ufc.br) on 2012-07-10T14:34:17Z No. of bitstreams: 1 2007_Tes_NTFilho.pdf: 840956 bytes, checksum: d655076b1043c961097d33ba9b1a426e (MD5) / Approved for entry into archive by Maria Josineide Góis(josineide@ufc.br) on 2012-07-10T15:06:02Z (GMT) No. of bitstreams: 1 2007_Tes_NTFilho.pdf: 840956 bytes, checksum: d655076b1043c961097d33ba9b1a426e (MD5) / Made available in DSpace on 2012-07-10T15:06:02Z (GMT). No. of bitstreams: 1 2007_Tes_NTFilho.pdf: 840956 bytes, checksum: d655076b1043c961097d33ba9b1a426e (MD5) Previous issue date: 2007 / This study had as its objective the identification in the results of SAEB/2003, here in Ceará, of a multilinear model with variables that gave a greater degree of explaination for the results in mathematics of tests given in the randomic sample of the fourth years students in public schools, the fourth year students in private schools, the eight year students in public schools and the eight year students in private schools. The following variables were taken into account: the director, the teacher, the student, the physical state of the school as variables that had significant relevance with the results of the tests in mathematics in each one of the samples, using the resources of the software SPSS (Statical Package for the School Sciences), a linear regression in each sample, using the method "stepware". Four multilinear models with variables were obtained that permitted a greater degree of explaination for the results of the mathematic tests in each sample. The study concluded affirming that an analysis of this type permits the formulation of public politics capable of overcoming the search for better forms of teaching with punctual interventions. / O presente estudo teve como objetivo identificar nos resultados do SAEB/2003, no Ceará, um modelo multilinear com variáveis que garantam o maior grau de explicação do rendimento em matemática nos testes aplicados nas amostras de 4ª série da escola pública; 4ª série da escola particular; 8ª série da escola pública e 8ª série da escola particular. Tomando-se, entre as variáveis do diretor, do professor, do aluno e das condições físicas da escola, as variáveis que se relacionavam significativamente com o rendimento no teste de matemática em cada uma das amostraS, com os recursos do software SPSS (Statical Package for the Social Sciences), uma regressão linear em cada amostra, com o método “stepware”. Obtiveram-se quatro modelos lineares múltiplos com variáveis que permitem um maior grau de explicação do rendimento no teste em matemática em cada uma das amostras. Conclui-se que a análise desse tipo permite a formulação de políticas públicas capazes de superar a busca da melhoria do ensino por intervenções pontuais.

Submitted by MARCIA RODRIGUES LUIZ DA SILVA null (marcia_rodrigues_fucamp@yahoo.com.br) on 2016-05-08T02:05:44Z No. of bitstreams: 1 TESE Márcia Luiz.pdf: 15629727 bytes, checksum: 663e5af045c005752feac3a5049ea727 (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-05-09T19:25:17Z (GMT) No. of bitstreams: 1 silva_mrl_dr_rcla.pdf: 15629727 bytes, checksum: 663e5af045c005752feac3a5049ea727 (MD5) / Made available in DSpace on 2016-05-09T19:25:17Z (GMT). No. of bitstreams: 1 silva_mrl_dr_rcla.pdf: 15629727 bytes, checksum: 663e5af045c005752feac3a5049ea727 (MD5) Previous issue date: 2016-03-21 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O presente estudo insere-se no campo da formação inicial de professores de Matemática em nível superior, em Cursos de Graduação. Tendo como contexto o Curso de Graduação em Matemática na Universidade Federal de Uberlândia (UFU), em Uberlândia/Minas Gerais, dialoga acerca da questão da Prática Como Componente Curricular (PCC) inserida nos currículos dos Cursos de Licenciatura como modalidade diferenciada de prática curricular a partir da Resolução CNE/CP nº. 01/2002 que instituiu as Diretrizes Curriculares Nacionais para a formação de Professores nesse nível. De caráter qualitativo, a pesquisa investigou, no âmbito da disciplina Estatística e Probabilidade do currículo do referido Curso, o processo de implementação do Projeto Integrado de Prática Educativa (PIPE) – componente curricular criada pela UFU para o desenvolvimento dessa modalidade de prática instituída pelas Diretrizes. Como objetivo geral o estudo buscou investigar, neste Curso de Matemática, a implementação do PIPE como PCC no desenvolvimento dessa disciplina e suas implicações na formação inicial do Professor de Matemática, norteando-se pela seguinte questão diretriz: Como vem ocorrendo o processo de implementação do Projeto Integrado de Prática Educativa (PIPE) na disciplina Estatística e Probabilidade no Curso de Graduação em Matemática da Universidade Federal de Uberlândia a partir de sua inserção como Prática como Componente Curricular neste Curso? O estudo desenvolveu-se por meio da pesquisa documental e de campo, tomando como sujeitos os professores e estudantes nessa disciplina e Curso, durante cinco semestres letivos (período de 2012 a 2014). A produção de dados se deu, além da parte documental e dos registros da pesquisadora no diário de campo, também por meio de entrevistas com os docentes, questionários aplicados aos alunos e um ambiente virtual criado pela pesquisadora no desenvolvimento da pesquisa. Os principais resultados evidenciaram a deficiência de registros de experiências com relação ao desenvolvimento do PIPE. Mostraram também que os diferentes sujeitos participantes da Pesquisa consideram o PIPE importante e necessário no Curso de Matemática por possibilitar, no desenvolvimento dessa Prática Curricular, um espaço diferenciado de formação, no entanto, há dúvidas conceituais em relação a essa componente e divergências de visão dos docentes entre si e deles com o Projeto Pedagógico do Curso quanto à concepção da PCC via PIPE, o que tem levado a diferentes formas de interpretá-lo e, portanto, efetivá-lo. Apontaram carência de esclarecimentos sobre essa Prática nos documentos institucionais e de uma maior comunicação dentro do Curso, sugerindo-se, para tanto, a implementação de um espaço de troca de experiências no âmbito do desenvolvimento do PIPE, aliado a um processo contínuo e permanente de acompanhamento e avaliação, para seu aprimoramento e efetividade. Por meio das cinco experiências vivenciadas no campo concluiu-se que o PIPE caracteriza-se como um tipo de prática que demanda um trabalho interdisciplinar e coletivo e por isso tem representado ainda um grande desafio para o Curso de Matemática, mas que, apesar disso não é uma proposta frágil, mas possível e viável, especialmente mediante a possibilidade de socialização de experiências e de uma responsabilidade que seja compartilhada entre todos os envolvidos e não exclusiva dos docentes. / This study is in the initial teacher training in Mathematics at higher education in undergraduate courses. With the context the Undergraduate course in Mathematics at the Federal University of Uberlandia (UFU) in Uberlandia/Minas Gerais, dialogue on the issue of the practice as Curriculum Component (PCC ) inserted in the curricula of undergraduate courses as differentiated mode of the practice from the CNE / CP Nº. 01/2002 resolution that instituted the National Curricular Guidelines for teacher training in this level. From a qualitative character, the research investigated, under the Statistics and Probability discipline, the curriculum of the mentioned course, the implementation process of the Integrated Project of Educational Practice (PIPE) – a curricular component created by UFU to the development of this type of practice established by the Guidelines. The general objective of the study was to investigate, in the Mathematics course, the implementation of the PIPE as PCC in the development of this discipline and its implications for initial training of Mathematic teachers, guiding by the guideline question : How has occurred the implementing process of the Integrated Project of Educational Practice (PIPE ) in Statistics and Probability discipline in the Undergraduate Course in Mathematic of the Federal University of Uberlandia from its insertion as Practice as Curricular Component in this course? The study was developed through the documental research and of field, taking as subject the teachers and students in this discipline and course, for five semesters (from 2012 to 2014). The production data was, beyond the documentary part and the researcher records in the field diary, also through interviews with the teachers, questionnaires to students and a virtual environment created by the researcher in the development of the research. The main results showed the deficiency of experience records regarding the development of the PIPE. They also showed that the different participants in the research consider the PIPE important and necessary in the Mathematics Course for enabling, in the development of this Curriculum Practice, a differential space training, however, there are conceptual questions regarding this component and view differences of the teachers with the pedagogical project of the course on the design of the PCC via PIPE, which has led to different ways of interpreting it and, thus, accomplish it. They showed lack of clarification on this practice in the institutional documents and greater communication within the course, suggesting, therefore, the implementation of an exchange experiences space in the PIPE development, combined with a continuous and ongoing process of monitoring and evaluation for its improvement and effectiveness. Through the five experiences in the field it concluded that the PIPE characterized as a kind of practice that requires an interdisciplinary and collective work and so has also represented a major challenge for the Mathematic course, but, nevertheless it is not a weak proposal, but possible and feasible, especially by the possibility of socialization and of a responsibility that is shared between the involved participants and not exclusive for teachers.