Publicação
Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers
| Resumo: | This chapter presents a perspective about the exploratory approach as a possible way to enact inquiry based mathematics teaching. In this approach, the teacher, instead of beginning the class by presenting explanations and examples to the students, proposes them to work on tasks that may lead to the construction of new knowledge. We use as illustration the work of a grade 6 class of students solving tasks involving rational numbers. Our aim is to know how students use representations and reasoning processes, seeking to find out how they deal with different representations and how they formulate generalizations and justifications. We follow a qualitative and interpretative approach, with participant observation of a teaching experiment that included five lessons that were integrally videotaped and transcribed. We analyse episodes from the work of the students in two tasks, one involving a complex relationship between fractions and the other involving the use of fractions as operators. The results show that when solving a task that involves rational numbers given as fractions, the students mostly use the decimal representation, with which they feel rather comfortable. In another task, involving rational numbers as operators, most students use fractions, but some of them also use of decimal numbers and pictorial representations. In both cases, the students chose the representation that they considered best suit their needs. In their written work, the students justify their choices by presenting the computations done when solving a task, adding explanations in natural language. Just by themselves, they are able to use counterexamples to refute a statement, and, during whole class discussions, prompted by the teacher, they are able to make generalizations and justifications based on definitions. |
|---|---|
| Autores principais: | Ponte, João Pedro da |
| Outros Autores: | Quaresma, Marisa |
| Assunto: | Generalization Justification Reasoning Rational numbers Representations |
| Ano: | 2020 |
| País: | Portugal |
| Tipo de documento: | capítulo de livro |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866809072113680384 |
|---|---|
| author | Ponte, João Pedro da |
| author2 | Quaresma, Marisa |
| author2_role | author |
| author_facet | Ponte, João Pedro da Quaresma, Marisa |
| author_role | author |
| contributor_name_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Ponte, João Pedro da\",\"Person.identifier.orcid\":\"0000-0001-6203-7616\"},{\"Person.name\":\"Quaresma, Marisa\",\"Person.identifier.orcid\":\"0000-0002-0861-6016\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Ponte, João Pedro da Quaresma, Marisa |
| datacite.date.Accepted.fl_str_mv | 2020-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2023-01-01T01:30:31Z |
| datacite.date.embargoed.fl_str_mv | 2023-01-01T01:30:31Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Generalization Justification Reasoning Rational numbers Representations |
| datacite.titles.title.fl_str_mv | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| dc.contributor.none.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Ponte, João Pedro da Quaresma, Marisa |
| dc.date.Accepted.fl_str_mv | 2020-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2023-01-01T01:30:31Z |
| dc.date.embargoed.fl_str_mv | 2023-01-01T01:30:31Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10451/45680 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Nova Science Publishers |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Generalization Justification Reasoning Rational numbers Representations |
| dc.title.fl_str_mv | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_3248 |
| description | This chapter presents a perspective about the exploratory approach as a possible way to enact inquiry based mathematics teaching. In this approach, the teacher, instead of beginning the class by presenting explanations and examples to the students, proposes them to work on tasks that may lead to the construction of new knowledge. We use as illustration the work of a grade 6 class of students solving tasks involving rational numbers. Our aim is to know how students use representations and reasoning processes, seeking to find out how they deal with different representations and how they formulate generalizations and justifications. We follow a qualitative and interpretative approach, with participant observation of a teaching experiment that included five lessons that were integrally videotaped and transcribed. We analyse episodes from the work of the students in two tasks, one involving a complex relationship between fractions and the other involving the use of fractions as operators. The results show that when solving a task that involves rational numbers given as fractions, the students mostly use the decimal representation, with which they feel rather comfortable. In another task, involving rational numbers as operators, most students use fractions, but some of them also use of decimal numbers and pictorial representations. In both cases, the students chose the representation that they considered best suit their needs. In their written work, the students justify their choices by presenting the computations done when solving a task, adding explanations in natural language. Just by themselves, they are able to use counterexamples to refute a statement, and, during whole class discussions, prompted by the teacher, they are able to make generalizations and justifications based on definitions. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | bookPart |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/357e3528-b337-4a75-a969-bb0fdefc963b/download |
| id | ul_ac09ffacf247bd28710fb0a4e804ecc6 |
| identifier.url.fl_str_mv | http://hdl.handle.net/10451/45680 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
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| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10451/45680 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Ponte, João Pedro da Ponte, João Pedro da https://www.ciencia-id.pt/6D1A-43D8-25B4 6D1A-43D8-25B4 http://orcid.org/0000-0001-6203-7616 0000-0001-6203-7616 Quaresma, Marisa Quaresma, Marisa https://www.ciencia-id.pt/0414-A3E4-8BA3 0414-A3E4-8BA3 http://orcid.org/0000-0002-0861-6016 0000-0002-0861-6016 |
| publishDate | 2020 |
| publisher.none.fl_str_mv | Nova Science Publishers |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
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| spelling | engNova Science Publisherspt_PTThis chapter presents a perspective about the exploratory approach as a possible way to enact inquiry based mathematics teaching. In this approach, the teacher, instead of beginning the class by presenting explanations and examples to the students, proposes them to work on tasks that may lead to the construction of new knowledge. We use as illustration the work of a grade 6 class of students solving tasks involving rational numbers. Our aim is to know how students use representations and reasoning processes, seeking to find out how they deal with different representations and how they formulate generalizations and justifications. We follow a qualitative and interpretative approach, with participant observation of a teaching experiment that included five lessons that were integrally videotaped and transcribed. We analyse episodes from the work of the students in two tasks, one involving a complex relationship between fractions and the other involving the use of fractions as operators. The results show that when solving a task that involves rational numbers given as fractions, the students mostly use the decimal representation, with which they feel rather comfortable. In another task, involving rational numbers as operators, most students use fractions, but some of them also use of decimal numbers and pictorial representations. In both cases, the students chose the representation that they considered best suit their needs. In their written work, the students justify their choices by presenting the computations done when solving a task, adding explanations in natural language. Just by themselves, they are able to use counterexamples to refute a statement, and, during whole class discussions, prompted by the teacher, they are able to make generalizations and justifications based on definitions.application/pdfpt_PTExploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbersPersonalPonte, João Pedro daDSpacehttp://dspace.org/items/7f7f6671-c6f0-4f10-8b88-822e768553bfDSpacehttp://dspace.org/items/7f7f6671-c6f0-4f10-8b88-822e768553bfMENDES DA PONTEJOÃO PEDROCiência IDhttps://www.ciencia-id.pt6D1A-43D8-25B4ORCIDhttp://orcid.org0000-0001-6203-7616PersonalQuaresma, MarisaDSpacehttp://dspace.org/items/9e4af501-1c72-4075-8be7-70d358a2e2b2DSpacehttp://dspace.org/items/9e4af501-1c72-4075-8be7-70d358a2e2b2QuaresmaMarisaCiência IDhttps://www.ciencia-id.pt0414-A3E4-8BA3ORCIDhttp://orcid.org0000-0002-0861-6016Researcher IDhttps://www.researcherid.comAAT-5779-2020Scopus Author IDhttps://www.scopus.com56471538400HostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.ptISBNIsPartOf978-1-53618-334-42023-01-01T01:30:31Z20202020-01-01T00:00:00ZHandlehttp://hdl.handle.net/10451/45680http://purl.org/coar/access_right/c_abf2open accessGeneralizationJustificationReasoningRational numbersRepresentations1773154 bytesliteraturehttp://purl.org/coar/resource_type/c_3248book parthttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/357e3528-b337-4a75-a969-bb0fdefc963b/downloadScience and mathematics education for 21st century citizens: Challenges and ways forwards131148New York |
| spellingShingle | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers Ponte, João Pedro da Generalization Justification Reasoning Rational numbers Representations |
| status | SINGLETON |
| subject.fl_str_mv | Generalization Justification Reasoning Rational numbers Representations |
| title | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| title_full | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| title_fullStr | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| title_full_unstemmed | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| title_short | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| title_sort | Exploratory mathematics teaching and the development of students’ use of representations and reasoning processes: An illustration with rational numbers |
| topic | Generalization Justification Reasoning Rational numbers Representations |
| topic_facet | Generalization Justification Reasoning Rational numbers Representations |
| url | http://hdl.handle.net/10451/45680 |
| visible | 1 |