Publicação
The study of pictorial sequences as a support to the development of algebraic thinking
| Resumo: | The purpose of this article is to study the contribution of a teaching unit that introduces algebra through pictorial sequences and problem solving with an exploratory and investigative approach towards the development of the algebraic thinking of grade 7 students. The study focuses on the work of a student, Joana, in different algebraic tasks. Data were collected by means of two interviews, audio recording and a research journal. Prior to the teaching unit, working with a pictorial sequence, the student fails to recognize the algebraic language except in a simple situation. During the teaching unit, the work in the classroom promotes the analysis of different strategies and justifications and the use of the algebraic language. After the teaching unit, the student decomposes the pictures in a sequence and identifies the relation between the order of the picture and the number of its elements, expressing it algebraically. Besides, she uses different strategies to solve equations, showing aunderstanding. She also recognizes the meaning of unknowns and generalized numbers in the symbols that appear in different contexts. Joana’s performance suggests that the teaching unit promoted the development of essential aspects of algebraic thinking like the ability to generalize in pictorial sequences, the understanding of symbols, expressions, and equations, and the use of informal and formal strategies for solving equations. |
|---|---|
| Autores principais: | Branco, Neusa |
| Outros Autores: | Ponte, João Pedro da |
| Assunto: | Algebra Algebraic thinking Equations Sequences |
| Ano: | 2012 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866809932054003712 |
|---|---|
| author | Branco, Neusa |
| author2 | Ponte, João Pedro da |
| author2_role | author |
| author_facet | Branco, Neusa Ponte, João Pedro da |
| author_role | author |
| contributor_name_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Branco, Neusa\",\"Person.identifier.orcid\":\"0000-0003-4695-0098\"},{\"Person.name\":\"Ponte, João Pedro da\",\"Person.identifier.orcid\":\"0000-0001-6203-7616\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Branco, Neusa Ponte, João Pedro da |
| datacite.date.Accepted.fl_str_mv | 2012-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2016-02-08T12:59:32Z |
| datacite.date.embargoed.fl_str_mv | 2016-02-08T12:59:32Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Algebra Algebraic thinking Equations Sequences |
| datacite.titles.title.fl_str_mv | The study of pictorial sequences as a support to the development of algebraic thinking |
| dc.contributor.none.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Branco, Neusa Ponte, João Pedro da |
| dc.date.Accepted.fl_str_mv | 2012-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2016-02-08T12:59:32Z |
| dc.date.embargoed.fl_str_mv | 2016-02-08T12:59:32Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10451/22609 |
| dc.language.none.fl_str_mv | eng |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Algebra Algebraic thinking Equations Sequences |
| dc.title.fl_str_mv | The study of pictorial sequences as a support to the development of algebraic thinking |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | The purpose of this article is to study the contribution of a teaching unit that introduces algebra through pictorial sequences and problem solving with an exploratory and investigative approach towards the development of the algebraic thinking of grade 7 students. The study focuses on the work of a student, Joana, in different algebraic tasks. Data were collected by means of two interviews, audio recording and a research journal. Prior to the teaching unit, working with a pictorial sequence, the student fails to recognize the algebraic language except in a simple situation. During the teaching unit, the work in the classroom promotes the analysis of different strategies and justifications and the use of the algebraic language. After the teaching unit, the student decomposes the pictures in a sequence and identifies the relation between the order of the picture and the number of its elements, expressing it algebraically. Besides, she uses different strategies to solve equations, showing aunderstanding. She also recognizes the meaning of unknowns and generalized numbers in the symbols that appear in different contexts. Joana’s performance suggests that the teaching unit promoted the development of essential aspects of algebraic thinking like the ability to generalize in pictorial sequences, the understanding of symbols, expressions, and equations, and the use of informal and formal strategies for solving equations. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/c82bd175-f492-4e40-9d8d-af41efc923aa/download |
| id | ul_55bbcd4c2b2cdf19cd6f82ffbaaa963e |
| identifier.url.fl_str_mv | http://hdl.handle.net/10451/22609 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
| network_acronym_str | ul |
| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10451/22609 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Branco, Neusa Branco, Neusa https://www.ciencia-id.pt/D411-2049-433B D411-2049-433B http://orcid.org/0000-0003-4695-0098 0000-0003-4695-0098 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 |
| publishDate | 2012 |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
| service_str_mv | urn:repositoryAcronym:ul |
| spelling | engpt_PTThe purpose of this article is to study the contribution of a teaching unit that introduces algebra through pictorial sequences and problem solving with an exploratory and investigative approach towards the development of the algebraic thinking of grade 7 students. The study focuses on the work of a student, Joana, in different algebraic tasks. Data were collected by means of two interviews, audio recording and a research journal. Prior to the teaching unit, working with a pictorial sequence, the student fails to recognize the algebraic language except in a simple situation. During the teaching unit, the work in the classroom promotes the analysis of different strategies and justifications and the use of the algebraic language. After the teaching unit, the student decomposes the pictures in a sequence and identifies the relation between the order of the picture and the number of its elements, expressing it algebraically. Besides, she uses different strategies to solve equations, showing aunderstanding. She also recognizes the meaning of unknowns and generalized numbers in the symbols that appear in different contexts. Joana’s performance suggests that the teaching unit promoted the development of essential aspects of algebraic thinking like the ability to generalize in pictorial sequences, the understanding of symbols, expressions, and equations, and the use of informal and formal strategies for solving equations.application/pdfpt_PTThe study of pictorial sequences as a support to the development of algebraic thinkingPersonalBranco, NeusaDSpacehttp://dspace.org/items/7e82fa6f-5029-41ee-b3a8-84e0e3559f12DSpacehttp://dspace.org/items/7e82fa6f-5029-41ee-b3a8-84e0e3559f12BrancoNeusaCiência IDhttps://www.ciencia-id.ptD411-2049-433BORCIDhttp://orcid.org0000-0003-4695-0098PersonalPonte, 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.org0000-0001-6203-7616HostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.ptISSNIsPartOf0973-56312016-02-08T12:59:32Z20122012-01-01T00:00:00ZHandlehttp://hdl.handle.net/10451/22609http://purl.org/coar/access_right/c_abf2open accessAlgebraAlgebraic thinkingEquationsSequences391823 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/c82bd175-f492-4e40-9d8d-af41efc923aa/downloadFar East Journal of Mathematical Education8Allahabad, India |
| spellingShingle | The study of pictorial sequences as a support to the development of algebraic thinking Branco, Neusa Algebra Algebraic thinking Equations Sequences |
| status | SINGLETON |
| subject.fl_str_mv | Algebra Algebraic thinking Equations Sequences |
| title | The study of pictorial sequences as a support to the development of algebraic thinking |
| title_full | The study of pictorial sequences as a support to the development of algebraic thinking |
| title_fullStr | The study of pictorial sequences as a support to the development of algebraic thinking |
| title_full_unstemmed | The study of pictorial sequences as a support to the development of algebraic thinking |
| title_short | The study of pictorial sequences as a support to the development of algebraic thinking |
| title_sort | The study of pictorial sequences as a support to the development of algebraic thinking |
| topic | Algebra Algebraic thinking Equations Sequences |
| topic_facet | Algebra Algebraic thinking Equations Sequences |
| url | http://hdl.handle.net/10451/22609 |
| visible | 1 |