INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS

Parodi, Sebastián

Resumen:

Natural number bias (NNB) has been widely documented as a persistent difficulty in learning rational numbers. However, less is known about how prospective mathematics teachers (PMTs) interpret student responses, in which this bias becomes evident when working with fractions and decimals. This paper examines how PMTs reconstruct the reasoning underlying such responses by asking: What characterizes PMTs’ interpretations of student productions involving manifestations of NNB? The study draws on two complementary frameworks. First, professional noticing (PN), focusing on interpretation as inferring students’ mathematical understanding from the details of their productions and from knowledge of mathematical thinking (Jacobs et al., 2010). Second, conceptual change research provides the basis for understanding students’ NNB as a persistent reasoning framework arising from the overgeneralization of natural number properties to rational numbers (Van Dooren et al., 2015). Nine PMTs participated in a qualitative exploratory case study within a teacher education course. The study was based on a sequence of two teacher-role concept cartoons (TRCC) whose characters are PMTs discussing authentic student productions involving NNB. Data consisted of audio-recorded plenary discussions. Segments containing explicit inferences about students’ thinking were analysed and coded into three levels (Jacobs et al., 2010): lack, limited, and robust evidence (LaE, LiE, RoE). Analysis of the data showed the levels to be characterized as follows. At LaE, errors were reduced to procedural shortcomings; NNB was explicitly ruled out. At LiE, errors were attributed to the inappropriate transfer of learned rules or analogies, with NNB implicitly suggested but not conceptualized as an underlying framework. At RoE, errors were interpreted as coherent results of reasoning with rational numbers as if they were natural numbers, reconstructing NNB as an overgeneralization of natural number properties. These levels capture qualitative differences in interpretive depth rather than developmental stages, positioning TRCC as a resource for inquiring into PMTs’ noticing of NNB in students’ mathematical thinking.

Detalles Bibliográficos
2026
Agencia Nacional de Investigación e Innovación
Natural number bias
Professional noticing
Prospective mathematics teachers
Ciencias Sociales
Ciencias de la Educación
Educación General
Inglés
Agencia Nacional de Investigación e Innovación
REDI
https://hdl.handle.net/20.500.12381/5677
Acceso abierto
Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND)
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author Parodi, Sebastián
author_facet Parodi, Sebastián
author_role author
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bb840984b108cb9f667a972525badc0e
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
bitstream.url.fl_str_mv https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5677/2/license.txt
https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5677/1/PME49_Natural_number_bias.pdf
collection REDI
dc.creator.none.fl_str_mv Parodi, Sebastián
dc.date.accessioned.none.fl_str_mv 2026-09-15T13:49:28Z
dc.date.available.none.fl_str_mv 2026-09-15T13:49:28Z
dc.date.issued.none.fl_str_mv 2026-07-31
dc.description.abstract.none.fl_txt_mv Natural number bias (NNB) has been widely documented as a persistent difficulty in learning rational numbers. However, less is known about how prospective mathematics teachers (PMTs) interpret student responses, in which this bias becomes evident when working with fractions and decimals. This paper examines how PMTs reconstruct the reasoning underlying such responses by asking: What characterizes PMTs’ interpretations of student productions involving manifestations of NNB? The study draws on two complementary frameworks. First, professional noticing (PN), focusing on interpretation as inferring students’ mathematical understanding from the details of their productions and from knowledge of mathematical thinking (Jacobs et al., 2010). Second, conceptual change research provides the basis for understanding students’ NNB as a persistent reasoning framework arising from the overgeneralization of natural number properties to rational numbers (Van Dooren et al., 2015). Nine PMTs participated in a qualitative exploratory case study within a teacher education course. The study was based on a sequence of two teacher-role concept cartoons (TRCC) whose characters are PMTs discussing authentic student productions involving NNB. Data consisted of audio-recorded plenary discussions. Segments containing explicit inferences about students’ thinking were analysed and coded into three levels (Jacobs et al., 2010): lack, limited, and robust evidence (LaE, LiE, RoE). Analysis of the data showed the levels to be characterized as follows. At LaE, errors were reduced to procedural shortcomings; NNB was explicitly ruled out. At LiE, errors were attributed to the inappropriate transfer of learned rules or analogies, with NNB implicitly suggested but not conceptualized as an underlying framework. At RoE, errors were interpreted as coherent results of reasoning with rational numbers as if they were natural numbers, reconstructing NNB as an overgeneralization of natural number properties. These levels capture qualitative differences in interpretive depth rather than developmental stages, positioning TRCC as a resource for inquiring into PMTs’ noticing of NNB in students’ mathematical thinking.
dc.description.sponsorship.none.fl_txt_mv Agencia Nacional de Investigación e Innovación
dc.identifier.anii.es.fl_str_mv FMV_3_2024_1_181336
dc.identifier.issn.none.fl_str_mv 3081-0833
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12381/5677
dc.language.iso.none.fl_str_mv eng
dc.relation.none.fl_str_mv https://hdl.handle.net/20.500.12381/5676
https://hdl.handle.net/20.500.12381/5678
https://hdl.handle.net/20.500.12381/5679
https://hdl.handle.net/20.500.12381/5682
https://hdl.handle.net/20.500.12381/5690
https://hdl.handle.net/20.500.12381/5683
dc.rights.*.fl_str_mv Acceso abierto
dc.rights.license.none.fl_str_mv Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.es.fl_str_mv Psychology of Mathematics Education (PME 49)
dc.source.none.fl_str_mv reponame:REDI
instname:Agencia Nacional de Investigación e Innovación
instacron:Agencia Nacional de Investigación e Innovación
dc.subject.anii.none.fl_str_mv Ciencias Sociales
Ciencias de la Educación
Educación General
dc.subject.es.fl_str_mv Natural number bias
Professional noticing
Prospective mathematics teachers
dc.title.none.fl_str_mv INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
dc.type.es.fl_str_mv Documento de conferencia
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
dc.type.version.es.fl_str_mv Publicado
dc.type.version.none.fl_str_mv info:eu-repo/semantics/publishedVersion
description Natural number bias (NNB) has been widely documented as a persistent difficulty in learning rational numbers. However, less is known about how prospective mathematics teachers (PMTs) interpret student responses, in which this bias becomes evident when working with fractions and decimals. This paper examines how PMTs reconstruct the reasoning underlying such responses by asking: What characterizes PMTs’ interpretations of student productions involving manifestations of NNB? The study draws on two complementary frameworks. First, professional noticing (PN), focusing on interpretation as inferring students’ mathematical understanding from the details of their productions and from knowledge of mathematical thinking (Jacobs et al., 2010). Second, conceptual change research provides the basis for understanding students’ NNB as a persistent reasoning framework arising from the overgeneralization of natural number properties to rational numbers (Van Dooren et al., 2015). Nine PMTs participated in a qualitative exploratory case study within a teacher education course. The study was based on a sequence of two teacher-role concept cartoons (TRCC) whose characters are PMTs discussing authentic student productions involving NNB. Data consisted of audio-recorded plenary discussions. Segments containing explicit inferences about students’ thinking were analysed and coded into three levels (Jacobs et al., 2010): lack, limited, and robust evidence (LaE, LiE, RoE). Analysis of the data showed the levels to be characterized as follows. At LaE, errors were reduced to procedural shortcomings; NNB was explicitly ruled out. At LiE, errors were attributed to the inappropriate transfer of learned rules or analogies, with NNB implicitly suggested but not conceptualized as an underlying framework. At RoE, errors were interpreted as coherent results of reasoning with rational numbers as if they were natural numbers, reconstructing NNB as an overgeneralization of natural number properties. These levels capture qualitative differences in interpretive depth rather than developmental stages, positioning TRCC as a resource for inquiring into PMTs’ noticing of NNB in students’ mathematical thinking.
eu_rights_str_mv openAccess
format conferenceObject
id REDI_23ca3f3ccc8e5db0d8ff35dd4ad19068
identifier_str_mv 3081-0833
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instacron_str Agencia Nacional de Investigación e Innovación
institution Agencia Nacional de Investigación e Innovación
instname_str Agencia Nacional de Investigación e Innovación
language eng
network_acronym_str REDI
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oai_identifier_str oai:redi.anii.org.uy:20.500.12381/5677
publishDate 2026
reponame_str REDI
repository.mail.fl_str_mv jmaldini@anii.org.uy
repository.name.fl_str_mv REDI - Agencia Nacional de Investigación e Innovación
repository_id_str 9421
rights_invalid_str_mv Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND)
Acceso abierto
spelling Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND)Acceso abiertoinfo:eu-repo/semantics/openAccess2026-09-15T13:49:28Z2026-09-15T13:49:28Z2026-07-313081-0833https://hdl.handle.net/20.500.12381/5677FMV_3_2024_1_181336Natural number bias (NNB) has been widely documented as a persistent difficulty in learning rational numbers. However, less is known about how prospective mathematics teachers (PMTs) interpret student responses, in which this bias becomes evident when working with fractions and decimals. This paper examines how PMTs reconstruct the reasoning underlying such responses by asking: What characterizes PMTs’ interpretations of student productions involving manifestations of NNB? The study draws on two complementary frameworks. First, professional noticing (PN), focusing on interpretation as inferring students’ mathematical understanding from the details of their productions and from knowledge of mathematical thinking (Jacobs et al., 2010). Second, conceptual change research provides the basis for understanding students’ NNB as a persistent reasoning framework arising from the overgeneralization of natural number properties to rational numbers (Van Dooren et al., 2015). Nine PMTs participated in a qualitative exploratory case study within a teacher education course. The study was based on a sequence of two teacher-role concept cartoons (TRCC) whose characters are PMTs discussing authentic student productions involving NNB. Data consisted of audio-recorded plenary discussions. Segments containing explicit inferences about students’ thinking were analysed and coded into three levels (Jacobs et al., 2010): lack, limited, and robust evidence (LaE, LiE, RoE). Analysis of the data showed the levels to be characterized as follows. At LaE, errors were reduced to procedural shortcomings; NNB was explicitly ruled out. At LiE, errors were attributed to the inappropriate transfer of learned rules or analogies, with NNB implicitly suggested but not conceptualized as an underlying framework. At RoE, errors were interpreted as coherent results of reasoning with rational numbers as if they were natural numbers, reconstructing NNB as an overgeneralization of natural number properties. These levels capture qualitative differences in interpretive depth rather than developmental stages, positioning TRCC as a resource for inquiring into PMTs’ noticing of NNB in students’ mathematical thinking.Agencia Nacional de Investigación e Innovaciónenghttps://hdl.handle.net/20.500.12381/5676https://hdl.handle.net/20.500.12381/5678https://hdl.handle.net/20.500.12381/5679https://hdl.handle.net/20.500.12381/5682https://hdl.handle.net/20.500.12381/5690https://hdl.handle.net/20.500.12381/5683Psychology of Mathematics Education (PME 49)reponame:REDIinstname:Agencia Nacional de Investigación e Innovacióninstacron:Agencia Nacional de Investigación e InnovaciónNatural number biasProfessional noticingProspective mathematics teachersCiencias SocialesCiencias de la EducaciónEducación GeneralINTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIASDocumento de conferenciaPublicadoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectSociedad de Educación Matemática Uruguaya//Ciencias Sociales/Ciencias de la Educación/Educación GeneralParodi, SebastiánLICENSElicense.txtlicense.txttext/plain; charset=utf-84967https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5677/2/license.txta4ce09f01b5dd771727aa05c73851623MD52ORIGINALPME49_Natural_number_bias.pdfPME49_Natural_number_bias.pdfapplication/pdf6418https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5677/1/PME49_Natural_number_bias.pdfbb840984b108cb9f667a972525badc0eMD5120.500.12381/56772026-10-01 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- Agencia Nacional de Investigación e Innovaciónfalse
spellingShingle INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
Parodi, Sebastián
Natural number bias
Professional noticing
Prospective mathematics teachers
Ciencias Sociales
Ciencias de la Educación
Educación General
status_str publishedVersion
title INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
title_full INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
title_fullStr INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
title_full_unstemmed INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
title_short INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
title_sort INTERPRETING STUDENTS’ MATHEMATICAL THINKING INVOLVING NATURAL NUMBER BIAS
topic Natural number bias
Professional noticing
Prospective mathematics teachers
Ciencias Sociales
Ciencias de la Educación
Educación General
url https://hdl.handle.net/20.500.12381/5677