The Role of Different Arguments: Upper Secondary School Students’ Collective Mathematical Reasoning in Algebra The Role of Different Arguments: Upper Secondary School Students’ Collective Mathematical Reasoning in Algebra

Algebra is a core aspect of mathematics, often functioning as a gatekeeper to further studies in mathematics. Although a well-researched area, we still do not know how students’ algebraic reasoning can vary, including the understanding of the roles of various mathematical arguments. In an explorativ...

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Veröffentlicht in:International journal of science and mathematics education Jg. 23; H. 7; S. 3153 - 3177
Hauptverfasser: Johansson, Anders, Sumpter, Lovisa
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Singapore Springer Nature Singapore 01.10.2025
Springer Nature B.V
Schlagworte:
Addition
Algebra
Algebraic reasoning
Argumentation
Arithmetic
Arithmetic sequences
Collective mathematical reasoning
Communicative Competence (Languages)
Competence
Definitions
Education
matematikämnets didaktik
Mathematical analysis
Mathematical arguments
Mathematics
Mathematics Education
Mathematics Instruction
Mathematics Skills
Reasoning
Science Education
Secondary school students
Sequences
Students
Syntax
Validity
Algebraic reasoning
Mathematical arguments
Arithmetic sequences
Argumentation
Collective mathematical reasoning
ISSN:1571-0068, 1573-1774, 1573-1774
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Abstract Algebra is a core aspect of mathematics, often functioning as a gatekeeper to further studies in mathematics. Although a well-researched area, we still do not know how students’ algebraic reasoning can vary, including the understanding of the roles of various mathematical arguments. In an explorative study, using semi-structured, non-participant observations and Interpersonal Process Recall interviews, we analyse eight upper secondary students’ collective mathematical reasoning when solving algebraic tasks about arithmetic sequences. The results show that the majority of expressed arguments were anchored in relevant mathematical properties covering a wide spectrum of algebraic reasoning. The results indicate that it is in the first instance of the reasoning, the task situation, where the students interpreted the pattern differently, where the biggest variation of different aspects of algebraic reasoning was displayed. In addition, the identifying arguments constituted the main part of all expressed arguments, indicating that the core part of the reasoning was in the interpretation of the task. There were few arguments about the choice of strategy and its implementation, signalling that once an interpretation was made and agreed upon, the strategy choice did not have as dominant role as previous research has suggested. In most cases, the arguments provided for the conclusion, evaluative arguments, were implicit and connected with previously expressed identifying arguments. The results also show that identifying arguments was connected to the mathematical content of the task, whereas the difference in algebraic reasoning appears depends on students' solution constructions and their degree of conventional syntax.
AbstractList Algebra is a core aspect of mathematics, often functioning as a gatekeeper to further studies in mathematics. Although a well-researched area, we still do not know how students’ algebraic reasoning can vary, including the understanding of the roles of various mathematical arguments. In an explorative study, using semi-structured, non-participant observations and Interpersonal Process Recall interviews, we analyse eight upper secondary students’ collective mathematical reasoning when solving algebraic tasks about arithmetic sequences. The results show that the majority of expressed arguments were anchored in relevant mathematical properties covering a wide spectrum of algebraic reasoning. The results indicate that it is in the first instance of the reasoning, the task situation, where the students interpreted the pattern differently, where the biggest variation of different aspects of algebraic reasoning was displayed. In addition, the identifying arguments constituted the main part of all expressed arguments, indicating that the core part of the reasoning was in the interpretation of the task. There were few arguments about the choice of strategy and its implementation, signalling that once an interpretation was made and agreed upon, the strategy choice did not have as dominant role as previous research has suggested. In most cases, the arguments provided for the conclusion, evaluative arguments, were implicit and connected with previously expressed identifying arguments. The results also show that identifying arguments was connected to the mathematical content of the task, whereas the difference in algebraic reasoning appears depends on students' solution constructions and their degree of conventional syntax.
Author Sumpter, Lovisa
Johansson, Anders
Author_xml – sequence: 1
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  surname: Sumpter
  fullname: Sumpter, Lovisa
  email: lovisa.sumpter@su.se
  organization: Department of Teaching and Learning, Stockholm University
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Issue 7
Keywords Algebraic reasoning
Mathematical arguments
Arithmetic sequences
Argumentation
Collective mathematical reasoning
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  year: 2012
  ident: 10579_CR14
  publication-title: International Journal of Science and Mathematics Education
  doi: 10.1007/s10763-011-9310-3
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Snippet Algebra is a core aspect of mathematics, often functioning as a gatekeeper to further studies in mathematics. Although a well-researched area, we still do not...
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SubjectTerms Addition
Algebra
Algebraic reasoning
Argumentation
Arithmetic
Arithmetic sequences
Collective mathematical reasoning
Communicative Competence (Languages)
Competence
Definitions
Education
matematikämnets didaktik
Mathematical analysis
Mathematical arguments
Mathematics
Mathematics Education
Mathematics Instruction
Mathematics Skills
Reasoning
Science Education
Secondary school students
Sequences
Students
Syntax
Validity
Subtitle The Role of Different Arguments: Upper Secondary School Students’ Collective Mathematical Reasoning in Algebra
Title The Role of Different Arguments: Upper Secondary School Students’ Collective Mathematical Reasoning in Algebra
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