Supporting grades 1-8 pre-service teachers' argumentation skills: constructing mathematical arguments in situations that facilitate analyzing cases

We report on a teaching experiment with pre-service teachers (PSTs) intended to support their understanding of the validity of mathematical arguments, and their ability to formulate mathematical arguments by conducting case analysis. PSTs used Toulmin's framework (1958/2003) and engaged in coll...

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Vydáno v:International journal of mathematical education in science and technology Ročník 51; číslo 8; s. 1196 - 1223
Hlavní autoři: Zambak, Vecihi S., Magiera, Marta T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Taylor & Francis 16.11.2020
Taylor & Francis Ltd
Témata:
Algorithms
Arithmetic
case analysis
collective argumentation
crypto-arithmetic problems
Elementary School Mathematics
Inferences
Learning Activities
Mathematical analysis
mathematical arguments
Mathematical Logic
Mathematics Education
Mathematics Skills
Mathematics Teachers
Middle School Mathematics
Persuasive Discourse
Pre-service teacher education
Preservice Teacher Education
Preservice Teachers
Private Colleges
Problem Solving
Reasoning
Skill Development
Skills
Teacher education
Teacher Educators
Teachers
Thinking Skills
Validity
ISSN:0020-739X, 1464-5211
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Abstract We report on a teaching experiment with pre-service teachers (PSTs) intended to support their understanding of the validity of mathematical arguments, and their ability to formulate mathematical arguments by conducting case analysis. PSTs used Toulmin's framework (1958/2003) and engaged in collective argumentation while solving crypto-arithmetic problems about a multi-digit addition algorithm. The problems facilitated reasoning about cases. Results show the evolution of PSTs' reasoning skills over time. A significant proportion of PSTs moved away from providing unsupported claims, towards constructing all-encompassing deductive-like arguments with clearly stated claims, supporting evidence, and reasons. We suggest a plausible sequence of learning activities for mathematics teacher educators to consider in an effort to strengthen PSTs' argumentation skills. The goal is to support PSTs' ability to reason about and analyze cases while solving problems that lend themselves to drawing logical inferences with strategic approaches.
AbstractList We report on a teaching experiment with pre-service teachers (PSTs) intended to support their understanding of the validity of mathematical arguments, and their ability to formulate mathematical arguments by conducting case analysis. PSTs used Toulmin's framework (1958/2003) and engaged in collective argumentation while solving crypto-arithmetic problems about a multi-digit addition algorithm. The problems facilitated reasoning about cases. Results show the evolution of PSTs’ reasoning skills over time. A significant proportion of PSTs moved away from providing unsupported claims, towards constructing all-encompassing deductive-like arguments with clearly stated claims, supporting evidence, and reasons. We suggest a plausible sequence of learning activities for mathematics teacher educators to consider in an effort to strengthen PSTs’ argumentation skills. The goal is to support PSTs’ ability to reason about and analyze cases while solving problems that lend themselves to drawing logical inferences with strategic approaches.
Audience Higher Education
Postsecondary Education
Junior High Schools
Middle Schools
Elementary Education
Secondary Education
Author Magiera, Marta T.
Zambak, Vecihi S.
Author_xml – sequence: 1
  givenname: Vecihi S.
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  surname: Zambak
  fullname: Zambak, Vecihi S.
  organization: Department of Curriculum and Instruction, Monmouth University
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  givenname: Marta T.
  orcidid: 0000-0003-2944-9787
  surname: Magiera
  fullname: Magiera, Marta T.
  email: marta.magiera@marquette.edu
  organization: Department of Mathematical and Statistical Sciences, Marquette University
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SubjectTerms Algorithms
Arithmetic
case analysis
collective argumentation
crypto-arithmetic problems
Elementary School Mathematics
Inferences
Learning Activities
Mathematical analysis
mathematical arguments
Mathematical Logic
Mathematics Education
Mathematics Skills
Mathematics Teachers
Middle School Mathematics
Persuasive Discourse
Pre-service teacher education
Preservice Teacher Education
Preservice Teachers
Private Colleges
Problem Solving
Reasoning
Skill Development
Skills
Teacher education
Teacher Educators
Teachers
Thinking Skills
Validity
Title Supporting grades 1-8 pre-service teachers' argumentation skills: constructing mathematical arguments in situations that facilitate analyzing cases
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