Linking comparing and contrasting, generalising and justifying: a case study of primary students’ levels of justifying

Wanty Widjaja, Colleen Vale, Sandra Herbert, Esther Y-K Loong, Leicha A Bragg

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of justifying and the connections to other reasoning processes of comparing and contrasting, forming conjectures and generalising observed among Year 3–4 Australian and Canadian students (9–10-year olds) using the mathematical reasoning actions and levels (MRAL) framework (Authors 2017). The findings revealed that examining commonalities and differences was critical to allow Year 3–4 students to form conjectures and generalise for themselves. Justifying by examples and seeking counterexamples to evaluate the conjecture were prevalent with some students attempting to develop logical argument. The findings have implications for frameworks that assess students’
levels of justifying and for teacher actions that encourage students to communicate their reasoning through oral and non-verbal as well as written communications.
Original languageEnglish
Number of pages23
JournalMathematics Education Research Journal
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • conjectures
  • generalising
  • justifying
  • mathemtical reasoning

Cite this

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title = "Linking comparing and contrasting, generalising and justifying: a case study of primary students’ levels of justifying",
abstract = "Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of justifying and the connections to other reasoning processes of comparing and contrasting, forming conjectures and generalising observed among Year 3–4 Australian and Canadian students (9–10-year olds) using the mathematical reasoning actions and levels (MRAL) framework (Authors 2017). The findings revealed that examining commonalities and differences was critical to allow Year 3–4 students to form conjectures and generalise for themselves. Justifying by examples and seeking counterexamples to evaluate the conjecture were prevalent with some students attempting to develop logical argument. The findings have implications for frameworks that assess students’levels of justifying and for teacher actions that encourage students to communicate their reasoning through oral and non-verbal as well as written communications.",
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Linking comparing and contrasting, generalising and justifying : a case study of primary students’ levels of justifying. / Widjaja, Wanty; Vale, Colleen; Herbert, Sandra; Loong, Esther Y-K; Bragg, Leicha A.

In: Mathematics Education Research Journal, 2020.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Herbert, Sandra

AU - Loong, Esther Y-K

AU - Bragg, Leicha A

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N2 - Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of justifying and the connections to other reasoning processes of comparing and contrasting, forming conjectures and generalising observed among Year 3–4 Australian and Canadian students (9–10-year olds) using the mathematical reasoning actions and levels (MRAL) framework (Authors 2017). The findings revealed that examining commonalities and differences was critical to allow Year 3–4 students to form conjectures and generalise for themselves. Justifying by examples and seeking counterexamples to evaluate the conjecture were prevalent with some students attempting to develop logical argument. The findings have implications for frameworks that assess students’levels of justifying and for teacher actions that encourage students to communicate their reasoning through oral and non-verbal as well as written communications.

AB - Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of justifying and the connections to other reasoning processes of comparing and contrasting, forming conjectures and generalising observed among Year 3–4 Australian and Canadian students (9–10-year olds) using the mathematical reasoning actions and levels (MRAL) framework (Authors 2017). The findings revealed that examining commonalities and differences was critical to allow Year 3–4 students to form conjectures and generalise for themselves. Justifying by examples and seeking counterexamples to evaluate the conjecture were prevalent with some students attempting to develop logical argument. The findings have implications for frameworks that assess students’levels of justifying and for teacher actions that encourage students to communicate their reasoning through oral and non-verbal as well as written communications.

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