An investigation of an undergraduate student’s reasoning with zero-divisors and the zero-product property

Cook, John Paul

doi:10.1016/j.jmathb.2017.11.001

Cited by 6 publications

(1 citation statement)

References 19 publications

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“…www.ejel.org 80 ©The Authors Mal's statement is consistent with Cook's (2018) that teachers frequently overlook the importance of reinforcing students' understanding of the zero-product property. High school students already have a lot of mathematics knowledge in their mathematics experience.…”

Section: Evidence Of Participants' External Transpositionsmentioning

confidence: 56%

Providing Online Learning Situations for In-Service Mathematics Teachers' External Transposition Knowledge During COVID-19 Pandemic: Case of Indonesia

Marfuah¹,

Suryadi²,

Turmudi³

et al. 2022

EJEL

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Updating mastery of mathematics scholarly knowledge is vital for mathematics teachers' professional development in Indonesia. External transposition refers to the transposition of mathematics scholarly knowledge to the school curriculum. During the COVID-19 pandemic, online learning becomes the primary strategy for strengthening the external transposition knowledge of mathematics teachers in Indonesia. This study aims to describe the process of providing online learning situations in lifting the in-service mathematics teachers' external transposition knowledge during the COVID-19 pandemic. The online learning involved 57 in-service high school mathematics teachers in Indonesia as participants. The scholarly knowledge to be delivered was the visualization of matrix multiplication. This qualitative study is a didactical design research that includes a prospective learning situation analysis, a meta-technopedadidactic analysis, and a retrospective analysis. In the prospective learning situation, the solutions for re-situating face-to-face learning to online learning were disclosed. Moodle was used as the Learning Management System, and GeoGebra Classroom was used as the Task Response System. A meta-technopedadidactic is an educator's ability to comprehensively analyze pedagogic interaction, didactic interaction, and didactic pedagogy anticipation in using technology in a learning situation. The finding in the meta-technopedadidactic analysis showed the role of technology as a visualization tool in online learning, evidence of participants' external didactic transposition, constraints, and collaboration in learning. Finally, the retrospective analysis suggested some future improvements for better online learning situations. This study contributes to the comprehensive organization of e-learning courses in Indonesia for mathematics teachers' professional development based on pedagogic interaction, didactic interaction, and didactic pedagogy anticipation in the use of technology. Despite some of the study's limitations, the findings have the potential to be an advantage for the long-term sustainability of e-learning as a new norm for teachers' professional development programs, rather than just a foreshadowing of the pandemic.

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Section: Evidence Of Participants' External Transpositionsmentioning

confidence: 56%

Providing Online Learning Situations for In-Service Mathematics Teachers' External Transposition Knowledge During COVID-19 Pandemic: Case of Indonesia

Marfuah¹,

Suryadi²,

Turmudi³

et al. 2022

EJEL

View full text Add to dashboard Cite

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Monster-Barring as a Catalyst for Bridging Secondary Algebra to Abstract Algebra

Cook

2018

Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers

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“I’ll just try to mimic that”: an exploration of students’ analogical structure creation in abstract algebra

Hicks

2024

Educ Stud Math

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Despite the prominence of analogies in mathematics, little attention has been given to exploring students’ processes of analogical reasoning, and even less research exists on revealing how students might be empowered to independently and productively reason by analogy to establish new (to them) mathematics. I argue that the lack of a cohesive framework for interpreting students’ approaches to analogical reasoning in mathematics contributes to this issue. To address this, I introduce the Analogical Reasoning in Mathematics (ARM) framework. Constructed from an analysis of interviews with four abstract algebra students, ARM identifies several analogical activities that serve to analyze students’ analogical reasoning with a finer grain size than was previously possible with existing frameworks. Using this framework, I present an analysis of the students’ constructions of a ring-theoretic analogy to subgroup, thus revealing that even constructing simple analogies can elicit diverse pathways of analogical reasoning across students. Implications for further research related to analogies and analogical reasoning in mathematics education are discussed.

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An investigation of an undergraduate student’s reasoning with zero-divisors and the zero-product property

Cited by 6 publications

References 19 publications

Providing Online Learning Situations for In-Service Mathematics Teachers' External Transposition Knowledge During COVID-19 Pandemic: Case of Indonesia

Providing Online Learning Situations for In-Service Mathematics Teachers' External Transposition Knowledge During COVID-19 Pandemic: Case of Indonesia

Monster-Barring as a Catalyst for Bridging Secondary Algebra to Abstract Algebra

“I’ll just try to mimic that”: an exploration of students’ analogical structure creation in abstract algebra

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