Knowledge Organisers for learning: Examples, non-examples and concept maps in university mathematics

Inae Jeong; Tanya Evans; Inae Jeong; Tanya Evans

doi:10.3934/steme.2023008

STEM Education

2023, Volume 3, Issue 2: 103-129. doi: 10.3934/steme.2023008

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Research article

Knowledge Organisers for learning: Examples, non-examples and concept maps in university mathematics

Inae Jeong ^{1
,},
Tanya Evans ^{2
,
,}

1.
Department of Mathematics, University of Auckland, Auckland CBD, Auckland, New Zealand; 0407jia@gmail.com
2.
Department of Mathematics, University of Auckland, Auckland CBD, Auckland, New Zealand; t.evans@auckland.ac.nz

Academic Editor: Chris Tisdell

Received: 24 April 2023 Revised: 29 June 2023 Accepted: 29 June 2023 Published: 30 June 2023

Finding effective ways to engage students in sense-making while learning is one of the central challenges discussed in mathematics education literature. One of the big issues is the prevalence of summative assessment tasks prompting students to demonstrate procedural knowledge only, which is a common problem at the tertiary level. In this study, in a large university classroom setting (N = 355), an instructional innovation was designed, developed, implemented and evaluated involving novel tasks–Knowledge Organisers. The tasks comprised prompts for students to generate examples/non-examples and construct a concept map of the key mathematical concepts in the course. The initiative's design was based on the current understanding of human cognitive architecture. A concept map is a visualisation of a group of related abstract concepts with their relationships identified by connections using directed arrows, which can be viewed as an externalisation of a schema stored in a learner's long-term memory. As such, we argue for a distinction between a local conceptual understanding (e.g., example space) versus a global conceptual understanding, manifesting through a high-quality concept map linking a group of related concepts. By utilising a mixed-methods approach and triangulation of the findings from qualitative and quantitative analyses, we were able to discern critical aspects pertaining to the feasibility of implementation and evaluate learners' perceptions. Students' performance on concept mapping is positively correlated with their perceptions of the novel tasks and the time spent completing them. Qualitative analysis showed that students' perceptions are demonstrably insightful about the key mechanisms that supposedly make the tasks beneficial to their learning. Based on the results of the data analyses and their theoretical interpretations, we propose pedagogical strategies for the effective use of Knowledge Organisers.
- Knowledge Organisers,
- concept maps,
- examples,
- variation theory,
- global conceptual understanding,
- undergraduate mathematics
Citation: Inae Jeong, Tanya Evans. Knowledge Organisers for learning: Examples, non-examples and concept maps in university mathematics[J]. STEM Education, 2023, 3(2): 103-129. doi: 10.3934/steme.2023008

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Abstract

Finding effective ways to engage students in sense-making while learning is one of the central challenges discussed in mathematics education literature. One of the big issues is the prevalence of summative assessment tasks prompting students to demonstrate procedural knowledge only, which is a common problem at the tertiary level. In this study, in a large university classroom setting (N = 355), an instructional innovation was designed, developed, implemented and evaluated involving novel tasks–Knowledge Organisers. The tasks comprised prompts for students to generate examples/non-examples and construct a concept map of the key mathematical concepts in the course. The initiative's design was based on the current understanding of human cognitive architecture. A concept map is a visualisation of a group of related abstract concepts with their relationships identified by connections using directed arrows, which can be viewed as an externalisation of a schema stored in a learner's long-term memory. As such, we argue for a distinction between a local conceptual understanding (e.g., example space) versus a global conceptual understanding, manifesting through a high-quality concept map linking a group of related concepts. By utilising a mixed-methods approach and triangulation of the findings from qualitative and quantitative analyses, we were able to discern critical aspects pertaining to the feasibility of implementation and evaluate learners' perceptions. Students' performance on concept mapping is positively correlated with their perceptions of the novel tasks and the time spent completing them. Qualitative analysis showed that students' perceptions are demonstrably insightful about the key mechanisms that supposedly make the tasks beneficial to their learning. Based on the results of the data analyses and their theoretical interpretations, we propose pedagogical strategies for the effective use of Knowledge Organisers.

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Author's biography Inae Jeong is a former postgraduate student at the University of Auckland, New Zealand, specialising in Mathematics Education. She completed her Master's degree in 2022; Dr. Tanya Evans is a senior lecturer in the Department of Mathematics at the University of Auckland. She specialises in mathematics education. Her research interests include secondary and undergraduate mathematics education, mathematical practice, professional development, and curriculum studies

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