Impact and Prevalence of Diagrammatic Supports in Mathematics Classrooms

Matlen, Bryan J.; Richland, Lindsey E.; Klostermann, Ellen C.; Lyons, Emily McLaughlin

doi:10.1007/978-3-319-91376-6_16

Cited by 3 publications

(8 citation statements)

References 26 publications

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“…Japanese and Hongkongese teachers used more linking gestures (e.g., hand and arm motions linking the two representations) and tied their use more effectively to students' needs, for example, by intensifying gesture use with novice students (Richland, 2015). Another study yielded similar conclusions (i.e., greater use of gestures and visual diagrams by Japanese and Hongkongese teachers) and also confirmed in experimental settings that such supports improve learning outcomes (Matlen et al, 2018).…”

Section: Gesturesmentioning

confidence: 66%

“…Across studies, three points emerge: First, teachers from all cultures view analogies as useful and important instructional tools (Richland, Zur, & Holyoak, 2007). Second, teachers from Japan and Hong Kong are more effective than American teachers in using analogies as instructional tools (Matlen, Richland, Klostermann, & Lyons, 2018). Third, students' learning outcomes correlate with analogical use: Students from cultures with greater classroom use of analogy perform more optimally than those with less use (Richland et al, 2007).…”

Section: Analogy As An Instructional Tool In Classroomsmentioning

confidence: 99%

“…A simple remedy is visual support: an explicit portrayal of the required mapping. For example, in one study, students learned to conduct mathematical comparisons most successfully when they were provided fully visible problems and solutions (i.e., when all problems and solutions were available visually, as opposed to being available partially, as when only the problem and not the solution are visible; Matlen et al, 2018).…”

Section: Visual Supportmentioning

confidence: 99%

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Development of Analogical Reasoning: A Novel Perspective From Cross‐Cultural Studies

Christie

2020

Child Dev Perspectives

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Analogical reasoning allows children to generate new abstractions from experience, which drives early learning. But our current understanding of analogical learning is based primarily on evidence from the West, and new data from Asia seem to call into question that information. In this article, we describe our finding that East Asian children do not share their Western peers’ strong bias for object similarity—often cited as the major reason for difficulties in relational reasoning. We analyze how this difference affects the ways analogy shapes learning in different cultures, such as what children use as base analogs and their likelihood of using comparison that results in relational abstraction. We also address cross‐cultural differences, which are evident in classroom contexts, since teachers from the United States and East Asia use analogy differently. Overall, cross‐cultural data are necessary to answer critical questions in theories of analogical learning; in this article, we chart pressing research questions and look ahead at directions for the field.

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Section: Gesturesmentioning

confidence: 66%

Section: Analogy As An Instructional Tool In Classroomsmentioning

confidence: 99%

Section: Visual Supportmentioning

confidence: 99%

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Development of Analogical Reasoning: A Novel Perspective From Cross‐Cultural Studies

Christie

2020

Child Dev Perspectives

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“…The results showed that even though there were different errors in solving the geometric tasks in each category of spatial intelligence, learners with low spatial intelligence often made errors in their solutions due to deficiencies in their visual abilities. This means that learners with low spatial intelligence were unable to see unseen features embedded in geometric tasks, limiting their ability to draw relational structures and connections about the tasks, to aid their understanding (Arcavi, 2003;Matlen et al, 2018).…”

Section: Spatial Abilitymentioning

confidence: 99%

“…Those who were able to solve the task used appropriate words about the governing properties of the parallelogram. Success and proficient geometric thinking rely on the ability to identify the properties related to the task's structure, through which geometric properties are connected to the visual properties of the tasks (Matlen et al, 2018;Ndlovu, 2014). The successful participants seemed to produce properties based on how they individualised and interpreted the task.…”

mentioning

confidence: 99%

An analysis of pre-service mathematics teachers’ geometric thinking and classroom discourse using a commognitive lens.

Larbi

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five keywords from the following Abstract: Learning geometry equips learners with cognitive skills such as visualisation, critical thinking, spatial reasoning and problem-solving abilities, that are necessary for learning mathematics in general. However, geometry is noted to be difficult for learning as well as teaching. An investigation of this difficulty, especially with teachers, will help address its teaching and learning. The purpose of this study was to analyse pre-service teachers’ geometric thinking and classroom discourse using the commognitive lens. The study was guided by three objectives, which were to analyse the pre-service teachers' discursive thinking in geometry; the nature of their routine thinking in solving the geometric tasks, and how these informed their classroom geometric discourse. The study aligned itself to the qualitative approach and was underpinned by the interpretivist research paradigm. Eight pre-service teachers who were second-year university students and had taken geometry as part of their programme modules, participated in the study. The study site was conveniently selected, whilst the participants were selected on purposively. Geometry worksheet (test), interview and classroom observation, were used to generate written, verbal (oral) response, and visual data in relation to the study objectives. The data was analysed using the themes of the commognitive framework. The results show that both literate and colloquial word use were found in the discourses of the pre-service teachers. Many participants in Group A used more literate words to define and explain geometric concepts and how they solved the geometry problems, than the participants in Group B, who used both literate and colloquial words. Also, the routine solution strategies of many in Group A showed more of an explorative way of thinking compared to those in Group B, who demonstrated more of a ritualised way of thinking. In addition, multiple solutions to tasks were found by many of Group A participants than those in Group B. Generally, many of the study participants demonstrated limited geometric thinking. Misconceptions were evident in the discourses of some pre-service teachers in both groups. Other key findings from the classroom observation were that, many participants in Group A demonstrated an explorative instruction that is characterised by developing learner understanding and using different kinds of visual mediators as compared to participants in Group B, whose classroom geometric discourse was ritualised in nature. In other words, their teaching was more procedure-driven than conceptual. The study concludes that many of the PSTs possess limited geometric thinking. In addition, those who possessed good geometric thinking were more capable of engaging learners in explorative instruction compared to those with limited geometric thinking. These findings may have an influence on mathematics teacher educators’ efforts to develop teaching competence among pre-service teachers.

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From One Language to the Next: Applications of Analogical Transfer for Programming Education

Kao

Matlen

Weintrop

2022

ACM Trans. Comput. Educ.

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The 1980s and 1990s saw a robust connection between computer science education and cognitive psychology as researchers worked to understand how students learn to program. More recently, academic disciplines such as science and engineering have begun drawing on cognitive psychology research and theories of learning to create instructional materials and teacher professional development materials based on theories of learning, to some success. In this paper, we follow a similar approach by highlighting common areas of interest between computer science education and cognitive psychology–specifically theories of analogical transfer–and discuss how cross-pollination of theoretical constructs between disciplines can support research on the teaching and learning of multiple programming languages. We will also discuss areas where computing education research can adapt the existing theories from cognitive psychology to develop domain-specific theories of knowledge transfer in computing and feed back into cognitive psychology research to inform larger debates about the nature of cognition and learning.

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Impact and Prevalence of Diagrammatic Supports in Mathematics Classrooms

Cited by 3 publications

References 26 publications

Development of Analogical Reasoning: A Novel Perspective From Cross‐Cultural Studies

Development of Analogical Reasoning: A Novel Perspective From Cross‐Cultural Studies

An analysis of pre-service mathematics teachers’ geometric thinking and classroom discourse using a commognitive lens.

From One Language to the Next: Applications of Analogical Transfer for Programming Education

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