Authority and whole-class proving in high school geometry: The case of Ms. Finley

Otten, Samuel; Bleiler-Baxter, Sarah K.; Engledowl, Christopher

doi:10.1016/j.jmathb.2017.04.002

Cited by 17 publications

(14 citation statements)

References 34 publications

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“…Learners across the spectrum of grade levels experience challenges in relation to mathematical reasoning in: 1) recalling of prior knowledge regarding definitions in spatial objects; 2) comprehending mathematical statements; 3) manipulating statements to make sense; 4) blending of mathematical concepts; and 5) validating blended mathematical statements (Otten, Bleiler-Baxter & Engledowl, 2017). These challenges, on the one hand, emanate from misunderstanding the tenets of mathematical reasoning and on the other hand, it is from learners' inabilities to prove mathematical statements using, analogies, deductions and induction (Amir-Mofidi, Amiripour, & Bijanzadeh, 2012;Yopp, 2015).…”

Section: Mathematical Reasoningmentioning

confidence: 99%

“…The third category requires learners to validate blended mathematical statements (Lee, 2016). Otten et al (2017) contend that teachers promote procedural rules of proof, but not the logic regarding the connection of mathematics concepts. Such a trichotomy on mathematical reasoning is problematic because it conflates mathematical reasoning and reduces it to mere proofs.…”

Section: Eurasia J Math Sci and Tech Edmentioning

confidence: 99%

“…In most classrooms, only procedures of proofs are taught, which conflates proofs to a reproduction of theorems (Otten et al, 2017). Consequently, learners grapple when recalling and manipulating properties of spatial figures (Fujita, Kondo, Kumakura & Kunimune, 2017;Heyd-Metzuyanim, Munter & Greeno, 2018).…”

Section: Geometry Spatial Reasoningmentioning

confidence: 99%

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Exploring Grade Nine Geometry Spatial Mathematical Reasoning in the South African Annual National Assessment

Dhlamini

Chuene

Masha

et al. 2019

EURASIA J MATH SCI T

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The purpose of this study was to explore geometry spatial mathematical reasoning in Grade nine Annual National Assessments, South Africa. Conceptual Blending was the guiding theory. Document analysis within the exploratory case study was used to explore available data, the 2014 Annual National Assessment learners' scripts (n=1250). Results revealed that on average 70.5 percent of the total number of learners remembered and blended irrelevant prior knowledge not reflective to the contexts of the geometry problems. For learners who recalled the correct prior knowledge, its manipulation was either fragmented or irrelevant. The use of recalled information in wrong contexts could be due to the incorrect manipulation of the meaning of the problems. Also, responses reveal challenges on the quality of mathematics education on geometry. Therefore, the teaching and learning of geometry should focus on empowering learners with skills of recalling, blending and on manipulating problems in their contexts.

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Section: Mathematical Reasoningmentioning

confidence: 99%

Section: Eurasia J Math Sci and Tech Edmentioning

confidence: 99%

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Exploring Grade Nine Geometry Spatial Mathematical Reasoning in the South African Annual National Assessment

Dhlamini

Chuene

Masha

et al. 2019

EURASIA J MATH SCI T

View full text Add to dashboard Cite

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“…Regarding the individual actions in a proof, specifically in geometry, Otten, Bleiler-Baxter, and Engledowl (2017) studied authority in a high school geometry classroom by investigating actions occurred during proving process. Otten and colleagues developed a framework (Figure 2.4) to code actions employed by the classroom teacher and students in a high school geometry classroom setting.…”

Section: Sample Proving Frameworkmentioning

confidence: 99%

“…Otten and colleagues developed a framework (Figure 2.4) to code actions employed by the classroom teacher and students in a high school geometry classroom setting. Although this framework was used for the teacher-student interaction during proving, it was also claimed that it might serve for the analysis of students' actions while proving (Otten et al, 2017). The frameworks discussed thus far highlighted the stages that may be involved in a typical proving process, and particularly the framework developed by Otten and colleagues (2017) is utilized for this study since it provides a practical scheme for coding actions that appear moment by moment in the proving process.…”

Section: Sample Proving Frameworkmentioning

confidence: 99%

High school students interpretations and use of diagrams in geometry proofs

Karaman¹

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In high school geometry, proving theorems and applying them to geometry problems is an expectation from high school students (CCSSI, 2010). Diagrams are considered as an essential part of the geometry proofs because diagrams are included in a typical geometric statement such as a claim or problem (Manders, 2008; Shin et al., 2001). This interview-based study investigated how high school students interpret and use diagrams during the process of proving geometric claims. Particular attention is given to the semiotic resources such as symbols, visuals, and gestures that students draw from the diagrams to develop their proving activities. Hence, the goal of the current study is to contribute to the mathematics education field by providing insights into the details of semiotic aspects of diagrammatic reasoning. Study participants were grade 10-12 high school students and data was collected through one-on-one task- based clinical interviews. In general, students focused on the figural properties of the diagrams more frequently than the conceptual properties of the diagrams in their proofs even when they produced a new diagram or multiple diagrams. Regarding the semiotic structure of students' proving process, gesture resources were prominent in the semiotic structure of students' proving process in diagram-given tasks. The findings also suggested that, in general, some visual resources such as drawing a new figure or multiple figures occurred regularly in particular tasks such as diagram-free tasks with non- diagrammatic register or truth-unknown features. Overall, the frameworks used in this study showed how important it is to consider the mathematics as multi semiotic, understanding the role of gestures in students' geometrical reasoning.

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