Assessing high school students’ understanding of geometric proof

McCrone, Sharon; Martin, Tami S.

doi:10.1080/14926150409556607

Cited by 33 publications

(30 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It seems that even if students might be able to construct a correct proof, they may still verify its correctness via empirical data (e.g., Harel & Sowder, 2007), and when asked to produce a proof they tend to construct an empirical-numeric proof (Stylianou, Blanton, & Rotou, 2015). Paralleling this evidence is research reporting that students at school, or even at undergraduate level, show difficulties when they try to read proofs that have been provided for them (e.g., Inglis & Alcock, 2012;Lin & Yang, 2007), when they are asked to judge the suitability of a proof (e.g., Hoyles & Healy, 2007), and when they are asked to write deductive proofs (e.g., McCrone & Martin, 2004;Senk, 1989).…”

Section: Introductionmentioning

confidence: 81%

Students’ understanding of the structure of deductive proof

2016

View full text Add to dashboard Cite

While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the structure of deductive proofs and, in this paper, we propose a theoretical framework based on this aspect of proof education. In our framework, we capture students' understanding of the structure of deductive proofs in terms of three levels of increasing sophistication: Prestructural, Partial-structural, and Holistic-structural, with the Partial-structural level further divided into two sub-levels: Elemental and Relational. In this paper, we apply the framework to data from our classroom research in which secondary school students (aged 14) tackled a series of lessons that provided an introduction to proof problems involving congruent triangles. Using data from the transcribed lessons, we focus in particular on students who displayed the tendency to accept a proof that contained logical circularity. From the perspective of our framework, we illustrate what we argue are two independent aspects of Relational understanding of the Partial-structural level, those of universal instantiation and hypothetical syllogism, and contend that accepting logical circularity can be an indicator of lack of understanding of syllogism. These findings can inform how teaching approaches might be improved so that students develop a more secure understanding of deductive proofs and proving in geometry.

show abstract

Section: Introductionmentioning

confidence: 81%

Students’ understanding of the structure of deductive proof

2016

View full text Add to dashboard Cite

show abstract

“…Studies show that both secondary teachers and students have encountered challenges in teaching and learning proofs (Cirillo, 2009;Knuth, 2002;McCrone & Martin, 2004; National Center for Education Statistics (NCES), 1998; Senk, 1985). In order to develop knowledge about pre-service secondary mathematics teachers' (PSMTs) conceptions of theorems and provide mathematics educators and researchers with a possible means to unpack their conceptions, the researcher investigated the essential elements of four PSMTs' conceptions of the nature of theorems (NoT) through research-informed task-based interviews in 2016-2017.…”

Section: Recommended Citationmentioning

confidence: 99%

“…For example, understanding of the axiomatic system of Euclidean geometry is ranked as higher level geometric thinking by the van Hiele levels (van Hiele, 1959). Despite the important role of proof and theorems in school mathematics, many secondary students have difficulty in writing valid geometry proofs (McCrone & Martin, 2004;NCES, 1998;Senk, 1985). Their difficulties may relate to incomplete conceptions or confusion about proof and theorems, such as accepting empirical evidence as formal proofs, questioning the generalizability of deductive reasoning, not accepting counterexamples as refutation, and overemphasizing the forms without logical coherence in proofs (Chazan, 1993;McCrone & Martin, 2004;Schoenfeld, 1994;Weber, 2001).…”

Section: Literature Review Challenges In Learning and Teaching Proof mentioning

confidence: 99%

“…Despite the important role of proof and theorems in school mathematics, many secondary students have difficulty in writing valid geometry proofs (McCrone & Martin, 2004;NCES, 1998;Senk, 1985). Their difficulties may relate to incomplete conceptions or confusion about proof and theorems, such as accepting empirical evidence as formal proofs, questioning the generalizability of deductive reasoning, not accepting counterexamples as refutation, and overemphasizing the forms without logical coherence in proofs (Chazan, 1993;McCrone & Martin, 2004;Schoenfeld, 1994;Weber, 2001). Studies also show that teachers' conceptions, knowledge, and prior learning experiences of proof and theorems can have significant impact on their teaching of proof and theorems and thus affect their students' understanding and achievement in learning proof and theorems (Cirillo, 2009;Knuth, 2002;Lacourly & Varas, 2009;Oehrtman & Lawson, 2008;Rozner, Noblet, & SotoJohnson, 2010).…”

Section: Literature Review Challenges In Learning and Teaching Proof mentioning

confidence: 99%

“…The researcher created a set of principles of theorems which served as the conceptual framework for the development of the data collection instrument: task-based interviews. The principles were developed by incorporating Cirillo's (2014) conceptual model of mathematical proof tools, Dreyfus and Hadas' (1987) six logical principles of geometry theorems and proofs with additional revisions by McCrone and Martin (2004), and Duval's (2007) indicators of misunderstandings in proof writing. The principles of theorems included three aspects: (a) nature of theorems (NoT), (b) logic of theorems (LoT), and (c) application of theorems (AoT).…”

Section: Conceptual Framework For Task Designmentioning

confidence: 99%

See 2 more Smart Citations

Volume 2. Proceedings of the Interdisciplinary STEM Teaching and Learning Conference

2018

stem

View full text Add to dashboard Cite

Full version of volume 2 of the Proceedings of the Interdisciplinary STEM Teaching and Learning ConferenceThis complete issue is available in Proceedings of the Interdisciplinary STEM Teaching and Learning Conference:https://digitalcommons.georgiasouthern.edu/stem_proceedings/vol2/iss1/1 Conference Proceedings AbstractSpatial reasoning is defined as the ability to generate, retain, and manipulate abstract visual images. In chemistry, spatial reasoning skills are typically taught using 2-D paper-based models, 3-D handheld models, and computerized models. These models are designed to aid student learning by integrating information from the macroscopic, microscopic, and symbolic domains of chemistry. Research has shown that increased spatial reasoning abilities translate directly to improved content knowledge. The recent explosion in the popularity of smartphones and the development of augmented reality apps for them provide, a yet to be explored, way of teaching spatial reasoning skills to chemistry students. Augmented reality apps can use the camera on a smartphone to turn 2-D paper-based molecular models into 3-D models the user can manipulate. This paper will discuss the development, implementation, and assessment of an augmented reality app that transforms 2-D molecular representations into interactive 3-D structures.

show abstract

Proving in Geometry: A Sociocultural Approach to Constructing Mathematical Arguments Through Multimodal Literacies

Taylor¹

2018

J Adolescent & Adult Lit

View full text Add to dashboard Cite

Multimodal literacies have been incorporated as social learning practices in content areas, but research regarding multimodality within secondary mathematics instruction has often lacked the sociocultural lens. The author describes practitioner action research in the form of a case study (with one focal participant) from a public high school. The author explored the use of multimodal literacies through geometry students’ projects, work samples, classroom videos, and interviews. Students created and presented arguments (through PowerPoint, Word, videos, and storybooks) on court cases in efforts to relate proving and justifying in geometry to evidence and claims in court. Findings reveal ways that multimodal literacies served as a vehicle for students to engage with their social context of learning in a mathematics classroom, demonstrating that sociocultural approaches to multimodal literacies can apprentice students into disciplinary literacy practices of mathematics. Moreover, these sociocultural perspectives toward multimodal literacies pose possible instructional applications in multiple content areas.

show abstract

Assessing high school students’ understanding of geometric proof

Cited by 33 publications

References 8 publications

Students’ understanding of the structure of deductive proof

Students’ understanding of the structure of deductive proof

Volume 2. Proceedings of the Interdisciplinary STEM Teaching and Learning Conference

Proving in Geometry: A Sociocultural Approach to Constructing Mathematical Arguments Through Multimodal Literacies

Contact Info

Product

Resources

About