Technology and the Role of Proof: The Case of Dynamic Geometry

Sinclair, Nathalie; Robutti, Ornella

doi:10.1007/978-1-4614-4684-2_19

Cited by 35 publications

(23 citation statements)

References 38 publications

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“…Stacey and Wiliam (2013) state that dynamic geometry programs allow students to "demonstrate a wide range of abilities" (p. 745). It stands to reason that they could also be used to reveal a teacher's abilities to experiment, investigate, make and test hypotheses, and create proofs (Sinclair and Robutti 2013). Also, there is a body of literature which states that when the virtual manipulative is designed so that the users can explore it (e.g., move it, change its features and parameters), its users may achieve more than when using physical manipulatives, although for the largest effect, it is advisable to combine virtual and physical manipulatives in mathematics teaching (Moyer-Packenham and Westenskow 2013).…”

Section: Virtual Manipulatives As Special Mathematics Machines or Digmentioning

confidence: 99%

Developing an Interactive Instrument for Evaluating Teachers’ Professionally Situated Knowledge in Geometry and Measurement

Manizade

Martinović

2016

International Perspectives on Teaching and Learning Mathematics With Virtual Manipulatives

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In this study, we propose a content specific, short, interactive, on-line, scenario-based instrument that incorporates virtual manipulatives developed in GeoGebra, as one of the many ways for evaluating and describing teachers' professionally situated knowledge (PSK) in the domains of geometry and measurement. To define PSK of mathematics teachers, we use a combination of Shulman's Pedagogical Content Knowledge (PCK) and its corresponding mathematical knowledge. We describe the methodology used to develop the instrument as well as the corresponding rubrics. The study design followed a concurrent mixed-methods approach, in which the quantitative and qualitative phases of data collection were intermingled to explore the research questions related to identifying components of the PSK. As a case study, we used PSK of the area of a trapezoid, since (a) this topic is familiar to most middle school and secondary mathematics teachers; and (b) a narrow focus was most advantageous when using Delphi methodology to draft an instrument, which was then fully developed using methods of grounded theory. This comprehensive approach led to a deep investigation of multiple and diverse data sources collected from practicing teachers, which we used to create their PSK profiles in the area of trapezoid.

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Section: Virtual Manipulatives As Special Mathematics Machines or Digmentioning

confidence: 99%

Developing an Interactive Instrument for Evaluating Teachers’ Professionally Situated Knowledge in Geometry and Measurement

Manizade

Martinović

2016

International Perspectives on Teaching and Learning Mathematics With Virtual Manipulatives

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“…The teacher plays an important role in moderating and leading classroom discussion by identifying necessary prompts, providing promising inputs, or taking advantage of "hiccups" (Clark-Wilson, 2010). Sinclair and Robutti (2013) reported the essential role of the teacher in two case studies in which the teacher helped students to make links between dynamic representations and theoretical geometry.…”

Section: Communication and Collaboration Through And Of Technologymentioning

confidence: 99%

Uses of Technology in Lower Secondary Mathematics Education

Drijvers

Ball

Barzel

et al. 2016

ICME-13 Topical Surveys

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Digital technology1 is omnipresent in society. Revolutionary technological developments change the character of professional environments, and therefore put new demands on workers (Hoyles, Noss, Kent, & Bakker, 2010). Consequently, there are new demands on educational systems in order to prepare students for future professions. Importantly, technology also offers opportunities for teaching and learning (see for example, Clark-Wilson, 2010;Sacristán et al. 2010); exploiting these opportunities requires rethinking educational paradigms and strategies. With the advent of such technology, the question arises as to what the impact on education and teaching practices should be in order to prepare the next generation of students for future careers.Both in professional practice and in personal life, it is particularly striking how digital technologies such as software-controlled engines, smart phones, tablets, and GPS devices rely on mathematical algorithms that are invisible to the user, but play essential roles "under the hood". Implications of these technology-rich environments have the potential to influence the nature of mathematics education and the concepts and skills that future students will possess.Roberts, Leung, and Lin (2013) comment on the complexity of the interplay between technology, mathematics, and education, noting that this complexity related to the use of tools in mathematics is not a phenomenon that is due to current technologies, but one that has been evident whenever people use tools in mathematics. The rapid development of digital technologies features new capabilities not even considered possible in the past. Despite advances in digital technologies, there is still strong value in using a combination of physical tools and digital technologies in mathematics education (Maschietto & Trouche, 2010). Different types of technologies are available for teaching mathematics, and different technologies are appropriate for different purposes. General technologies for communication, 1 To avoid constantly repeating the terms "digital technology" in this text we will often refer to "technology"; while doing so, we refer to digital technology in mathematics education.

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“…More research is needed on how other types of problems may or may not support the identification of the links between discursive apprehensions and the process of inferring new information about figures as a way of helping pre-service teachers construct essential relations between geometrical facts. Today, one Downloaded by [University of Massachusetts, Amherst] at 07:25 05 October 2014 particular new area of interest should be how configural reasoning is developed to solve geometrical proof problems in dynamic geometry environments, since these contexts can modify the learning of geometrical knowledge (Gómez-Chacón & Kuzniak, 2013;Sinclair & Robutti, 2013). In this context, it is possible that a conceptual control requiring explicit geometrical knowledge is needed to trigger configural reasoning.…”

Section: Discussionmentioning

confidence: 97%

Characteristics of Pre-Service Primary School Teachers’ Configural Reasoning

Llinares

Clemente

2014

Mathematical Thinking and Learning

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The goal of this study is to identify the characteristics of pre-service primary teachers' configural reasoning, understood as the relationships between concepts and figures set to solve geometrical proof problems. Ninety-seven primary teachers were asked to solve two geometrical proof problems in which a geometrical figure was provided. The results suggest the existence of two levels of the pre-service primary teachers' discursive organization. The first, when pre-service primary teachers link the geometrical facts to the figure by discursive apprehensions, and the second, when several geometrical facts are related by logical chains to infer new information. The identification of a relevant configuration and the way in which geometrical facts are logically organized from discursive apprehensions are key factors in the shift between these moments. We contend that these factors help to explain how the image component stimulates thought and how conceptual constraints control the formal rigor of the process.

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Technology and the Role of Proof: The Case of Dynamic Geometry

Cited by 35 publications

References 38 publications

Developing an Interactive Instrument for Evaluating Teachers’ Professionally Situated Knowledge in Geometry and Measurement

Developing an Interactive Instrument for Evaluating Teachers’ Professionally Situated Knowledge in Geometry and Measurement

Uses of Technology in Lower Secondary Mathematics Education

Characteristics of Pre-Service Primary School Teachers’ Configural Reasoning

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