Automatic deduction in (dynamic) geometry: Loci computation

Botana, Francisco; Abánades, Miguel A.

doi:10.1016/j.comgeo.2013.07.001

Cited by 9 publications

(6 citation statements)

References 38 publications

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“…As a result, this circumstance will lower their motivation level and their performance in the academic level as well. To date, many researchers have conducted researches on GeoGebra on attitudes towards the technology in education in many topics such as Geometry (Botana & Abánades, (2014), Intergers (Reisa, 2010), Trigonometry (Zengin, Furkan, & Kutluca, 2012), Calculus (Volk & Yip, 1999), Algebra (Hohenwarter & Fuchs, 2004;Hohenwarter & Jones, 2007). But researches on specific topics like Loci in Two Dimensions still as countable as the fingers on one hand.…”

Section: Introductionmentioning

confidence: 99%

Attitude of Secondary Students towards the Use of GeoGebra in Learning Loci in Two Dimensions

Rajagopal¹,

Ismail²,

Ali³

et al. 2015

IES

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The use of computer software has good chance to form an efficient and powerful learning among the students. On the other hand, using open source software to teach mathematics in the school system of Malaysia, particularly in secondary school is still an uncertain issue. As a result, in an attempt to bring in a freeware, GeoGebra, this paper studies the attitude of form two students towards the utilization of GeoGebra in learning Loci in Two Dimensions. This study was conducted with 30 form two students from a secondary school in Johor Bharu district. In the beginning, GeoGebra was used to teach Loci in Two Dimensions and then followed by a survey. Questionnaires were provided to investigate the attitude of the students towards GeoGebra. A research model which was modified from the Technology Acceptance Model (TAM) was used to develop the questionnaires in order to study the students' attitude. Later on, the data were analyzed by using Statistical Packages for Social Sciences 19.0 (SPSS) software to find the correlation coefficient and regression results. The result revealed that the students showed positive attitudes towards the use of GeoGebra in learning Loci in Two Dimensions. At the same time, there was a significant relationship between perceived ease of use, perceived usefulness and attitude of students towards GeoGebra. This positive attitude of students will bring to positive behavioral intention to use GeoGebra in the future. At last, the implication of the research and recommendations for the future research also are discussed in this paper.

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Section: Introductionmentioning

confidence: 99%

Attitude of Secondary Students towards the Use of GeoGebra in Learning Loci in Two Dimensions

Rajagopal¹,

Ismail²,

Ali³

et al. 2015

IES

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“…In [10] Botana and Abánades write the following definition of ADG, "as the study and development of computer programs designed to prove geometry theorems". Then they traced the domain back to 1963 when Gelernter [49] connected it to Artificial Intelligence.…”

Section: Cognitive Neighborhood Of a Mathematical Notionmentioning

confidence: 99%

Computer Assisted Proofs and Automated Methods in Mathematics Education

Dana-Picard

2023

Electron. Proc. Theor. Comput. Sci.

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This survey paper is an expanded version of an invited keynote at the ThEdu '22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in Mathematics Education, and in the broader frame of STEAM Education. In particular, we discuss the transformation of Mathematics Education into explorationdiscovery-conjecture-proof scheme, avoiding usage as a black box . This scheme fits well into the so-called 4 C's of 21st Century Education. Communication and Collaboration are emphasized not only between humans, but also between machines, and between man and machine. Specific characteristics of the outputs enhance the need of Critical Thinking. The usage of automated commands for exploration and discovery is discussed, with mention of limitations where they exist. We illustrate the topic with examples from parametric integrals (describing a "cognitive neighborhood" of a mathematical notion), plane geometry, and the study of plane curves (envelopes, isoptic curves). Some of the examples are fully worked out, others are explained and references are given.

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“…A locus or envelope construction is described by a polynomial system The fact that for all elements in a segment the types of system solutions are the same (finite, infinite or no solution) helps to decide about the membership of each segment to the sought locus or envelope. Since a detailed description of the procedure is in [17] and the goal of this note is the illustration of new GeoGebra abilities by means of SingularWS, we will use it here without further explanation.…”

Section: The Groebnercover Algorithmmentioning

confidence: 99%

A Singular web service for geometric computations

Botana

Kovács

2014

Ann Math Artif Intell

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Outsourcing algebraic computations in dynamic geometry is a possible strategy used when software distribution constraints apply. Either if the target user machine has hardware limitations, or if the computer algebra system cannot be easily (or legally) packaged inside the geometric software, this approach can solve current shortcomings in dynamic environments. We report the design and implementation of a web service using Singular, a program specialized in ideal theory and commutative algebra. Besides its canonical address, a virtual appliance and a port to a low-cost ARM based computer are also provided. Any interactive geometric environment can then outsource computations where Singular is used, and incorporate their results into the system. In particular, we illustrate the capabilities of the web service by extending current abilities of GeoGebra to deal with algebraic loci and envelopes by means of a recent algorithm for studying parametric polynomial systems.

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Automatic deduction in (dynamic) geometry: Loci computation

Cited by 9 publications

References 38 publications

Attitude of Secondary Students towards the Use of GeoGebra in Learning Loci in Two Dimensions

Attitude of Secondary Students towards the Use of GeoGebra in Learning Loci in Two Dimensions

Computer Assisted Proofs and Automated Methods in Mathematics Education

A Singular web service for geometric computations

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