Daila Silva Seabra de Moura Fonseca;Regina Helena de Oliveira Lino Franchi
{"title":"Exploring the convergence of sequences in the embodied world using GeoGebra","authors":"Daila Silva Seabra de Moura Fonseca;Regina Helena de Oliveira Lino Franchi","doi":"10.1093/teamat/hrw012","DOIUrl":"https://doi.org/10.1093/teamat/hrw012","url":null,"abstract":"This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts, with the use of software, to the understanding of the convergence of numerical sequences and to the transition of mathematical thinking from elementary to advanced. Such activities had an exploratory nature and were constructed based on the theoretical frameworks of Advanced Mathematical Thinking and the Three Worlds of Mathematics. For the data collection were used the recordings of the computer screens, audio recordings of the discussion between students, student records in the responses of the activities and field notes of the researchers. The data were analyzed considering relations between the embodiment of the concept of convergence and proceptualization processes and axiomatization and also considering the transition from elementary mathematical thinking to advanced. The results indicate that the activities enabled the formation of the mental image that the convergence of sequences occurs when the sequence terms are approaching a certain value, and thus propitiated the embodiment of the concept of convergence and established cognitive roots for formal definition of convergence by the limit and further theoretical development. They also indicate that relations between different representations were established, which contributed to abstraction of the concept of convergence of sequences and thus for the transition between elementary and advanced mathematical thinking.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 2","pages":"88-101"},"PeriodicalIF":0.8,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50311275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ana Maria D’azevedo Breda;José Manuel Dos Santos Dos Santos
{"title":"Complex functions with GeoGebra","authors":"Ana Maria D’azevedo Breda;José Manuel Dos Santos Dos Santos","doi":"10.1093/teamat/hrw010","DOIUrl":"https://doi.org/10.1093/teamat/hrw010","url":null,"abstract":"Complex functions, generally feature some interesting peculiarities, seen as extensions of real functions. The visualization of complex functions properties usually requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study and exploration of complex functions of one complex variable not only through the traditional techniques but also by the use of Domain Colouring techniques. Here, we will show how we can use GeoGebra to explore complex functions, using several representations obtained by the creation of new tools, which complement the ones already provided by this software. Our tools were designed to be used by students attending the first academic year of engineering or science courses. They can and should be used as an educational tool in collaborative learning environments. The main advantage in their use is the promotion of deductive reasoning (conjecture/proof) in individual terms, and the promotion of mathematical discussions in collective terms. In the literature review done so far, few references were found involving the study of this topic by the use of a single software.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 2","pages":"102-110"},"PeriodicalIF":0.8,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50311276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
da Fonseca, Regina Helena de Oliveira Lino Franchi
{"title":"Exploring the Convergence of Sequences in the Embodied World Using GeoGebra.","authors":"da Fonseca, Regina Helena de Oliveira Lino Franchi","doi":"10.1093/TEAMAT/HRW012","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRW012","url":null,"abstract":"This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts, with the use of software, to the understanding of the convergence of numerical sequences and to the transition of mathematical thinking from elementary to advanced. Such activities had an exploratory nature and were constructed based on the theoretical frameworks of Advanced Mathematical Thinking and the Three Worlds of Mathematics. For the data collection were used the recordings of the computer screens, audio recordings of the discussion between students, student records in the responses of the activities and field notes of the researchers. The data were analyzed considering relations between the embodiment of the concept of convergence and proceptualization processes and axiomatization and also considering the transition from elementary mathematical thinking to advanced. The results indicate that the activities enabled the formation of the mental image that the convergence of sequences occurs when the sequence terms are approaching a certain value, and thus propitiated the embodiment of the concept of convergence and established cognitive roots for formal definition of convergence by the limit and further theoretical development. They also indicate that relations between different representations were established, which contributed to abstraction of the concept of convergence of sequences and thus for the transition between elementary and advanced mathematical thinking.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 1","pages":"88-101"},"PeriodicalIF":0.8,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRW012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61090106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Angle concept: a high school and tertiary longitudinal perspective to minimize obstacles","authors":"M. Barabash","doi":"10.1093/TEAMAT/HRW008","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRW008","url":null,"abstract":"","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"36 1","pages":"31-55"},"PeriodicalIF":0.8,"publicationDate":"2016-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRW008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61090500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Teaching mathematics with intelligent support in natural language. Tertiary education students working with parametrized modelling activities","authors":"T. Rojano, Montserrat García-Campos","doi":"10.1093/TEAMAT/HRW009","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRW009","url":null,"abstract":"","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"36 1","pages":"18-30"},"PeriodicalIF":0.8,"publicationDate":"2016-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRW009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61090511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Students’ views of example generation tasks","authors":"S. Breen, A. O’Shea, Kirsten Pfeiffer","doi":"10.1093/TEAMAT/HRV017","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRV017","url":null,"abstract":"We report here on students’ views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we found that on the whole they viewed the example generation tasks as unfamiliar and sometimes difficult, but also as beneficial for promoting conceptual understanding and independent thinking. In addition, some students characterized these tasks as ‘the backwards ones’.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 1","pages":"27-40"},"PeriodicalIF":0.8,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRV017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61089819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Using DEWIS and R for multi-staged statistics e-Assessments","authors":"D. Rhys Gwynllyw;Iain S. Weir;Karen L. Henderson","doi":"10.1093/teamat/hrv018","DOIUrl":"https://doi.org/10.1093/teamat/hrv018","url":null,"abstract":"We demonstrate how the DEWIS e-Assessment system may use embedded R code to facilitate the assessment of students’ ability to perform involved statistical analyses. The R code has been written to emulate SPSS output and thus the statistical results for each bespoke data set can be generated efficiently and accurately using standard R routines. This enables students’ answers, generated from their application of SPSS, to be marked and appropriate feedback supplied back to them automatically. Staging is used between different parts of the e-Assessment to replicate the natural stages of a complete statistical analysis. This allows students the freedom to work away from the e-Assessment; they may view the relevant stage an unlimited number of times prior to submitting their answers for that stage. The technical challenges of setting up the e-Assessment in this way are discussed as well as the rationale for adopting this pioneering approach.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 1","pages":"14-26"},"PeriodicalIF":0.8,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrv018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50408598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Front matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 1","pages":"1-2"},"PeriodicalIF":0.8,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016818/8207914/08207919.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50305887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Subtleties of hidden quantifiers in implication","authors":"B. Shipman","doi":"10.1093/TEAMAT/HRV007","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRV007","url":null,"abstract":"Barbara Shipman is an Associate Professor and Distinguished Teaching Professor at the University of Texas at Arlington. She completed her doctoral studies in mathematics at the University of Arizona, where she initiated the Department’s student-led graduate seminar. Before coming to Texas, Dr. Shipman held a three-year position at the University of Rochester, New York. To complement her work at the interface of differential geometry and dynamical systems, she enjoys rethinking foundational concepts and definitions in new and insightful ways. Dr. Shipman has received support from the National Science Foundation, as well as many teaching awards, for her creative work in the classroom, including the 2010 Regents’ Outstanding Teaching Award from the University of Texas System.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 1","pages":"41-49"},"PeriodicalIF":0.8,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRV007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61089727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Back matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 1","pages":"1-2"},"PeriodicalIF":0.8,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016818/8207914/08207921.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50305886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}