Pub Date : 2023-12-18DOI: 10.1080/0020739x.2023.2289794
Brian Winkel
{"title":"Using modelling to motivate and teach differential equations","authors":"Brian Winkel","doi":"10.1080/0020739x.2023.2289794","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2289794","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":" 7","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138995307","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}
Pub Date : 2023-12-18DOI: 10.1080/0020739x.2023.2290627
Zahra Pourazima, Vahid Borji, Hassan Alamolhodaei
{"title":"Third-grade students’ strategies for presenting permutations of three or four objects","authors":"Zahra Pourazima, Vahid Borji, Hassan Alamolhodaei","doi":"10.1080/0020739x.2023.2290627","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2290627","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":" 5","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138963547","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}
Pub Date : 2023-12-10DOI: 10.1080/0020739x.2023.2288818
Wes Maciejewski
{"title":"Flexibility of differentiation procedures in calculus","authors":"Wes Maciejewski","doi":"10.1080/0020739x.2023.2288818","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2288818","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"14 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138982001","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}
Pub Date : 2023-12-10DOI: 10.1080/0020739x.2023.2288822
K. Arnesen, A. Valenta
{"title":"Lesson plays as an approach to learning to teach proving","authors":"K. Arnesen, A. Valenta","doi":"10.1080/0020739x.2023.2288822","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2288822","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"671 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138982615","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}
Pub Date : 2023-12-10DOI: 10.1080/0020739x.2023.2289068
Peter Rowlett, Chris Graham, Christian Lawson-Perfect
{"title":"Demonstration of a partially automated assessment approach to create an individualised, open-ended modelling worksheet","authors":"Peter Rowlett, Chris Graham, Christian Lawson-Perfect","doi":"10.1080/0020739x.2023.2289068","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2289068","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"25 9","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138982031","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}
Pub Date : 2023-12-05DOI: 10.1080/0020739x.2023.2283346
V. Hatisaru
{"title":"Mathematical connections – a growing construct","authors":"V. Hatisaru","doi":"10.1080/0020739x.2023.2283346","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2283346","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"111 8","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138599972","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}
Pub Date : 2023-11-17DOI: 10.1080/0020739X.2023.2282343
Dr Colin Foster, Dr. M. McCartney, Professor G. Oates, Dr. Katherine Seaton, Professor S. Abramovich, Professor B. Bradie, Dr Cornelia Connolly, Professor T. Dana-Picard – Applied, Mathematics, Dr Peter Dunn, Professor J. Engelbrecht, Professor M. Goos, Dr Suzanne E. Hiller, Professor B. Loch, Dr. Elizabeth Lugosi, Dr. Andrea Maffia, Dr. Alan McCarthy, Dr L. Rylands, Professor A. G. Shannon, Dr Giovanni Vincenzi, Professor L. Wood, Professor R. Zazkis, Avi C. Bajpai, W. T. Martin, M. Harrison
{"title":"International Journal of Mathematical Education in Science and Technology","authors":"Dr Colin Foster, Dr. M. McCartney, Professor G. Oates, Dr. Katherine Seaton, Professor S. Abramovich, Professor B. Bradie, Dr Cornelia Connolly, Professor T. Dana-Picard – Applied, Mathematics, Dr Peter Dunn, Professor J. Engelbrecht, Professor M. Goos, Dr Suzanne E. Hiller, Professor B. Loch, Dr. Elizabeth Lugosi, Dr. Andrea Maffia, Dr. Alan McCarthy, Dr L. Rylands, Professor A. G. Shannon, Dr Giovanni Vincenzi, Professor L. Wood, Professor R. Zazkis, Avi C. Bajpai, W. T. Martin, M. Harrison","doi":"10.1080/0020739X.2023.2282343","DOIUrl":"https://doi.org/10.1080/0020739X.2023.2282343","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"39 2","pages":"i - iv"},"PeriodicalIF":0.9,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139265358","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}
Pub Date : 2023-11-08DOI: 10.1080/0020739x.2023.2268101
Ana Isabel Sacristán, Marisol Santacruz-Rodríguez
AbstractThis paper reports some results of a study on how Colombian primary-school teachers, experienced in the use of technological tools, integrate digital resources into their practice. Specifically, we investigate the processes of selection and integration (including appropriation and orchestration) of these resources in the teaching of geometry. We aim to illustrate the potential paths (along with associated criteria) that teachers follow when selecting and integrating digital resources into their practice, using the Documentational Approach to Didactics. Accordingly, we present case studies of a 1st-grade teacher and a 5th-grade teacher, which describe their paths during their respective geometry lessons. The paths followed by the teachers were influenced by their knowledge and beliefs regarding the utilisation of digital technology resources and the potential student engagement with such resources. All these aspects come into play as teachers select and orchestrate digital resources. Our empirical data analysis enabled us to infer several criteria for resource selection and levels of orchestration and appropriation manifested by the teachers as they integrated digital resources into their classes. This work can provide valuable insights for further exploration of how teachers integrate digital resources, and can contribute to the development of professional development programmes.Keywords: Teachers’ practicesprimary-schoolgeometrydigital resourcesselectionappropriationorchestrationDocumentational Approach to Didactics AcknowledgmentsThe authors thank Prof. Luc Trouche for his help in preparing the initial version of this document.We also acknowledge that the research presented in this paper was ethically approved by the Colombian schools where it took place, after written and oral presentations to the authorities, parents and participants. The research project was also approved by the Department of Mathematics Education of the Centre for Research and Advanced Studies (Cinvestav), Mexico. Additionally, all research participants in our study provided their informed signed consent, although the names given in this paper are pseudonyms.Partial funding for the research study was provided by Mexico’s National Council for Research and Technology (CONACYT), through the Becario #678019 grant.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThis work was supported by Mexico's Consejo Nacional de Ciencia y Tecnologia (Conacyt): [Grant Number Becario 678019].
{"title":"Paths of integration of digital resources for geometry by two primary-school teachers","authors":"Ana Isabel Sacristán, Marisol Santacruz-Rodríguez","doi":"10.1080/0020739x.2023.2268101","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2268101","url":null,"abstract":"AbstractThis paper reports some results of a study on how Colombian primary-school teachers, experienced in the use of technological tools, integrate digital resources into their practice. Specifically, we investigate the processes of selection and integration (including appropriation and orchestration) of these resources in the teaching of geometry. We aim to illustrate the potential paths (along with associated criteria) that teachers follow when selecting and integrating digital resources into their practice, using the Documentational Approach to Didactics. Accordingly, we present case studies of a 1st-grade teacher and a 5th-grade teacher, which describe their paths during their respective geometry lessons. The paths followed by the teachers were influenced by their knowledge and beliefs regarding the utilisation of digital technology resources and the potential student engagement with such resources. All these aspects come into play as teachers select and orchestrate digital resources. Our empirical data analysis enabled us to infer several criteria for resource selection and levels of orchestration and appropriation manifested by the teachers as they integrated digital resources into their classes. This work can provide valuable insights for further exploration of how teachers integrate digital resources, and can contribute to the development of professional development programmes.Keywords: Teachers’ practicesprimary-schoolgeometrydigital resourcesselectionappropriationorchestrationDocumentational Approach to Didactics AcknowledgmentsThe authors thank Prof. Luc Trouche for his help in preparing the initial version of this document.We also acknowledge that the research presented in this paper was ethically approved by the Colombian schools where it took place, after written and oral presentations to the authorities, parents and participants. The research project was also approved by the Department of Mathematics Education of the Centre for Research and Advanced Studies (Cinvestav), Mexico. Additionally, all research participants in our study provided their informed signed consent, although the names given in this paper are pseudonyms.Partial funding for the research study was provided by Mexico’s National Council for Research and Technology (CONACYT), through the Becario #678019 grant.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThis work was supported by Mexico's Consejo Nacional de Ciencia y Tecnologia (Conacyt): [Grant Number Becario 678019].","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135393169","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}
Pub Date : 2023-10-31DOI: 10.1080/0020739x.2023.2259388
Jean Marie Linhart
AbstractThe historic total global human population dataset is available on Wikipedia and provides an opportunity for modelling with simple models such as the exponential and logistic differential equations for population. Using the per-capita population growth rate (PPGR) predicted by these two models and estimated PPGR from the data, we are able to estimate parameters for the exponential model and discover that we cannot estimate parameters for the logistic model. However, we are able to create a new differential equation that models this data using ideas from the derivation of the logistic model. This is the superexponential model that goes to infinity in finite time. While the initial exponential and superexponential models are good for approximating the population data, neither really matches the PPGRs estimated from the data. We switch to a hybrid model that better matches the estimated PPGRs. It is superexponential for the first portion of the data and logistic for the rest. This hybrid model greatly reduces the modelling error and can extrapolate from the data. We note that the model switches between superexponential and logistic around 1960, the year the FDA-approved oral contraceptives, a fascinating historical tie-in with our modelling.KEYWORDS: Populationper-capita population growth ratelogistic modelexponential modelsuperexponential modelMATHEMATICAL SUBJECT CLASSIFICATIONS: 97M1092-10 Disclosure statementNo potential conflict of interest was reported by the author.
{"title":"Modelling the historic total global human population","authors":"Jean Marie Linhart","doi":"10.1080/0020739x.2023.2259388","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2259388","url":null,"abstract":"AbstractThe historic total global human population dataset is available on Wikipedia and provides an opportunity for modelling with simple models such as the exponential and logistic differential equations for population. Using the per-capita population growth rate (PPGR) predicted by these two models and estimated PPGR from the data, we are able to estimate parameters for the exponential model and discover that we cannot estimate parameters for the logistic model. However, we are able to create a new differential equation that models this data using ideas from the derivation of the logistic model. This is the superexponential model that goes to infinity in finite time. While the initial exponential and superexponential models are good for approximating the population data, neither really matches the PPGRs estimated from the data. We switch to a hybrid model that better matches the estimated PPGRs. It is superexponential for the first portion of the data and logistic for the rest. This hybrid model greatly reduces the modelling error and can extrapolate from the data. We note that the model switches between superexponential and logistic around 1960, the year the FDA-approved oral contraceptives, a fascinating historical tie-in with our modelling.KEYWORDS: Populationper-capita population growth ratelogistic modelexponential modelsuperexponential modelMATHEMATICAL SUBJECT CLASSIFICATIONS: 97M1092-10 Disclosure statementNo potential conflict of interest was reported by the author.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"127 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135927889","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}
Pub Date : 2023-10-29DOI: 10.1080/0020739x.2023.2268076
Klára Kelecsényi, Éva Osztényiné Krauczi, Attila Végh
AbstractThe study examines the levels of understanding logarithmic expressions within the frames of a mathematical card game. The game is based on the popular card game Saboteur. In this paper, we analyse the progress of a group of six undergraduate students participating in a remedial course using games for recalling some fundamental mathematical concepts. The context of the game allowed us to observe and rank their levels of understanding logarithm and the change of these levels during the game.KEYWORDS: Games and mathematicsunderstandinglogarithmcard gamesAPOS theorySubject classification codes: 97C30 Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 PhotoMath is a freely available mobile application for solving mathematical problems. It identifies the handwritten problem, provides the detailed solution and the corresponding explanations.
{"title":"Understanding logarithm in a mathematical card game environment","authors":"Klára Kelecsényi, Éva Osztényiné Krauczi, Attila Végh","doi":"10.1080/0020739x.2023.2268076","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2268076","url":null,"abstract":"AbstractThe study examines the levels of understanding logarithmic expressions within the frames of a mathematical card game. The game is based on the popular card game Saboteur. In this paper, we analyse the progress of a group of six undergraduate students participating in a remedial course using games for recalling some fundamental mathematical concepts. The context of the game allowed us to observe and rank their levels of understanding logarithm and the change of these levels during the game.KEYWORDS: Games and mathematicsunderstandinglogarithmcard gamesAPOS theorySubject classification codes: 97C30 Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 PhotoMath is a freely available mobile application for solving mathematical problems. It identifies the handwritten problem, provides the detailed solution and the corresponding explanations.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"21 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136134887","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}
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