International Journal of Mathematical Education in Science and Technology最新文献

{"title":"Generic examples in undergraduate topology: a case study","authors":"Keith Gallagher, Nicole Engelke Infante","doi":"10.1080/0020739x.2023.2256732","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2256732","url":null,"abstract":"AbstractExpert mathematicians use examples and visual representations as part of their informal mathematics reasoning when constructing proofs. In contrast, the ways undergraduates reason and work toward creating proofs is an open area of investigation, particularly in advanced mathematics. Furthermore, research on students’ reasoning in topology is largely unexplored. Building on findings from Gallagher [(2020). Identifying Structure in Introductory Topology: Diagrams, Examples, and Gestures. Doctoral Dissertation, West Virginia University, Morgantown, West Virginia. https://researchrepository.wvu.edu/etd/7599/ (MS #8610)], we present a case study of an undergraduate taking a first course in general topology and her use of generic examples in argumentation prior to producing formal proofs and counterexamples. We discuss patterns that emerged in her use of generic examples when proving true statements and disproving false claims. We compare and contrast this student’s generic examples with other generic examples in the literature from other content areas within mathematics, and we argue that generic examples are not one-size-fits-all but rather must be fit-for-purpose. Our results suggest that generic examples may be particularly useful for students writing proofs when they may not have access to specific examples.KEYWORDS: Generic examplesdiagramstopologyproofargumentation AcknowledgementsThe results presented in this manuscript are derived from an analysis of data collected by the lead author for their doctoral dissertation (Gallagher, 2020).Disclosure statementNo potential conflict of interest was reported by the authors.Human participants disclosureHuman participants took part in this research. This research was classified as minimal risk; no physical or mental risks were anticipated during the study. Ethics approval for this research was granted by the Institutional Review Board at West Virginia University under protocol/approval number 1711838593. All subjects were informed that they would be video and audio recorded solving mathematics problems, and any data they provided may be used for research purposes and published in scholarly manuscripts. All research subjects signed consent forms and were free to withdraw their consent and/or request to have their data removed from our data corpus at any time.Notes1 The facilitator neglected to include the condition that the sets U and V must be nonempty to form a separation of X. Neither Stacey nor the facilitator acknowledged this omission during Session 7.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135731505","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":"Design principles of inquiry-oriented tasks in integral calculus","authors":"Houssein El Turkey, Yasanthi Kottegoda, Lochana Siriwardena","doi":"10.1080/0020739x.2023.2257699","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2257699","url":null,"abstract":"AbstractDesigning and implementing purposefully developed tasks have been linked to students’ understanding of mathematical topics. We report on design principles and intentions that guided the development of inquiry-oriented tasks. Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design intentions: Provide Review; Introduce New Content; Provide Guidance; Prompt Graphing and Visualisation; Prompt Generalisation; Foster Mathematical Creativity; and Prompt Reflection. In the discussion, we align these themes with existing literature and recognise an intersection between designing inquiry-oriented tasks, creativity-fostering tasks and reflective assignments. We additionally provide some recommendations for practitioners and report on students’ feedback on these tasks.KEYWORDS: Calculustask designinquiryundergraduate mathematics educationMSC: 97D99 Disclosure statementNo potential conflict of interest was reported by the authors.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136185729","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":"A Rasch-model-based hierarchical framework for statistical literacy and learning","authors":"Danny L'Boy, R. Nazim Khan","doi":"10.1080/0020739x.2023.2261453","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2261453","url":null,"abstract":"Statistical literacy has a large and important role in the teaching of statistics. Most mathematics and statistics courses are hierarchical, and the earlier material forms the foundation for later material. We construct a hierarchical structure for an introductory statistics course using Rasch analysis of the student scripts for the final examination. This forms the basis of a statistical literacy construct that has wider implications than just an undergraduate course. The world is overwhelmed with data from an exponentially increasing number of sources. Such data is of various types and contexts, ranging from social, commercial, scientific, survey and human. Statistical literacy has therefore assumed a larger and more important role.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014263","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":"Mathematical modelling using scenarios, case studies and projects in early undergraduate classes","authors":"G. R. Fulford","doi":"10.1080/0020739x.2023.2244490","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2244490","url":null,"abstract":"Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area, particularly models involving only two or three coupled differential equations. These models were amenable to students as well as interesting and relevant to students because they came from real research papers. I will describe the use of scenarios and case studies in lectures, and group projects for assessment. The scenarios and case studies were published in a textbook that I wrote. Scenarios, case studies and projects provided an opportunity to expose students to some novel applications of differential equations. One example is developed here as a Classroom Note: modelling the dynastic cycles in Chinese history.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014132","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":"Re-envisioning our journey of learning in mathematics","authors":"Ingrid M. Rewitzky","doi":"10.1080/0020739x.2023.2257698","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2257698","url":null,"abstract":"ABSTRACTWhen embarking on our journey of learning in mathematics, we may envision a linear path of modules for acquiring mathematical knowledge and understanding to reach a predetermined outcome. However, this is a partial representation since the outcome and path are developing and adapting and our learning is continuously emerging. In this paper, our journey of learning in mathematics is re-envisioned as a complex adaptive system with agents, internal diversity, internal redundancy, decentralised control, sources of disruption and sources of coherence. As will be illustrated through the adaptive cycle of a complex adaptive system, learning may emerge between phases of destabilisation and development. For this emergence there needs to be openness to embrace a disruption, reflection to interpret the disruption, connection to respond to the disruption and inspiration to grow and adapt in response to the disruption. There also needs to be a balance between individual and collective learning. Through navigating these cycles along our journey of learning there may be emergence of learning experiences within and beyond mathematics.KEYWORDS: Complexity adaptive systemlearninguniversity mathematics Disclosure statementNo potential conflict of interest was reported by the author.Additional informationFundingThis project was supported by the Stellenbosch University Teaching Fellowship Award .","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136212040","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":"Seventh-grade students’ understanding of risk and reward arising from mathematical modelling activities*","authors":"Melike Tural-Sonmez, Ayhan Kursat Erbas","doi":"10.1080/0020739x.2023.2258881","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2258881","url":null,"abstract":"AbstractThis study examined seventh-grade students’ emergent and progressive financial literacy in the context of risk and reward while working on two mathematical modelling tasks. The participants were six seventh-grade students identified as ‘good at mathematics’ by their teachers. The data sources comprised videotaped group discussions, group presentations, worksheets, and researchers’ field notes. The results revealed that students’ financial experience and mathematical knowledge influenced the mathematical modelling process in the context of risk and reward. Students with experience in financial contexts, similar to those in the modelling tasks, were more successful in making financial comments and linking mathematical knowledge. We conclude that mathematical modelling tasks would have encouraged students to discuss and adopt different approaches that facilitated more advanced financial thinking. How mathematical modelling activities might activate students’ financial knowledge in the context of risk and reward was discussed, and limitations and recommendations for further research are included.KEYWORDS: Financial literacymathematical modellingmiddle schoolrisk and reward Disclosure statementNo potential conflict of interest was reported by the authors.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136098021","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":"Is mathematics a barrier for engineering?","authors":"Terrence Tsui, R. Nazim Khan","doi":"10.1080/0020739x.2023.2256319","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2256319","url":null,"abstract":"Mathematics is traditionally considered necessary for engineering courses. Over the last three decades, the mathematics requirements for entry into engineering programmes has steadily weakened in Australia. Further, the mathematics component of engineering programmes has progressively decreased. This research aims to investigate the following two questions. First, is mathematics a barrier for students to complete an engineering programme? And second, is performance in mathematics associated with performance in engineering? We identified the significant factors associated with weighted average mark and the completion status of engineering studies at both an undergraduate level and a Masters level. Of particular interest was the students' mathematical background. Furthermore, a survey of students enrolled in engineering at the University of Western Australia was conducted to obtain more in depth views of student attitudes and perceptions towards how mathematics has affected their engineering studies. Binary logistic models were fitted to the survey data. Additionally, focus group interviews were conducted to gain insight on student perspectives regarding the effectiveness of mathematics teaching in engineering. The results are discussed in relation to the importance of mathematics and statistics for the engineering curriculum.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136212048","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":"Exploring growth mindset experiences in university students","authors":"Anita L. Campbell","doi":"10.1080/0020739x.2023.2255212","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2255212","url":null,"abstract":"AbstractStudents that classify as having growth mindsets rather than fixed mindsets enjoy greater academic success. This finding has been repeated in a variety of contexts and encourages teachers and researchers to develop growth mindsets in students. However, neutral and negative conclusions from some mindset intervention studies raise questions about the conditions in which growth mindsets develop. This study contributes evidence and suggestions to guide the development and assessment of growth mindsets in university students. The five-stage behaviour change model provides a framework to explain why mindset interventions may cause shifts that are not detected in the short term. Mindset assessment methods with original and adapted scales are presented and critiqued. I compare literature-sourced experiences used in growth mindset interventions with interview data from seven first-year engineering students at a South African university to help determine if growth mindset interventions for university students are worth implementing. I summarise implications for practice when assessing mindsets or using growth mindset interventions.KEYWORDS: Academic achievementuniversity studentsfixed mindsetimplicit theories of intelligencestudent successinterventionbehaviour change AcknowledgementsI am grateful to helpful suggestions from my PhD supervisors Tracy Craig and Brandon Collier-Reed, anonymous reviewers, and members of Helen Sword's WriteSPACE. Special thanks to the students who generously volunteered their time for interviews. This work is adapted from a chapter in my PhD (Campbell, Citation2020).Disclosure statementNo potential conflict of interest was reported by the author.Additional informationFundingThis work was supported by National Research Foundation [grant number TTK160531166788]; University of Cape Town.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135645179","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":"Analysing signs emerging from students’ work on a designed dependency task in dynamic geometry*","authors":"Ingi Heinesen Højsted, Maria Alessandra Mariotti","doi":"10.1080/0020739x.2023.2246979","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2246979","url":null,"abstract":"AbstractThis article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students’ awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design principles used in the study and present analysis of four Danish grade 8 students (age 13–14) working in pairs on the very first task of the sequence. The Theory of Semiotic Mediation frames the design of the study and the analysis of data, which was collected in the form of screencast, video and written products. The results show that grasping logical relationships is not immediate, on the contrary, the results indicate that students expect dependencies to be non-hierarchical in DGE and that low achieving students describing the behaviour of constructions during dragging refer to their global appearance, rather than to geometrical properties. Such results suggest that specific prompts in the task design can shift students’ attention on specific elements of constructions and that explicitly asking the students to explain any unexpected observation seems to be necessary for active reflection.KEYWORDS: Dynamic geometry environmentstask design principlesmathematical reasoning competencydesign-based researchtheory of semiotic mediation Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 The mathematical reasoning competency is one of eight mathematical competencies in the Danish KOM framework (Niss & Højgaard, Citation2019).2 We omit the formulation of 1.c., 1.e. and 1.f. since it is not discussed in this article. 1.c. was a repetition of 1.b. in relation to point B, while 1.e. and 1.f. concern choice (v) – explain.3 Arzarello (Citation2006) introduced and elaborated (Arzarello et al., Citation2009) the terms semiotic set and semiotic bundle. A semiotic set comprises three components: signs; modes of production/transformation of signs; and relationships among signs. A semiotic bundle is a collection of semiotic sets and a set of relationships between the semiotic sets of the bundle (Arzarello, Citation2006, p. 281).4 E.g. Geometer Sketchpad 3, as mentioned in Talmon and Yerushalmy (Citation2004).","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135425943","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":"Mathematical inquiry with the Steiner ellipse using GeoGebra and numerical analysis","authors":"Özlem Çeziktürk","doi":"10.1080/0020739x.2023.2254762","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2254762","url":null,"abstract":"AbstractI explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.KEYWORDS: Steiner ellipseanalytic geometrycentral ellipsesmathematical inquirynumerical analysis AcknowledgementsThe author of this paper feels obliged to thank her department and her colleagues for letting her study what interests her most.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":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135425932","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}