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

{"title":"Issue 54-9: Covers and Table of Contents","authors":"","doi":"10.1080/0020739x.2023.2277093","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2277093","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514090","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 the complexities of swapping the order of integration in double integrals","authors":"Khemane Thabiso, Padayachee Pragashni, Shaw Corrinne","doi":"10.1080/0020739x.2023.2265948","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2265948","url":null,"abstract":"AbstractThis article explores the conceptual challenges that engineering students encounter with double integrals in a vector calculus course. Drawing on previous literature and utilising APOS (Activity- Process- Objects- Schema) as a theoretical framework, this study investigates the difficulties that students face in understanding and applying double integrals. By analysing responses to a written test that assesses students’ conceptual understanding of double integrals and student responses in interviews, this research sheds light on specific areas where students struggle, such as curve sketching, identifying regions of integration and changing the order of integration. Swapping the order of integration in double integrals is the focus of this research study. The findings of this study have the potential to contribute to the enhancement of teaching and learning strategies for double integrals to better support engineering students’ conceptual comprehension and proficiency in this important mathematical concept.KEYWORDS: Double integralsorder of integrationconceptual understandingAPOS theory 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":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135512857","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":"Table mountain delta: Reflect. Connect. Be inspired!","authors":"Tracy S. Craig, Claire Blackman, Greg Oates","doi":"10.1080/0020739x.2023.2270241","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2270241","url":null,"abstract":"","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135513357","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":"Transforming mathematical identity: changes in one international student’s positioning during first-year mathematics tutorials","authors":"Kim Locke, Igor’ Kontorovich, Lisa Darragh","doi":"10.1080/0020739x.2023.2259917","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2259917","url":null,"abstract":"In many countries, international students form a distinct cohort in first-year mathematics courses. For these students, the transition to university mathematics may demand significant adaptation. A research-based understanding of their experiences would enable host universities to provide effective support as they transition from school mathematics in their home countries to a foreign university context. In this study we analyse four episodes in which an international student from China interacted with the tutor during collaborative first-year tutorials at a New Zealand university. The first two episodes occurred near the start of the semester, and the others towards the end. The analysis reveals changes in the student’s positioning of herself over successive episodes as she embraced local classroom norms. We propose that her positioning shift facilitated a process through which the tutor was able to support her mathematics learning more effectively.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135513436","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":"Coordinated topics as transitional enablers towards higher-level conceptualisations of the range concept","authors":"Hamide Dogan","doi":"10.1080/0020739x.2023.2260790","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2260790","url":null,"abstract":"AbstractThis paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualisation of linear transformations from the perspective of Action (A), Process (P), Object (O), and Schema (S) (APOS) theory. Data reported in this paper came from 44 first-year linear algebra students’ responses on a task regarding the range of a linear transformation. Our analysis revealed parallels between Levels/Stages of the range concept and the use of representations of matrix multiplications. More importantly, these representations appeared to have been the enablers of transitions from lower to higher APOS Stages for the range. Conversely, mental mechanisms employing other means showed little to no progressions, some, furthermore, revealed faulty knowledge structures.KEYWORDS: Linear transformationsrangeAPOS theorymental mechanismstransitional pointscoordinated topics AcknowledgementsWe thank the Editors and the reviewers for their valuable input towards the improvement of the earlier versions of the paper.Disclosure statementNo potential conflict of interest was reported by the author.Additional informationFundingThis material is based upon work supported by a grant from the University of Texas System and the Consejo Nacional de Ciencia y Tecnología de México (CONACYT). The opinions expressed are those of the authors and do not necessarily represent the views of these funding agencies.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135513356","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":"Proof of the small angle approximation sin <i>θ</i> ≈ <i>θ</i> using the geometry and motion of a simple pendulum","authors":"J. J. Bissell","doi":"10.1080/0020739x.2023.2258885","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2258885","url":null,"abstract":"The small angle approximation sin(θ)≈θ is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum itself offers a route to understanding the origin of the small angle approximation without recourse to calculus. Rather charmingly, our approach exploits the motion of the pendulum to visualise the process of taking an important limit and can be used to explore the meaning of mathematical approximation in physical systems.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617067","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":"Elementary proof of a theorem about hexagons with parallel opposite sides","authors":"Rolfdieter Frank, Heinz Schumann","doi":"10.1080/0020739x.2023.2243944","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2243944","url":null,"abstract":"AbstractThe perpendicular bisectors of the sides of a hexagon, whose opposite sides are parallel, produce a point symmetric hexagon. Michael de Villiers already gave two proofs of this theorem, firstly an elaborate one with the aid of dynamic geometry and secondly a merely verifying one with the help of coordinates and computer algebra. In this note, we present a short elementary proof. Our proof uses the fact, that the three altitudes of a triangle intersect in a common point, and it also covers degenerate cases.KEYWORDS: Hexagonperpendicular bisectorpoint symmetry 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":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135779132","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":"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}