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

{"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":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":"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}

{"title":"Love stories in a differential equations classroom","authors":"Yanping Ma, Gail Tang","doi":"10.1080/0020739x.2023.2251016","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2251016","url":null,"abstract":"AbstractWe believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (Citation2009) and Gutiérrez (Citation2018), we present a five-part bundle of activities for undergraduate differential equations course instructors, including one pre-activity reflection assignment, three modeling activities, and a final project. The Pre-Activity Assignment engages students to draw on their own personal and/or cultural experiences with the concept of love. Three activities focus on developing revision skills in mathematical modeling and practicing methods of solving systems of ordinary differential equations (ODEs). In these activities, students would collaborate to construct a relationship model consisting of a system of first-order linear ODEs and solve different model iterations with the characteristic polynomial, matrix form, or Laplace transform method. The final project connects the reflections in Pre-Activity Assignment with the skills developed in the three activities by inviting students to create a relationship scenario, model, revise, solve it, and present the conclusions. By engaging in this set of assignments, students connect personal and cultural experiences with the concept of love and perceive themselves and their peers in the curriculum, fostering a sense of belonging and relevance.Keywords: Mathematical modelingculturally relevant pedagogysystems of linear ordinary differential equationscharacteristic polynomial methodLaplace transform methodmatrix form Data availability statementDetailed solutions, sample MATLAB live scripts, and grading rubrics are available upon request. We purposefully do not include them here in case students attempt to search for solutions online.AcknowledgementsThe authors would like to express our gratitude to the guest editors and reviewers for providing valuable feedback and insightful suggestions. The authors also appreciate the organizations of SIMIODE EXPO 2022, where the idea of this project started.Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 This section tests future SAT questions. These unscored sections look just like the scored sections of the SAT so students do not know which sections are scored or unscored.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135815337","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":"The supportive role of active learning in a calculus course on low precalculus proficiency students","authors":"Charity N. Watson, Pablo Duran, Adam Castillo, Edgar Fuller, Geoff Potvin, Laird Kramer","doi":"10.1080/0020739x.2023.2255189","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2255189","url":null,"abstract":"AbstractCollege calculus plays an important role in STEM students’ degree and career aspirations. One of the key factors considered in assessing a student’s ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students’ precalculus proficiency on their achievement in introductory calculus based on their classroom environment. Results from the implementation of the Modeling Practices in Calculus (MPC) model, an innovative, active learning approach, are presented. Using a randomized-controlled trial research design, students were randomly assigned to MPC and traditional, lecture-based calculus sections. The Precalculus Concept Assessment inventory was administered to gauge students’ precalculus proficiency. We found that students exposed to the MPC model were more likely to be successful in their calculus course, even if they began with low precalculus proficiency. Also, students enrolled in the MPC sections saw significant growth in their precalculus proficiency from the beginning to the end of the semester. Additionally, we observed this model providing support for students in key demographics (low proficiency, female, first and second year undergraduates) in terms of the development of their proficiency that they may not receive in traditional classrooms.KEYWORDS: Active learningcalculusprecalculus proficiencycalculus achievementSubject classification code: 97D40 AcknowledgementsWe thank the instructors, students, and Learning Assistants involved in this study for their support during the administration and collection of data. We also thank our institution and the State of Florida for the initial support that made this project possible. Any opinions, findings, and conclusions in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThis work was supported by the US National Science Foundation [grant number: 1832450].","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136061584","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":"Investigating how lower secondary school students reason about quadrilaterals emerging in dynamic constructions","authors":"Lukáš Vízek, Libuše Samková, Jon R. Star","doi":"10.1080/0020739x.2023.2255184","DOIUrl":"https://doi.org/10.1080/0020739x.2023.2255184","url":null,"abstract":"This contribution focuses on reasoning about quadrilaterals provided by lower secondary school students when working with pre-prepared dynamic constructions. On this topic, we present an exploratory empirical qualitative study carried out within a GeoGebra Classroom environment, and our diagnostic instrument consists of a set of dynamic constructions of quadrilaterals that are based just on a composition of lines and circles. The dynamic constructions consist of the same construction steps as with a straightedge and a compass on paper, without any relational or measurement information provided by the software. The hierarchy in the dynamic constructions is tied to properties of diagonals and takes on various levels and structure (one level, two consecutive levels, two parallel pairs of consecutive levels). For each of the constructions, the participants of the study reasoned which shapes could be found in the construction and why. Various levels of reasoning as well as various levels of students’ understanding of quadrilaterals appeared in data. The findings indicate that, at least for the lower secondary school students, the combination of dynamic manipulations and geometric constructions could form a significant space for scaffolding the identification of the features of quadrilaterals and the comprehension of the inclusive relations between them.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136314848","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}