Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)            First | 1 2 3 4 | Last

Showing 201 - 400 of 538 Journals sorted alphabetically
Educação Matemática Debate     Open Access  
Edumatica : Jurnal Pendidikan Matematika     Open Access  
EduMatSains     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 3)
Em Teia : Revista de Educação Matemática e Tecnológica Iberoamericana     Open Access  
Emergent Scientist     Open Access  
Energy for Sustainable Development     Hybrid Journal   (Followers: 13)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Open Access   (Followers: 2)
Euclid     Open Access  
European Journal of Applied Mathematics     Hybrid Journal  
European Journal of Combinatorics     Full-text available via subscription   (Followers: 3)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 1)
Examples and Counterexamples     Open Access  
Experimental Mathematics     Hybrid Journal   (Followers: 5)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Extracta Mathematicae     Open Access  
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 5)
Fixed Point Theory and Applications     Open Access  
Formalized Mathematics     Open Access  
Forum of Mathematics, Pi     Open Access   (Followers: 1)
Forum of Mathematics, Sigma     Open Access   (Followers: 1)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 6)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)
Foundations and Trends® in Stochastic Systems     Full-text available via subscription   (Followers: 1)
Foundations and Trends® in Theoretical Computer Science     Full-text available via subscription   (Followers: 1)
Foundations of Computational Mathematics     Hybrid Journal  
Fractal and Fractional     Open Access  
Fractals     Hybrid Journal   (Followers: 1)
Frontiers of Mathematics in China     Hybrid Journal  
Fuel Cells Bulletin     Full-text available via subscription   (Followers: 9)
Functional Analysis and Other Mathematics     Hybrid Journal   (Followers: 4)
Fundamental Journal of Mathematics and Applications     Open Access  
Funktsional'nyi Analiz i ego Prilozheniya     Full-text available via subscription  
Fuzzy Optimization and Decision Making     Hybrid Journal   (Followers: 8)
Game Theory     Open Access   (Followers: 2)
Games     Open Access   (Followers: 4)
Games and Economic Behavior     Hybrid Journal   (Followers: 26)
Gamm - Mitteilungen     Hybrid Journal  
GANIT : Journal of Bangladesh Mathematical Society     Open Access  
GEM - International Journal on Geomathematics     Hybrid Journal   (Followers: 1)
General Mathematics     Open Access  
Glasgow Mathematical Journal     Full-text available via subscription  
Global Journal of Mathematical Sciences     Full-text available via subscription  
Graphs and Combinatorics     Hybrid Journal   (Followers: 4)
Grey Systems : Theory and Application     Hybrid Journal  
Groups, Complexity, Cryptology     Open Access   (Followers: 2)
GSTF Journal of Mathematics, Statistics and Operations Research     Open Access   (Followers: 1)
Historia Mathematica     Full-text available via subscription  
Historical Methods: A Journal of Quantitative and Interdisciplinary History     Hybrid Journal   (Followers: 28)
IMA Journal of Applied Mathematics     Hybrid Journal  
IMA Journal of Numerical Analysis - advance access     Hybrid Journal  
ImmunoInformatics     Open Access   (Followers: 1)
Indagationes Mathematicae     Open Access  
Indian Journal of Pure and Applied Mathematics     Hybrid Journal   (Followers: 4)
Indonesian Journal of Combinatorics     Open Access  
Indonesian Journal of Science and Mathematics Education     Open Access   (Followers: 2)
Infinite Dimensional Analysis, Quantum Probability and Related Topics     Hybrid Journal   (Followers: 1)
Infinity Jurnal Matematika dan Aplikasinya     Open Access   (Followers: 4)
Information and Inference     Free  
InfoTekJar : Jurnal Nasional Informatika dan Teknologi Jaringan     Open Access  
InfraMatics     Open Access  
Insight - Non-Destructive Testing and Condition Monitoring     Full-text available via subscription   (Followers: 114)
International Electronic Journal of Algebra     Open Access  
International Journal for Numerical Methods in Engineering     Hybrid Journal   (Followers: 37)
International Journal for Numerical Methods in Fluids     Hybrid Journal   (Followers: 20)
International Journal of Advanced Mathematical Sciences     Open Access  
International Journal of Advanced Mechatronic Systems     Hybrid Journal   (Followers: 2)
International Journal of Advanced Research in Mathematics     Open Access  
International Journal of Advances in Engineering Sciences and Applied Mathematics     Hybrid Journal   (Followers: 10)
International Journal of Algebra and Computation     Hybrid Journal   (Followers: 1)
International Journal of Algebra and Statistics     Open Access   (Followers: 3)
International Journal of Applied and Computational Mathematics     Hybrid Journal  
International Journal of Applied Mathematical Research     Open Access   (Followers: 1)
International Journal of Applied Mathematics and Computer Science     Open Access   (Followers: 7)
International Journal of Applied Mechanics     Hybrid Journal   (Followers: 8)
International Journal of Applied Nonlinear Science     Hybrid Journal  
International Journal of Autonomic Computing     Hybrid Journal   (Followers: 1)
International Journal of Bifurcation and Chaos     Hybrid Journal   (Followers: 4)
International Journal of Biomathematics     Hybrid Journal   (Followers: 2)
International Journal of Computational Complexity and Intelligent Algorithms     Hybrid Journal  
International Journal of Computational Economics and Econometrics     Hybrid Journal   (Followers: 6)
International Journal of Computational Geometry and Applications     Hybrid Journal   (Followers: 2)
International Journal of Computational Intelligence and Applications     Hybrid Journal   (Followers: 2)
International Journal of Computational Methods     Hybrid Journal   (Followers: 4)
International Journal of Computer Processing Of Languages     Hybrid Journal   (Followers: 1)
International Journal of Control, Automation and Systems     Hybrid Journal   (Followers: 15)
International Journal of Dynamical Systems and Differential Equations     Hybrid Journal   (Followers: 1)
International Journal of Economics and Accounting     Hybrid Journal   (Followers: 1)
International Journal of Foundations of Computer Science     Hybrid Journal   (Followers: 3)
International Journal of Fuzzy Computation and Modelling     Hybrid Journal   (Followers: 2)
International Journal of Image and Graphics     Hybrid Journal   (Followers: 5)
International Journal of Industrial Electronics and Drives     Hybrid Journal   (Followers: 3)
International Journal of Low-Carbon Technologies     Open Access   (Followers: 1)
International Journal of Mathematical Education in Science and Technology     Hybrid Journal   (Followers: 9)
International Journal of Mathematical Modelling & Computations     Open Access   (Followers: 3)
International Journal of Mathematical Modelling and Numerical Optimisation     Hybrid Journal   (Followers: 5)
International Journal of Mathematical Sciences and Computing     Open Access  
International Journal of Mathematics     Hybrid Journal   (Followers: 4)
International Journal of Mathematics & Computation     Full-text available via subscription  
International Journal of Mathematics and Mathematical Sciences     Open Access   (Followers: 4)
International Journal of Mathematics in Operational Research     Hybrid Journal   (Followers: 2)
International Journal of Metaheuristics     Hybrid Journal   (Followers: 1)
International Journal of Modelling in Operations Management     Hybrid Journal   (Followers: 2)
International Journal of Modern Nonlinear Theory and Application     Open Access   (Followers: 1)
International Journal of Number Theory     Hybrid Journal   (Followers: 2)
International Journal of Partial Differential Equations     Open Access   (Followers: 2)
International Journal of Polymer Science     Open Access   (Followers: 25)
International Journal of Pure Mathematical Sciences     Open Access  
International Journal of Reliability, Quality and Safety Engineering     Hybrid Journal   (Followers: 14)
International Journal of Research in Undergraduate Mathematics Education     Hybrid Journal   (Followers: 5)
International Journal of Sediment Research     Full-text available via subscription   (Followers: 2)
International Journal of Shape Modeling     Hybrid Journal   (Followers: 1)
International Journal of Theoretical and Mathematical Physics     Open Access   (Followers: 13)
International Journal of Trends in Mathematics Education Research     Open Access   (Followers: 5)
International Journal of Ultra Wideband Communications and Systems     Hybrid Journal  
International Journal of Wavelets, Multiresolution and Information Processing     Hybrid Journal  
International Journal on Artificial Intelligence Tools     Hybrid Journal   (Followers: 9)
International Mathematics Research Notices     Hybrid Journal   (Followers: 1)
Internet Mathematics     Hybrid Journal   (Followers: 1)
Inventiones mathematicae     Hybrid Journal   (Followers: 3)
Inverse Problems in Science and Engineering     Hybrid Journal   (Followers: 3)
Investigations in Mathematics Learning     Hybrid Journal  
Iranian Journal of Optimization     Open Access   (Followers: 2)
Israel Journal of Mathematics     Hybrid Journal  
Ithaca : Viaggio nella Scienza     Open Access  
ITM Web of Conferences     Open Access  
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya     Full-text available via subscription  
Jahresbericht der Deutschen Mathematiker-Vereinigung     Hybrid Journal  
Japan Journal of Industrial and Applied Mathematics     Hybrid Journal  
Japanese Journal of Mathematics     Hybrid Journal  
JIPM (Jurnal Ilmiah Pendidikan Matematika)     Open Access  
JMPM : Jurnal Matematika dan Pendidikan Matematika     Open Access  
JOHME : Journal of Holistic Mathematics Education     Open Access   (Followers: 3)
Johnson Matthey Technology Review     Open Access  
Jornal Internacional de Estudos em Educação Matemática     Open Access  
Journal d'Analyse Mathématique     Hybrid Journal   (Followers: 2)
Journal de Mathématiques Pures et Appliquées     Full-text available via subscription   (Followers: 3)
Journal for Research in Mathematics Education     Full-text available via subscription   (Followers: 29)
Journal für Mathematik-Didaktik     Hybrid Journal  
Journal of Advanced Mathematics and Applications     Full-text available via subscription   (Followers: 1)
Journal of Algebra     Full-text available via subscription   (Followers: 3)
Journal of Algebra and Its Applications     Hybrid Journal   (Followers: 3)
Journal of Algebraic Combinatorics     Hybrid Journal   (Followers: 3)
Journal of Algorithms & Computational Technology     Open Access  
Journal of Applied Mathematics     Open Access   (Followers: 3)
Journal of Applied Mathematics and Computation     Open Access   (Followers: 2)
Journal of Applied Mathematics and Computing     Hybrid Journal  
Journal of Applied Mathematics, Statistics and Informatics     Open Access   (Followers: 1)
Journal of Artificial Intelligence and Data Mining     Open Access   (Followers: 10)
Journal of Classification     Hybrid Journal   (Followers: 5)
Journal of Combinatorial Designs     Hybrid Journal   (Followers: 4)
Journal of Combinatorial Optimization     Hybrid Journal   (Followers: 7)
Journal of Combinatorial Theory, Series A     Full-text available via subscription   (Followers: 5)
Journal of Combinatorial Theory, Series B     Full-text available via subscription   (Followers: 3)
Journal of Complex Analysis     Open Access   (Followers: 2)
Journal of Complex Networks     Hybrid Journal   (Followers: 1)
Journal of Complexity     Hybrid Journal   (Followers: 6)
Journal of Computational and Applied Mathematics     Hybrid Journal   (Followers: 6)
Journal of Computational Biology     Hybrid Journal   (Followers: 9)
Journal of Computational Mathematics and Data Science     Open Access  
Journal of Computational Multiphase Flows     Open Access   (Followers: 1)
Journal of Computational Physics     Hybrid Journal   (Followers: 60)
Journal of Computational Physics : X     Open Access   (Followers: 1)
Journal of Computer Engineering, System and Science (CESS)     Open Access  
Journal of Contemporary Mathematical Analysis     Hybrid Journal  
Journal of Cryptology     Hybrid Journal   (Followers: 5)
Journal of Difference Equations and Applications     Hybrid Journal  
Journal of Differential Equations     Full-text available via subscription   (Followers: 1)
Journal of Discrete Mathematics     Open Access   (Followers: 1)
Journal of Dynamics and Differential Equations     Hybrid Journal  
Journal of Engineering Mathematics     Hybrid Journal   (Followers: 2)
Journal of Evolution Equations     Hybrid Journal  
Journal of Experimental Algorithmics     Full-text available via subscription  
Journal of Flood Risk Management     Hybrid Journal   (Followers: 14)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 3)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 4)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 6)
Journal of Global Research in Mathematical Archives     Open Access  
Journal of Homotopy and Related Structures     Hybrid Journal  
Journal of Honai Math     Open Access  
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Journal of Hyperbolic Differential Equations     Hybrid Journal  
Journal of Indian Council of Philosophical Research     Hybrid Journal  
Journal of Industrial Mathematics     Open Access   (Followers: 2)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 3)
Journal of Integrable Systems     Open Access  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 2)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal   (Followers: 1)
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 3)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 3)

  First | 1 2 3 4 | Last

Similar Journals
Journal Cover
International Journal of Research in Undergraduate Mathematics Education
Number of Followers: 5  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2198-9745 - ISSN (Online) 2198-9753
Published by Springer-Verlag Homepage  [2469 journals]
  • The Evolution of Students’ Learning from Calculus to Analysis: How
           Students Solve Analysis Tasks that look like Calculus Tasks

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      Abstract: Abstract Research using the Anthropological Theory of the Didactic suggests different models of how student learning may evolve in the progression of undergraduate mathematics coursework: from elementary courses in Calculus to more advanced courses in Analysis. An ideal model suggests that the theory-driven learning in the latter serves as a natural complement and extension to the primarily procedural focus of the former. A contrasting model points to a potential didactic obstacle to the ideal evolution of students’ knowledge: When the types of tasks in Analysis courses (e.g., “prove a specified limit”) resemble those in Calculus courses (e.g., “find a specified limit”). To gain insight into the actual evolution experienced by students, we contributed an exploratory study of one introductory Analysis course, including an analysis of assessment activities provided in the course and task-based interviews with 15 students shortly after they passed the course. Results suggest that when faced with “Analysis tasks” that look like “Calculus tasks,” most students do not mobilize the proof-based knowledge that was expected to be learned in Analysis. Moreover, this could be linked not only to the non-empty intersection of students’ Calculus and Analysis courses, but also to the place of Calculus and Analysis in the intersection of their differing future professional institutions.
      PubDate: 2022-06-24
       
  • Derivatives and the Study of Motion at the Intersection of Calculus and
           Mechanics: a Praxeological Analysis of Practices at the College Level

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      Abstract: Abstract Of the many disciplines that rely on calculus, physics is among those with the strongest connections to this branch of mathematics. For instance, the derivative—one of the key notions of calculus—is used to describe velocity and acceleration, which play a central role in mechanics. In post-secondary education, in particular at the college level, it is not unusual for students to enroll in calculus and mechanics courses in the same year, and even the same term. In mathematics education, however, there is scant research focusing on students’ construction of the notion of derivative in a mechanics context, and existing studies offer contradictory views on the effectiveness of using mechanics to teach derivatives. To shed light on the use of derivatives in mechanics and calculus courses, our study focuses on practices involving the use of derivatives to study motion in both courses. We first conducted a praxeological analysis of five differential calculus textbooks and five mechanics textbooks to pinpoint their use of derivatives in the study of motion. This analysis was complemented by interviews with four mathematics teachers and three mechanics teachers, to compare their praxeologies with those of the textbooks. We then identified consistencies and inconsistencies between practices employed in both courses, which may have an impact on students’ learning, and formulated recommendations for teaching the notion of derivative in kinematics.
      PubDate: 2022-06-22
       
  • The Limit Notion at Three Educational Levels in Three Countries

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      Abstract: Abstract This paper documents how the limit concept is treated in high school, at a university and in teacher education in England, France and Sweden. To this end we make use of vignettes, data-grounded accounts of the situation at the three levels in the three countries. These are analysed using the Anthropological Theory of the Didactic (ATD). While university praxeologies are relatively similar across the three countries, greater differences manifest themselves in high school and teacher education. For instance, at the high school level, in France a local praxeology on the limits of sequences is taught, which is not the case in England or Sweden. Results from the analysis of limits are extrapolated to comment on implications for the teaching of calculus, and for teacher education, in the three countries. The paper also raises methodological issues in our approach.
      PubDate: 2022-06-22
       
  • The Inextricability of Students’ Mathematical and Physical Reasoning in
           Quantum Mechanics Problems

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      Abstract: Abstract Reasoning with mathematics plays an important role in university students’ learning throughout their courses in the scientific disciplines, such as physics. In addition to understanding mathematical concepts and procedures, physics students often must mathematize physical constructs in terms of their associated mathematical structures and interpret mathematical entities in terms of the physical context. In this study, we investigate physics students’ reasoning about mathematics in relation to physics content addressed in two quantum mechanics problems. Through qualitative analysis of interview data from twelve students, results show that 1) students use intricate, nonuniform problem-solving methods with reasoning that moves fluidly between structural (mathematizing and interpreting) and technical (conceptual and procedural) skills in quick succession, and 2) student reasoning about orthonormal bases, change of basis, inner products, and probability informed their flexibility in choosing problem-solving approaches. We illustrate the results with examples of student reasoning and discuss the inextricability of mathematics and physics in students’ reasoning.
      PubDate: 2022-06-16
       
  • Calculus at the intersection of institutions, disciplines and communities:
           a special issue Guest Editorial

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      PubDate: 2022-06-11
       
  • Support for All' Confronting Racism and Patriarchy to Promote
           Equitable Learning Opportunities through Undergraduate Calculus
           Instruction

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      Abstract: Abstract Undergraduate calculus instruction is a contributor to racialized and gendered trends of STEM persistence and disidentification with mathematics. However, the nature of instruction that promotes equitable learning opportunities for disrupting such negative outcomes and experiences among historically marginalized populations is underexplored. To fill this gap, this paper presents an analysis of 34 undergraduate Black and Latina/o students’ perceptions of discouraging events and alternatives for supportive practices in calculus instruction to build theory of equitable practices. Our findings show how supportive-for-all practices – instructional practices supportive for all students (e.g., creating space for questions and mistakes, extending out-of-class support) – were perceived as necessary yet insufficient to cultivate equitable opportunities for classroom participation and access to content. Black and Latina/o participants’ perceptions of instruction addressed how, without challenging broader influences of racism and patriarchy (e.g., stereotypes of mathematical ability), historically marginalized students have limited access to learning opportunities afforded by supportive-for-all practices. The present study, therefore, demonstrates how equitable calculus instruction requires race- and gender-conscious enactment of supportive practices, which challenges colorblind and gender-neutral assumptions of uniformity in students’ experiences of instruction that leave structural forms of exclusion unchecked. We conclude with implications for practice and research.
      PubDate: 2022-06-10
       
  • You Don’t Want to Come Into a Broken System: Perspectives for Increasing
           Diversity in STEM Among Undergraduate Calculus Program Stakeholders

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      Abstract: Abstract As attention grows towards the disparities and underrepresentation of minoritized groups within undergraduate STEM education, there is a need for understanding how university calculus program stakeholders perceive the issue of increasing diversity. Calculus is a subject crucial to many STEM disciplines, and thus can play an outsized role in facilitating necessary change across STEM fields. We present a research-driven framework from a thematic analysis of interviews and focus groups with calculus program stakeholders (students, faculty, staff, and administrators) at two universities in the United States. The framework juxtaposes various stakeholders’ motivations for diversifying STEM fields along critical and dominant axes with four primary recipients that benefit from diversifying STEM. This framework prompts critical analysis of increasing access and achievement within the current system while also attending to the need to fundamentally change mathematical structures to bolster individual identities and increase the power of marginalized individuals in STEM disciplines.
      PubDate: 2022-06-10
       
  • Geometrical Reasoning in the Teaching and Learning of Integrals of
           Multivariable Functions

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      Abstract: Abstract This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R2 and R3. Adopting the framework of the Anthropological Theory of the Didactic, we approached the problem by performing a praxeological analysis of typical tasks in a multivariable calculus course to describe the geometry involved, and to support the transition from textbook knowledge where geometry seems to be hidden. Our analysis reveals a collection of geometrical praxeologies that are used in the tasks but are not explicitly taught. Interviews with students show that we cannot consider that students are equipped with these praxeologies prior to taking the course on multivariable calculus.
      PubDate: 2022-06-10
       
  • Sameness in Mathematics: a Unifying and Dividing Concept

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      Abstract: Abstract While many aspects of the teaching and learning of specific advanced mathematics courses have been studied, limited work has examined mathematical themes like sameness or its instantiations across disciplines. In this paper, we explore algebraists’ collective example space for mathematical sameness. We used qualitative methods to analyze survey responses from 197 algebraists in order to identify specific mathematical concepts that the algebraists associated with sameness and relevant factors to consider when determining sameness of objects. Using variation theory, we introduce the notion of a community example space for algebraists to highlight specific dimensions of variation in sameness as well as the range of variation for each dimension through specific instantiations given by multiple participants. Dimensions of sameness included contexts, concepts, objects, properties, and qualities. These results suggest potential for building connections across levels and branches of mathematics by highlighting how different choices for each dimension of sameness can produce different instantiations of sameness.
      PubDate: 2022-06-07
       
  • From the Front lines of active learning: Lessons learned from those who
           are trying

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      Abstract: Abstract Active learning is becoming more widely accepted in mathematics as a superior teaching method for student learning and, as a result, faculty are increasingly convinced of the benefits. Our study was designed to close a research gap by determining how to support mathematics faculty in transforming their instruction to active learning. We investigated actual challenges of faculty during the transition to more active pedagogy, then researched and tested solutions to reported challenges. To do so, we executed a participant observation study of six diverse faculty members from a mathematics department and followed typological analysis techniques of focus group and interview transcripts. Participants’ challenges include overcoming a dominant culture of teaching through lecture in the mathematics community, combatting a tendency to default to lecture, and acquiring specific skills and confidence to implement active learning. We suggest that specific characteristics of a robust department-wide professional development program could provide solutions to many challenges faced by faculty. This paper reports on the challenges for faculty, alongside proposed solutions through purposefully defined faculty professional development.
      PubDate: 2022-06-03
       
  • ‘Scaffolding’ or ‘Filtering’: A Review of Studies on the Diverse
           Roles of Calculus Courses for Students, Professionals and Teachers

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      Abstract: Calculus courses have been attracting the attention of mathematics education researchers over the last decades. Recent publications and special issues dedicated to calculus highlight the diverse roles of calculus courses in the pathways for STEM studies within and across educational levels, as well as issues related to the academic preparation of future STEM professionals, including mathematicians, non-mathematics professionals (NMPs) and teachers. In this paper, we review recent literature, mostly since 2015, to identify and characterize explicit references to such diverse roles of calculus courses. The review highlights an intrinsic tension between two institutional roles of calculus: scaffolding and filtering. We find nuanced yet substantial variation in how the dual role of calculus is experienced and managed across different groups of students and stakeholders. With regard studies on calculus for mathematics students, recent studies attend to changes in the rules underpinning calculus notions and processes, and highlight the scaffolding potential of calculus courses towards abstraction and reasoning. In contrast, studies on calculus for NMPs report that such courses often promote filtering rather than scaffolding and question transferability and relevance of those courses for NMPs. Finally, studies challenge the perception that traditional tertiary calculus courses scaffold school teaching and underline the need for empirical research that would explain the nature of this scaffolding and how it can be realized in practice. We conclude that further empirical research, in particular theory development, is needed to address the diverse roles of calculus at the intersection of institutions, disciplines and communities.
      PubDate: 2022-06-01
       
  • Collectively engaging with others’ reasoning: Building intuition through
           argumentation in a paradoxical situation

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      Abstract: Abstract One goal of inquiry-oriented instruction is student engagement with others’ mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others’ ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the apparently paradoxical zero area and infinite perimeter of the Sierpiński triangle. The instructor strategically facilitated collective argumentation centered on their reasoning, resulting in several ideas that functioned-as-if-shared in the classroom community. In this report we capitalize on this classroom discussion to contribute to theory and methods for investigating the complex intersection of engagement and argumentation.
      PubDate: 2022-05-18
       
  • Transition to University Mathematics in Turkey: Examining the Views of
           Students and Faculty Members on Student Difficulties

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      Abstract: Researchers from many countries have pointed out the difficulty of transitioning from high school to university settings, especially within the context of mathematics courses. With its abstract content, deductive thinking structure, and unique language, university mathematics is quite different from high school mathematics for students encountering such courses at the undergraduate level for the first time; often, they may perceive themselves as though they are in a different world. The two main actors playing a role in students’ transition from high school to university mathematics are the students themselves and the faculty members who are attempting to guide them through the process. This study aims to reveal the difficulties experienced by 17 to 19-year-old first-year students in the undergraduate departments of mathematics education and mathematics from the perspectives of students and faculty members. Within the scope of the study, the mathematics courses offered in the first year of a Faculty of Education program and a Faculty of Science program in Turkey were observed for one semester. Interviews were then conducted with volunteer students, as well as faculty members who were instructing the courses. We present the cognitive, epistemological, sociocultural, didactic, and affective aspects of the difficulties experienced by first-year students, as well as the reasons underlying these difficulties.
      PubDate: 2022-05-14
       
  • When the Problem Seems Answerable yet the Solution is Unavailable:
           Affective Reactions Around an Impasse in Mathematical Discourse

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      Abstract: Abstract Situations where students encounter mathematical "impasses" – instances where their current discourse is incommensurable with the discourse demanded to solve a task – have the potential to stir emotional responses of different types. They can engender feelings of confusion and bafflement, or even embarrassment, or alternatively open students' curiosity to the ways by which more advanced mathematics can solve a problem. In this study, we closely examine the subjectifications (affective communication) of a group of graduate students encountering such an impasse in the form of a request to account for the area and perimeter of the Sierpiński triangle. We analyze these subjectifications in relation to an a priori mathematical analysis of the impasse inherent in the task. We show two major types of subjectifications, found to be communicated by distinct members of the classroom: "I'm baffled", and "this is not a problem". We show how the students subjectifying "this is not a problem" were those who avoided engagement with the impasse by attending only to the infinite process that defines the fractal, while those students who subjectified "I'm baffled" were those who engaged with the process as well as its outcome. Moreover, despite the lack of substantial contribution to the exploration of the impasse by those students who subjectified "this is not a problem", they were positioned as the "explainers", in a position of power relative to those students who expressed bafflement. We conclude by discussing the dialectical relationship between identity and engagement with mathematical impasses.
      PubDate: 2022-05-13
       
  • Constructing the Self-similarity Concept

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      Abstract: Abstract Fractals describe many natural phenomena; their strong visual-figurative nature found its mathematical conceptualization in the concept of self-similarity. In the current study, we investigate how students construct (fully or partially) the self-similarity concept while recursively constructing the Sierpiński triangle, working in small group and whole class settings in an inquiry-based MA level mathematics education course. We follow shifts of knowledge from individuals to groups and/or to the whole class community during the process of constructing the self-similarity concept. Our theoretical and methodological approach is based on networking between Abstraction in Context and Documenting Collective Activity. We found that the knowledge constructing processes of different students varied, some thinking recursively about finite cases and others thinking more directly about the infinite case. Some students acted as knowledge agents, with shifts of knowledge occasionally occurring in chains. We also observed a tendency to report results of group discussions back to the plenum only partially and in a purified manner.
      PubDate: 2022-04-27
       
  • Students’ Thinking about the Structure of Constructive Existence
           Proofs

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      Abstract: Abstract Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students’ thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural error while the second was a valid argument of the claim. We found that the students often considered the logical structures of the arguments when validating them. They provided reasons for their evaluations, including why they thought the structure of the first argument functioned to prove the claim and why they thought the structure of the second argument did not function to prove the claim. We discuss how these reasons provide insights into why constructive existence proofs might be challenging for students. We end the paper with implications for the teaching and learning of constructive existence proofs and their proof frameworks.
      PubDate: 2022-04-22
       
  • Analyzing the Structure of the Non-examples in the Instructional Example
           Space for Function in Abstract Algebra

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      Abstract: The concept of function is critical in mathematics in general and abstract algebra in particular. We observe, however, that much of the research on functions in abstract algebra (1) reports widespread student difficulties, and (2) focuses on specific types of functions, including binary operation, homomorphism, and isomorphism. Direct, detailed examinations of the function concept itself–and such fundamental properties as well-definedness and everywhere-definedness–are scarce. To this end, in this paper we examine non-examples of function in abstract algebra by conducting a textbook analysis and semi-structured interviews with abstract algebra instructors. In doing so, we propose four key categories based upon the definitive function properties of well-definedness and everywhere-definedness. These categories identify specific characteristics of the kinds of non-examples of function that abstract algebra instruction should emphasize, enabling us to hypothesize how students might be able to develop a robust view of function and explain in greater detail the nature of the reported difficulties that students experience.
      PubDate: 2022-04-07
      DOI: 10.1007/s40753-022-00166-z
       
  • ConcepTests in Undergraduate Real Analysis: Comparing Peer Discussion and
           Instructional Explanation Settings

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      Abstract: Abstract Peer Instruction, first introduced by Eric Mazur in the late '90 s, is a method aiming at active student participation in lectures. It includes conceptual questions (so-called ConcepTests) presented to the students, who vote on answer alternatives presented to them and then discuss their answers in small groups. As professors have been reported to implement several variants of this method, it is highly desirable to understand the specific effects of the individual elements of the method (tasks, voting, and discussions in small groups). In the present study, we focus on the role of the discussion phase (peer discussion). Our study implemented two conditions: Peer Instruction in classical fashion, and a variant, in which peer discussion was replaced with instructional explanation by a tutor. Students in a course on Real Analysis were randomly assigned to the two conditions for two semesters. As far as learning outcomes are concerned, we do not measure these in terms of voting results within Peer Instruction cycles but we are focusing on transfer in terms of results in the final exams of the two semesters. Interestingly, we found no significant difference between the two conditions. Additionally, we had positive evaluations of the use of Peer Instruction in both variants, with no significant differences between the groups either. Regarding affective variables and learning strategies, no difference in the development could be detected. As an important practical implication, these results show that both implemented variants of the Peer Instruction method are justifiable as far as learning outcomes, measured by exam results, or students’ assessment of the method are concerned. Our results put the widespread belief that it is mainly the peer discussion that accounts for the success of the use of ConcepTests into question.
      PubDate: 2022-04-07
      DOI: 10.1007/s40753-022-00167-y
       
  • Abell, Braddy, Ensley, Ludwig, Soto: MAA Instructional Practices Guide

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      PubDate: 2022-04-01
       
  • Exploring Shifts in Student Attitudes Toward Group Exams in College
           Calculus: The Case of Dane

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      Abstract: Abstract As university instructors update modes of teaching and student engagement in STEM classes, concerns often arise about student resistance to different methods of teaching and learning. This research examines what it looks like from a student perspective to experience a shift in attitude by exploring the case of Dane, a white male student who changed his perspective from opposition to support of group exams in calculus. Part of this shift included a change in Dane’s view of his relation to others, as he began to see how working with others benefited himself, consider others’ experiences, and recognize how group exams can be helpful to everyone. We consider how Dane’s experience and attitudes are likely influenced by the racialized and gendered nature of mathematics, and we explore factors of Dane’s calculus classes that contributed to his shift in beliefs. Dane’s story raises questions about instructors’ role in not only working to garner student support for new teaching and learning practices, but interrogating deeper beliefs about what it means to do mathematics and the role of others in students’ mathematics engagement. This research also highlights the importance of exploring students’ experiences and attitudes in relation to the larger sociopolitical context of mathematics.
      PubDate: 2022-04-01
       
 
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