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Teaching Mathematics and Its Applications最新文献

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Conceptual Understanding Weighting System: a targeted assessment tool 概念理解权重系统：一种有针对性的评估工具
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2017-03-01 DOI: 10.1093/teamat/hrw003
Mairead Greene;Paula Shorter
{"title":"Conceptual Understanding Weighting System: a targeted assessment tool","authors":"Mairead Greene;Paula Shorter","doi":"10.1093/teamat/hrw003","DOIUrl":"https://doi.org/10.1093/teamat/hrw003","url":null,"abstract":"The goal of this article is to introduce the revised Conceptual Understanding Weighting System (CUWS) Greene & Shorter (2012, Trans. Dial.), a tool for categorizing and weighting a mathematical task in order to identify the level of conceptual understanding being assessed by the task. In addition, there is discussion of how this weighting system relates to other frameworks that are currently used to classify mathematical tasks and student reasoning. Examples are provided to demonstrate how the revised CUWS can be used to calculate a conceptual understanding score for a particular exam, to create mathematical tasks that assess understanding at different levels and to analyse student understanding within those different levels. This in turn allows instructors to identify concepts with which students are struggling and quickly adapt classroom activities to improve students’ understanding. The ability to use the CUWS to create mathematical tasks (not just categorize them) is one of the important goals of the CUWS and one that is not regularly emphasized when working with other frameworks to categorize mathematical tasks.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50274530","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}
引用次数: 1
Weekly online quizzes to a mathematics course for engineering students 工科学生数学课程每周在线测验
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2017-03-01 DOI: 10.1093/teamat/hrw011
Sandra Gaspar Martins
{"title":"Weekly online quizzes to a mathematics course for engineering students","authors":"Sandra Gaspar Martins","doi":"10.1093/teamat/hrw011","DOIUrl":"https://doi.org/10.1093/teamat/hrw011","url":null,"abstract":"A set of weekly optional online quizzes was used with 104 students on a Multivariable Calculus course (MC), via the Moodle online system. These quizzes contributed a maximum of two extra points, and this was awarded if the student scored more than 9 points (out of 20) on the exam. All the students got the same questions and could resubmit the answers without penalty. There were usually several sub-questions embedded in each item. The effectiveness of these quizzes, applied with this set of strategies, was studied using students’ adherence and performance. Students’ vision of quizzes was also studied: usefulness, fairness, effect on the amount of study, awareness of the student’s level of understanding, and influence on outcome scores.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50274624","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}
引用次数: 11
Angle concept: a high school and tertiary longitudinal perspective to minimize obstacles 角度概念：高中和高等教育的纵向视角，最大限度地减少障碍
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2017-03-01 DOI: 10.1093/teamat/hrw008
Marita Barabash
{"title":"Angle concept: a high school and tertiary longitudinal perspective to minimize obstacles","authors":"Marita Barabash","doi":"10.1093/teamat/hrw008","DOIUrl":"https://doi.org/10.1093/teamat/hrw008","url":null,"abstract":"The concept of angle emerges in numerous forms as the learning of mathematics and its applications advances through the high school and tertiary curriculum. Many difficulties and misconceptions in the usage of this multifaceted concept might be avoided or at least minimized should the lecturers in different areas of pure and applied mathematics be aware of the way their students have learned the concept in their previous studies. The article presents an analysis of the literature on the mathematical and didactical origins of the concept of angle. The purpose of the analysis is to identify the principal characteristics of the concept required in various contexts of pure-mathematical and applied courses, and to trace the way these appearances might have been previously presented. Attentiveness to students’ possible lack of mastery of the notion will hopefully help to prevent or at least minimize difficulties related to it.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50274623","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}
引用次数: 2
Teaching mathematics with intelligent support in natural language. Tertiary education students working with parametrized modelling activities 在自然语言的智能支持下教授数学。从事参数化建模活动的高等教育学生
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2017-03-01 DOI: 10.1093/teamat/hrw009
Teresa Rojano;Montserrat García-Campos
{"title":"Teaching mathematics with intelligent support in natural language. Tertiary education students working with parametrized modelling activities","authors":"Teresa Rojano;Montserrat García-Campos","doi":"10.1093/teamat/hrw009","DOIUrl":"https://doi.org/10.1093/teamat/hrw009","url":null,"abstract":"This article reports the outcomes of a study that seeks to investigate the role of feedback, by way of an intelligent support system in natural language, in parametrized modelling activities carried out by a group of tertiary education students. With such a system, it is possible to simultaneously display on a computer screen a dialogue window and a window with a microworld that are dynamically hot-linked to each other. While users work in the microworld, they can enter into dialogue with the system in natural language. The article discusses the case of one pair of participating students. In their case, the feedback provided by the intelligent support and by the microworld at key moments of the modelling activities, such as understanding the phenomenon, building the model or predicting, was crucial to their ability to build a spreadsheet model and, consequently, to their understanding of the long-term behaviour of the phenomenon being modelled.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50274529","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}
引用次数: 5
Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking 通过数学思维的三个世界发展线性代数的概念理解和定义清晰度
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2016-12-01 DOI: 10.1093/TEAMAT/HRW001
J. Hannah, Sepideh Stewart, Mike Thomas
{"title":"Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking","authors":"J. Hannah, Sepideh Stewart, Mike Thomas","doi":"10.1093/TEAMAT/HRW001","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRW001","url":null,"abstract":"Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall’s three worlds (embodied, symbolic and formal) of mathematical thinking, and use a framework combining these with Dubinsky’s Action, Process, Object and Schema (APOS) theory to analyse students’ resulting levels of understanding. Through interviews and analysis of test and examination scripts, we investigate students’ understanding of the basic concepts of linear algebra, their ability to use and explain these concepts and their relationship to definitional clarity. The results show that, while students tend not to learn definitions by rote and can be imprecise when expressing them in words, they seem to understand the concepts, can talk sensibly about them and are able to use their essential features in solving problems.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRW001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61089920","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}
引用次数: 17
Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking 通过数学思维的三个世界发展线性代数的概念理解和定义清晰度
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2016-12-01 DOI: 10.1093/teamat/hrw001
John Hannah;Sepideh Stewart;Michael Thomas
{"title":"Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking","authors":"John Hannah;Sepideh Stewart;Michael Thomas","doi":"10.1093/teamat/hrw001","DOIUrl":"https://doi.org/10.1093/teamat/hrw001","url":null,"abstract":"Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall’s three worlds (embodied, symbolic and formal) of mathematical thinking, and use a framework combining these with Dubinsky’s Action, Process, Object and Schema (APOS) theory to analyse students’ resulting levels of understanding. Through interviews and analysis of test and examination scripts, we investigate students’ understanding of the basic concepts of linear algebra, their ability to use and explain these concepts and their relationship to definitional clarity. The results show that, while students tend not to learn definitions by rote and can be imprecise when expressing them in words, they seem to understand the concepts, can talk sensibly about them and are able to use their essential features in solving problems.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50323955","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}
引用次数: 17
Flipping the calculus classroom: an evaluative study 翻转微积分课堂：一项评估性研究
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2016-12-01 DOI: 10.1093/teamat/hrv019
Wes Maciejewski
{"title":"Flipping the calculus classroom: an evaluative study","authors":"Wes Maciejewski","doi":"10.1093/teamat/hrv019","DOIUrl":"https://doi.org/10.1093/teamat/hrv019","url":null,"abstract":"Classroom flipping is the practice of moving new content instruction out of class time, usually packaging it as online videos and reading assignments for students to cover on their own, and devoting in-class time to interactive engagement activities. Flipping has garnered a large amount of hype from the popular education media and has been adopted in a variety of contexts. Despite this high amount of interest, few studies have evaluated the effectiveness of classroom flipping on student academic outcomes. Specifically, no rigorous studies of the effects of flipping a mathematics course on students’ mathematical understandings and achievement appear in the literature. This article reports results from a control group study of flipping a large (N = 690), first-year university calculus course for life sciences students. Students in the flipped course sections on average outperformed their counterparts in the traditional sections on the final exam, though only by approximately 8%. A more detailed analysis reveals the true beneficiaries in a flipped classroom—those with high basic mathematical ability and low initial calculus knowledge. Gains for this group are considerable: approximately 10% on the final, with an effect size of d = 0.56, and comparable gains on an independent measure of calculus concept mastery. This study positions classroom flipping as an effective practice in undergraduate mathematics and calls for further research into the mechanisms behind its effectiveness.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrv019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50324647","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}
引用次数: 73
Trigonometric integration without trigonometric functions 没有三角函数的三角积分
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2016-12-01 DOI: 10.1093/TEAMAT/HRV020
J. Quinlan, J. Kolibal
{"title":"Trigonometric integration without trigonometric functions","authors":"J. Quinlan, J. Kolibal","doi":"10.1093/TEAMAT/HRV020","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRV020","url":null,"abstract":"Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals. It introduces a framework in which students can better understand more advanced mathematical ideas such as the inverse Laplace transform and also affords an opportunity to work with detailed algebraic manipulations involving the binomial expansion.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRV020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61089905","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}
引用次数: 0
Trigonometric integration without trigonometric functions 没有三角函数的三角积分
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2016-12-01 DOI: 10.1093/teamat/hrv020
James Quinlan;Joseph Kolibal
{"title":"Trigonometric integration without trigonometric functions","authors":"James Quinlan;Joseph Kolibal","doi":"10.1093/teamat/hrv020","DOIUrl":"https://doi.org/10.1093/teamat/hrv020","url":null,"abstract":"Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals. It introduces a framework in which students can better understand more advanced mathematical ideas such as the inverse Laplace transform and also affords an opportunity to work with detailed algebraic manipulations involving the binomial expansion.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrv020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50323954","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}
引用次数: 0
Pre-service teachers’ mathematics content knowledge: implications for how mathematics is taught in higher education 职前教师的数学内容知识：对高等教育数学教学的启示
IF 0.8
Teaching Mathematics and Its Applications Pub Date : 2016-12-01 DOI: 10.1093/teamat/hrv008
Tom Lowrie;Robyn Jorgensen
{"title":"Pre-service teachers’ mathematics content knowledge: implications for how mathematics is taught in higher education","authors":"Tom Lowrie;Robyn Jorgensen","doi":"10.1093/teamat/hrv008","DOIUrl":"https://doi.org/10.1093/teamat/hrv008","url":null,"abstract":"This investigation explored pre-service teachers’ mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is acquired; and (3) the applicability of mathematics. These factors were used in subsequent multivariate analyses to determine whether teachers’ mathematics competence influenced their personal mathematics viewpoints and perspectives. There was no difference between those students who had studied advanced and standard mathematics at school on the three belief and attitude measures, despite distinct differences in their MCK.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrv008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50323956","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}
引用次数: 23
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