An ongoing reform programme of the post-16 Advanced ‘A’-level qualifications in England and Wales means that pre-university mathematics content and assessment will change from 2017. Undergraduate engineering is a subject that relies heavily on mathematics, and applicants to engineering degree programmes in the UK are required to have studied A-level Mathematics in order to be accepted. Therefore, the planned reforms are likely to have an impact on students’ transition to undergraduate engineering. To investi-gate this, we conducted an online questionnaire survey of 462 current undergraduate engineering students who had taken A-levels. Participants reported on their experiences of studying post-compulsory mathematics and the preparation it provided for their degrees. Those who had studied the more advanced A-levelçFurther Mathematicsçin addition to A-level Mathematics, considered it to be good preparation. They also believed that the A-level structure, which allows specialization in certain areas of applied mathematics, to be advantageous. In particular, possibilities for in-depth study of mechanics and pure mathematics were highly valued by participants. It is recommended that university engineering departments do more to encourage prospective students to study Further Mathematics. However, it should not necessarily be made compulsory because of con-straints regardingaccess, uptake and provisionof FurtherMathematics in certain schools.
{"title":"Engineering Undergraduates' Views of A-Level Mathematics and Further Mathematics as Preparation for Their Degree.","authors":"Ellie Darlington, Jessica Bowyer","doi":"10.1093/TEAMAT/HRW020","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRW020","url":null,"abstract":"An ongoing reform programme of the post-16 Advanced ‘A’-level qualifications in England and Wales means that pre-university mathematics content and assessment will change from 2017. Undergraduate engineering is a subject that relies heavily on mathematics, and applicants to engineering degree programmes in the UK are required to have studied A-level Mathematics in order to be accepted. Therefore, the planned reforms are likely to have an impact on students’ transition to undergraduate engineering. To investi-gate this, we conducted an online questionnaire survey of 462 current undergraduate engineering students who had taken A-levels. Participants reported on their experiences of studying post-compulsory mathematics and the preparation it provided for their degrees. Those who had studied the more advanced A-levelçFurther Mathematicsçin addition to A-level Mathematics, considered it to be good preparation. They also believed that the A-level structure, which allows specialization in certain areas of applied mathematics, to be advantageous. In particular, possibilities for in-depth study of mechanics and pure mathematics were highly valued by participants. It is recommended that university engineering departments do more to encourage prospective students to study Further Mathematics. However, it should not necessarily be made compulsory because of con-straints regardingaccess, uptake and provisionof FurtherMathematics in certain schools.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"36 1","pages":"200-216"},"PeriodicalIF":0.8,"publicationDate":"2016-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRW020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61090234","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}
M. Carr, Mark Prendergast, C. Breen, Fiona Faulkner
In the Dublin Institute of Technology, high threshold core skills assessments are run in mathematics for third-year engineering students. Such tests require students to reach a threshold of 90% on a multiple choice test based on a randomized question bank.The material covered by the test consists of the more important aspects of undergraduate engineering mathematics covered in the first 2 years of the Honours degree programme and the 3 years of the Ordinary degree programme. Students are allowed to resit the assessment as frequently as required until they pass. In order to measure the effectiveness of such an exercise, a follow-up assessment was given to students on their first day of their fourth year. A comparison is made with the level of basic mathematical knowledge of these students on their first day in third year, exactly a year previously. For the majority of the students we see a significant decrease in the performance of the students from the beginning of third year to the beginning of fourth year. In addition, students were surveyed for their perception of both how much knowledge had been retained and how effective they felt that this approach had been. Overall the students felt positive about the process of online testing and that it would make it easier for them to regain this information in the future.
在都柏林理工学院(Dublin Institute of Technology)，对三年级工程专业学生的数学进行了高门槛的核心技能评估。这类考试要求学生在基于随机题库的多项选择题中达到90%的阈值。该测试涵盖的材料包括在荣誉学位课程的前两年和普通学位课程的三年中涵盖的更重要的本科工程数学方面。学生可以根据需要随时重新进行评估，直到他们通过。为了衡量这种练习的有效性，在学生第四年的第一天对他们进行了后续评估。与这些学生在一年前的三年级第一天的基础数学知识水平进行比较。对于大多数学生来说，我们发现从三年级开始到四年级开始，学生的表现明显下降。此外，还调查了学生对保留了多少知识以及他们认为这种方法的有效性的看法。总体而言，学生们对在线测试的过程持积极态度，认为这将使他们在未来更容易重新获得这些信息。
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A. Reyes-Rodriguez, Manuel Santos-Trigo, Fernando Barrera-Mora
{"title":"The construction of a square through multiple approaches to foster learners’ mathematical thinking","authors":"A. Reyes-Rodriguez, Manuel Santos-Trigo, Fernando Barrera-Mora","doi":"10.1093/TEAMAT/HRW022","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRW022","url":null,"abstract":"","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"36 1","pages":"167-181"},"PeriodicalIF":0.8,"publicationDate":"2016-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRW022","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61090268","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}
Drawing on large-scale survey data and interviews with students during their first year at university, and case studies in their institutions, we explore the problems faced by students taking mathematically demanding courses, e.g. physics and engineering. These students are often taught mathematics as a service subject by lecturers of mathematics. Analysis of students’ perceptions of transition suggests that ‘the lecture’ in Higher Education continues to pose problems. Thematic analysis of interview data shows that these problems relate to the way lectures involve ‘time pressure’ and ‘lack of dialogue/interaction’ which are practices that we associate with transmissionist pedagogy generally and can also create negative dispositions. A case study of one mathematics course for engineering that we argue made a difference is presented, and conclusions drawn for developing practice which are especially pertinent with the introduction of the Teaching Excellence Framework to monitor and assess teaching in universities.
{"title":"‘They [the lecturers] have to get through a certain amount in an hour’: first year students’ problems with service mathematics lectures","authors":"Diane Harris;Maria Pampaka","doi":"10.1093/teamat/hrw013","DOIUrl":"https://doi.org/10.1093/teamat/hrw013","url":null,"abstract":"Drawing on large-scale survey data and interviews with students during their first year at university, and case studies in their institutions, we explore the problems faced by students taking mathematically demanding courses, e.g. physics and engineering. These students are often taught mathematics as a service subject by lecturers of mathematics. Analysis of students’ perceptions of transition suggests that ‘the lecture’ in Higher Education continues to pose problems. Thematic analysis of interview data shows that these problems relate to the way lectures involve ‘time pressure’ and ‘lack of dialogue/interaction’ which are practices that we associate with transmissionist pedagogy generally and can also create negative dispositions. A case study of one mathematics course for engineering that we argue made a difference is presented, and conclusions drawn for developing practice which are especially pertinent with the introduction of the Teaching Excellence Framework to monitor and assess teaching in universities.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 3","pages":"144-158"},"PeriodicalIF":0.8,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/teamat/hrw013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50302567","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":"Front matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 3","pages":"1-2"},"PeriodicalIF":0.8,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016818/8151516/08237128.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50302568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Drawing on large-scale survey data and interviews with students during their first year at university, and case studies in their institutions, we explore the problems faced by students taking mathematically demanding courses, e.g. physics and engineering. These students are often taught mathematics as a service subject by lecturers of mathematics. Analysis of students’ perceptions of transition suggests that ‘the lecture’ in Higher Education continues to pose problems. Thematic analysis of interview data shows that these problems relate to the way lectures involve ‘time pressure’ and ‘lack of dialogue/interaction’ which are practices that we associate with transmissionist pedagogy generally and can also create negative dispositions. A case study of one mathematics course for engineering that we argue made a difference is presented, and conclusions drawn for developing practice which are especially pertinent with the introduction of the Teaching Excellence Framework to monitor and assess teaching in universities.
{"title":"‘They [the lecturers] have to get through a certain amount in an hour’: first year students’ problems with service mathematics lectures","authors":"D. Harris, M. Pampaka","doi":"10.1093/TEAMAT/HRW013","DOIUrl":"https://doi.org/10.1093/TEAMAT/HRW013","url":null,"abstract":"Drawing on large-scale survey data and interviews with students during their first year at university, and case studies in their institutions, we explore the problems faced by students taking mathematically demanding courses, e.g. physics and engineering. These students are often taught mathematics as a service subject by lecturers of mathematics. Analysis of students’ perceptions of transition suggests that ‘the lecture’ in Higher Education continues to pose problems. Thematic analysis of interview data shows that these problems relate to the way lectures involve ‘time pressure’ and ‘lack of dialogue/interaction’ which are practices that we associate with transmissionist pedagogy generally and can also create negative dispositions. A case study of one mathematics course for engineering that we argue made a difference is presented, and conclusions drawn for developing practice which are especially pertinent with the introduction of the Teaching Excellence Framework to monitor and assess teaching in universities.","PeriodicalId":44578,"journal":{"name":"Teaching Mathematics and Its Applications","volume":"35 1","pages":"144-158"},"PeriodicalIF":0.8,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/TEAMAT/HRW013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61090133","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}
A wide body of literature has highlighted how high achievement in mathematics in secondary school does not necessarily motivate students to both choose and succeed on mathematically demanding programmes at post-compulsory level. The recent Enterprising Science project (Archer et al. (2015, J. Res. Sci. Teach., 52, 922–948)) and before that, the ASPIRES project (Archer et al. (2013, London: Kings College)), have both highlighted that access to science capital is perhaps more important than prior achievement in shaping students’ aspirations and their future trajectories in Science, Technology, Engineering and Mathematics. In this article, we critically analyse the notion of science capital and its role in mediating students’ choice of and experience of studying mathematically demanding degree programmes at university. Drawing on data from the TransMaths project, we present two cases—Stacey and Elton—who are both enrolled on the same ‘Mathematics for Physics’ course at university. We show that although both discuss access to science capital in narrating their choice of degree, they do so in different ways and this invariably interplays with different forms of identification with ‘Mathematics for Physics’. We conclude that there is a need to re-conceptualize science capital so that the dialectic relationship between its exchange and use value is theorized more fully. Whilst some students may access science capital as a means to accumulate capital (e.g. qualifications) for its own sake (exchange value), others appear to recognize the ‘use value’ of science learning and knowledge and this produces different forms of engagement with science (and mathematics). We therefore argue that authoring oneself in the name of a STEM identity is crucial in mediating how one perceives science capital. Finally, we argue that mathematics should be a central part of this framework since it significantly contributes to the exchange value of science as a form of capital (especially Physics), but it also offers use value in scientific labour (e.g. in modelling scientific problems).
大量文献强调，中学数学成绩优异并不一定能激励学生在义务教育后选择并成功完成对数学要求很高的课程。近期创业科学项目(Archer et al.， 2015, J. Res. Sci.)教书。， 52, 922-948))以及在此之前的aspire项目(Archer等人(2013年，伦敦:国王学院))都强调，在塑造学生在科学、技术、工程和数学方面的抱负和未来轨迹方面，获得科学资本可能比先前的成就更重要。在本文中，我们批判性地分析了科学资本的概念及其在中介学生选择和学习数学要求高的大学学位课程的经验中的作用。根据TransMaths项目的数据，我们提出了两个案例——stacey和elton——他们都在大学里参加了同一门“数学为物理”课程。我们表明，尽管两者都在叙述他们的学位选择时讨论了获取科学资本的途径，但他们以不同的方式这样做，这总是与对“物理数学”的不同形式的认同相互作用。我们认为，有必要重新定义科学资本的概念，以便更充分地理论化科学资本的交换与使用价值之间的辩证关系。虽然一些学生可能为了自己的利益(交换价值)而将科学资本作为积累资本(例如资格)的手段，但其他人似乎认识到科学学习和知识的“使用价值”，这产生了不同形式的科学(和数学)参与。因此，我们认为，以STEM身份的名义创作自己对于调解一个人如何感知科学资本至关重要。最后，我们认为数学应该是这个框架的核心部分，因为它显著地促进了科学作为一种资本形式的交换价值(尤其是物理学)，但它也提供了科学劳动的使用价值(例如，在科学问题建模中)。
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In this editorial we explain the background to the research papers reported in this special issue, and to some extent how each paper relates to this body of work. In particular we outline the research projects and research teams that worked together between 2006 and 2014 on projects that related to the theme of transition, and we provide the knowledge base on which these papers build.
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A wide body of literature has highlighted how high achievement in mathematics in secondary school does not necessarily motivate students to both choose and succeed on mathematically demanding programmes at post-compulsory level. The recent Enterprising Science project (Archer et al. (2015, J. Res. Sci. Teach., 52, 922–948)) and before that, the ASPIRES project (Archer et al. (2013, London: Kings College)), have both highlighted that access to science capital is perhaps more important than prior achievement in shaping students’ aspirations and their future trajectories in Science, Technology, Engineering and Mathematics. In this article, we critically analyse the notion of science capital and its role in mediating students’ choice of and experience of studying mathematically demanding degree programmes at university. Drawing on data from the TransMaths project, we present two cases—Stacey and Elton—who are both enrolled on the same ‘Mathematics for Physics’ course at university. We show that although both discuss access to science capital in narrating their choice of degree, they do so in different ways and this invariably interplays with different forms of identification with ‘Mathematics for Physics’. We conclude that there is a need to re-conceptualize science capital so that the dialectic relationship between its exchange and use value is theorized more fully. Whilst some students may access science capital as a means to accumulate capital (e.g. qualifications) for its own sake (exchange value), others appear to recognize the ‘use value’ of science learning and knowledge and this produces different forms of engagement with science (and mathematics). We therefore argue that authoring oneself in the name of a STEM identity is crucial in mediating how one perceives science capital. Finally, we argue that mathematics should be a central part of this framework since it significantly contributes to the exchange value of science as a form of capital (especially Physics), but it also offers use value in scientific labour (e.g. in modelling scientific problems).
大量文献强调，中学数学成绩高并不一定能激励学生在义务教育后选择数学要求高的课程并取得成功。最近的创业科学项目（Archer et al.（2015，J.Res.Sci.Thech.，52922-948））和在此之前的ASPIRES项目（Archeret al.（2013，伦敦：国王学院））都强调，在塑造学生在科学、技术、，工程和数学。在这篇文章中，我们批判性地分析了科学资本的概念及其在调节学生在大学学习数学要求高的学位课程的选择和体验中的作用。根据TransMaths项目的数据，我们介绍了两个案例——Stacey和Elton——他们都在大学学习同一门“数学换物理”课程。 我们发现，尽管两人在讲述他们的学位选择时都讨论了获得科学资本的途径，但他们以不同的方式这样做，这总是与“数学换物理”的不同认同形式相互作用。 我们得出的结论是，有必要重新概念化科学资本，以便更充分地理论化其交换和使用价值之间的辩证关系。虽然一些学生可能为了自己的利益（交换价值）而获得科学资本作为积累资本（如资格）的一种手段，但其他学生似乎认识到科学学习和知识的“使用价值”，这产生了不同形式的科学（和数学）参与。因此，我们认为，以STEM身份的名义创作自己，对于中介人们如何看待科学资本至关重要。最后，我们认为数学应该是这个框架的核心部分，因为它作为一种资本形式（尤其是物理学）对科学的交换价值做出了重大贡献，但它也为科学劳动提供了使用价值（例如，为科学问题建模）。
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