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1.
Making the transition to formal proof 总被引：1，自引：0，他引：1
Robert C. Moore 《Educational Studies in Mathematics》1994,27(3):249-266
This study examined the cognitive difficulties that university students experience in learning to do formal mathematical proofs. Two preliminary studies and the main study were conducted in undergraduate mathematics courses at the University of Georgia in 1989. The students in these courses were majoring in mathematics or mathematics education. The data were collected primarily through daily nonparticipant observation of class, tutorial sessions with the students, and interviews with the professor and the students. An inductive analysis of the data revealed three major sources of the students' difficulties: (a) concept understanding, (b) mathematical language and notation, and (c) getting started on a proof. Also, the students' perceptions of mathematics and proof influenced their proof writing. Their difficulties with concept understanding are discussed in terms of a concept-understanding scheme involving concept definitions, concept images, and concept usage. The other major sources of difficulty are discussed in relation to this scheme.This article is based on the author's doctoral dissertation completed in 1990 at the University of Georgia under the direction of Jeremy Kilpatrick. 相似文献
2.
This paper reports a qualitative inquiry on teaching a British undergraduate management programme to Chinese students in China. The research objectives were to develop a deeper understanding of challenges students face in their academic learning within an English speaking and study environment, and to enhance organisational learning through developing practical pedagogical techniques to improve classroom interactions. A longitudinal participatory action research strategy was employed. The subjects were second and third year undergraduate students who were studying for dual-degrees in international tourism management at a Sino-Foreign educational institute. The inquiry found that various instructional techniques could help the students engage with fellow students and the lecturer in the classroom setting. We conclude that, in addition to linguistic factors, normative values of education in Chinese culture ought to be appreciated so that Chinese students’ learning needs can be better served. 相似文献
3.
Ruth Stavy 《科学教学研究杂志》1991,28(4):305-313
A new approach to change misconceptions of students is to build on ideas which match their students' existing intuitive knowledge. This can be done by analogy. The use of an analogical relation between the known and the unknown can help students learn new information and discard or modify misconceptions. Previous studies have confirmed this result in such areas as mathematics. The present study examined the use of analogical instruction to overcome misconceptions about conservation of matter. Students who understood the concept of conservation of matter when iodine was evaporated were able to transfer their understanding to the evaporation of acetone. This indicates that teaching by analogy can be an effective tool in science. The author is now studying the relative effectiveness of conflict training and learning by analogy. 相似文献
4.
Paola Iannone Matthew Inglis Juan Pablo Mejía-Ramos Adrian Simpson Keith Weber 《Educational Studies in Mathematics》2011,77(1):1-14
Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is
an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked
undergraduate students to study a novel concept by either tackling example generation tasks or reading worked solutions to
these tasks. Contrary to suggestions in the literature, we found no advantage for the example generation group on subsequent
proof production tasks. From a second study, we found that undergraduate students overwhelmingly adopt a trial and error approach
to example generation and suggest that different example generation strategies may result in different learning gains. We
conclude by arguing that the teaching strategy of example generation is not yet understood well enough to be a viable pedagogical
recommendation. 相似文献
5.
AbstractThis study examined learning strategy use in mathematics among East Asian students in East Asian educational systems. By employing latent class analysis on the Programme for International Student Assessment (PISA) 2012 data, we found four classes of learning strategy types, namely memorization with metacognitive strategies (17.49%), metacognitive strategies with memorization (50.70%), elaboration only (10.33%), and metacognitive strategies with elaboration (16.47%). The results showed that the majority of the students in all seven East Asian educational systems belonged to the ‘metacognitive strategies with memorization’ class, and most students adopted more than one type of learning strategy when learning mathematics. Additionally, students who reported the use of metacognitive strategies along with either memorization or elaboration showed higher mathematics achievement. We conclude that the cognitive processes employed by students of East Asian backgrounds are more complex and nuanced than the previous perception that they relied heavily on memorization. 相似文献
6.
We believe that professional mathematicians who teach undergraduate mathematics courses to prospective teachers play an important role in the education of secondary school mathematics teachers. Thus, we explored the views of research mathematicians on the mathematics that should be taught to prospective mathematics teachers, on how the courses they teach can serve teachers in their work with school students, and on the changes they would implement if their courses were designed specifically for prospective teachers. We constructed profiles of the four mathematicians based on their responses to a clinical interview. We employed the construct of mathematics teacher-educators’ triad in the reflective analysis of our findings and extended the construct based on the results of this study. In conclusion, we commented on potential ways to draw stronger connections between university mathematics and the mathematics taught in schools. 相似文献
7.
P. L. Galbraith 《Higher Education》1984,13(6):675-685
An acute shortage of mathematics teachers has emerged in the Western world. This article describes a study of the influence of tertiary education experiences on the attitudes of potential mathematics teachers towards their subject.Parallel questionnaires were given to groups of students who were respectively entering university mathematics courses as new undergraduates, and entering postgraduate teacher training courses. Both groups of students answered items pertaining to their experiences within secondary mathematics courses.The undergraduate students were also asked a series of questions about their expectations of tertiary mathematics courses. For the postgraduates a parallel set of questions was provided that required them to rate their actual tertiary experiences.An analysis of responses indicated that the postgraduate students were more positive about their recollection of secondary mathematics than were the undergraduate students with their more recent experience of it. They were also less positive about the reality of their tertiary courses than were the undergraduates about their expectations. Responses of the postgraduates suggested that tertiary mathematics is not merely an extension of secondary mathematics, but a subject with which distinctive and, in general, more negative reactions are associated.Mathematics emerges as a subject which progressively loses its appeal with further study and implications are drawn for both tertiary education and teacher supply. 相似文献
8.
Owe Kågesten 《European Journal of Engineering Education》2007,32(3):303-314
In this study we created an environment for peer learning, where students teach students by making oral presentations in groups about solving mathematical problems and explaining the theoretical background in mathematics, during the first year of an undergraduate engineering programme at the Norrköping campus of the Linköping University. In order to strengthen the students’ understanding and perception of central mathematical concepts, the study was designed to take the students through five different learning experiences, preparing the presentation, presenting the mathematics, listening to others presenting, discussion by all students after the presentation and feedback by the teacher to the small group of students separate from the other students. We study how oral presentations work as a learning and assessment method. The study consisted of three stages. After a first run of the presentations as a learning instrument, three guidebooks with recommendations for students and teachers were developed in order to assist students as well as teachers about their role in this learning environment. Students’ and teachers’ views on the student presentations as learning instrument were surveyed before and after the intervention. In stage three, students were interviewed individually to ascertain the relevant success of the different learning experiences. 相似文献
9.
Joshua K. Strakos 《Decision Sciences Journal of Innovative Education》2016,14(1):51-66
Inventory management is widely researched and the topic is taught in business programs across the spectrum of operations and supply chain management. However, the concepts are notoriously difficult for students to practice once they finish school and become managers responsible for inventory control. This article explains the structure and details of an inventory management class module designed to bridge the gap between learning inventory management theory and applying the learning to practice. Through an active learning exercise, groups of logistics management graduate students in two sections of an introductory inventory management class (in‐residence and online) are taught the exchange curve concept, introduced to its use in practice, and given a tool for implementing this learning in a variety of practical scenarios. The exercise is valuable as it is well suited for students with a limited math background because it allows the exchange curve concept to be taught and demonstrated without presenting complicated mathematics. A three‐tiered assessment of the exercise reveals its effectiveness in meeting the goals of providing an engaging and interesting use of learning time and giving the students an in‐depth practical understanding of the exchange curve concept. The exercise is designed to be equally useful for application in an undergraduate class. 相似文献
10.
Alla T. Alzhanova-Ericsson Christina Bergman Patrik Dinnétz 《Journal of Further & Higher Education》2017,41(1):1-15
The value and importance of lectures in higher education is part of a modern education discourse worldwide. This study aims to estimate the importance of lectures for prospective teachers of kindergarten, preschool and early primary school. We analysed academic achievements of prospective teachers who had either mandatorily or voluntarily attended lectures in the subject of teaching and learning mathematics. Students’ examination grades in a maths course with mandatory or voluntary lecture attendance were analysed with a logistic model testing the association between lecture attendance requirement and grades. We show that mandatory lecture attendance (1) more than double the odds of students receiving a pass grade when their situated and tacit knowledge was examined and (2) quadrupled the odds of students achieving the highest grade (pass with distinction) when both their understanding of elementary mathematics and their situated and tacit knowledge of teaching and learning mathematics were examined. Our study provides evidence for a significant positive role of lecture attendance for students acquiring skills in Teaching and Learning Mathematics. While attending lectures students receive situated tacit knowledge of the subject which is otherwise difficult, if not impossible, for them to obtain in a different way. The observed improvement may have an additional positive effect in being a step towards overcoming a maths anxiety, which is otherwise relatively common among prospective teachers. 相似文献
11.
Kathryn Paige 《Asia-Pacific Journal of Teacher Education》2017,45(3):285-301
Educating for sustainability has been a key principle underpinning the primary/middle undergraduate teacher education programme at an Australian University for the past decade. Educating for sustainability seeks to provide knowledge and understanding of the physical, biological, and human world, and involves students making decisions about a range of ethical, social, environmental and economic issues, and acting upon them. This study (a part of the ongoing evaluation of our courses) focuses on pre-service teachers (PSTs) who have selected a minor in science and mathematics. Participatory and inclusive learning processes, transdisciplinary collaborations, experiential learning, and the use of local environment and community as learning resources as outlined by Sterling (2001) have formed the basis of much of our practice to develop PSTs’ confidence and competence to teach science. This paper explores one pedagogical practice, environmental pledges which the preservice teachers undertook for 15 weeks. The focus is on the impact that undertaking an environmental pledge has had on the personal and professional lives of two groups, first, four cohorts of final-year science and mathematics pathway PSTs, and second, a small group of early-career teachers who had completed the course in previous years. Data have been collected from final-year science and mathematics students and early-career teachers using ethnographic methods to provide insight into their experiences of using the pledge. 相似文献
12.
In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students
in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted
and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection
was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working
with two different groups of students. Case study methods were used to identify and analyze critical events that occurred
throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with
students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches
to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies;
(3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with
students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations
to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent
with the nature of their interactions and perceived role with students. The implications inform the development of an expanded
learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics
in technology-rich environments. 相似文献
13.
Incorporation of mathematics into biology curricula is critical to underscore for undergraduate students the relevance of mathematics to most fields of biology and the usefulness of developing quantitative process skills demanded in modern biology. At our institution, we have made significant changes to better integrate mathematics into the undergraduate biology curriculum. The curricular revision included changes in the suggested course sequence, addition of statistics and precalculus as prerequisites to core science courses, and incorporating interdisciplinary (math-biology) learning activities in genetics and zoology courses. In this article, we describe the activities developed for these two courses and the assessment tools used to measure the learning that took place with respect to biology and statistics. We distinguished the effectiveness of these learning opportunities in helping students improve their understanding of the math and statistical concepts addressed and, more importantly, their ability to apply them to solve a biological problem. We also identified areas that need emphasis in both biology and mathematics courses. In light of our observations, we recommend best practices that biology and mathematics academic departments can implement to train undergraduates for the demands of modern biology. 相似文献
14.
This study examined the relationships between university mathematics classroom environments, mathematics beliefs, and achievement in the context of mainland China. As a type of affect in mathematics learning, mathematics beliefs including mathematics conceptions and efficacy were examined as mediators. Based on analysis of a sample of 1443 undergraduate students from a university in northern China, the study not only found that the mathematics classroom environment was associated with both affective and cognitive mathematics outcomes, but also confirmed the mediating role of mathematics beliefs. Specifically, a desirable classroom environment was related to students’ cohesive conceptions, enhanced self-efficacy, and higher mathematics achievement. In contrast, students’ perceived difficulty of learning mathematics was connected to their fragmented conceptions, reduced self-efficacy and lower mathematics achievement. Implications of the study are discussed. 相似文献
15.
We analyze the interrelations between prospective and practicing teachers' learning of the mathematics of change and the development
of their emerging understanding of effective mathematics teaching. The participants in our study, who were all interested
in teaching secondary mathematics, were mathematics majors who had significant formal knowledge of the fundamental concepts
of calculus prior to taking our courses, but who often experienced and expressed procedural orientations toward the teaching
of mathematics. To address this difficulty, we developed novel computer-based activities to challenge the participants' mathematical
understandings and required them to use technology during short teaching episodes they conducted with younger students. To
analyze our participants' understandings, we developed a framework that juxtaposes the roles of the participants as students
and teachers, and their understanding of mathematics and of pedagogical strategies. Our analysis of the participants' views
from these different perspectives enabled us to see simultaneously the intertwined development of subject matter insights
and specific views of teaching.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
16.
Gaining insights into students' attitudes and beliefs is a crucial step in understanding how the learning environment for mathematics is affected by the introduction of computers and other technology. We review research into the impact of technology on the teaching and learning of mathematics, although systematic evaluations are sparse. We discuss the relationship between affective variables and performance and having constructed appropriate measures of attitude, we present results from an extensive initial study. The study disentangles affects relating to mathematics and to computing and in doing so identifies attributes which are important where mathematics and computing interact. We report on the application of six Galbraith–Haines scales to 156 students, we discuss the implications of confidence, motivation, engagement and interaction with the technology in the learning environment and we demonstrate that the computing and mathematics attitude scales capture distinctive properties of student behaviour in this respect. 相似文献
17.
We describe how a team approach that we developed as a mentoring strategy can be used to recruit, advance, and guide students to be more interested in the interdisciplinary field of mathematical biology, and lead to success in undergraduate research in this field. Students are introduced to research in their first semester via lab rotations. Their participation in the research of four faculty members-two from biology and two from mathematics-gives them a first-hand overview of research in quantitative biology and also some initial experience in research itself. However, one of the primary goals of the lab rotation experience is that of developing teams of students and faculty that combine mathematics and statistics with biology and the life sciences, teams that subsequently mentor undergraduate research in genuine interdisciplinary environments. Thus, the team concept serves not only as a means of establishing interdisciplinary research, but also as a means of incorporating new students into existing research efforts that will then track those students into meaningful research of their own. We report how the team concept is used to support undergraduate research in mathematical biology and what types of team-building strategies have worked for us. 相似文献
18.
This article describes a study about a service learning project at a small undergraduate university. We examined how professors
and students became involved in service learning through course work and related activities. This study sought to find out
why participation in service learning is low in post-secondary education science and mathematics courses. Participants described
challenges to participation as well as benefits which, if emphasized, may allow for some growth in participation by science
degree students. 相似文献
19.
The phenomenon in which students enter university under-prepared for the mathematical demands of their undergraduate courses, regularly referred to as the ‘Maths Problem’, has been widely reported in Ireland, UK, Australia, and the US. This issue has been of particular concern in Ireland recently, with beginning undergraduates’ performance of basic mathematical skills showing signs of significant decline in recent years. New mathematics curricula, commonly referred to as ‘Project Maths’, were gradually introduced into the Irish secondary school education system from 2010 onwards. These new curricula aim to place greater emphasis on student understanding of mathematical concepts, use of contexts, and applications of mathematics. This study analyses, through mathematics diagnostic test data gathered between 2008 and 2014, the change in the basic mathematical skills of beginning undergraduates over the time period in which the new mathematics curricula were introduced to secondary education in Ireland. It was found that students’ basic mathematical skills have declined over the time period during which the new mathematics curricula were introduced. Significant declines in beginning undergraduates’ performance of basic mathematical skills were observed during the period 2008–2014, particularly among students who have achieved Higher Level C grades and Higher Level D grades. 相似文献
20.
In entry-level university courses in science, technology, engineering, and mathematics fields, students participating in associated laboratory sessions generally do better than those who have no related lab classes. This is a problem when, for various reasons, not enough lab sections can be offered for students and/or when students opt out of optional available lab courses. Faced with such a situation, this study evaluated the efficacy of the peer-led team-learning (PLTL) instructional model as a potential method for narrowing the achievement gap among undergraduate students electing not to enroll in an optional laboratory component of an introductory biology course. In peer-led workshops, small groups of students participated in solving problems and other activities that encouraged active learning. Students led by peer leaders attained significantly higher exam and final course grades in introductory biology than comparable students not participating in PLTL. Among the introductory biology students who opted not to enroll in the optional lab course, those who participated in PLTL averaged more than a letter grade higher than those who did not. This difference was statistically significant, and the PLTL workshops almost entirely closed the achievement gap in lecture exam and final grades for students who did not take the lab. 相似文献