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1.
The challenges facing those charged with teaching mathematics to engineers are enormous. Faced with large groups of students possessing a considerable range of abilities, prior experiences, and motivations, it is incumbent upon the developers and deliverers of mathematics programmes to engineers to ensure that such programmes are as inclusive as possible and take into account the particular and often individual needs of the student. Often a mathematics lecturer is caught between the demands of an engineering department expecting students to know and apply advanced techniques, and the needs of groups of students who lack confidence, have serious gaps in their knowledge and sometimes lack ability in mathematics. This paper describes an innovative approach to these challenges which involves a mix of traditional and modern technologies and which has been used with some effect at Loughborough University, for the teaching of mathematics to first year undergraduate engineering students.  相似文献   

2.
Too difficult, too abstract, too theoretical – many first-year engineering students complain about their mathematics courses. The project MathePraxis aims to resolve this disaffection. It links mathematical methods as they are taught in the first semesters with practical problems from engineering applications – and thereby shall give first-year engineering students a vivid and convincing impression of where they will need mathematics in their later working life. But since real applications usually require more than basic mathematics and first-year engineering students typically are not experienced with construction, mensuration and the use of engineering software, such an approach is hard to realise. In this article, we show that it is possible. We report on the implementation of MathePraxis at Ruhr-Universität Bochum. We describe the set-up and the implementation of a course on designing a mass damper which combines basic mathematical techniques with an impressive experiment. In an accompanying evaluation, we have examined the students' motivation relating to mathematics. This opens up new perspectives how to address the need for a more practically oriented mathematical education in engineering sciences.  相似文献   

3.
Effective Classroom Organisation in Primary Schools: Mathematics   总被引：1，自引：0，他引：1  
One of the greatest problems in teaching mathematics arises from the diversity of pupils' attainments. For decades, this has been managed by primary class teachers in England by adopting an approach of within-class grouping or differentiation according to attainment-level. During the last two years, however, government initiatives have increased the focus on a whole-class approach to teaching mathematics. This has led to an increase in the number of schools adopting a policy of grouping between parallel classes, or 'setting' by attainment within classes in order to contain the range of attainment in each teaching group and to make whole-class teaching a realistic possibility. Earlier research studies have outlined the benefits of grouping by attainment for subsequent learning in mathematics, especially for higher-attaining pupils; the results this article uses challenge the findings of earlier studies. Newly available data from a large-scale primary mathematics project are examined which indicate that the attainments of pupils taught in mixed-ability classes are at least equal to those of pupils in schools set by attainment.  相似文献   

4.
Current changes, especially the wide application of information technology, in all fields of our life, mean that mathematical knowledge becomes necessary in almost every domain. It implies new expectations for mathematical education. An urgent need of a new mathematical literacy for all—also a new mathematical literacy for engineers—is evident. It is necessary to consider a process of mathematics learning at tertiary level from the epistemological perspective and to investigate students’ ways of mathematical thinking. This epistemological knowledge is especially indispensable when students use information technology. In this article current requirements regarding mathematical education are discussed, especially those for future engineers. Analysis of examples of learning elementary statistics, using graphing calculators as supporting tools, leads to the formulation of essential aims for mathematics educators concerning mathematics teaching for future engineers.  相似文献   

5.
It has been proposed that playing chess enables children to improve their ability in mathematics. These claims have been recently evaluated in a meta-analysis (Sala & Gobet, 2016, Educational Research Review, 18, 46–57), which indicated a significant effect in favor of the groups playing chess. However, the meta-analysis also showed that most of the reviewed studies used a poor experimental design (in particular, they lacked an active control group). We ran two experiments that used a three-group design including both an active and a passive control group, with a focus on mathematical ability. In the first experiment (N = 233), a group of third and fourth graders was taught chess for 25 hours and tested on mathematical problem-solving tasks. Participants also filled in a questionnaire assessing their meta-cognitive ability for mathematics problems. The group playing chess was compared to an active control group (playing checkers) and a passive control group. The three groups showed no statistically significant difference in mathematical problem-solving or metacognitive abilities in the posttest. The second experiment (N = 52) broadly used the same design, but the Oriental game of Go replaced checkers in the active control group. While the chess-treated group and the passive control group slightly outperformed the active control group with mathematical problem solving, the differences were not statistically significant. No differences were found with respect to metacognitive ability. These results suggest that the effects (if any) of chess instruction, when rigorously tested, are modest and that such interventions should not replace the traditional curriculum in mathematics.  相似文献   

6.
Abstract

To determine whether patterning instruction was as useful or more useful than other forms of instruction, kindergarten children (age five) were taught either patterning or early literacy or mathematics or social studies in matched sessions. Instruction was conducted in 15-minute sessions from November through mid-April. Posttests on patterning, mathematics, early literacy, and three executive functions showed that the children taught patterning became significantly better at patterning than those in the other instructional conditions. No differences were found between the children taught mathematics, early literacy, or social studies. Correlational analyses indicated that the relations of patterning ability, working memory, and inhibitory control to mathematics achievement were similar. Cognitive flexibility was not very strongly related to any other measure and the executive functions were relatively independent of each other for the children who were age five.  相似文献   

7.
The initial phase of undergraduate engineering degree programmes often comprises courses requiring mathematical expertise which in some cases clearly exceeds school mathematics, but will be imparted only later in mathematics courses. In this article, an approach addressing this challenge by way of example within a fundamentals of electrical engineering course is presented. The concept focuses on gaining specific mathematical knowledge and competencies in the technical context of this course. For this purpose, a complementary blended learning scenario centring around a web-based learning platform and involving an adaptation of the course was developed. The concept particularly considers the heterogeneity of today's student groups and is discussed with regard to related approaches, didactical considerations, and technical implementation. For the interventions, the results of a questionnaire-based evaluation proving students' acceptance and positive influence on examination performance are presented.  相似文献   

8.
Abstract

The central subject matter of the paper is the attempt to assess the learning gains exhibited by university students who were taught by the Case Method rather than the conventional lecture method in a relatively unpropitious non-case environment. Based on a systematic approach developed by educational psychologists, the project monitored the relative gains in terms of cognitive performance and change in motives and attitudes. The methodological approach is explained comprehensively and the quantitative results are discussed in a frank and an objective manner with a view to stimulating university teachers to rethink prevailing teaching methods and goals.  相似文献   

9.
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10.
Science and mathematics education needs to serve several (possibly contradictory) motivating goals. One is found in the movement for a universal literacy in the central principles and methods of the disciplines. The second is the need to provide the experiences and background that makes possible the production of scientists and engineers. A complication in both efforts is that the formal education takes place over many years, and the application of the layers of information, understanding, and sophistication need also be aware of the age of the student and what has come before. These efforts require clear ideas as to the end goal of the process and attention to assessment. Receiving less attention is the need to also feed and nurture the creative side of those who would become professionals, as creative approaches will be a central and necessary aspect of their work and thought. In this paper, I address the use of a course in mathematical modeling taught over a period of 25 years to undergraduate students of mathematics, mathematics education, computer science, and engineering, as a method to open up creative pathways. Through an historical discussion of the role and nature of creativity in the sciences and mathematics, a process to have students find their creative voice is described in the context of this course.  相似文献   

11.
Gila Hanna 《Interchange》2000,31(1):21-33
Proof seems to have been losing ground in the secondary mathematics curriculum despite its importance in mathematical theory and practice. The present paper critically examines three specific factors that have lent impetus to the decline of proof in the curriculum: a) The idea that proof need be taught only to those students who intend to pursue post-secondary education, b) the view that deductive proof need no longer be taught because heuristic techniques are more useful than proof in developing skills in reasoning and justification, c) the idea that deductive proof might profitably be abandoned in the classroom in favour of a dynamic visual approach to mathematical justification. The paper concludes that proof should be an essential component in mathematics education at all levels and compatible with both heuristic techniques and dynamic visual approaches.  相似文献   

12.
We have already conducted cross-cultural studies of mathematical thinking ability and the capacity to study the schools' mathematics curriculum of Tibetan and Han students. Our study methods and results have been discussed in detail in "Study on the Differences in the Development of Mathematical Thinking Ability of Tibetan and Han Children"1 and "Comparative Study of the Development of Mathematical Ability in Han and Tibetan Secondary School Students."2 The results of the study show that Tibetan students' mathematical thinking ability and capacity to learn the school mathematics curriculum are lower than these skills in Han students in the same locality. What produces these differences? And what are the influences affecting the development of Tibetan and Han students' ability to think mathematically? In the previous studies, we carried out preliminary analysis on school conditions, family environment, language, and other areas, but analyzing these external factors is insufficient to explain these differences. Educational circles in China and overseas have recently considered that the primary factors influencing learning activities were intelligence and nonintelligence psychological factors. Therefore we can only accurately state the reasons for the differences in mathematical ability of Tibetan and Han students by analyzing the individuals' intellectual and nonintellectual factors. There have been studies that have looked at the influences of intellectual and nonintellectual factors in students' schoolwork, but they are usually limited to the Han nationality and only deal with cross-cultural issues in their conclusions. We therefore went to Tibetan areas to carry out field-work to examine the differences in mathematical ability of Tibetan and Han students. This paper endeavors to analyze the data comprehensively in order to probe the intellectual and nonintellectual factors influencing the development of mathematical ability in Tibetan and Han students.  相似文献   

13.
This paper explores the nature of the language used when teaching mathematics to young children. It proposes that an important part of the teaching of a mathematical concept is the introduction of specific terminology. Children may need to be taught new meanings for already familiar words. The timing of these introductions to new words or meanings is critical to their understanding of the concepts being taught. It will be argued that there are two aspects of the children's learning that need to be considered. First, their understanding of the concept being introduced, and secondly, their learning the appropriate word to describe that concept. By assessing children's understanding of new mathematical concepts through their own use of the terminology, the teacher can then negotiate new meanings with them through practical experiences, introducing new word meanings only when the concepts have been understood.  相似文献   

14.

Enrichment for mathematically gifted students in the elementary school needs to extend beyond puzzles or busywork and support the development of mathematical power through a differentiated curriculum. This article describes a series of enrichment experiences that were designed to develop young gifted children's understanding of large numbers, which was central to their investigation of space travel. Although large numbers are not traditionally included in the mathematics curriculum for young children, the children in this group responded enthusiastically to the enrichment experiences. These experiences provided the children with an opportunity to understand the large numbers they encountered in science resource material and to develop their mathematical power.  相似文献   

15.
The present paper describes the design, implementation and evaluation of a cryptography module for final-year software engineering students. The emphasis is on implementation architectures and practical cryptanalysis rather than a standard mathematical approach. The competitive continuous assessment process reflects this approach and rewards experimentation. Students who excel at mathematics will invariably do well in cryptography. A key aim of the module is to try to extend this relationship to include good software engineers who may find mathematics more difficult. The approach is evaluated quantitatively by statistical analysis. The results of the statistical analysis show a significantly higher correlation between a student's performance in software engineering and cryptography than in mathematics and cryptography. These results indicate that this teaching approach is a better fit for software engineers than a standard approach.  相似文献   

16.
ABSTRACT

Research suggests that a significant reason that a large number of students earn low grades in the fundamental engineering science course Statics is that they may be entering the course with incorrect conceptual knowledge of mathematics and physics. The self-explanation learning approach called collective argumentation helps k-12 students to understand their misconceptions of mathematical principles that often appear abstract to them. This study investigated collective argumentation as an instructional approach that helps engineering students identify and correct their misconceptions of topics taught in Statics. Results suggest that argumentation improves student performance as measured by grades earned on semester exams. Survey and focus group results suggest that students did not understand the argumentation process. Therefore, the students did not like using it as a learning approach.  相似文献   

17.
SOMMAIRE

The curricula used to educate engineers have been the subject of study in recent years. This effort has arisen from the perceived mismatch between the topics taught, and the long term requirements of the engineering graduate. A strategic review has been hampered by a sufficiently useful definition of what an engineer should be. This paper suggests such a definition, based upon the idea that engineers are general problem-solvers within a financial and technical set of co-ordinates. Using this definition as an analytical tool, it is possible to see the strengths and limitations of the current programmes, and to approach curriculum development on a more rational basis. It is concluded that, in general, current engineering education concentrates upon the treatment of a class of problems whose solution is rather obvious, even if the tools used to produce the solution may be complex and arcane. It is suggested that engineering curricula should address a wider set of problems, with less obvious solutions, since this is closer to reality, and also since it will allow an engineering-orientated viewpoint to be brought to bear in complex problems. A modified curriculum is proposed, based upon these ideas.

On a étudié depuis longtemps les programmes d'enseignement pour la formation des ingénieurs. Ces recherches ont, pour leur origine, les differences entre les sujets qu 'un ingénieur doit étudier pendant son formation, et ceux qu'il utilise actuellement en train de sa vie profes-sionelle. Pour mieux comprendre ces differences, on a examine surtout ces cours elles-meme, et les méthodes pedagogiques. On n'a pas reussi parce qu' on n'a pas pu repondre à la question “Qu'est-ce que c'est un ingenieur?” lei, on essai de donner un reponse, vis.: “Un ingenieur se conceme avec la resolution des problemes”, souvent dans un cadre financier, Avec cette definition, on peut analyser les programmes d'enseignement qui existe à ce moment. Aussi, on peut proposer des modifications basées sur la raison. On peut dire que les cours de la formation des ingénieurs fixent leur attention sur une catégoric de probleme pour laquelle la solution est evident, meme si les méthodes d'analyse. (mathematique, ordinateur etc) peuvent etre assez difficile. On propose que, pour la formation des ingénieurs, les cours se concernent avec une categorie des problemes plus larges, avec des solutions qui ne sont pas immediatement evident (et pour lesquelles on peut souvent proposer plusieurs bons solutions). Enfin, on propose un cours modifié, en prenant compte de ces pensées.  相似文献   


18.
If what is taught is important but how well it is taught has only a trivial impact, then much of the work on 'school effectiveness' may be studying short term effects which quickly disappear from the system and have no long term consequences. If such were the case, then school effectiveness researchers would need to give greater consideration to what is studied, rather than simply how well it is studied. The influence of schools on curriculum choices may be more important than their influence on relative performance or "value added". In the UK 'A' levels represent a useful point at which to look at the impact of curriculum choice since students typically have to choose to study only two or three subjects for the final 2 years of secondary school. The choices are made at the age of 16 with little evidence available regarding the long term consequences. This article presents an exploration of the consequences of taking or not taking 'A' level mathematics. Evidence was available from a 5 year follow-up study of students who took 'A' levels in 1988. There were substantial differences between institutions in the extent to which students were attracted into mathematics, that is in the "Pulling Power" of mathematics departments. Focusing on students who appeared sufficiently able to have taken mathematics at A-level it was found that those who did and who were in high "Pulling Power" institutions, reported, 5 years later, a higher quality of life and a higher expectation for salaries than similarly able students who had been in institutions with low "Pulling Power" for mathematics and who had taken English at A-level.  相似文献   

19.
An experiment was conducted to examine the effects of metacognitive instruction on mathematics achievement and attitude towards mathematics of low mathematics achievers at a middle school in the North‐West Province of South Africa. Forty standard (std) 7 pupils were identified whose non‐verbal general ability and previous mathematics achievements were significantly lower than those of other std 7 pupils. These subjects were randomly assigned to an experimental group and a control group. Metacognitive strategies in solving mathematical problems related to four mathematics topics were individually taught to the members of the experimental group, while the pupils in the control group were taught the four mathematics topics through the conventional method of teaching mathematics. The comparisons of pretest and posttest measures of general ability, metacognitive awareness, attitude towards mathematics, and mathematics achievement revealed that the posttest scores of all the four variables for the experimental group were significantly higher than those for the control group.  相似文献   

20.
Abstract

As experimental studies to compare a control group with an experimental group in new mathematics programs were introduced, experimenters became aware that many variables which could have an observable effect on test scores were not being measured. Among these was the student-subject's attiude toward his preparation for the course work under comparison. In order to ascertain a subject's attitude toward his mathematical preparation for college Calculus an attitude scale of the Thurstone type was developed. Students at two institutions in Oklahoma were used to obtain statements regarding their attitude toward their mathematical preparation, and to scale these statements. Two final scales were developed, one with a high face validity, and one with an abstract, research oriented base.  相似文献   

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