Attitudes of Engineering Students to Mathematics--A Comparison across Universities.
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| Title: | Attitudes of Engineering Students to Mathematics--A Comparison across Universities. |
|---|---|
| Language: | English |
| Authors: | Shaw, C. T., Shaw, V. F. |
| Source: | International Journal of Mathematical Education in Science and Technology. Jan-Feb 1999 30(1):47-63. |
| Peer Reviewed: | Y |
| Page Count: | 17 |
| Publication Date: | 1999 |
| Intended Audience: | Practitioners; Teachers |
| Document Type: | Guides - Classroom - Teacher Journal Articles |
| Descriptors: | College Students, Engineering Education, Foreign Countries, Higher Education, Mathematics Education, Questionnaires, Student Attitudes, Student Surveys |
| Geographic Terms: | United Kingdom |
| ISSN: | 0020-739X |
| Abstract: | Surveys engineering students' attitudes towards mathematics in three different United Kingdom universities. Reports that students can be placed into five groupings; members of groups recorded significantly different responses to many of the questions posed, including their university, gender, home or overseas status, mathematics qualification on entry to university, and so on. Contains 22 references. (Author/ASK) |
| Entry Date: | 1999 |
| Accession Number: | EJ580454 |
| Database: | ERIC |
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| FullText | Links: – Type: pdflink Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwH01eA8UCi2lbXSNP6RS5x8AAAA4TCB3gYJKoZIhvcNAQcGoIHQMIHNAgEAMIHHBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDINKpuvYbm_eDKql2gIBEICBmf2VsJDgyeKNkuWJfxl440hiXBYExJWn_fGoj-ksviFLtN2DfbqKy30u2F9gWkU_70ERpnJ5Z3rlx3bkiQsYoQuQfbbZIDPlO31PmiyZulUbdd9SRKkWkvcj-xDKaN8adRiwDow_OA03pm7shLIxB4xtoaD2WNgOqHoqBnNBNfup1ef8ec5vnWIF-3Ovz_fWyTALS5reGyDOOA== Text: Availability: 1 Value: <anid>AN0001602966;IMT01JAN.99;2000Oct18.16:16;v4.1</anid> <title id="AN0001602966-1">ATTITUDES OF ENGINEERING STUDENTS TO MATHEMATICS--A COMPARISON ACROSS UNIVERSITIES </title> <p>There is much debate about the level of mathematics ability of students starting engineering courses at university. However, attempts to determine a student's performance in mathematics as a function of their mathematics qualification on entry is very difficult, as a wide range of performance is achieved by students with the same qualifications. Clearly other factors are at work, including the attitudes of students towards mathematics teaching. This paper presents the results of a survey of the attitude of engineering students to mathematics in three different UK universities. Further, information has also been obtained on students' ratings of teaching methods and mathematics topics. From this, it is found that students can be placed into five groupings known as High Flyers, Downhillers, Ambivalents with Good Pre-University Teaching, Ambivalents with Poor Pre-University Teaching and Haters. The members of each of these groups record significantly different responses to many of the questions posed, but in particular to their university, gender, home or overseas status, mathematics qualification on entry to university, the rating of the difficulty of mathematics topics and the rating of the usefulness of teaching methods. Finally, a factor analysis shows that three independent factors are important in determining students' attitudes: the pre-university experience, the university experience and the perceived difficulty and workload at university. </p> <hd id="AN0001602966-2">1. Introduction</hd> <p>At present the mathematical education of engineering students in the UK is the subject of much debate. There are many facets to this debate including the changes in the way that mathematics is taught within schools, the increase in the number of routes of entry to higher education (each with a different mathematical content), the reduction in the mathematics content in undergraduate engineering courses and the increasing use of calculators and computer software in mathematics teaching. For example, many changes have been brought about by the replacement of GCE O-level and CSE qualifications by GCSE qualifications [<reflink idref="bib1" id="ref1">1</reflink>, 2], as well as by the introduction of the National Curriculum [<reflink idref="bib3" id="ref2">3</reflink>, 4], the changes to A-level syllabi [<reflink idref="bib4" id="ref3">4</reflink>, 5] and then the introduction of core syllabi at both A- and AS-level [<reflink idref="bib6" id="ref4">6</reflink>, 7]. These changes have led to considerable disquiet about the preparation of students in mathematics before university and about the ability of many engineering students to cope with mathematics. </p> <p>Further, the entry qualifications of engineering students are becoming much broader. University engineering departments have traditionally recruited a majority of students with A-level and a minority with qualifications such as those offered by BTEC either at National or Higher National level. Now, however, students are also recruited from one-year Access (or similar) courses and with Advanced GNVQs. Such a broad spectrum of entry qualifications has led to some engineering courses reducing their mathematics content to enable students to survive the experience. All of this has led to the publication, and Europe-wide promotion, of a common core syllabus for mathematics within engineering degrees as well as a list of assumed pre-requisite knowledge [<reflink idref="bib8" id="ref5">8</reflink>]. While this common core syllabus is widely discussed within the engineering mathematics community, it is difficult to know what its influence on courses has been to date. </p> <p>It must be stated here that some changes might well be for the better, removing what some students see as the boring or difficult elements of mathematics and so increasing motivation and interest. An example of this is the use of powerful calculators and computer tools, such as computer algebra packages, which is becoming more widespread within universities [<reflink idref="bib9" id="ref6">9</reflink>, 10]. Such has been the nature of the debate in the UK that several organizations including the Institute of Mathematics and Its Applications (IMA) and the Engineering Council have issued reports on these topics [<reflink idref="bib11" id="ref7">11</reflink>] and also sponsored major conferences to promote discussion [<reflink idref="bib12" id="ref8">12</reflink>, 13]. It was in reponse to these conferences that the work presented here was initiated. </p> <p>In an initial study [<reflink idref="bib14" id="ref9">14</reflink>] the performance of engineering students in mathematics within their degree programme at Warwick was compared to their entry qualification in mathematics. It was found that for students with the same mathematics qualification on entry there was a large amount of variability in their examination performance. Consequently, factors other than the entry qualification appeared to affect performance in the examination. In an attempt to determine what these other factors might be, a survey of student attitudes to mathematics was carried out using a structured questionnaire. Similar surveys have also been carried out in subsequent years at Warwick, and the results of these are reported by Shaw and Shaw [<reflink idref="bib15" id="ref10">15</reflink>]. </p> <p>When analysing the data, Shaw and Shaw [<reflink idref="bib14" id="ref11">14</reflink>, 15] used cluster analysis [<reflink idref="bib16" id="ref12">16</reflink>] to produce a set of five attitude groupings of students: the High Flyers, the Downhillers, the Averages (or Ambivalents), the Haters and the Realistics. Considerable information has been found about the characteristics of the groups and their members, in terms of the size of the groups, the mathematics entry qualification, the school or college background before university, the preferred instruction media, the perceived level of difficulty of various topics in mathematics and the time spent working on mathematics. This information has proved useful to other institutions, for example in preparing tutors of mathematics for the types of students that they are likely to encounter in their teaching. However, as the students of only one institution have been surveyed, the results may not be representative of the situation in other institutions. </p> <p>This study aims to address this issue by assessing the situation in a wider range of institutions. As a result, the questionnaire survey has been repeated in three further universities in the UK. From this more comprehensive survey it should be possible to validate the attitude groupings of students, to investigate the composition of the groups across the three universities and to understand the driving forces behind the attitudes of students. This paper gives the results of the latest survey, including the new attitude groupings that are identified. Further, a factor analysis of the data is carried out to see if independent factors can be found that affect the attitudes of the engineering students to mathematics education. </p> <hd id="AN0001602966-3">2. The survey process</hd> <hd id="AN0001602966-4">2.1. The questionnaire</hd> <p>Before this work commenced, little was known about students' attitudes to mathematics, with the exception of work carried out by Heard [<reflink idref="bib17" id="ref13">17</reflink>], which explores the changes that students would like to make to their mathematics courses and the topics causing difficulty, and Keys and Wardman [<reflink idref="bib18" id="ref14">18</reflink>] which reveals that difficulty with mathematics is a major reason for students to leave an engineering degree course. </p> <p>So that a better understanding of students' attitudes to mathematics might be obtained, a questionnare has been developed. The questionnaire used in this work reported here is similar to that used in the previous studies at Warwick with some small changes to cater for other institutions. Using the questionnaire, information has been requested in four categories: </p> <ulist> <item> Personal background. Questions on gender, age, previous type of educational establishment, the highest qualification in mathematics prior to entry, home or overseas student status, the degree course applied for and the current year of study. </item> <item> Mathematics before coming to university. Questions asking students to rate, on a five-point scale, the helpfulness of mathematics teachers or lecturers, the level of difficult of mathematics, the enjoyment of mathematics courses. </item> <item> Mathematics at university. Questions asking students to rate, on a five-point scale, the usefulness of mathematics lectures, course notes and handouts, course textbook, computer-assisted learning, tutorials in mathematics, the difficulty with mathematics in comparison to other subjects, the enjoyment of the mathematics course and the comparative workload for the course. A single question also asks for the time spent studying mathematics outside formal sessions. </item> <item> General questions. Questions asking students to rate, on a five-point scale, the difficulty of the following topics: integration, differentiation, differential equations, matrices, vectors, probability, statistics, trigonometric functions, logarithmic functions, geometry, algebra, complex numbers, hyperbolic functions and series. Two further questions ask students to rate, on a five-point scale, their motivation for mathematics and their desire to improve their capability in mathematics. </item> </ulist> <hd id="AN0001602966-5">2.2. The universities surveyed</hd> <p>While the previous study [<reflink idref="bib14" id="ref15">14</reflink>, 15] of the attitudes of engineering students to mathematics at a single university has produced results which are both interesting and of use to the community, it is clear that a broader study is required. Such research is necessary to see how the attitudes of students vary across what is now a very diverse range of universities in the UK. In this study, the questionnaire has been issued to students at three universities, with each institution being typical of one particular type of university within the UN system. All three universities will be referred to in an anonymous form, i.e. Universities X, Y and Z. In all three institutions, staff members issued the questionnaire during a formal teaching period and asked the students to complete and return the questionnaire at the end of the session. This has enabled high response rates to be achieved which are much better than the minimum rates suggested in the literature [<reflink idref="bib19" id="ref16">19</reflink>] for this type of research. </p> <hd id="AN0001602966-6">University X</hd> <p>University X is a typical so-called 'Old University' which aims to have departments that are strong in both research and teaching. This institution was chosen in an attempt to provide a control for the data gathered previously at Warwick. Hence the results from University X should provide a direct check on the results obtained previously. </p> <p>Each year University X recruits several hundred engineers across a range of disciplines, mainly from what might be classed as traditional students, i.e. those coming to university immediately after leaving school at about 18 years of age and having three A-levels. However, as with most university engineering courses, a significant minority of students are recruited from other backgrounds. For example, these might be students with BTEC qualifications or those returning to study after a gap of several years during which they have been in employment. To cater for the needs of both traditional and non-traditional students, the mathematics course at University X is split into two. In both cases the students receive two one-hour lectures and one one-hour example class per week. However, different staff members teach the two groups and different textbooks are used. When discussing these groups, the traditional students will be labelled X<subs>Trad</subs> and the non-traditional students as X<subs>Ntrad</subs>. </p> <p>In this survey, data has been obtained from 108 first-year students in the traditional category out of a total of 162 students in the class, representing a response rate of 67% (note, however, that in total there are 445 traditional first-year students at University X). Also data has been obtained from 50 students in the non-traditional category out of a total of 70 such students, a response rate of 71%. </p> <hd id="AN0001602966-7">University Y</hd> <p>University Y is a typical former Polytechnic, known for the quality of its engineering education. Engineering students come to University Y with a wide range of qualifications including A-levels and BTEC certificates and diplomas at all levels. Many have also undertaken Access or Foundation courses or arrive with a range of overseas qualifications. Data has been collected from students across a range of engineering programmes. In total, 50 first-year students have been surveyed out of a total of 70 such students, giving a response rate of 71%, and 66 second-year students have been surveyed out of a total of 91 students, giving a response rate of 73%. The teaching methods at University Y include formal lectures, course notes, a course text, computer-assisted learning and tutorials. </p> <hd id="AN0001602966-8">University Z</hd> <p>University Z represents a former College of Higher Education which achieved university status directly. It represents a small group of such institutions in the UK. Typical students have non-traditional qualifications and are following nontraditional modes of study, such as part-time study. Data has been collected from 29 students out of a total of 34 students who are studying engineering in what is effectively their second year of study at degree level. This gives a response rate of 85%. Students are taught in one evening session per week with a mixture of lecture, seminar and examples classes given in a two-hour period. </p> <hd id="AN0001602966-9">3. An overview of the data</hd> <hd id="AN0001602966-10">3.1. A respondent profile</hd> <p>For all respondents, 91% are male. Looking at the age profile, 73% of respondents are aged 21 or younger and 96% are aged 30 or younger. In terms of Home and European Union students, 84% of the total are in this category, with the remainder coming from other countries. </p> <p>The previous educational establishments attended by the respondents included comprehensive schools (12%), grammar schools (9%), secondary schools (11%), sixth-form colleges (14%), public (private) schools (11%), further education colleges (28%) and other universities or higher education institutions (15%). </p> <p>Finally, 69% of respondents are in their first year of study and 31% in their second year of study. </p> <hd id="AN0001602966-11">3.2. The key attitude variables</hd> <p>As in the previous study, use will be made of eight key attitude variables when using cluster analysis to produce the groupings of students. Cross-tabulation of the responses for the four groups of students considered yield significant differences at the 5% level or better for five of the eight variables. These are the helpfulness of staff before university (significance level 0.001), difficulty of mathematics before university (significance level 0.023), enjoyment of mathematics before university (significance level 0.004), difficulty of mathematics at university (significance level 0.000) and mathematics workload at university (significance level 0.000). The variables showing no significant differences at the 5% level are enjoyment of mathematics at university (significance level 0.057), motivation for mathematics at university (significance level 0.591) and desire to improve mathematics capability (significance level 0.345). </p> <p>To gain a feel for the data collected in this present survey and so understand the reasons behind the appearance, or lack of it, of significant differences, the results for these eight variables are shown in table 1. There they are also compared with the results obtained previously. </p> <p>From table 1, it can be seen that for traditional students, at University X and at Warwick, around 10% found that the staff that taught mathematics previously were not helpful. This percentage increases to around 20% for the non-traditional students at Universities X and Y, but is very low at University Z. The increase for non-traditional students might be expected, but the reduction at University Z is against this trend and probably reflects the care taken in preparing these students before entry. Differences are also found for the rating of mathematics difficulty before university, where 23% of traditional students at University X record previous difficulties, a level much lower than elsewhere. Also, the rating of previous enjoyment of mathematics is lower than the average level for traditional students at University X and higher than the average for students at University Y. Mathematics difficulty at university also varies widely across the four groups of students sampled here, as does the perception of workload. In particular, students at University Z record high levels of difficulty and workload. </p> <p>As would be expected for the variables with no significant differences, i.e. enjoyment of mathematics at university, motivation towards mathematics and a desire to improve, these are rated similarly across all four groups of students. Also, while it is disappointing that only around one-third are motivated towards mathematics, it is encouraging that four-fifths wish to improve their capability in mathematics. </p> <p>By comparing the data for Warwick students with that for the other groups of students, it can be seen that for the three variables concerned with mathematics teaching at university, i.e. enjoyment, difficulty and comparative load, Warwick is seen as being a much tougher option than Universities X and Y. Hence it may be that these universities provide a more sympathatic approach in their teaching, as the number of students responding negatively to these three questions is typically halved in these institutions compared to Warwick. </p> <p>One interesting feature of the data is the trend in enjoyment and difficulty of mathematics when comparing the responses given for experiences before university and then at university. The data from the previous survey at Warwick showed a marked increase in those not enjoying the subject and also in those finding it difficult. A much more encouraging trend is found for the three universities surveyed here. In particular, the percentage of students at University Y that do not enjoy mathematics at university is lower than the percentage not enjoying mathematics before university and also fewer find it difficult at university. Again, it could be that this is due to a more sympathetic approach to teaching, but it might also be that difficult parts of the syllabus, which by the nature of the general engineering course at Warwick must be taught in the first year, are left out at X, Y and Z. </p> <p>Finally, it is worth looking at the time spent by students working on mathematics outside formal teaching. In Universities X, Y and Z, about half of the students spend less than 2 hours per week working on mathematics, whereas for the Warwick survey only 19% recorded spending so little time on mathematics. This might well be due to the increased formal contact time at Universities X, Y and Z, which amounts to typically three hours per week compared with the single one-hour plenary sessions plus tutorial at Warwick. The increase in formal contact time could lead to a reduced amount of independent working, but equally the reduction in independent working could be due to a reduced amount of work being expected of the students. </p> <hd id="AN0001602966-12">3.3. Ratings of the mathematics topics</hd> <p>Students were asked to rate the level of perceived difficulty of a range of mathematics topics. By taking the mean score for each group of students, a league table of difficulty has been drawn up for the 14 topics. The results of this are shown in table 2, together with the mean score from each group of students for these topics. Note that the ranking found in the previous study at Warwick has been used to order the topics. </p> <p>In the previous study at Warwick, the mean ratings of the topics were used to arbitrarily split the list into three categories, namely, difficult topics (hyperbolic functions, differential equations and series), topics of average difficulty (integration, matrices, statistics, vectors, probability, complex numbers, logarithmic functions, differentiation and trigonometric functions) and easy topics (algebra and geometry). These results can then be compared to the results of Heard [<reflink idref="bib17" id="ref17">17</reflink>], who found that vectors and differential equations were rated as the most difficult topics, followed by, in order, statistics, integration, complex numbers, matrices, limits and series, and then differentiation in the next grouping. Heard [<reflink idref="bib17" id="ref18">17</reflink>] then found that other topics caused fewer problems. While some differences were found between the order of the rankings at Warwick and Heard's results, there are many similarities between the two sets of results. </p> <p>Moving to the results shown in table 2 for the universities surveyed in this study, it is clear that students in the various institutions rated the topics differently. Despite this, in the order of ranking, the three topics identified as the most difficult are the same for Warwick, University X (both groups) and University Y. These topics are hyperbolic functions, differential equations and series. Only University Z produces a different list of the three most difficult topics, i.e. series, integration and statistics. Equally the two topics identified as the easiest at Warwick, algebra and geometry, are rated as being in the easiest four topics everywhere except at University Z. The anomalies in the ratings by the students at University Z show other interesting differences when compared to the ratings from elsewhere. For example, algebra is ranked fifth not thirteenth or fourteenth. One cause of these discrepancies in the ratings from students at University Z might be alluded to in the fact that many students there did not give a rating for many of the topics, perhaps suggesting that this range of topics has not been covered in their mathematics course. </p> <hd id="AN0001602966-13">3.4. Ratings of teaching methods</hd> <p>As the teaching methods between Warwick and the other universities studied are quite different, no comparison between Warwick and the others is made here. However, the mean scores for the rankings of the teaching methods are shown in table 3. From this it is clear that lectures and course notes are rated across all universities as being the most useful teaching media. Course textbooks are rated as being of neutral usefulness, again across all groups. The results for computer-assisted learning (CAL) are interesting as this medium is generally thought to be not useful except at University Y where it is of neutral usefulness. This might be explained by the fact that at University Y CAL is a formal part of the course, whereas at the other universities little or no use of it has been made with the students questioned. Finally, tutorials are rated as being of neutral usefulness, except at University Y where they are seen to be useful. This might be because some students see tutorials as threatening situations thereby reducing the usefulness of the sessions. </p> <hd id="AN0001602966-14">4. A cluster analysis using the eight key attitude variables</hd> <hd id="AN0001602966-15">4.1. The cluster analysis procedure</hd> <p>From the overview of the data in section 3, it can be seen that there are some similarities with the data collected at Warwick in terms of students' attitude and ranking of the different mathematical topics. However, it also clear that the students surveyed at Universities X, Y and Z are not as negative about mathematics as the students at Warwick. Given this overview, it is now interesting to undertake a cluster analysis [<reflink idref="bib16" id="ref19">16</reflink>] of the eight key attitude variables to assess whether clear groupings exist at these three universities as they did at Warwick. These variables are the responses of students to questions on the helpfulness of mathematics teachers or lecturers before university, the difficulty of mathematics before university, the enjoyment of mathematics before university, the difficulty of mathematics at university, the enjoyment of mathematics at university, the mathematics workload at university, the students' motivation for mathematics and their desire to improve their capability in mathematics. </p> <p>For each student questioned, the responses to these eight questions form a vector which represents their attitude to mathematics before university and at university. The cluster analysis calculates the differences between these vectors and then forms groups by first of all linking the two students with the smallest difference in attitude. These two students are agglomerated into a single group, i.e. the two vectors are replaced by a single composite vector representing the group. Then the differences are recalculated across all uncombined students and the new group, and the two groups of students with the smallest difference are combined. This process is repeated until all students have been combined into a single group. In this case, Ward's method [<reflink idref="bib20" id="ref20">20</reflink>] has been used to carry out the agglomeration in which the vector representing a new group is calculated as being the centroid of the vectors of the group members. This method of agglomeration is preferred for sociological research for this kind [<reflink idref="bib22" id="ref21">22</reflink>]. At each stage in the agglomeration process, the difference between the groups that are combined is recorded. This list of differences can then be used to calculate the number of clusters that it is reasonable to assume exist for the data used. The analysis for all the students produced five clusters. </p> <hd id="AN0001602966-16">4.2. Classifying the five clusters</hd> <p>To classify the clusters of students, the mean value of each of the eight variables is calculated from the responses of the cluster members. These mean values are shown in table 4. From this the following classification can be obtained: </p> <hd id="AN0001602966-17">Table 4.</hd> <ct id="AN0001602966-18"> Mean score for cluster members. Based on five-point scales for helpfulness from 1 (not at all helpful) to 5 (very helpful), for difficulty from 1 (not at all difficult) to 5 (very difficult), for enjoyment from 1 (not at all enjoyable) to 5 (very enjoyable), for workload from 1 (very light) to 5 (very heavy), for motivation from 1 (not at all motivated) to 5 (very motivated) and for desire to improve from 1 (not at all important) to 5 (very important). Legend for Chart: A - Variable B - Ambivalent PTs C - Downhillers D - Haters E - Ambivalent GTs F - High Flyers A B C D E F Helpfulness of staff previously 2.1 4.5 3.2 4.1 4.7 Difficulty of maths before university 3.3 2.2 2.8 3.6 1.5 Enjoyment of maths before university 2.9 4.0 2.3 3.2 4.8 Enjoyment of maths at university 3.4 3.2 1.6 3.2 4.4 Difficulty of maths at university 3.0 2.8 3.9 3.1 1.9 Workload of maths at university 3.0 3.1 3.3 3.2 2.2 Motivation for maths 3.3 2.9 1.8 3.3 4.2 Desire to improve maths 4.6 3.7 3.6 4.1 4.7</ct> <ulist> <item> Cluster One is made up of 15% of the students. These students give average ratings for most variables, except that they found that their mathematics teachers or lecturer before university was not helpful and they are very keen to improve their mathematics skill. This cluster might be called Ambivalent With Poor Pre-University Teaching (Ambivalent PT). </item> <item> Cluster Two is larger with 31% of the students. They found that before university mathematics was easy, they enjoyed it then and found their teacher or lecturer to be very helpful. At university the picture is different with only average scores being recorded. However, these students do show some willingness to improve their mathematics capability. This cluster can be said to be Downhillers. </item> <item> Cluster Three has only 11% of the students. It is characterized by students who did not enjoy mathematics before university and do not enjoy it at university. Further they have no motivation for mathematics at university and are ambivalent about improving their mathematics capability. In terms of the level of difficulty of mathematics, these students found mathematics to be of average difficulty before university and they find it more difficult now. This cluster can be classified as Haters. </item> <item> Cluster Four is the largest group with 35% of the students. Their responses are very similar to those given by Cluster One, as they record average scores in the main. However, these students found their mathematics teacher or lecturer before university to be very helpful, not unhelpful as was found by Cluster One. This cluster might be called Ambivalent With Good Pre-University Teaching (Ambivalent GT). </item> <item> Cluster Five is the smallest cluster with 8% of the students. These students enjoyed mathematics before university and they enjoy it at university. Also they found mathematics easy before university and they still find it easy at university. Before university, they found their teacher or lecturer to be very helpful. At university, they are very motivated towards mathematics and they are very keen to improve their capability in mathematics. These are the High Flyers. </item> </ulist> <hd id="AN0001602966-19">4.3. Comparison with the clusters found previously</hd> <p>It is interesting to compare this classification of the clusters with the classification of the clusters found at Warwick. In both cases the clusters known as the High Flyers have a similar profile, and the size of the clusters is similar with the Warwick cluster comprising 9% of the students and the current cluster comprising 8% of the students. The Downhillers clusters are also of similar size, with the Warwick cluster containing 28% of the students, and the current cluster containing 31% of the students. The Downhillers also record similar attitudes, except that this group of Downhillers is less negative about mathematics at university than were those at Warwick. Moving to the Haters, this is now a slightly smaller cluster with 11% of students compared to 18% at Warwick. Again the current Haters cluster is similar to the Warwick cluster in that these clusters both show poor enjoyment and motivation ratings, but the two clusters are different in that the current cluster records less negative values for the other questions. In the previous work at Warwick, two clusters--the Ambivalents (or Averages) and the Realisics--were found. In this survey, two different clusters of Ambivalents are identified that give average scores to most of the variables, but had helpful or not helpful mathematics teachers before university. </p> <hd id="AN0001602966-20">4.4. Analysis of the clusters by university type</hd> <p>As table 5 shows there is a higher proportion of Downhillers at University X<subs>Trad</subs> than at any other of the institutions studied (42.1%), but there is also a higher percentage of High Flyers (12.1%). This is not a dissimilar picture to that at Warwick where a high number of Downhillers was also observed. Meanwhile, at University X<subs>Ntrad</subs> there is a much lower number of High Flyers with the highest number of students coming into the Ambivalent GT category. It is interesting that there are significantly fewer Downhillers in the X<subs>Ntrad</subs> group, which is possibly a reflection of the fact that these students are taught separately and are perhaps given more attention. University Y displays many similar characteristics to X<subs>Ntrad</subs>, probably because of the similarity in the background of the student population in the two groups. At University Z there are notably no High Flyers and over half of the respondents are in the Ambivalent GT cluster. Given that many of these students have entered university through access and foundation courses, in which they have received a good level of pre-university mathematics training, this is perhaps not surprising. </p> <hd id="AN0001602966-21">4.5. Analysis of the membership of the clusters</hd> <p>Now that the classification of the five clusters is known, the membership of the clusters can be analysed in more detail. This involves analysing each cluster in terms of gender, home/overseas student status, the type of pre-university educational establishment attended by the students, the performance of the students in mathematics on entry to university, the ranking of the teaching methods and the perceived difficulty of the mathematics topics. </p> <p>Considering the gender of the respondents, significant differences are found across the clusters (significance level 0.010). Here the major difference is in the High Flyer cluster, where the male to female ratio is 72:28 not 91:9 as in the dataset as a whole. Clearly many more women are High Flyers which suggests that mainly brighter females apply to study engineering. Similarly the High Flyers cluster has significantly fewer Home and EU than overseas students--a home (EU) to overseas ratio of 60:40 compared with 84:16 for the total number of respondents (significance level 0.002). </p> <p>Significant differences are not found between the clusters for the previous educational establishment attended by the students. Nevertheless, some of the differences observed are interesting. The Ambivalent PT cluster shows a membership similar to that of the overall respondent profile, whereas the Downhillers cluster has more Grammar School, Public or Private School and Sixth Form College students. These differences are possibly a reflection of the change in teaching method from smaller group tuition at school to large lectures at university. The Haters cluster, meanwhile, has more Secondary School students, but fewer former comprehensive pupils and the Ambivalent GT cluster has most Comprehensive and FE College students. Finally the High Flyers cluster has more Comprehensive, Public or Private School and Sixth Form College students than other groups. </p> <p>Comparing the highest mathematics qualification on entry to university, there are again significant differences between the clusters (significance level 0.000). The Ambivalent PT cluster has an even distribution of pre-university mathematics qualifications, but notably more students with A-Level grades of D and E (23.3%) than the respondents as a whole (11.9%). The Downhillers and High Flyers have a significantly higher proportion of A-Level students achieving grades from A to C (60.9% and 56%, respectively) than any other cluster. This suggests there is potentially a fine line between becoming a Downhiller or a High Flyer. Significantly more Haters (35.5%) enter university with BTEC qualifications suggesting that many such students find mathematics particularly difficult, although the Ambivalent GT cluster also has an above average number of former BTEC students. </p> <p>Further significant differences have been identified in the ratings given by respondents to the usefulness of some of the teaching methods used in the different universities. While members of all clusters considered lectures to be of above average usefulness, the High Flyers and the Ambivalent PTs rated them significantly higher (significance level 0.001). The High Flyers also rate the tutorials much higher, while the Downhillers and Haters give the lowest ratings for this teaching method (significance level 0.018). This is possibly because the tutorials give the High Flyers a chance to show how well they can cope with the mathematics material in their course, but might expose the weaknesses of the Downhillers and Haters. This might be particularly true where there is a mix of the different types of students in tutorials. Other teaching methods displayed no significant differences between the clusters. </p> <p>Finally the mean scores for the perceived difficulty of the various mathematics topics are considered. Significant differences were observed for six of the 14 topics. The High Flyers found all of the six topics (integration, trigonometric functions, logarithmic functions, geometry, algebra and series) to be of below average difficulty, while the Haters found them all, with the exception of algebra (significance level 0.009), to be of above average difficulty. This cluster did though appear to have particular problems with series. Interestingly, the Downhillers found all of these topics to be of only average or below average difficulty which suggests that many of their problems stem from their attitude and motivation for mathematics rather than from the perceived level of difficulty with the subject. Given the large number of students who fall into this cluster all universities need to recognize their existence and work with them in order to help them improve their levels of motivation for mathematics enabling them to take a more positive attitude to this important subject. Ambivalent PTs and Ambivalent GTs, as might be expected, found most of the mathematics topics to be of average difficulty with the former having the most problems with integration (significance level 0.005) and the latter with series (significance level 0.001). </p> <hd id="AN0001602966-22">5. Factors behind the attitudes</hd> <p>In an attempt to confirm the cluster analysis findings and to determine any underlying factors behind the attitudes of students, a factor analysis [<reflink idref="bib21" id="ref22">21</reflink>] has been carried out. Such methods extract from the data, which in this case is the vector formed from the responses to the eight key attitude questions for each student, the typical trends that exist in the data. The process is equivalent to a least-squares fitting to two-dimensional data. For the data gathered here, three factors have been extracted and these factors account for 64.5% of the data. The factors that have been extracted are: </p> <ulist> <item> Factor 1: where enjoyment of mathematics and motivation are always high and the difficulty is low. This factor would be positive for the members of the High Flyers cluster and negative for those in the Haters cluster. </item> <item> Factor 2: where mathematics is seen as being difficult but enjoyment of the subject is improving and motivation and willingness to improve are both high. Such a factor might be typical of the two Ambivalent clusters. </item> <item> Factor 3: where there is a change is perception from pre-university study to university study. The difficulty of mathematics is increasing and the enjoyment of it is reducing. This is combined with poor motivation and indifference about improving. This is typical of those in the Downhillers cluster. </item> </ulist> <p>Hence, as these factors can be related directly to each of the clusters, confirmation of the accuracy of the analysis is achieved. However, a clearer picture can be obtained by rotation of these factors through the 8-dimensional space. This can be used to maximize or minimize the scores of each of the variables and so clarify the underlying relationships between the factors. In this case rotation gives the following three factors: </p> <ulist> <item> Factor A--Positive University Experience where the enjoyment of mathematics at university is linked to high levels of motivation and a desire to improve. </item> <item> Factor B--Perception of Difficulty and Workload where the perceived difficulty of mathematics at university is linked to a high workload. </item> <item> Factor C--Positive Pre-University Experience where the enjoyment of mathematics before university is linked to the perception that mathematics before university was easy and to the helpfulness of mathematics teachers or lecturers before university. </item> </ulist> <p>By looking at the mean values for these rotated factors across university groupings, it can be seen that University X<subs>Trad</subs> can be characterized by students having a positive pre-university experience and finding mathematics easy at university; University X<subs>Ntrad</subs> is associated with students who find mathematics difficult at university; University Y with those who have had a negative pre-university experience and University Z with those who find mathematics extremely difficult. </p> <hd id="AN0001602966-23">6. Discussion</hd> <p>This survey has revealed a large amount of information about the attitudes of engineering students to mathematics across three very different universities. In this section it is intended that this information be brought together, such that the implications of this for the teaching of mathematics within university engineering courses can be ascertained. </p> <p>Looking at the data for the students in the four university groupings, there is considerable similarity for the key attitude variables with the data collected in previous surveys at Warwick. However, there are some signs that the students surveyed here are enjoying their mathematics more at university and finding it less difficult than students at Warwick. This could be due to Warwick demanding more of their students, or to Universities X, Y and Z being more sympathetic in their teaching style or to Universities X, Y and Z demanding less of their students. From discussions with staff at X, Y and Z there is some evidence that it could be due to a combination of reduced expectation and more sympathetic teaching. </p> <p>In terms of the ratings of the individual mathematics topics there is again remarkable agreement as to the order of difficulty of these topics across Warwick and both Universities X and Y. This ranking should enable mathematics teachers to focus on the topics that students find difficult, ensuring that students have a firm grasp of the pre-requisites for these topics and being sensitive to the difficulties that students find when teaching them. Perhaps changes in teaching methods need to be considered for these difficult topics. This might include the use of more computer-assisted learning software which could guide students through the difficulties at a pace determined by the student. Also, perhaps, the order in which topics are taught needs to be considered. Easier topics should appear first so that students gain confidence before moving to the more difficult topics. Grouping students by ability might also improve the student experience, enabling students to be taught at a pace that suits them. </p> <p>Also it is interesting to note that traditional methods of teaching such as lectures and course notes are regarded by students as being the most useful, with tutorials, textbooks and computer-assisted learning being seen as in need of improvement. As computer-assisted learning is a novel use of technology this is not surprising, but tutorials and textbooks have been in use for some time and so one might think that they would have been refined by now into useful media of instruction. Also lectures might be seen as useful because of the direct relation students perceive between lectures and examination content, or it could be that students prefer lectures as they involve less effort on their part. </p> <p>Moving to the membership of the attitudinal clusters, the High Flyers cluster is perhaps the easiest to understand. These students tend to be found in traditional universities, having come from traditional schools with good A-level results. They find lectures and tutorials to be useful and find many mathematics topics easy. The Haters are also easy to understand. They tend to be non-traditional students having come from secondary schools with the poorest A-level grades or BTEC Ordinary level qualifications. They find some subjects hard and do not like tutorials, where they possibly find the small group situation threatening. Tutors, therefore, need to ensure that their tutorials take into account the different needs of the various clusters identified in this research and to ensure that, for example, High Flyers and Haters are not taught in the same groups. </p> <p>By their nature the other three clusters are much more interesting. The Downhillers tend to be found in the traditional universities, having come from good quality traditional schools with good A-level results. They also do not like tutorials, perhaps for the same reasons as the Haters, but they find trigonometric and logarithmic functions hard and geometry and algebra easy. There appears to be a fine line between becoming a Downhiller and a High Flyer so given the large number of students who are in the former cluster much work needs to be done to identify these students early on in their engineering degrees such that efforts can be made, in terms of teaching methods and style, to maintain their earlier levels of enjoyment such that they too might become High Flyers. </p> <p>Students in the two Ambivalent clusters tend to be those with the middle to poor A-level grades, good teaching producing the middle grades and poor teaching the lower grades. Those with good teaching tend to come from comprehensive schools and FE colleges. The implications of the trends in cluster membership are serious, especially as the grades of some students can depend on the quality of mathematics teaching before university. </p> <p>Finally the factor analysis has shown that the three factors, related to the university experience, the pre-university experience and the perceived difficulty and workload at university, are completely independent. Hence it is possible to take students who have had bad experiences with mathematics before university and provide a sufficiently sympathetic regime at university that these students actually change from hating the subject to enjoying it. </p> <p>If engineering students in the UK are to compete internationally, and be able to understand the detail of advanced engineering methods, then they need to be comfortable with mathematics as a topic and capable of using it with ease. For this to happen, those students who are Haters or Downhillers need to be provided with sufficient support that they are transformed from being Haters into a new grouping of Uphillers, or from being Downhillers into High Flyers. The work here has shown that this is possible as the factors relating to the pre-university experience and the university experience are independent. </p> <hd id="AN0001602966-24">7. Conclusions</hd> <p>In this study the attitudes of engineering students to mathematics teaching have been analysed across three very different UK universities. The students surveyed are a much broader cross-section of the student population, and hence more representative, when compared to those surveyed in previous studies at the University of Warwick. Use is made in this work of the responses to eight key questions, which relate to the students' attitudes. Five of these questions produce significant differences across the university groups, namely the helpfulness of staff before university, difficulty of mathematics before university, enjoyment of mathematics before university, difficulty of mathematics at university and mathematics workload at university. Also, students were asked to rate the difficulty of mathematics topics and considerable agreement has been found across the university groups with, in general, hyperbolic functions and differential equations being seen as the most difficult and algebra and geometry seen as the easiest. </p> <p>From the responses to the eight key attitude questions, cluster analysis has been used to produce five clusters of students across the three different universities. These clusters of students have been named High Flyers, Downhillers, Ambivalents with Good Pre-University Teaching, Ambivalents with Poor Pre-University Teaching and Haters. These clusters are, in three cases, very similar to those found in a previous study at Warwick and they show significant differences for variables such as pre-university educational establishment, pre-university mathematics qualification and ratings of difficulty of mathematics topics. </p> <p>To determine underlying factors behind the attitudes of students, a factor analysis has been carried out that produces three factors that can be used to describe the attitudes. These factors can be summarized as the pre-university experience, the perception of difficulty and workload at university and the university experience. From this, mathematics education at university is seen to be decoupled from the student's experiences before university, and enjoyment and motivation at university are decoupled from the perception of difficulty. Consequently it is possible for students, regardless of background, to have a positive experience of mathematics at university, while still being challenged intellectually. </p> <hd id="AN0001602966-25">8. Further work</hd> <p>From this study across three UK universities, it is clear that a slightly different picture has emerged as to the attitudes of engineering students when compared to the study at Warwick alone. While this is no doubt an improved picture of the national situation, further work is required to confirm the results. A broader survey across many more universities is required to establish the true picture within the UK. Also, as mathematics training for engineers can be a factor in economic success, so can differences in the attitudes of students between those in the UK and other European nations as well as those in other trading competitors of the UK such as the United States and countries in the Far East and Pacific Rim. </p> <p>As well as looking at the broader picture, each lecturer in engineering mathematics must try to ascertain the attitudes of the students that they teach. This can be done by being aware of the various mindsets that students have, i.e. the cluster groupings found here, when dealing with the problems that students bring, and also by trying to understand the composition of the student group being taught by issuing a questionnaire similar to the one used here. Finally it is possible that a self-administered questionnaire could be developed suitable for all engineering departments to make an assessment of the attitude of their students to mathematics. </p> <hd id="AN0001602966-26">Table 1. Percentage of students agreeing with propositions describing the eight key attitude variables.</hd> <ct id="AN0001602966-27"> Legend for Chart: A - Proposition B - X<subs>Trad</subs> (%) C - X<subs>NTrad</subs> (%) D - Y (%) E - Z (%) F - Warwick (%) A B C D E F Staff previously not helpful 8 22 18 3 11 Maths difficult previously 23 34 37 31 30 Did not enjoy maths previously 12 16 24 17 16 Do not enjoy maths at university 23 16 20 20 51 Maths difficult at university 20 46 32 66 62 Maths load above average at university 12 36 17 59 68 Motivated towards maths 27 22 36 41 31 Wish to improve maths capability 75 82 77 69 83</ct> <hd id="AN0001602966-28">Table 2. League table of difficulty for mathematics topics. The mean score on a five-point scale ranging from 1 (not at all difficult) to 5 (very difficult) is also given in parentheses.</hd> <ct id="AN0001602966-29"> Legend for Chart: A - Topic B - Ranking of difficulty at Warwick C - Ranking of difficulty at X<subs>Trad</subs> D - Ranking of difficulty at X<subs>Ntrad</subs> E - Ranking of difficulty at Y F - Ranking of difficulty at Z A B C D E F Hyperbolic functions 1 1 1 1 = 5 (3.6) (3.3) (4.0) (3.4) (3.3) Differential equations 2 2 = 3 2 4 (3.5) (3.1) (3.5) (3.3) (3.4) Series 3 3 2 3 1 (3.4) (3.0) (3.6) (3.2) (3.8) Integration = 4 = 4 = 3 = 4 2 (3.2) (2.9) (3.5) (3.1) (3.7) Matrices = 4 = 9 13 = 12 = 11 (3.2) (2.6) (2.7) (2.6) (2.6) Statistics = 4 = 6 6 = 4 3 (3.2) (2.8) (3.4) (3.1) (3.5) Vectors = 4 = 9 = 10 = 12 = 11 (3.2) (2.6) (2.9) (2.6) (2.6) Probability 8 = 6 8 = 4 8 (3.1) (2.8) (3.1) (3.1) (2.8) Complex numbers 9 = 4 = 10 9 = 9 (3.0) (2.9) (2.9) (3. O) (2.7) Logarithmic functions 10 8 = 3 = 4 = 9 (2.9) (2.7) (3.5) (3.1) (2.7) Differentiation = 11 = 12 9 = 10 = 5 (2.8) (2.3) (3.0) (2.7) (3.3) Trigonometric functions = 11 = 9 7 = 4 14 (2.8) (2.6) (3.2) (3.1) (2.5) Algebra = 13 = 12 14 14 7 (2.6) (2.3) (2.6) (2.5) (3.0) Geometry = 13 = 12 = 10 = 10 = 11 (2.6) (2.3) (2.9) (2.7) (2.6)</ct> <hd id="AN0001602966-30">Table 3. The mean score given in ranking the teaching methods encountered. This is based on a five-point scale ranging from 1 (not at all useful) to 5 (very useful).</hd> <ct id="AN0001602966-31"> Legend for Chart: A - Method of instruction B - X<subs>Trad</subs> C - X<subs>Ntrad</subs> D - Y E - Z A B C D E Lectures 4.0 3.7 4.0 3.7 Course notes/handouts 3.8 3.7 4.1 3.7 Course textbook 2.6 2.9 3.1 2.9 Computer-assisted learning 1.9 1.9 3.1 1.9 Tutorials 2.6 3.1 4.0 3.4</ct> <hd id="AN0001602966-32">Table 5. Cluster membership by university.</hd> <ct id="AN0001602966-33"> Legend for Chart: A - University B - Ambivalent PTs C - Downhillers D - Haters E - Ambivalent GTs F - High Flyers A B C D E F X<subs>Trad</subs> 10.3% 41.2% 5.6% 29.9% 12.1% X<subs>Ntrad</subs> 20.0% 24.0% 14.0% 38.0% 4.0% Y 20.4% 23.9% 13.3% 33.6% 8.8% Z 3.4% 31.0% 13.8% 51.7% 0%</ct> <ref id="AN0001602966-34"> <title>References</title> <blist> <bibl id="bib1" idref="ref1" type="bt">[1]</bibl> <bibtext>BORRIE, M., 1986, IMA Bull., 22, 44-45. </bibtext> </blist> <blist> <bibl id="bib2" type="bt">[2]</bibl> <bibtext>CRANK, J., 1986, IMA Bull., 22, 113-118. </bibtext> </blist> <blist> <bibl id="bib3" idref="ref2" type="bt">[3]</bibl> <bibtext>MUSTOE, L. R., 1992, IMA Bull., 28, 99-102. </bibtext> </blist> <blist> <bibl id="bib4" idref="ref3" type="bt">[4]</bibl> <bibtext>HIRST, K., 1993, IMA Bull., 29, 9-15. </bibtext> </blist> <blist> <bibl id="bib5" type="bt">[5]</bibl> <bibtext>IMA Bull., 1987, 23, 168-169. </bibtext> </blist> <blist> <bibl id="bib6" idref="ref4" type="bt">[6]</bibl> <bibtext>IMA Bull., 1994, 30, 16-18. </bibtext> </blist> <blist> <bibl id="bib7" type="bt">[7]</bibl> <bibtext>EASINGWOOD, T., 1997, Math. Today, 33, 56-58. </bibtext> </blist> <blist> <bibl id="bib8" idref="ref5" type="bt">[8]</bibl> <bibtext>BARRY, M. D. J., and STEELE, N. C., 1992, A Core Curriculum in Mathematics for the European Engineer, SEFI Document, 92.1. </bibtext> </blist> <blist> <bibl id="bib9" idref="ref6" type="bt">[9]</bibl> <bibtext>CHALLIS, N., and GRETON, H., 1997, Mathematical Education of Engineers, Proceedings of the second IMA conference (London: Institute of Mathematrics and Its Applications), 145-150. </bibtext> </blist> <blist> <bibl id="bib10" type="bt">[10]</bibl> <bibtext>SIMONS, F., 1997, Mathematical Education of Engineers, Proceedings of the second IMA conference (London: Institute of Mathematics and Its Applications), 133-140. </bibtext> </blist> <blist> <bibl id="bib11" idref="ref7" type="bt">[11]</bibl> <bibtext>IMA Bull., 1995, 31, 159. </bibtext> </blist> <blist> <bibl id="bib12" idref="ref8" type="bt">[12]</bibl> <bibtext>MUSTOE, L, and HIBBERD, S., 1995, Mathematical Education of Engineers (Oxford: Oxford University Press). </bibtext> </blist> <blist> <bibl id="bib13" type="bt">[13]</bibl> <bibtext>MUSTOE, L., and HIBBERD, S., 1997, Second Conference on Mathematical Education of Engineers, Proceedings of the second IMA conference (London: Institute of Mathematics and Its Applications). </bibtext> </blist> <blist> <bibl id="bib14" idref="ref9" type="bt">[14]</bibl> <bibtext>SHAW, C. T., and SHAW, V. F., 1995, In Mathematical Education of Engineers (Oxford: Oxford University Press), pp. 161-174. </bibtext> </blist> <blist> <bibl id="bib15" idref="ref10" type="bt">[15]</bibl> <bibtext>SHAW, C. T., and SHAW, V. F., 1997, Int. J. Math. Educ. Sci. Technol., 28, 289-301. </bibtext> </blist> <blist> <bibl id="bib16" idref="ref12" type="bt">[16]</bibl> <bibtext>ALDENDERFER, M. S., and BLASHFIELD, R. K., 1984, Clustrer Analysis, Sage University Paper Series on Quantitative Applications in the Social Sciences, 07-044 (Newbury Park, CA: Sage). </bibtext> </blist> <blist> <bibl id="bib17" idref="ref13" type="bt">[17]</bibl> <bibtext>HEARD, T. J., 1978, The Mathematical Education of Engineers at School and University, BP Schoolteacher Fellow Report. </bibtext> </blist> <blist> <bibl id="bib18" idref="ref14" type="bt">[18]</bibl> <bibtext>KEYS, W., and WARDMAN, M., 1991, Research Into Engineering Education, National Foundation for Educational Research. </bibtext> </blist> <blist> <bibl id="bib19" idref="ref16" type="bt">[19]</bibl> <bibtext>TULL, D. S., and HAWKINS, D. J., 1993, Marketing Research (New York: Macmillan). </bibtext> </blist> <blist> <bibl id="bib20" idref="ref20" type="bt">[20]</bibl> <bibtext>WARD, J., 1963, J. Amer. Stat. Assoc., 58, 236-244. </bibtext> </blist> <blist> <bibl id="bib21" idref="ref22" type="bt">[21]</bibl> <bibtext>KIM, J.-O., and MUELLER, C. W., 1978, Introduction to factor analysis: What it is and how to do it, Sage University Paper series on Quantiative Applications in the Social Sciences, 07-013 (Newbury Park, CA: Sage). </bibtext> </blist> <blist> <bibl id="bib22" idref="ref21" type="bt">[22]</bibl> <bibtext>ANDERBERG, M. R., 1973, Cluster Analysis for Applications (New York: Academic Press). </bibtext> </blist> </ref> <p>(Received 6 August 1997; Revised 23 October 1997) </p> <aug> <p>By C. T. Shaw, Department of Engineering University of Warwick, Coventry, CV4 7AL, England and V. F. Shaw, Warwick Business School, University of Warwick, Coventry, CV4 7AL, England </p> </aug> |
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| Items | – Name: Title Label: Title Group: Ti Data: Attitudes of Engineering Students to Mathematics--A Comparison across Universities. – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Shaw%2C+C%2E+T%2E%22">Shaw, C. T.</searchLink><br /><searchLink fieldCode="AR" term="%22Shaw%2C+V%2E+F%2E%22">Shaw, V. F.</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22International+Journal+of+Mathematical+Education+in+Science+and+Technology%22"><i>International Journal of Mathematical Education in Science and Technology</i></searchLink>. Jan-Feb 1999 30(1):47-63. – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: Y – Name: Pages Label: Page Count Group: Src Data: 17 – Name: DatePubCY Label: Publication Date Group: Date Data: 1999 – Name: Audience Label: Intended Audience Group: Audnce Data: Practitioners; Teachers – Name: TypeDocument Label: Document Type Group: TypDoc Data: Guides - Classroom - Teacher<br />Journal Articles – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22College+Students%22">College Students</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+Education%22">Engineering Education</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Higher+Education%22">Higher Education</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Questionnaires%22">Questionnaires</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Attitudes%22">Student Attitudes</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Surveys%22">Student Surveys</searchLink> – Name: Subject Label: Geographic Terms Group: Su Data: <searchLink fieldCode="DE" term="%22United+Kingdom%22">United Kingdom</searchLink> – Name: ISSN Label: ISSN Group: ISSN Data: 0020-739X – Name: Abstract Label: Abstract Group: Ab Data: Surveys engineering students' attitudes towards mathematics in three different United Kingdom universities. Reports that students can be placed into five groupings; members of groups recorded significantly different responses to many of the questions posed, including their university, gender, home or overseas status, mathematics qualification on entry to university, and so on. Contains 22 references. (Author/ASK) – Name: DateEntry Label: Entry Date Group: Date Data: 1999 – Name: AN Label: Accession Number Group: ID Data: EJ580454 |
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| RecordInfo | BibRecord: BibEntity: Languages: – Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 47 Subjects: – SubjectFull: College Students Type: general – SubjectFull: Engineering Education Type: general – SubjectFull: Foreign Countries Type: general – SubjectFull: Higher Education Type: general – SubjectFull: Mathematics Education Type: general – SubjectFull: Questionnaires Type: general – SubjectFull: Student Attitudes Type: general – SubjectFull: Student Surveys Type: general – SubjectFull: United Kingdom Type: general Titles: – TitleFull: Attitudes of Engineering Students to Mathematics--A Comparison across Universities. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Shaw, C. T. – PersonEntity: Name: NameFull: Shaw, V. F. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 1999 Identifiers: – Type: issn-print Value: 0020-739X Numbering: – Type: volume Value: 30 – Type: issue Value: 1 Titles: – TitleFull: International Journal of Mathematical Education in Science and Technology Type: main |
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