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Education for Mathematics in the Workplace : Mathematics Education Library - Annie Bessot

Education for Mathematics in the Workplace

Mathematics Education Library

By: Annie Bessot (Editor), Jim Ridgway (Editor), G. Vergnaud (Introduction by)


Published: 31st December 2000
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Education must achieve a range of goals - it must provide academic knowledge, knowledge and skills which young people need in order to enter the world of work, and must lay the foundations for lifelong learning. This volume brings together the ideas and research findings from experts in mathematical education around the world. It raises issues concerning the nature of school mathematics and mathematics at work, and the challenges of teaching valuable mathematics in school and providing appropriate training for a variety of careers. It offers lively commentaries on important topics - transferring knowledge and skill across contexts; the concept of "authentic mathematics"; comparability of different types of assessment; and analyzes research methods which can be used to inform our understanding of all these issues. It should be of interest to everyone concerned with vocational education and with training, and everyone interested in cultural and cognitive aspects of mathematics.

Acknowledgmentp. xv
Introductionp. xvii
Mathematical Knowledge in School and at Workp. 1
Prefacep. 3
The Transfer of Mathematics Learning From School to Work Not Straightforward But Not Impossible Either!p. 5
Introductionp. 5
Views on the Transfer of Learning in Mathematicsp. 6
Conceptualising Boundaries and Bridgesp. 7
Teaching for Transferp. 9
Implications for Researchp. 11
Conclusion and Directions for Researchp. 13
Referencesp. 14
Notesp. 15
Working Knowledge: Mathematics in Usep. 17
The Studyp. 19
Documentary Analysis and Interviewsp. 20
Ethnographic observationp. 21
Simulation interviewsp. 21
Questionnaires and teaching experimentsp. 22
Data Collection and Analysisp. 22
Visible Mathematics and Routine Activityp. 23
Breakdown Episodes and Underlying Modelsp. 28
Mathematising Workplace Activityp. 31
Referencesp. 34
Notesp. 35
Forms of Mathematical Knowledge Relating to Measurement in Vocational Training for the Building Industryp. 37
Combining two approaches to knowledge: the construction schoolp. 37
The central role of measurements in practicep. 38
The transfer of measurements as a basic practice for setting outp. 40
Dimensions in structural drawingsp. 40
Cumulated dimensions, a technique for transferring dimensions from plans to groundp. 41
An incident at the construction schoolp. 45
Mathematics and knowledge relating to cumulated dimensions at schoolp. 47
Conclusionp. 48
Referencesp. 49
Notesp. 50
The Integration of Mathematics Into Vocational Coursesp. 53
Mathematics within vocational education in England and Walesp. 53
Key Skills--including Application of Numberp. 54
Ways of providing support for Application of Numberp. 55
Views from two culturesp. 55
Adding value to vocational work by integrating mathematics into itp. 56
Taking charge of learningp. 56
Forming hypothesesp. 57
Integrating or embedding mathematical skillsp. 57
Project examplesp. 57
Examples from Health and Social Carep. 58
Examples from Art and Designp. 60
Conclusion and suggestionsp. 63
Referencesp. 64
Mathematical Means and Models From Vocational Contexts--A German Perspectivep. 65
Vocational Education in Germany: the organisationp. 65
Teaching Mathematics in German Vocational Educationp. 66
Aims of mathematics education and trainingp. 66
Mathematics education in part-time vocational collegesp. 67
Mathematics education in full-time vocational collegesp. 68
Modelling versus Legitimate Peripheral Participationp. 69
Two pedagogies: modelling versus legitimate peripheral participationp. 69
An aside on 'transfer'p. 71
Proposing a way forwardp. 72
Mathematical and other means in vocational contextsp. 73
Means ('primary' artefacts)p. 73
Teaching and means ('secondary' artefacts)p. 74
Teaching and learning with information technologyp. 75
Conclusionp. 77
Lessons to Learn for General Mathematics Educationp. 77
Speculating on the futurep. 78
Referencesp. 78
Bringing School and Workplace Togetherp. 81
Prefacep. 83
Working Mathematics for Learners with Lower Abilitiesp. 87
Introductionp. 87
Designing of the investigationp. 88
Exploring the shop floorp. 90
The mathematics of the shop floorp. 92
The translation to worksheetsp. 94
An examplep. 95
Influence on curriculum documents and examination syllabip. 98
Final conclusionsp. 99
Referencesp. 99
Notesp. 100
Classroom Teachers Doing Research in the Workplacep. 101
Introductionp. 101
Backgroundp. 101
The Key Competenciesp. 102
The RIUMIT Projectp. 103
The Workplace Research Methodologyp. 103
The aimp. 104
The planp. 104
Data gathering methodsp. 104
The trialp. 105
Outcomes of the Researchp. 108
The workplace storiesp. 108
Reflections by the teachersp. 109
Conclusionp. 112
Appendix: Education in Australiap. 113
Referencesp. 113
Making Authentic Mathematics Work for all Studentsp. 115
The Standards Movementp. 117
Status, Equity, and Trackingp. 118
Beyond Eighth Gradep. 119
Authentic Tasksp. 120
Challengesp. 123
Appendix A: Occupational Skill Standardsp. 124
Appendix B. Selected Web Sitesp. 125
Referencesp. 126
Mathematics Knowledge as a Vocational Qualificationp. 127
Introductionp. 127
Some basic conceptsp. 128
Mathematics in the Danish Adult Education Systemp. 129
Two different conceptions of mathematics knowledgep. 130
Mathematics knowledge as a qualificationp. 131
The objective and subjective perspectivep. 133
Referencesp. 135
Notesp. 136
Educating Future Workersp. 137
Prefacep. 139
Geometry at Work-Examples from the Building Industryp. 143
Introductionp. 143
Geometry and the reading of plans on the building-sitep. 144
Between geometry and space: the drawing as a basis for marking out the building linesp. 144
Linking drawings with objects in space: teaching strategiesp. 146
Didactical engineering: basic training procedures for the reading of technical drawingsp. 148
Variables of basic plan readingp. 149
A teaching scenario for reading technical drawings within the micro-space of modelsp. 149
Conclusionp. 154
Appendix: Organizational diagram of the French Education systemp. 155
Referencesp. 156
Notesp. 156
Teaching Mathematics to Shop-Assistant Apprentices Exploring Content and Didactical Situationsp. 159
Mathematics Used by a Jewelry Shop Assistantp. 159
The Mathematics Coursep. 160
Students' Skills With Percentagesp. 161
Suitable Didactical Situationsp. 163
Conclusionp. 165
Referencesp. 165
Notesp. 165
Developing a New Mathematics Curriculum for Post-Compulsory Educationp. 167
Introductionp. 167
Pre-vocational coursesp. 167
General Mathematical Competencep. 169
Exemplifying the general mathematical competence in students' work in Sciencep. 170
Specifying new qualificationsp. 173
Taxonomy of Learningp. 177
Further research questionsp. 179
Referencesp. 180
Research Methods for Mathematics at Workp. 181
Prefacep. 183
Assumptions about Mathematics in the Workplacep. 183
Methods for Research in Workplace Mathematicsp. 184
Future Researchp. 186
Referencesp. 187
The Mathematical Needs of Engineering Apprenticesp. 189
Exploring the Problem: Are the Number Skills of Apprentices in Decline?p. 191
What are the Mathematical Challenges of Engineering?p. 191
What are the Mathematical Challenges of School Mathematics?p. 192
How Do Apprentices Perceive Mathematics at School and Work?p. 193
What Predicts Apprentice Performance?p. 193
Mathematics at School versus Mathematics at Work-Resolving the Paradoxp. 195
Some Conclusionsp. 196
Referencesp. 196
Notesp. 197
Identification of Some Mathematical Needs Linked to the Use of Mathematics at Workp. 199
Is there a need for mathematics?p. 200
Sample 1. The counting of sardines by Breton fishermen at the beginning of the centuryp. 200
Sample 2. Present-day use of INRA tables by agricultural technicians for feeding dairy cowsp. 202
A calculating toolp. 203
Numbers arranged in the form of a diagonal cross serve to calculate proportions in mixturesp. 203
Working knowledge and basic knowledgep. 205
The ways of changep. 206
Conclusionp. 207
Referencesp. 207
Notesp. 208
Ethnography and the Situatedness of Workplace Numeracyp. 209
Ethnography and the study of mathematical culturesp. 210
A Rationale for Using Ethnographyp. 211
Situated learningp. 211
Ethnomathematicsp. 213
Constructivismp. 213
Key Assumptions of Ethnographyp. 214
Conducting Workplace Ethnographiesp. 216
Data Collectionp. 217
Participant observationp. 217
Interviewsp. 219
Artifactsp. 221
Conclusionp. 222
Referencesp. 223
Notesp. 224
Visibility of Mathematical Objects Present in Professional Practicep. 225
Actions and Device, a division between the visible and the invisiblep. 225
An a priori analysis of situations in which a wall is constructedp. 226
Need for checkingp. 226
Casing for a wall perpendicular to an existing wallp. 227
When formwork becomes problematicp. 228
Possible techniques for constructing the fillerp. 229
Operating conditions for techniques found on the construction sitep. 232
Investigation of a construction site training coursep. 233
Organisation of the investigation into the construction site training coursep. 233
An episode from the construction site training course or a forgotten rectificationp. 234
The forms taken by the notion of a slope within institutionsp. 235
The notion of slope within trades in the building industryp. 235
The notion of slope in 'vocational' teachingp. 236
The notion of slope in maths teaching in technical high schools for the building industryp. 236
Conclusionp. 237
Referencesp. 237
Notesp. 237
Conclusionp. 241
Maths at the work placep. 241
Maths for work taught in different settingsp. 242
Role of artefacts / technologyp. 244
Comment on research methodologyp. 245
Referencesp. 246
Index of Subjectsp. 247
Index of Authorsp. 257
Author Affiliationsp. 261
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792366638
ISBN-10: 0792366638
Series: Mathematics Education Library
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 265
Published: 31st December 2000
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.4 x 17.0  x 2.54
Weight (kg): 0.75