Numbers and mathematics in AVT___________________________________ Vocational Mathematics Tine Wedege Translated by Gail FitzSimons and Anna Folke Larsen 2 Contents Vocational Mathematics Preface 3 Tine Wedege Introduction 4 Malmö University, Malmö Chapter 1 8 © 2007 The author Numbers and technology Translation: Gail FitzSimons Chapter 2 14 Functional mathematics and and Anna Folke Larsen reading skills Chapter 3 20 Photos: Mathematics in work and in school 2Maj/Mira cover Chapter 4 26 Adults’ blocks towards learning Dreamstime p. 14, 26, 44 mathematics Apart from these: Tine Chapter 5 30 Wedege Numeracy in everyday life and in education Drawings: Anders Folke Chapter 6 38 Larsen Numbers and vocational mathematics First edition 1998: in semi-skilled jobs Fagmat – tal og matematik i Chapter 7 44 Numbers and vocational mathematics AMU. in AVT teaching The Danish Labour Market Chapter 8 50 Authority, Copenhagen Relevance and visibility of mathematics Literature 54 3 Preface It has been argued internationally in policy reports that numeracy as well as literacy are both necessary for work and for citizenship. Accordingly, there has been a focus on the lack of basic reading, writing and arithmetic skills of many adults. In the International Adult Literacy Surveys (IALS) from the 1990s, the focus was on quantitative literacy, and in the Adult Literacy and Life skills survey (ALL) from 2003 it was on numeracy. Following an initial survey, the Danish Labour Market Authority initiated the analytical project “Adult Vocational Mathematics” (Danish: Fagmat) on numbers and mathematics in semi-skilled job functions and in Adult Vocational Training (AVT). In this project, the focus was not solely on the adults’ problems with mathematics but also on the problems caused by mathematics educa- tion itself. As a senior adviser with the Authority at the time, I led this project from 1995- 1998. Together with Lena Lindenskov (then at Roskilde University), I organized four surveys on AVT-teaching, on AVT-students and on workplaces. The following people participated in the project for shorter or longer periods of time: Susan Møller, Bruno Clematide, Lothar Holek, Kim Foss Hansen, Tage Munch-Hansen, Dennis Karlsson, Nina Skov-Hansen, Per Gregersen and Tomas Højgaard Jensen. A series of AVT-centres, Vocational Schools, workplaces, employees and AVT- students participated in the empirical investigations. Four industry representatives from education committees participated in the reference group: Jan Mogensen (construction), Knud Madsen (commerce and office work), Gorm Holsteen Jessen (metal) and Jørgen Abildgaard Nielsen (transport). I thank all these people and institutions for engaging in the project. Also many thanks Anna Folke Larsen and Gail FitzSimons who did an excellent job translating FAGMAT from Danish into English. Finally, I want to thank the Danish Ministry of Education and the European Network for Motivational Mathematics for Adults (EMMA) who made this publication possible. I hope that this publication might lead to a further development of the mathematics (containing) instruction by teachers and educators in adult and vocational training. Tine Wedege Malmö University, September 2007 4 In the European labour market there is a need for functional understanding of numbers and mathematical skills just like there is a need for skills in rea- ding, writing and use of information technology. The needs are found both among the workers themselves and in workplaces where new technology with its changing techniques and work organisation places new requirements on the competences. 5 Introduction Why the project “Vocational One could be led to ask: “But aren’t Mathematics”? we well of without these competen- At Grundfos, one of the world's lea- ces?” Yes, it is accepted that many ding pump manufacturers, the semi- adults are immensely competent in skilled workers receive a special offer their work function after many years to learn mathematics (at the AVT- of experience, even though they do not centre or the Adult Educational have formal qualifications in mathe- Centre). One aim is to qualify the em- matics. If you do not feel comfortable ployees for education and work; a with numbers there are many strate- second aim is that a number of em- gies for avoiding them in the everyday ployees with blocks in the subject can life, but it will constrain your flexibi- move on. The Head of education at lity. Furthermore, quality certification Grundfos has not been in doubt that in the workplace implies rigid require- the basic qualifications in mathema- ments on the employees’ literacy and tics are necessary in the labour arithmetic skills. market today: “They are necessary in The teaching in most AVT-education order to enter work. That is one contains some calculation and voca- hundred per cent sure, as calculation tional mathematics of some kind or has not been automatised: the em- other - either as general arithmetic in ployee has to decide upon the special modules or fitted into the voca- numbers coming out of the machine.” tional teaching, or as vocational arith- In the 1990s, large national and metic integrated into the technical- international surveys of adults’ literacy vocational teaching. took place. Corresponding surveys did Within a number of areas during the not exist in the area of calculation and past 15-20 years, there have been mathematics, but it was striking that new/stronger requirements for the some of the reading tasks causing participants to have mathematics- especial difficulties among both semi- containing competences in the Danish skilled workers and others AVT-education. For example, this presupposed that the reader had an applies to the courses in sewerage, understanding of numbers and the CNC-turning, techniques of measure- skills of reading maps and tables. ment, and logistics and co-operation. 6 This can lead to some vocational and figure it out. I’ve never been good in educational problems in teaching; but maths.” also in other places with no new Many adults have a frozen attitude requirements, problems can arise in towards mathematics. Some people the classroom. A vocational teacher call it mathematics anxiety, while expressed it this way: others talk about blocks towards “Calculations and mathematics are numbers. considered as a problem by incredib- What is project “Vocational ly many students. “I’m simply not Mathematics”? able to do anything with numbers.” Vocational Mathematics is an analysis They give up beforehand. Maybe and development project about num- they have had bad experiences with bers and vocational mathematics in mathematics... It is women my age Adult Vocational training. We have who left school as thirteen-year-olds. posed three main questions in They don’t have faith in themselves Vocational Mathematics: and they are left out. Here is a speci- fic example illustrating the problem: • What skills and understandings in A pattern for a skirt is to be made calculation and mathematics are with a waist of 100cm. The 100cm needed in the semi-skilled jobs has to be divided by four. A typical compared with the requirements in student’s reaction is: “No, I can’t the AVT-teaching? 7 • What are the difficulties in (3) The workplace survey on the use numbers and mathematics that the of numbers, charts and formulas in AVT-students encounter, why do semi-skilled job functions in a number the problems arise, and what are of selected workplaces. The survey the implications for those returning consists of observations and short to vocational education. interviews with nine core employees and an examination of seven existing • How can the mathematics- qualification analyses. containing AVT-teaching be arranged such that it supports the In the surveys we were interested in students and provides them with numbers and vocational mathematics opportunities to exploit their within the following four areas: potentials? Construction, commerce and office In order to shed light on these ques- work, metal and transport. tions, project Vocational Mathema- Furthermore, our starting point was a tics consists of three surveys: questionnaire survey among vocatio- (1) The teaching survey on numbers nal teachers at the AVT-centres. The and vocational mathematics in AVT- survey was carried out in Spring 1995 teaching in selected education pro- in the framework of the cross-sectoral grams for semi-skilled workers. The development project “Profile in survey consists of observations of the Mathematics of Adults,” where the teaching in AVT-centres and exami- teachers were asked to evaluate the nation of educational documents. participants’ arithmetic and mathema- tical skills in relation to the vocational (2) The student survey on the AVT- teaching. students’ general understanding of numbers, arithmetic and mathemati- This publication is not a report on the cal skills, their experienced needs for three surveys but it is based upon the using these skills in the workplace, findings and on international research and their attitudes towards numbers on adults, mathematics and work. By and mathematics. The survey consists the translation in 2007, we have up- of qualitative interviews with 45 stu- dated the text and generalised it to the dents at AVT-centres and structured broader European context whereever interviews with 160 students at a possible. commercial school and four AVT- centres. 8 Technological development is about new techniques/machinery, work organisation and qualifications/ competences. Workplaces are swarming with numbers, but math- ematics is hidden in the technology and it is a widespread conception among adults that “mathematics is important, but not for me”. 9 Numbers and technology Everyone in the labour market experiences and participates in technological development. While some people experience that they are in control of their situation at work, others do not. Many people speculate about development – politicians, philosophers and educational planners. The great question for philosophers is the possibility of humans being able to control The tools are a setsquare, ruler, technological development. compass and pocket calculator But, how is the teacher to judge what in the small workshop.