ICME9 - WGA6
|ICME Conference - Tokyo, Japan, July 30 - August 6||Special Site|
back to WGA-6 program
Abstracts ICME-9, WGA-6:
Adult and Lifelong Education in Mathematics
|Assistant Organisers:||Local Organiser:|
|Diana Coben||Akihiko Takahashi|
‘Competence’ as a Construction in Adult and Mathematics Education
Roskilde University, Denmark
The term ‘competence’ usually appears in everyday language as a term for expertise and/or authority at the same time. However, the term is widespread in the world of education with the more closely defined specific meanings of a target in the learning and development processes. I regard the widespread use of concepts of competence in educational research as an expression of the wish to avoid the classical dichotomy of knowledge versus skills. Another line of demarcation could be drawn between, on the one hand, ‘technological logic’ which is illustrated by the formula: competence = explicit knowledge + rule-based skills, and on the other hand, a ‘holistic’ conception of competence which is presented thus: competence = explicit knowledge/current tacit knowledge + rule-based skills/rule-less skills.
Within the area of political and administrative problematiques, concepts of competence are construed for, respectively, general labour-market requirements with regard to people’s knowledge and skills (core competencies) and specific sub-competencies as aims in modularised adult education programmes where people’s competence is equated with their performance. The construction of competence concepts has consequences for the design of education programmes and teaching. There have been several attempts at defining a concept of competence in Danish adult education research. Most recently, it has been discussed how competencies and learning processes can be conceptualised to pave the way for the complexity and the interaction between learning processes within and outside the work process. In mathematics education research different sets of mathematical sub-competencies have been defined, partly as a consequence of administrative demands regarding the evaluation of competence development, and partly to put relevant competencies on the agenda in teaching. In other mathematics educational problematiques ‘numeracy’ and ‘matheracy’ appear as competence concepts that cover people’s competence in dealing with mathematical challenges in everyday life. Across the lines of different constructions in adult education programmes, I identify a number of common features: competence is linked to a certain context as a result of learning and development processes, and it is connected with the readiness for action and thought of a subject and their emotional readiness and/or mandate for action.
An Analysis of "Mathematical Museums" from Viewpoints of Life-long Education
Yoichi Hirano & Katsuhisa Kawamura
Tokai University, Japan
Nowadays, there are a many science museums in the world and some of them are specialized in mathematics. But, especially in Japan, we have very few mathematical museums. Since science museums play a important to extend various knowledge of sciences and technologies to the public (both children and adults), the realization of "mathematical museums" might be expected for the same reason. Mathematical museums could offer an opportunity of informal mathematics education and they could present, to the public, the importance, the interests and the joy of mathematics.
In Japan, a new curriculum of education is prepared for 2002. This educational reform is based on the importance of the "Life-Long Education" proposed by UNESCO and especially is aiming at the development of children's "creative potential (power) and ability to live". We think this reform should be related with the understanding of mathematics in a society. Many adults say: "I was not good at mathematics." But according to the data of our questionnaire about some mathematical exhibitions held in Japan, many adults seem to hope to understand mathematics not as a study at school, but as a human culture. Here, we can find a importance of mathematical museums. The key word of the mathematical museums is thought to be a set of the four following words: "wonder", "surprise", "understanding", "impression". In the mathematical museum, visitors see, for example, the mathematics hidden in the nature, in human life, etc. Through exhibits, visitors feel wonder and understand the mathematical principles experimentally and many exhibits give to the visitors "surprise" and "impression". These feelings attract visitors' interests and give them various images of mathematics. After all mathematical museums must be a place where visitors can feel the mathematics with various concrete, visual and experimental exhibits.
In this paper, we are to discuss what mathematical museums bring to the mathematics education for all people, children and adults, and to analyze a possibility of mathematics education for all people.
Numeracy in the International Life Skills Survey
Myrna Manly & Dave Tout
An international survey of the numeracy abilities of adults is to be part of the International Life Skills Survey (ILSS) planned for the year 2002. This comparative survey is being jointly developed by Statistics Canada and by the United States' National Center for Education Statistics (NCES), in cooperation with the Organisation for Economic Cooperation and Development (OECD). The ILSS project is a follow-up to the International Adult Literacy Survey (IALS), the world's first large scale comparative assessment of adult literacy. Tasks will assess performance in several skill domains, including Numeracy as well as Document and Prose Literacy, and Problem Solving; and other variables will be assessed via a background questionnaire.
Concept of numeracy
The conception of Numeracy utilized by ILSS is innovative in that it is built not only upon the IALS conception of Quantitative Literacy, but also upon recent research and work done in the Netherlands, Australia, the United States, and other countries. Our basic premise is that numeracy is the bridge that links mathematical knowledge, whether acquired via formal or informal learning, with functional and information-processing demands encountered in the real world. An evaluation of a person’s numeracy is far from being a trivial matter, as it has to take into account task and situational demands, type of mathematical information available, the way in which that information is represented, prior practices, individual dispositions, cultural norms, and more.
However, one cannot assess numeracy, but behavior (broadly defined). We have thus chosen to focus on numerate behavior, which is revealed in the response to mathematical information that may be represented in a range of ways and forms. The nature of a person’s responses to mathematical situations depends on the activation of various enabling knowledge bases, practices, and processes.
The development of a scale that attempts to predict the complexity/difficulty of numeracy tasks was an exciting and challenging aspect of the project A scheme of five factors was developed to account for the difficulty of different tasks, enabling an explanation of observed performance in terms of underlying cognitive factors. These five factors are: (1) Complexity of Mathematical information / data; (2) Type of operation / skill; (3) Expected number of operations; (4) Plausibility of distractors (including in text); (5) Type of match / problem transparency. These factors have been used to attempt to estimate, separately and in interaction, the difficulty level of the numeracy tasks.
Results so far
A pool of 80 items was developed and tested in a feasibility study in the U.S. and the Netherlands in June, 1999, along with a smaller follow up study in January, 2000. This presentation will share the results of the feasibility study and will present examples of the assessment tasks developed so far.
The Changing Adult Numeracy Curriculum in England
School of Continuing Education, University of Nottingham
World Mathematics Year 2001, sponsored by UNESCO, comes at a time when concern about standards of achievement in mathematics is high following the International Adult Literacy Survey (IALS) and the Third International Mathematics and Science Study (TIMSS). These and other studies have fuelled anxiety about the UK's capacity to compete in the global market and paved the way for the Moser Report's review of adults' basic skills (including numeracy) in England. The Report recommends a National Adult Basic Skills Strategy to include the development of a core curriculum in adult numeracy. For the first time there is to be a 'national curriculum' for adults in basic skills, a departure from the negotiated curriculum beloved of liberal adult educators. The proposal represents a continuation, in post-16 education, of policy already established in the school sector. This paper reviews the current situation and questions whether the imposition of a core curriculum in numeracy is appropriate for adult learners.
Language in Mathematics for Adult Second Language Learners
University of Western Sydney, Nepean,
Many adults who come to Australia, either for a short term or for permanent settlement, need to study mathematics for employment. This is particularly relevant for those who wish to become teachers or fulfil other roles in which their grasp of the second language is critical for communication or for the required study for their vocation, such as engineering. This paper will raise some of the issues related to the difficulties that learners of a second language have in learning mathematics. These will include learning styles, the use of written as well as oral work, the understanding of symbols and notations, and the interpretation of cultural differences.
Of particular interest is the role of the first language in the development of mathematical concepts, skills and understandings and their application in a number of different mathematical contexts. The treatment of errors and possible learning, production and communication strategies will be investigated in this regard. Affective issues such as motivation and attitude will also be considered, as will other differences that may exist among the second language learners. Attention will also be given to the way individual differences impact upon the learning of mathematics.
Because of the limitations of the author in speaking only English fluently, the examples used will be drawn from an English speaking context.
Adult Learners of Mathematics: Working with Parents
Rosi Andrade & Marta Civil
The University of Arizona
Our presentation will be based on two research projects located in minority and working-class communities in the Southwest of the USA. Both projects have as a key component the involvement of parents as learners of mathematics. Though both projects share some similarities in terms of participant characteristics (ethnicity, backgrounds, levels of education, where they live) there are also differences that need to be highlighted since they are relevant for this presentation. In project BRIDGE, the group of mothers who form the mathematics workshops attend primarily as adult learners, interested in advancing their knowledge and experience in mathematics so that they may in turn assist their children in learning mathematics. For quite some time, this group of women has been getting together in a literature group that holds as its credo that all participants are equal and come together to learn from one another. We emphasize this approach in our work in mathematics. Project MAPPS is more recent and its focus is on parental involvement in mathematics. It is larger in scope and works with several schools at the same time. Thus, the parents participating are primarily there as PARENTS, that is seeking ways to help their children in mathematics, and learning about how the school system works. But although this may be their primary role, we are already noticing their engagement as learners of mathematics themselves. We are interested in documenting this "switch" from their role as parents to their role as learners.
Our work with adults in mathematics is grounded on socio-cultural and social constructivist perspectives (Cobb, 1990; Ernest, 1996; van Oers, 1996) and on research on adult education (Benn, 1997; Coben, 1998; FitzSimons, Jungwirth, Maa? & Schloeglmann, 1996; Knijnik, 1996). Our presentation will focus on the two groups of adults as they come to learn mathematics for themselves. In particular we will focus on their work in exploring geometry (BRIDGE) and patterns and algebra (MAPPS). We want to highlight affective and cognitive components as the parents reflect on the mathematics they are working on. Our focus is on how they construct meaning in a mathematics context and on how this learning experience compares with their previous learning experiences. Furthermore, we are particularly interested in connecting the mathematical ideas that we present (through typical school-based, hands-on mathematics activities) with their own uses of mathematics in everyday life (e.g., through their knowledge of sewing, craft-making, cooking). In BRIDGE, we are exploring this connection as a group—the mothers and the university researchers together.
Address: Marta Civil, Department of Mathematics, Building #89, University of Arizona, Tucson, AZ 85721, USA
What is Numeracy? What is Mathematics?
Language Australia, the National languages and Literacy Institute of Australia
One significant debate in Australia has been about the use of the word "numeracy", and its relationship to mathematics. As an adult numeracy field we have debated and argued about what it was we do, and what we should call it. Was it "real" maths (or "big M" Mathematics) or was it numeracy? Numeracy could be seen as meaning just the basics - coping with numbers and associated arithmetic skills. Numeracy was often cast as the pretender - the junior, inferior partner. Should we reject its use as a term to describe our work and field? In recent times this has also extended to the school sphere where numeracy has become one of the hot topics and is now a priority with governments.
In Australia the debate has mainly centred on broadening the view of numeracy so that it wasn't narrowed to being just about numbers. There was an attraction to the use of the term mathematics, which whilst incorporating number skills, also included other strands of mathematics such as data, space and shape, measurement and even algebra. However, the term mathematics brought with it many of the negative aspects related to the traditional teaching of mathematics in schools where it was taught, mainly by rote, and where the maths was taught out of any real life context. So there was a need to explore what we meant by numeracy and how it was different from school or academic type maths.
This presentation will offer a number of ideas and concepts that have been instrumental in shaping the way that numeracy has been seen and taught in Australia, and look at some recent international developments as well. Some of these include Betty Johnston's five strands of meaning making in mathematics (Johnston, 1994) and the concept of multiple numeracies developed through Beth Marr and Dave Tout's writing of the numeracy and mathematics strand of Australia's most popular adult basic education accredited curriculum, the Certificates in General Education for Adults (CGEA) (Kindler et al, 1996). International cooperation is now also occurring on projects such as the numeracy component of the International Life Skills Survey, which also has extended the concept and meaning of numeracy, and helped to answer the questions of "what is numeracy?" and "what is its relationship with mathematics?"
Kindler, Jan; Kendrick, Robin; Marr, Beth; Tout, Dave and Wignall, Louise, Certificates in General Education for Adults, Adult, Community and Further Education Board, Victoria, Melbourne 1996
Johnston, Betty, "Critical Numeracy" in FinePrint, Vol. 16, No. 4, Summer 1994, VALBEC, Melbourne, 1994
Financial Mathematics Courses for Adults
Edmir Ribeiro Terra
Universidade Federal De Mato Grosso Do Sul/Brazil
I have been working since 1994 with Financial Mathematics teaching courses for adults who have little or no knowledge of Financial Mathematics or about the use in these courses of Calculator HP 12c, a tool very useful for the calculations of several financial functions. The courses are sponsored by SEBRAE ( Brazilian Service of Support for Micro Enterprise ), with time of duration of twenty hours per week each course, and directed to businessman, and the local community (salesmen, students and others). Sometimes there are have managers and/or CEOs in these courses, especially when they are a closed package.
The approach refers to calculations of initial capital which is related to a final capital which changes due to the time. These capitals have a changeable factor, which is called Factor of Variation or FV (FDV in Portuguese). This approach is different from that which is taught at schools because we work with a numeric calculator and with basic facts of Financial Mathematics. It is possible to calculate the common rates and also the accumulated ones in several continuous periods of time, using the same concept. The common calculators (algebraic calculators) can also be used for introducing the concepts which are pertinent to the theme. The ease of learning is due to the use of calculator HP 12c which can also operate with calculations between furnished dates. Besides these mathematical functions, others such as statistics and linear regression (usually used for the calculations of rates and current capital flow or cash flow) can be used in the courses.
My work has two aims: the first intends to show how the simple concepts drive us to some formula and at least show a deduction that the concept doesn't change when we work with several capitals. The first applicable capital is transformed in a another capital which is applicable again and so on, including the percentage concept which arrives at the second moment. My second proposal of work is just to show that this new approach doesn't contradict the traditional teaching of Financial Mathematics, and these approaches can change and to facilitate the learning of this matter.
The students starting from a simple idea get a better understanding and are able to learn more deep concepts in a better way, acquiring a good level of learning.
The Need for Innovative Math Curriculum in Japanese Primary and Secondary Schools: Introducing Polythetic Learning as an Approach Compatible with Lifelong Education
University of the Ryukyus
Following post-World War II reconstruction, Japanese society Developed rapidly, especially economically. In the wake of Japan's phenomenally rapid economical growth, one of the characteristics of the 1970s (exactly speaking, after the Oil-Crisis) was children's rough behavior: frustrated children often destroyed the doors of toilets and smashed windowpanes. The 1980's were a period of unprecedented violence in the schools for Japanese people. They were shocked to learn of junior secondary school students' violence against teachers. The latter half of 1980's was marked by an increase of bullying ('ijime' in Japanese) and children's refusal to attend school. People were also disturbed by repeated encounter of news of children's murder or suicide. Within the development of this situation, the four Recommendations of the National Task Force for Educational Reform (1984-87) were published by the Japanese along with the advocacy of renewal of Japanese education. However, concrete reference was made only to the defense and innovation of social education. No reference was made to the innovation of school education from the perspective of lifelong education. In the 1990's, the problems above ware aggravated. As for Mathematics education, children's lower achievement was an issue of concern after the war. Teachers endeavored to assure high achievement of all children. But by the 1970's, the existence of children who dislike learning Mathematics became an important issue: it was found that the more children were taught Mathematics, the more they came to dislike Mathematics. In particular, it was from their Math classes that many high school students escaped. Although Japanese teachers made the effort to plan and practice "enjoyable Mathematics" by using hand-made teaching materials, the number of children who hated Mathematics continued to increase. Children could find no reason for learning Mathematics except for passing the rigorous entrance exams for high school and university. From the 1980's, in addition to offering "enjoyable Mathematics," we have tried to emphasize Mathematics as a tool for understanding the real world. But the problem outlined above remained relatively unchanged even in the 1990's. Moreover, after collapse of the "bubble economy," teachers have been bewildered to face "Class-Melting": younger pupils will not listen to what their teacher says in the classroom. Japanese people are dismayed to find that children's cruel violence is apparently escalating. Many children refuse to go to school and often their parents now support their children in this refusal. Recently also, university students' sliding achievement in Mathematics has been added to the problems of education. The Japanese school system is clearly not working well at present.
In this deadlocked situation, the 15th Central Council for Education has put attention on the innovation of school education (1998), as a consequence of which the perspective of lifelong education has become a keyword for reconstructing Japanese school education. The new curriculum guide (2002-) establishes the framework "Comprehensive Learning" to emphasize the perspective of lifelong education. The fact that Japanese education at the primary and secondary level has reached an impasse is now undeniable. The reconstruction of school education from the perspective of lifelong education is imperative. As for Mathematics education, one of the core curriculum subjects, we must recognize that Japanese children have lost a feeling for the joy and the realities of learning. It is necessary to recognize that the reality which can be taught depends on the historical/economical stage and the cultural maturity of Japan. With these points in mind, I propose the Small-Core-And-Options Curriculum and "Polythetic Learning" in order to reconstruct and revitalize Mathematics education. The perspective of lifelong education is now the fundamental point of view to draw a curriculum design, with which a through revision of the present curriculum model is possible in Japan. The Polythetic Learning that I advocate here is based on the United Nations' Convention on the Rights of the Child and an approach compatible with lifelong education.
Fostering a National Desire to Learn Mathematics and the Establishment of a Mathematics Aptitude Certification System
The Mathematics Certification Association of Japan (SUKEN)
Overview: "Suken" is a system for measuring practical aptitude in the field of mathematics. In recent years this system has been instrumental in helping to increase the desire to study mathematics throughout Japan. In order to promote the Suken system, Japan’s Education Ministry formally recognized The Mathematics Certification Association of Japan as a legally incorporated foundation. Since then, the Suken system has successfully been promoting the lifelong study of mathematics. Due to the creation of the Suken system, Japan is enjoying a rapid increase in the number of people studying mathematics. This phenomenon has not been limited to only students, but also includes small children and adults. In 1999, roughly 100,000 people were studying mathematics outside of the classroom setting thanks to the establishment of the Suken system. This figure is all the more amazing when we consider that this system did not even exist in 1992. Furthermore, over the next five years, we expect this number to increase to 500,000 or even 600,000 people a year. There is tremendous potential for such a system to become popular in countries throughout the world, particularly in developed nations, and we can expect an increase in students of mathematics on a global scale.
What is ‘Suken’? People who are gifted in mathematics have many chances throughout their lives to have their skills assessed and praised. However, those who study hard without concrete results do not have the chance to see their earnest efforts rewarded. This being the case, the Suken system fundamentally changed the levels, standards and ways of thinking about the assessment of capabilities in order to create an assessment system that corresponds to different levels of mathematics. People successfully passing a set level of math problems will be awarded a certificate of merit. In this manner, even the efforts of students at the beginning stages of mathematics can be clearly seen. The certificate does not display the student’s score, but is instead intended as a means of recognizing the student’s achievement. The important point is to create a system that clearly recognizes that the student has reached a certain level. In this respect, Suken is not a test, but a certification method. A test usually serves the purpose of the institution administering the test, whereas a certification serves as a means for the people taking the test to meet their own individual goals. People take the Suken examination for a wide variety of reasons. Some want to have documented proof of their abilities to present when seeking employment. Others want to use the results from the test when applying to enter educational institutions. There are even parents and children that take the Suken examination together as a means of sharing the joys of learning. The Suken system is also different than a qualification test. A qualification test is like a door, once you pass through it, your journey is over. However, Suken is more like a flight of stairs. With the Suken system you progress one step at a time in accordance with your own abilities. You can continue moving upward until you reach your goal or a level that meets with your satisfaction.
Items to be presented at WGA6
An Educational Programme for Enhancing Adults' Quantitative Problem Solving and Decision Making
Noel Colleran (City of Limerick Vocational Education Committee), John O’Donoghue & Eamonn Murphy (University of Limerick)
The complexity of modern society has created an ever increasing demand for life-long learning. While this demand has implications for all areas and disciplines it will impact strongly on areas such as adult literacy and numeracy. Adults’ quantitative problem solving skills will be a key focus as educators grapple with the challenge of educating people for an Information Age and maintaining workers’ employability in a knowledge society. Against this backcloth , the authors have been working on innovative ways of improving adults’ quantitative problems skills.
This paper reports on the development of an educational programme aimed at improving the quantitative problem-solving and decision-making skills of adult learners. The programme is designed to generate the conditions in which adult learners can discover the processes through which they solve quantitative problems and make decisions. This is done in an incremental and developmental manner. The theoretical basis for the programme in Lonergan’s (1957) work is discussed as are its connections to problem solving in mathematics education. Lonergan claims to have uncovered a ‘cognitional structure’ which delineated the mental activities employed by each individual when s/he comes to understand and know. He suggests that this process occurs naturally and in the same manner for each individual.
Finally, the authors outline their initial findings when the programme is applied in Adult Basic Education in Ireland with two different groups of long-term unemployed learners.
Lonergan, B. (1957) Insight: A study of human understanding. Longmans, Greene and Company: London.
Mexican Adults’ Knowledge about Basic School Mathematics
Silvia Alatorre, Natalia de Bengoechea, Ignacio Mendez, & Elsa Mendiola
National Pedagogical University, Mexico City/ National Autonomous University of Mexico
A survey was conducted among Mexican adults in which twenty problems of Basic School Mathematics were posed, covering mainly Arithmetic. Two samples were taken in Mexico City, each of 792 subjects aged 25-60 (which covers three national primary school curricula) and representative of the city’s population in that age group. Each subject received one of two versions (A or B) of the questionnaire and also gave general data.
Examples of the questions are:
The overall average of correct answers was 10.75 over 20. There was a statistically significant effect of the following variables:
There was no significant effect of the following variables:
The effect of schooling may be interpreted in several ways: it could be thought that the topics covered in the questionnaire are finally learnt in upper levels, or that only those subjects who learnt them in basic school arrived there. The non effect of curriculum leads us to think that the national efforts in improving it may not be all that fruitful, and to ask if that is the way to increase people’s general knowledge of mathematics.
How is this situation in other countries?
Mathematics and Key Skills for the Working Place
Henk van der Kooij
In The Netherlands life-long learning is an important political issue nowadays. Because of the rapidly changing world of work, due to the influence of technology, the need for people who have some flexibility in handling non-routine problems is growing.
Vocational training and adult education in The Netherlands are brought together in Regional Education Centers. Courses are described in terms of qualifications for the working place.
In the recent past, these qualifications described in detail what (technical) knowledge a person should master. Now the (political) discussion is about describing skills and competencies for so-called key problems of the professional area.
For mathematics education it is interesting to see that flexibility, problem analysis, structuring and schematizing abilities and critical sense are among the most important key skills for the newly defined qualifications.
Between 1997 and 2000, a new mathematics program is developed for vocational education (engineering) for students in the age group 16-20 in the TWIN-project. Because mathematics should really support the vocational courses, it was decided to develop mathematical concepts starting in the context of engineering. Many mathematical algorithmic topics (that are taken for granted in general education) are of no use in vocational settings, while other aspects of mathematics turn out to be very important. Among them are the key skills mentioned in the new structure of qualifications for vocational education.
Learning mathematics that makes sense in professional life is quite different from learning mathematics just because of the discipline itself. In the project we have emphasized the qualitative skills more than the algorithmic skills. One way to reach our goals was the integration of technology (like the Graphing Calculator) in the learning process.
Some examples, situated in the context of both engineering and the new key skills will be presented
The Context of Nursing Mathematics
D.F. (Mac) McKenzie
Unitec, New Zealand
Problems involved in the transfer of learning have been widely researched over many years. The conflicting results of different studies have shown that the issue is a complex one, and that many factors are involved. One major factor in determining the success or failure of a transfer situation may be the context within which the original learning took place.
This paper presents the findings of the first stage of a study being done with student nurses in different years of study in a nursing degree programme. The purpose of the study is to determine whether or not the student nurses are able to transfer the mathematical skills learned on the programme into other contexts.
In this first stage of the study, nursing students were tested on questions related to nursing and on similar questions from a more general life-skills context. This was to find out if there was any statistically significant difference in the problem-solving ability of the students in the two areas. The paper then will examine literature relating to the issue, and suggest possible causes for any differences found.
There is some concern at the polytechnic where this study is being done, (as elsewhere), that the mathematical standards of nursing trainees are not sufficient for the needs of the profession. Here, one action being taken is to have some trainees do their mathematical learning in a different environment before commencing the degree programme. This paper will indicate how future stages of the study will proceed over the next three years in an attempt to determine the effectiveness of such an approach, compared to the present on-site training.
If differences are found, and the context in which learning takes place does have a significant effect on the depth of understanding of the principles within the learning, then the study could have important consequences for a number of training programmes which involve significant mathematical content.
Life-Long Learning and Values:
An Undervalued Legacy of Mathematics Education?
Philip C Clarkson (Australian Catholic University)
Alan J Bishop, Gail E FitzSimons and WeeTiong Seah (Monash University)
In a report on adult learning in an Australian daily newspaper (Proctor, 2000), it was noted that people over 65 when returning to a semi-formal gathering to learn new skills or discuss ideas are motivated, interested, and there because they want to be there; a situation clearly common to many places in the world. Although they may be slower in learning in some ways, for them ‘learning is creating meaning’. This for them is not just a theoretical statement used by educationists, but a statement of reality. To create meaning they have an extensive, broad data base of prior experiences upon which to draw. Although many of those experiences will be positive in creating meaning in their new learning environment, some past experiences may also be inhibitors. When it comes to mathematics, skills never learnt, or once learnt but now forgotten, may be not the only inhibitor. A more enduring legacy of their prior mathematical learning experiences may be more important: the values, affective notions or dispositions that were implicitly learnt in the mathematics classroom.
When a mathematics teacher suggests that, "Remember of course that when solving these problems, be sure to show all the steps in your solution", the way of doing the mathematics is not just driven by considerations of the content to be learnt. This teacher is insisting that the method a student uses, whatever that method might be, should be able to be set out in a logical step by step sequence. Such a teacher is at this point teaching a particular mathematics education value, either explicitly or implicitly. This teacher may justify this notion of ‘show all your steps in your solution’ to the students, or may not. If the teacher does not, then the reasons why this is a critical part of ‘doing mathematics’ may well become part of the mystery, the unknown, and even the unknowable, part of mathematics for some students. What then for these students when they return to mathematics some years later? How should they go about doing mathematics now? Are they to show ‘all their steps in solutions’ when they are less than confident that their working will be ‘correct’? If the teacher does justify the injunction to ‘show all the steps in your solution’, then the student may learn that part of doing mathematics is being very logical, and that every step does count, and that every step needs to be correct. But if a student does not regard themselves as being very logical, then may be ‘showing all their steps’ can be a rather traumatic instruction. What feelings will this student still have from those classroom days if they return to doing mathematics at some point later in life? On the other hand, some students will think about this instruction, and it may lead them to start viewing mathematics as an elegant system of ideas, each section, at least in theory, fitting together neatly with other ideas to form a systematic whole. They might realise after some time that the notion of ‘showing all the steps’ is important for themselves, as well as their teacher, when learning a new idea in mathematics, but once the idea is learnt, such an instruction can be disregarded. These students may well be able to return at some later point in their lives to learning mathematics with some confidence.
It has been suggested that education can be conceptualised as the realization of our creative potential. Education throughout life is the continuous process of forming whole beings - their knowledge and aptitudes, as well as critical faculties and the ability to act (Delors, 1996). This paper will draw on some early results from a study investigating how values are taught in mathematics classrooms, often implicitly by the teacher (see web address in references). From these results, some possible implications will be explored as to the ramifications such teaching has for students throughout the whole of their lives. There is also an imperative that all teachers need to become aware of the values that they are teaching, when they are teaching mathematics, no matter at what level they are teaching. Hence, depending on the values learnt in mathematics classrooms, students may be helped in their life long learning, or may sadly learn values that inhibit their in-built creative potential.
What Might Good Practice Look Like in On-Line Teaching for Numeracy and/or Mathematics?
Jennie Bickmore- Brand
Murdoch University, Australia
This session will engage participants in a criteria for evaluating on-line and multi media technology for teaching and learning of numeracy and/or mathematics. The given set of Principles of teaching and learning developed by Bickmore-Brand (1990) is a set of pedagogical principles of teaching and learning that have been widely used across secondary and post compulsory teacher professional development programs/ materials. The principles have been drawn from an extensive interpretive search to identify common principles of learning across disciplines.
The following is a summary of the key ideas behind each of the seven principles.
Context- creating a meaningful and relevant context for the transmission of knowledge, skills and values.
Interest/connections- realising that the starting point of learning must be from the knowledge, skills and/or values base of the learner.
Modelling- providing opportunities to see the knowledge, skills and/or values in operation by a ‘significant’ person.
Metacognition- making explicit the learning processes which are occurring in the learning environment.
Scaffolding- challenging learners to go beyond their current thinking, continually increasing their capacities.
Responsibility- developing in learners the capacity to accept increasingly more responsibility for their learning.
Community- creating a supportive learning environment where learners are free to take risks and be part of a shared community.
Participants will be exposed to a range of examples of on-line courses at secondary, tertiary and adult numeracy levels from Australian contexts and assess them against the criteria (power point using website and CD Rom examples). Participants are invited to include any sites of their own or of special interest to be discussed (ethernet connection).
Reference will be made to studies which have been made evaluating multi media instructional design materials and projects (Reference list and handouts).
A Summary of Research on Adult Mathematics Education
in The United States During the Past Twenty Years
Katherine Safford-Ramus, Ed.D.
Saint Peter's College, Jersey City, New Jersey 07306,
United States of America
During the coming months I will be reviewing published reports of research conducted in the area of adult mathematics education in the United States. Sources will include doctoral dissertations as well as reports from mathematics, mathematics education, and adult education research journals. The summary will report both quantitative and qualitative studies. For the purposes of the review, all studies dealing with students older than sixteen who are not in traditional secondary institutions will be included. They will be examined and reported according to delivery system: adult basic education (ABE), adult secondary education (ASE and GED), English as a Second Language (ESL), workplace literacy, and undergraduate mathematics programs. Whenever possible, the undergraduate program results will separate findings for traditional-age students (younger than 25) from those for adult students (25 years or older).
Since the research which will be reported in this presentation is currently being conducted, it is difficult at present to predict the categorizations which will develop from the findings. A qualitative synthesis of the analysis will constitute the major portion of the presentation. Since there will be an extensive bibliography, the presenter will make that available to attendees through some electronic medium, preferably a web page at her home institution.
Developing a Video Case Study to Engage Numeracy Teachers in Reflection on Their Practices
University of Pennsylvania
Case study methodology has long been used in medicine, law, and business to develop situated professional knowledge amongst practitioners. Research has shown that professional development activities based on case studies of teachers dealing with real life concerns is both effective and interesting to teachers. Video case studies have the potential to allow a group of adult educators to "visit" a colleague’s classroom, gain a sense of the environment, watch the interactions and ongoing decision-making and share their observations, concerns, and alternative ideas about what they view, learning from each other in a safe environment.
But, developing a video case study that is both engaging and useful is different from developing a paper scenario. Video of unrehearsed interactions between a teacher working with adult learners provides both a richness and an ordinariness that impact decisions on case study components and presentation. This presentation will share the trials and tribulations of developing video case study resources on adult numeracy instruction for adult education practitioners, envisioning the conversations they may encourage.
Mathematics and Lifelong Learning: In Whose Interests?
Gail E. FitzSimons,
The rhetoric of lifelong learning has been adopted by governments of many countries around the world. Although the notion of lifelong learning was posited by Dewey, the concept was given prominence by the UNESCO commissioned report (Faure et al., 1972) which emphasised the dual ideas of lifelong education and a learning society. At approximately the same time the Organisation for Economic Co-operation and Development [OECD] (1971) was focusing on what it termed Recurrent Education. It called for reform of the basic presuppositions of education as the monopoly of the young, arguing for the centrality of continuing education as part of normal programmes. The more recent UNESCO report Learning: The Treasure Within (Delors, 1996) appears to maintain a holistic approach to personal, social, and economic development, as well as including environmental awareness.
Marginson (1997) observed that, by the mid-1980s the OECD policy documents attributed to education a human capital function of contributing as both a socialisation and a screening mechanism. He continued that the OECD, if not all member governments, realised that simplistic assumptions about the nexus between education and productivity were tempered by the effects of market forces as well as the individual’s capacities. The OECD argued that the economic contribution of education was better understood as a private return to individuals or firms rather than a social investment. Not only has education been linked to productivity, it is also implicated in the production of a self-managing subject. This may be achieved partly through inculcation the aspirations of citizenship and partly through encouraging people to invest in themselves through education (Marginson, 1997). In Australia social marketing (as in health awareness campaigns, for example) is to be the vehicle used to instil a desire, even a passion, for skill acquisition and engagement in lifelong learning (Australian National Training Authority, 1999).
The shift, over the last two decades, in the orientation of lifelong learning discourse from social to economic goals is particularly noticeable in the approach of the OECD, as described by Marginson (1997); it is being operationalised as a more subtle yet nevertheless persuasive strategy in Australia. Not only has the discourse of lifelong learning been appropriated by economically-oriented governments, but the promotion of lifelong learning has in turn appropriated discourses of marketing and its associated psychologies.
This paper will examine the possible contradictory roles played by mathematics in lifelong learning campaigns as a means of developing and maintaining personal agency, on the one hand, while being harnessed by governments in the production of self-managing subjects, on the other.
Delors, J. (Chair)..(1996). Learning: The treasure within. Report to UNESCO of the International Commission on Education for the Twenty-first Century. Paris: United Nations Scientific, Cultural and Scientific Organization (UNESCO).
Faure, E., Herrera, F., Kaddoura, A-R., Lopes, H., Petrovsky, A. V., Rahnema, M., & Champion Ward, F. (1972). Learning to be: The world of education today and tomorrow. Paris: UNESCO.
Marginson, S. (1997). Markets in education. St Leonards, NSW: Allen & Unwin.
Organisation for Economic Co-operation and Development (1971). Conference on policies for educational growth, General report: Educational policies for the 1970’s. Paris: Author.
Without a Bridging Mathematics Course,
Can Distance Education Students Survive?
Presentation by Distribution
Sukhothai Thammathirat Open University (STOU) caters mainly for adults returning to study and consequently has students with widely varying mathematical backgrounds. Many students required to study a compulsory mathematics course find it hard to pass due to their lack of basic knowledge and the absence of close support from the university. The students rely on the text as their major means of learning. Face-to-face tutorials are the most popular supporting medium but only a small proportion of students participates.
This research is the result of the analysis of a questionnaire completed by students enrolled in a Mathematics for Social Science distance education course in1998 and attended face-to-face tutorials. While students who attended the tutorials felt that they had improved their understanding of the subject, and they also scored better on the final examination than those who did not attend, there is still much room for further improvement. A major problem for many students is a lack of knowledge of the basic fundamentals. A third of the students came from non-formal education where they did not have enough mathematics. A similar number of students who did not complete secondary school, or who studied in vocational colleges, had identical problems.
The results indicated that the students' performance is adversely effected by their lack of prior mathematical knowledge. Though the students found the face-to-face classes satisfactory, they did not gain sufficient support from them. Previous studies suggest that STOU students dropped out due to lack of basic knowledge, the teaching and learning system, and their inability to commit sufficient time to study. Therefore, the university has to revise the system to help the disadvantaged students. A bridging course should be introduced to boost their basic knowledge and skills as a foundation for further studies. It is the university's responsibility to provide extra support given the policy of open admission and the lack of an entrance examination. Without a bridging course for mathematics many cannot succeed. The university will gain from the change, as the students will continue until they graduate and graduates will be of higher quality.
Forging Links for Community Development:
Roles of Schools and
A. (Ken) Clements
last three decades of the 20th century witnessed the largest and