ADULTS LEARNING MATHS NEWSLETTER
Company No. 3901346 Charity No. 1079462	No. 11 November 2000

In this issue

From the chair
Let us begin this volume of the newsletter on a positive note. Members are, I hope, returning fresh and refreshed from holidays and conferences full of ideas and enthusiasm for the new term/year. My earnest hope (and project ) for the coming year is to harness some of that enthusiasm, experience and expertise for the benefit of ALM and adults learning mathematics.

It is fitting as we return to our workplaces at the beginning of the new academic year to assess the challenges and opportunities facing us. Already the newsletter team has been busy producing this issue and planning for the future. There are exciting plans in train to grow the ALM newsletter in stages into an ALM journal in the next few years. This major undertaking is supported by the trustees and will need the dedicated support of all members if it is to succeed. In practical terms we can show our support by continuing to send articles to the newsletter, offering ideas and advice, and generally making the repository of tacit knowledge of ALM members available to the editorial team. I am pleased to welcome Tine Wedege to a newsletter team that is likely to expand in the coming months by at least one more member.

Members should note that ALM has moved to its own corporate website, a move that was approved by members at the recent AGM. This move was instigated and subsequently ‘engineered’ by Mieke van Groenestijn who has expertly supervised our presence on the web until now and who will continue to act as webmaster. The new address is http://www.alm-online.org. Also I would like to alert members to a new electronic discussion group for members with a special interest in vocational education. Members can join by sending an email to voc-ed@list.hvu.nl .

I am pleased to report that ALM-7 in Boston was a big success, and I would like to take this opportunity to thank our hosts and sponsors Analucia Schliemann, Department of Education, Tufts University and John Comings, NSCALL, Harvard Graduate School of Education. Special thanks are due to the organising committee under Mary Jane Schmitt and Kathy Safford. As expected some of us continued on to ICME-9 in Tokyo to contribute to the working group, WGA6/ Adult and life-long Education in Mathematics, as organisers and presenters. This work is adding to ALM standing in the field of adults learning mathematics, together with the scholarly output of members that continues to grow.

This is a good time to congratulate colleagues who have published books this year, Iddo Gal, Jeff Evans, and jointly Diana Coben and Gail FitzSimons. I’ll sign off with a reminder to make a diary entry for ALM-8 at Roskilde University next summer. Details are available now on the ALM website.

Prof. John O’Donoghue, Chair, ALM
Dept of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
Fax: +353 61 334927. email: John.ODonoghue@ul.ie

Mathematics in Transition Between School and Work

King Beach, Transitions Research Group, Michigan State University

Keynote address from the ALM7 Conference

 

We learn and develop mathematical understandings not only within particular contexts,but also during our moves from one context to another.Learning transfer is one of the few conceptual tools that we have to study how people generalize knowledge and skill across contexts such as school, homes, and workplaces.Unfortunately, transfer is not useful in sorting through the complicated relations between culture, history, mathematics, and identity that intertwine schools with other institutions such as work, and are at the heart of how we generalize knowledge across contexts.

Our everyday use of the term “transfer” has a powerful metaphorical bearing on how we, as educators and researchers who also happen to lead everyday lives, think about learning transfer.In our everyday usage of the term, transfer involves the movement of a person, a transaction, or the shifting of an object from one place and time to another.As a construct in educational psychology, it refers to the appearance of a person carrying the product of learning from one task, problem, situation, or institution to another.It is here that the metaphor begins to break down.

•     Commonsense suggests that generalization happens regularly on a moment-to-moment basis in our lives.Yet when we seek to study or facilitate it as transfer, we are rarely successful.This suggest that though the underlying phenomena are quite real, the transfer concept is inadequate for understanding them.

•     Transfer either defines an extremely narrow and isolated aspect of learning (that learned on task/situation A that is applied on task/situation B), or is no different from “just plain learning,” i.e. all learning involves transfer.Both are make the concept relatively useless.

•     Transfer environments are assumed to be static and pre-given.This excludes the creation of environments as part of the transfer process itself.

•     Nothing new can be created in the process of transfer.Transfer assumes a model of person-environment relation that seals a person’s initial learning off from being transformed in the new problem or situation.

•     Transfer involves single processes such as recognizing isomorphisms or abstracting general representations.The actual generalization of mathematical reasoning from school to work is complex and cannot be reduced to single process explanations.

Despite these problems with the transfer metaphor, the important educational issues and challenges that underlie what we have called transfer remain central and important.I and the other members of our group at Michigan State University believe that the difficulties are significant enough that the transfer metaphor should be left behind in favor of a metaphor and a set of concepts that accept both changing persons and changing social contexts as central to understanding generalization between the classroom and the workplace.A sociocultural stance affords us this possibility.

To paraphrase Mike Cole in his 1996 book, Cultural Psychology, our distinctiveness as humans lies in our ability to modify our world through the construction of cultural artifacts in texts, technologies, symbols, and signs, along with our corresponding ability to reconstruct the modifications in subsequent generations through our schools, families, communities, and work.We thus transform our own learning and development.It is this recursive relation between changing individuals and a changing world that is central to sociocultural work, and to our conceptualization of consequential transition.

The Concept of Consequential Transition as an Alternative to Transfer

Experiences such as learning algebra after years of studying arithmetic, becoming a machinist, founding a community organization, teaching your first-born to walk, an elementary school class writing a letter to a local newspaper, collaborating with NASA scientists on a classroom project via the internet,making the transition from student to teacher, and learning to do manufacturing quality control in your first job out of high school are all potential examples of the sort of things we are concerned with.Clearly the forms of generalization involved go far beyond learning transfer, but cover an educational terrain that has been reduced, metaphorically, to the carrying and application of knowledge across tasks.Each of these experiences share a set of common features as consequential transitions.

•     Transitions involve the reconstruction of new knowledge, skills, and artifacts, or transformation, across time and through multiple social context, rather than the reproduction of something that has been acquired elsewhere.Transitions therefore involve a notion of progress for the learner and are best understood as a developmental process.

•     Consequential transitions involve a change in identity: a sense of self, social position, or a becoming someone new.Therefore individuals and institutions are often highly conscious of the development that is taking place, and have particular, sometimes publicly debated agendas for how and why it should happen.Identity is what makes these transitions consequential.

•     Consequential transitions are not changes in the individual or in the social context, per se, but rather are changes in their relationship.Both person and social context contribute to a consequential transition and are recursively linked to each other.

Illustrations of the Concept of Consequential Transition

One illustration of the concept comes from a study of Nepali high school students becoming shopkeepers and adult shopkeepersattending school for the first time (Beach, 1995a,;1995b).High school students near graduation were apprenticed to adult shopkeepers for a period of several months.Similarly, adult shopkeepers that had never attended school were enrolled in an adult literacy/numeracyclass for several months.Changes in arithmetic reasoningwere tracked during this period of time.

The high school students engaged in a lateral transition from school to work.Many students in rural Nepal go on to become shopkeepers, and therefore the transition was unidirectionaltoward their future career.The shopkeepers engaged in a collateral transition between the shop and the classroom.They participated in both activities with near simultaneity.They planned to remain shopkeepers.Their transition was not preparation for participation in a new activity.Rather, it wasfor the improvement of their existing activity—shopkeeping.Thus changesin both the students’ and shopkeepers’ sense of self and social position were engaged as a part of the consequential transition.

The high school students’ transformed their arithmetic reasoning as a part of the transition. Students retained a written form of arithmetic notation, but the notationwas changed to represent modified forms ofmental and finger calculation strategies used by the shopkeepers.By transforming their arithmetic reasoning the students retained the status associated with written arithmetic while acquiring the efficiency of the shopkeepers’ strategies.The transition involved a transformation ofthe students’ knowledge of arithmetic.Unlike students, shopkeepers added some aspects of paper and pencil calculation algorithms to their existing repertoire of calculation strategies, and rejected others asnot useful for shopkeeping, such as the writing-out of operation signs.They expanded and reorganized their existing knowledge of arithmetical calculation, but did not construct a new form for representing calculations.

A second illustration comes from a study of an industrial machine shop where machinists trainedon mechanical machines were learning to use computer numerical control (CNC) machines(Hungwe, 1998;Hungwe & Beach, 1995).Mechanical machines are controlled with a series of dials, levers, and gauges that the machinist manipulates in real time to make parts.In contrast to this, program code that is written at a location distant from the machines before producing parts control the CNCmachines. The social and technological organization of the shop changed with the introduction of the computerized machines.Many of the machinists experienced an encompassing transition, a form of consequential transition occurring within the boundaries of a single social organization that is itself changing.

Machinists with decades of experience running mechanical machines mapped the CNC programming codes onto their prior knowledge of tool movement through Cartesian space and trigonometric calculations, albeit with some adjustment.However, machinists without those many years of experience with mechanical machines relied more directly on the structure of the programming code to think about tool movement and organize calculations in learning CNC machining.It can be seen from this example that it is the particular intersection of the history of the individual with the history of the social organization that determines the nature of knowledge developed during encompassing transitions.

The introduction of CNC machining supported the division of machining into machine operation and machine programming. Some machinists in the shop opted for overseeing the operation of the machines, whereas others began to program the machines.Several of the more accomplished machinists experienced a loss of craftsmen identity as a part of the transition to CNC machines.They were no longer individually responsible for creating parts from start to finish. Despite having mastered the intricacies of CNC machining, these machinist returned to mechanical machines where they were fully responsible for the making of parts.Sense of self and social position, or identity, rather than knowledge and skill, drove the reversal of their earlier transition.

The final illustration comes from a study of high school students at work in fast food restaurants for the first time (Beach & Vyas,(1998).An exclusive focus on school subjects like math, science, and literacy gives the appearance that nothing new was gained during collateral transitions between high school and work in fast food.It fact, the situation appears to be very much one of classic transfer.Students’ subject knowledge from school is applied to work in the restaurant.New understandings of math, science, and literacy are not constructed during the transition when these categories of knowledge are looked at in isolation.

A closer analysis indicates that the high school students do develop during the transition.Theyare learning how to learn in a production activity for the first time, in contrast to learning within a social organization that has learning as an explicit part of its agenda.Uses of language, math, and science on the job are reconstructed “on the fly,” so to speak, while production is maintained.The students develop ways to learn how to avoid inefficient arithmetic calculations, call out orders that communicate without distracting, and avoid food spoilage, all without specific time and support for learning these things.Students do not see these as instances of math, literacy, or science.They are right in one sense.Math, literacy, and science each involve multiple concepts that reference each other within their respective domains, e.g., the concept of ratio is related to fractions, decimals, and division. Math-, science-, and literacy-like concepts in the fast food restaurant are referenced to aspects of production, and not to other mathematical, scientific, or communicative concepts.

Development can be found during collateral transitions when we move away from using the epistemological assumptions of one social organization—the school—to understand participation in the new organization, in this case the fast food restaurant.In doing so we are also putting aside ideological assumptions thatvalue knowledge organized in the form of subject matter over knowledge organized is other ways, such as for production.

Some New Understandings and Questions

What might this new conceptual tool of consequential transition “buy” us in understanding and facilitating mathematics learning during transitions between school and work, and what new unresolved questions does it raise?Here are a few described in brief.A fuller explication of the concept ofconsequential transition can be found is a recent volume of the annual Review of Research in Education (Beach, 1999).

•     Attempts to get mathematical reasoning to generalize by making the learning of mathematics in classrooms more like math at work, or by teaching core concepts “in the abstract” are misguided and not particularly effective.

•     It is more productive to think about differences in school and work as presenting opportunities for mathematical learning and development, rather than boundaries to be overcome or transferred across.This suggests that efforts should not be directed at making school and work similar to each other, nor should seamless transitions between the two be promoted as a goal.Rather, we need to think about ways to directly support consequential transitions themselves as important pedagogical opportunities.

•     Learning mathematics in classrooms engages adult learner identities in ways that are quite different from that of younger students.The sense of becoming someone new, or of not being someone, e.g. not being “educated” should be considered legitimate topics for discussion among adult learners of mathematics.

•     How do we engage workplaces as environments for learning mathematics when learning and production often present competing and contradictory agendas?

•     How do we maintain relations between that which the adult learner experiences as math, and that which she does not experience mathematically, though we can understand both experiences as mathematical from our vantage point as teacher or researcher?

References

Beach, K. D. (1995a).Sociocultural change, activity and individual development: Some methodological aspects.Mind, Culture, and Activity,2(4), 277-284.

Beach, K. D. (1995b).Activity as a mediator of sociocultural change and individual development: The case of school-work transition in Nepal. Mind, Culture, and Activity, 2(4), 285-302.

Beach, K.D.(1999). Consequential transitions: A sociocultural expedition beyond transfer in education.Review of Research in Education, 24, 124-149.

Beach, K.D. & Vyas, S.(1998).Light pickles and heavy mustard: Horizontal development among students negotiating how to learn in a production activity.Paper presented at the ThirdInternational Conference on Cultural Psychology and Activity Theory, Aarus,Denmark.

Cole, M.(1996).Cultural psychology: A once and future discipline.Cambridge: Harvard University Press.

Hungwe, K.(1999).Becoming a machinist in a changing industry.Unpublished PhDDissertation,MichiganState University.

Hungwe, K.& Beach, K.(1995).Learning to become a machinist in a technologically changing industry.Paper presented as part of an interactive session titled,“Learning and Development Through Work” at theAnnual Meeting of the Educational Research Association, San Francisco, CA .

A Teacher’s Transformation into Teacher-Researcher

Pam Meader, Portland, Maine USA

Keynote address from the ALM7 Conference

 

For many practitioners, the word “research” is not welcomed with openarms.Many practitioners feel inadequate and not a part of the researchworld.Many feel that the research has no connection to what they do in the classroom and that researchers care little about practitioner’s feedback.Until I became involved in NCSALL’s (National Center for the Study of Adult Learning and Literacy) Practitioner Dissemination and Research Network(PDRN), I had these feelings about research. I would read an occasional abstract but rarely would it influence my teaching practice.

My first real “connection” to the research world came during a national meeting at Harvard University in Cambridge, Massachusetts during the summer of 1996.As a PDRN representative for Maine, I joined other representatives from the New England and Southeast regions to meet the researchers of the various NCSALL projects.All of us felt intimidated and nervous as we walked into a glorious room of giant mahogany tables.We were strategically placed around this room to get “closer” to the researchers and share in the process.It wasn’t until I heard the researchers John Comings, Rima Rudd, and Victoria Purcell-Gates speak that I began to relax and feel welcomed in this research arena. Matching faces to the research helped me to better “connect” to the projects.

During the second year as a PDRN representative, I learned that my job description was changing.Each representative was asked to conduct their own practitioner research based on John Comings research on learner persistence.I was apprehensive at first not knowing what “practitioner research” was.I soon learned that practitioner research was much like scientific inquiry where one posed a question or hypothesis, collected data, and then analyzed the findings.Because I am a math teacher, I found this process exciting and relevant.

The support and training I received from the NCSALL staff provided me with the much needed tools for practitioner research.We met three times during the year for support in our journey into research.Our first meeting helped us to develop and refine the questions, what many of us found to be the hardest task of all.Once our data was gathered, we met a second time to talk about ways to analyse data and present our findings.At our final meeting, we actually presented our projects and received wonderful support and accolades for our work.

In John Comings’ research on persistence, he found four supports to persistence:awareness and management of the positive and negative forces that help or hinder persistence; student self-efficacy, establishing a goal by the student, and progress toward reaching a goal.The idea of “persistence” certainly resonated with me.It had been a constant struggle to see students complete the variety of math courses we offered.In analyzing past persistence performances, I found that our persistence rates fluctuated between 40% and 60%.The idea of exploring force field analysis and incorporating goal setting into my math classes intrigued me.After much thinking and revisions, I decided to base my research on what effect continuous goal setting in a math classroom had on persistence rates.

I decided to begin collecting data with the first class meeting.I explained to the students about John Coming’s findings on learner persistence and goal setting.I asked each student to fill out a goal setting questionnaire which incorporated force field analysis.That is, the survey asked students to consider what barriers would prohibit them from completing their goals and what positive forces would enable them to reach their goals.They were also asked to list daily action steps that they would follow to help reach their goal.Four weeks later we revisited their goals, then again at the half way mark of the semester and then toward the end.

What I learned from this research was far more than I had imagined.While Comings’ research found transportation, child care, and work as barriers, the greatest barrier for math students was math difficulties.

 

Students listed lack of understanding, fear of failure, fear of math, frustration with math, math anxiety, and motivation as barriers to fulfilling their math goal.Clearly psychological and academic barriers were at work here, not situational barriers such as transportation.

As far as the effect of goal setting on persistence the result was equally surprising.My higher level mathematics courses of Algebra showed no significant change while lower level courses showed a positive effect on persistence and goal setting.The following graph shows the class of greatest improvement.The non-goal setting group had only a 40% completion rate while the goal setting group was about 75% persistent.

 

The transformation from teacher to researcher has made an everlasting impact on myself and my students.I continue to use goal setting in my classroom and feel it has made a difference in persistence.More importantly, I now have introduced the research process to my algebra students.As a performance assessment task, my students must develop a research question, collect data, graph and analyze the findings and present their research to the class.

On another level, this research project has impacted my math department.Discovering that math difficulties were a clear barrier, I had my three math teachers conduct force field analysis in their classrooms.The results were synonymous with my findings.We then surveyed students who completed a required math class to see if their math attitudes changed.The majority of students went from hating and fearing math to liking math.Clearly a change in math attitude can have a direct effect on persistence.

As you can see, practitioner research has had a direct change on myself, my students and my staff.I feel practitioner research is a viable procedure to help effect change.However, in order to be a successful model, practitioners need to be supported, both administratively and financially.With the supports in place, practitioner research can cause immediate changes in the classroom.

Reference

John Comings, Andrea Parrella, and Lisa Soricone, (2000), “Helping Adults Persist: Four Supports” in Focus on Basics, Vol.4, Issue A, March 2000, pp 3-6

Challenging the Researcher/Practitioner Dichotomy: a voice from the south

Gelsa Knijnik, Universidade do Vale do Rio dos Sinos, Brasil

From the ALM7 Conference

In the last 10 years I have been working with the Brazilian’s Landless People Movement. It is a national organised social movement of rural workers now internationally acknowledged for its struggle for land reform in the country with the highest concentration of land ownership in the world, a land reform that will enable a more equitable distribution of wealth and promote social justice. The Landless Movement has also been internationally acknowledged for prioritising education as one of the central dimensions of its struggle, in particular the need of children, youths and adults for mathematical education.

The work that I have been developing with the Landless Movement can be summarised in what I have called the Ethnomathematics Approach. This consists of:

•     the investigation of the traditions, practices and mathematics concepts of a social group and the pedagogical work which is developed in order for the group to be able to interpret and decode its knowledge, to acquire the knowledge produced by academic mathematics; and

•     to establish comparisons between its knowledge and academic knowledge, thus being able to analyse the power relations involved in the use of both these kinds of knowledge.

Guiding an educational process in this approach means, necessarily, to articulate research and practice. The pedagogical practice here is linked with research in two dimensions. The first, relating to the process of investigation of the traditions, practices and mathematical concepts of a social group. This investigative process implies the need to carry out fieldwork, in which ethnographic techniques, such as participant observation, audio recordings, field diary and interviews are used. But this is not anthropological work, ethnography in the strictest sense of the word. However, in using elements of ethnographic techniques, inspired by anthropological knowledge, I have been watchful about questions which have been asked contemporarily by anthropology, an area strongly marked by its links with the colonial area, with the description of the “other”.

In a second dimension, the Ethnomathematics Approach also connects practice and research. This dimension concerns the follow up of the pedagogical process. Here I, as a practitioner, am dedicated to writing and examining my own practice, establishing an interlocution with the theorisations in the field of ethnomathematics, thus seeking to discuss the limitations and potentials of the work I am doing.

This research perspective which, in a more conservative view could be criticised as lacking neutrality and objectivity, now, as we live in a time when these myths have been undone, can produce other meanings for the act of researching, enabling a crossing of borders and a breaking of the dichotomies between “insider” and  “outsider”, between the language of research and the language of practice. This crossing of borders, which had previously been outlined with such accuracy, involves the act of writing about one’s own research, presenting it at conferences, which means definitely to take on, oneself, the act of self-representation.

In the third part of the paper my intention was to provide an example of an Ethnomathematics Approach.  The example is connected to the “Rice production project”, which I developed in a Landless Movement settlement (Knijnik, 2000). It was carried out with a group of young people who, at the time, were in 7th grade. However, the ideas that sprouted from it have inspired the work we are developing in the non-formal education of youths and adults in the Landless Movement.

In the project the past and present cultural practices were examined in the dimensions of conflict, of the struggle to impose meanings, in a dynamics in which non-official knowledges, vocalised by peasants coming from different regions of the state, whose life experiences are marked by different traditions, were recovered and confronted amongst themselves and in their relations with dominant knowledges, vocalised by the agronomist. The approach used in the pedagogical work focused on problems of practical and material needs. They were not transmuted into symbolic control problems, indicating other possibilities in the field of adult mathematics education, especially adult mathematics education which is carried out in diverse cultural settings such as the Landless Movement.

References:

KNIJNIK, Gelsa. (2000) Ethnomathematics and Political Struggles. In: COBEN, D. et al. (Ed.) Perspectives on Adults Learing Mathematics: Research and practice. Kluwer Academic Publishing

ICME-9: Working Group for Action (WGA) 6: Adult and Life-long Education in Mathematics

Chief Organiser: Gail FitzSimons [AUS]; Associate Organisers: Diana Coben [GBR], John O’Donoghue [IRL], Lynda Ginsburg [USA]; Local Assistant Organiser: Akihiko Takahashi [JAP/USA]

Over 60 people participated in this WGA during the three days of meeting in Tokyo. The stated goal of the group was to propose a set of recommendations related to mathematics education in relation to lifelong education. This orientation offered a very broad scope for presentations. Work is being undertaken in many countries to develop systematic and critical foundations for this research which needs to be grounded in the work of those practising in the field. The group welcomed the contributions of educators with experience of teaching mathematics to adults, whether on a formal or an informal basis, as well as those with observations and recommendations on the amelioration of compulsory schooling towards an ethos of life-long education, taken in the broadest sense in being of benefit to both the individual and the community at large.

As the programme evolved it became apparent that there were several distinctive themes, pertinent to countries at varying levels of industrial development. These included adult teaching and learning, family education, education for the workplace, distance education, professional development, and research and policy issues. The programme was structured to accommodate plenary sessions as well as parallel sessions. The abstracts are currently available on the Adults Learning Mathematics website: www.alm-online.org. It is intended that the full papers be published by the end of 2000.

Recommendations

The final session allowed time specifically for participants to make recommendations about life-long education in mathematics. The following is a synthesis of recommendations taken from this session, recognising that this working group represents an emerging field concerned with extremely diverse populations of learners in terms of variables such as age, and educational, social, cultural, and political backgrounds.

Political aspects of Life-long Education to be considered:

1.   We need to be aware that the discourses of lifelong learning/education have been appropriated by economically-oriented governments.

2.   We need to be aware of the risks associated with following government agendas in order to gain funding for research and/or programme delivery. Such agendas may, for example, be framed in the rhetoric of recognising urgent unmet community need while simultaneously demanding mathematics (or numeracy) curricula and pedagogies that are inappropriate ‑ that is, not grounded in adult or lifelong education research. These risks are well illustrated in the metaphor of Diana Coben: “It is like stepping on a rake-head!”

3.   We need to be aware of the relationships between the sectors of education, especially as education becomes commodified. For example, adults do not need simply ‘school mathematics’ (again), even if dressed in ‘adult’ contexts. Conversely, as highlighted by several presenters, school mathematics itself may be broadened in scope, in cognitive and affective domains, to encourage the formation of positive attitudes spanning a lifetime towards the study of mathematics.

Research aspects of Life-long Education to be considered:

1.   Whose interests are we, as adult and lifelong mathematics educators, serving? Is it government(s)? Industry? Individuals?

2.   Where does mathematics actually occur in industry?

3.   How does mathematics education fit in with government and industry priorities? For example, it may be perceived that adults are being enabled to critique government policy. Or, that adults are being empowered to make their own career decisions rather than complying with decisions made elsewhere.

4.   Ethics is a critical issue in Adult and Life-long Education. There is always an opportunity cost to adults in terms of time and/or money invested in undertaking study, and researchers need to be cognisant of this fact. Some adults, especially inhabitants of social institutions, have few if any rights over videotapes, audiotapes, or transcripts of dialogue.

Possible research questions:

1.   Is a broad mathematics education better than narrow training in improving economic and social productivity/output?

2.   Are we, as adult educators, being caught up in a mathematics-technology juggernaut? What might constitute a circumspect approach to the uses of technology as a tool and endpoint of teaching?

3.   Is there a function for adult mathematics education to involve the general public, not least decision-makers, in education processes concerning the realities of mathematics ¾ as distinct from the ‘school mathematics’ remembered by most?

4.   To what extent can learners in a system determine their own goals?

Other observations:

1.   Education for lifelong learning goes beyond a narrow context (e.g., ‘semi-skilled’ jobs).

2.   The conceptual shift from ‘mathematics’ to ‘numeracy’ may afford the opportunity for a broader curriculum.

3.   Parents, together with friends and other relations, who have experienced an enjoyable, successful, interesting, and engaging mathematics education are likely to support and encourage children’s learning through socialisation and enculturation.

4.   The timescale for adult education may be too restrictive under managerialist philosophies of education, as is the focus on small packages of atomised curricula. Adult education requires a long-term commitment to achieve its goals. However, longer time spans for formal education do not imply more time in the formal classroom. Education may take place formally, informally, or non-formally.

Conclusion

This WGA, Adult and Life-long Education in Mathematics, was broadly situated to encompass political, cultural, social, epistemological, pedagogical/andragogical discourses. Our thanks goes to all participants, and especially to the presenters.

A note on the reasons for the challenges in teaching mathematics to adult learners at the tertiary level in Trinidad and Tobago

Isaac Dialsingh, Lecturer, Department of Economics, University of the West Indies, St Augustine, Republic of Trinidad and Tobago.   Email:  consult@tstt.net.tt

This paper seeks to address some of the issues that are currently engaging the attention of educators in the Caribbean region. It is basically geared towards suggesting reasons for the poor performance of adult learners of Mathematics in the region and it addresses the current innovations/changes that are being used to address these problems.

A short presentation of the educational system that currently exists is presented in an attempt for the reader to gain an appreciation of the education scenario. Basically the educational system in Trinidad and Tobago is patterned after the British system and is made up of the primary, secondary, tertiary, and vocational levels. The child enters primary school at the age of about five and spends about six years there. The ‘Common Entrance Examination’ ( a multiple choice exam) is administered and then they are placed in the secondary school system where they normally spend another five years. Students opting to pursue vocational education have the option of applying to one of two technical institutes. Children who are academically inclined often choose to do two additional years at a secondary school where they would complete their General Certificate Examination at the Advanced Level. After completing their exams, they then have the option to pursue a degree in a subject of their choice at one of the many tertiary institutions in the country (both private and public).

Now we take a look at what actually happens in our educational system.

First, our educational system is very deep rooted in the idea of producing as much ‘passes’ as possible. With this in mind, and the syllabus that needs to be covered, there is little or no room left for innovation or creativity in the learning process. The learning process is restricted to the blackboard and chalk. The materials that are supplied are also limited to foreign text books and teaching aids. In the primary system the government has embarked upon a system of standardizing textbooks. This basically means that all schools throughout Trinidad and Tobago will be using the same Mathematics books (all locally produced) for the entire primary system. While this might be good news for the parents in terms of economics, it leaves the teacher in a bit of a dilemma in which he is restricted to only using textbooks that are ‘recommended’ by the state. The secondary school system is vastly different - teachers here have the ability to recommend textbooks of their choice. Again, because of economics most of the underprivileged children never get their hands on one. These textbooks are mostly published in the UK and as such, students often have a difficult time relating to the materials and examples presented in the texts. At university reliance is strictly on lecturer’s notes and ‘photocopies’. The Internet is now being seen as a valid and cheaper alternative of getting university level materials with little or no cost attached to it.

Teacher training is another area of contention. To be eligible to teach at the primary school level, you need to have five ordinary level passes or five ordinary level and at least two advanced levels. To teach at the secondary level, all that is needed is a degree in the relevant subject area. Therefore because of the lack of trained teachers the system or delivery process suffers. At the primary school I taught at for two years, 30% of all the teachers were untrained. In the secondary school that I am currently teaching at, only 10% of the staff possess a diploma in education. Teacher training does affect the teacher’s ability to properly deliver the basic foundation of mathematics. Failure to build a proper foundation only spells disaster at the tertiary level.

Class size too is an area of concern. The size of classes at both the primary level and secondary level range from 20 to 45. These large classes afford no one-on-one interaction and class discussion is greatly hampered, as a result, the class time is more of a lecture than an interactive session. One of the spin offs of this is the ‘lessons trade’—teachers are in high demand for private tuition. I thought that this lessons phenomena was restricted to the primary and secondary levels, but there are a substantial number of students who are asking for lessons at the University of the West Indies especially in Mathematics.

Now I turn my attention to the tertiary level system where the class size is no better. The class size for a lecture in introductory mathematics was about 200 a few years ago. However, today there are steps to decrease the class size to 50. The major reason for  splitting classes has been the high failure rate (60%). There has been some improvement as the failure rates has dropped to around 40%.  Tutorial sessions which are meant to be interactive are not that interactive. Students are satisfied with just getting a copy of the solutions. Questions are seldom asked by students. They simply accept the method given to them and adopt the method as ‘biblical’. The majority of adult learners that I have taught still rely on ‘mechanics’ than a thorough understanding of the concept at hand.

The major problems I see that adult learners have are:

1.   An unwillingness to ‘unlearn’ what they have learnt. Sometimes adult learners need to forget what they have learnt. A common example is prime numbers. Some adult learners insist that 1 is a prime number.

2.   The inability to think logically. A common mistake made by students is the ‘method’ mistake. They adopt a method and assume that it will work for all ‘similar’ problems. When to use which method is often a problem. For example, in proofs using set notation, do we use a contradiction or do we prove by using a counter example? Or even to prove that set A=B it is not uncommon for students to give examples of two sets that are equal instead of proving:

                  

3.   The inability to identify shorter methods of solving problems. For example a common problem given to students is:

           

 

will normally see students engaging integration by parts but almost no one will check that the function is odd and because of the limits, the integral will be zero.

My conclusion is that the heart of the problem with adults learning mathematics lies with the foundation that had been laid at the primary and secondary levels. As noted above there are serious problems to be addressed. But, the government is beginning to do a lot of work in this area. Teachers at the secondary levels will now be recruited only if the they have a diploma in education. Also training courses will be made available to teachers in the use of multimedia instructional resources. At the tertiary level too, the University of the West Indies has been doing a lot of work with respect to improving the delivery of the lectures. The main goal here is to get as much student interaction into the classroom as possible. So, very soon our ‘lectures’ would be highly participatory. The University has also spent enormous sums of money in putting the proper infrastructure in place. New lecture halls with overhead projectors and new computer labs with a lot of academic software is currently available. Internet access for all is quickly becoming a reality and education at the tertiary level will be expected to be less boring.

 

Reflections on ALM-7

Mark Schwartz <markdotmath@earthlink.net>

I just got back from my first ALM Conference. I’ve been talking to people on this Numeracy BB for several years and the timing was right for my going to meet them and others and to re-engage with the intimacies of teaching adults.

I was (and hope to continue to be)...

ENGULFED by a community of researchers and practitioners who are not satisfied with the current state of math education for adults. There is a delicious tension - people fidget and fuss and are in perpetual motion. It’s like a clutch of chickens eating - continually scratching and pecking at things that might ultimately be savory and nutritional and fortifying.

ENTHRALLED by concepts that I had seen before, but had never visited through other’s eyes.

ENLIVENED by discussions and debates and dialogues and polylogues about topics great and small, detailed and global conceptions.

ENAMOURED of the people and the ideas and practices presented.

ENMESHED in knotty little math dilemmas that have overwhelmed adults for a while and that have been (and still are) challenging ALMers to unravel - simple little things that encase curiosities and complexities that hide “AHA” from learners.

ELEVATED by seeing and hearing of the dedication, passion and sweat and tears of ALMers who see helping others as a natural event. 

ENTERTAINED by the continual and lively talkativeness. I think that, alternately, half of the ALMers talk in their sleep while the other half listens!

EMANCIPATED from some crusty perceptions I had and joyful of shedding them.

ENDANGERED by no one; only by some of the new ideas I saw (but hopefully I’ll get over it).

EQUILIBRATED by the comfort of hearing about good teaching/learning strategies, some consonant with my practices and perceptions.

and mainly EDUCATED. People at the conference teased and taunted and terrorized concepts that deserved that kind of attention. It was for me what Stephen Gould describes as “punctuated equilibrium”. It was not restful; rather it was refreshing. It was prickly and quirky in a most energizing way.

Thanks to all who were there. And, for those of you who enjoy what you experience on the Numeracy BB but haven’t had the opportunity to attend ALM (or for that matter any professional group of adult math educators), consider attending next year.

Reprinted with permission from Mark.  It was originally sent to the the ANN numeracy list.

Memories of two class visits

K.T. Elsdon

Practice makyth imperfect

Weekday evening; a mixed class, mostly late adolescent boys who might be in the last two years of school, early and middle-aged men, a few young and middle-aged women, meeting in an ill-lit room round two large tables.  Man school teacher in his early fifties; are the boys from his day school, and receiving extra tuition?  Blackboard is covered with sums which the class members have copied into exercise books and are now working to solve; teacher watches, circulates, and marks work on the spot: tick or cross, tick or cross.  At least he’s using a plain pencil, not red ink! Quiet, concentrated work by a class who don’t seem to understand what they are doing; it appears to be almost a matter of chance whether they get their sums right or not, and the marking is not accompanied by questions or explanations.  The atmosphere is as melancholy as the lighting.

The LEA [Local Education Authority, in England] has been generous:  there are stacks of exercise books and packets of pencils in the cupboard, and they’re free.  Puzzled what help I can offer here, I ask if they have a tape measure or at any rate some rulers.  “No, we don’t let them have those until the second year.”  Exeo, sadly, having done no good.

Another country, and the wench revives

Another slum class, this time in Nairobi, meeting in the morning in a community centre (a hut with a clean new earth floor and chairs).  Class ranges from young to mainly young middle-aged women and two old men; a few non-participant husbands keep watch at the back.  Teacher a woman in early middle age who works from the front, surveying the serried rows and getting individuals to sing out their answers to the rows of multiplication sums she has written on the blackboard.  People work in exercise books or on bits of paper, using pencils.  Apart from a quiet sense of hopeful commitment the work is in much the same rut as before: as I go round and ask questions it seems many students don’t understand what they are doing, but this teacher knows.  What can be done about it?  She really wants to be more effective.  Would I advise?  I take a deep breath, say yes, and ask if I may borrow the class.  The teacher agrees, with obvious relief at being off the hook (her area organiser being present!) and the class, surprised at being asked for their permission, begin to think there may be an adventure ahead.  The room is utterly bare except for a  poster or two about nutrition and hygiene.  Nothing there on which to hang a lesson to explain the principles of multiplication. Then: the floor!

Let’s pretend we’re rich, that this is our own house, and that we’re going to have a CONCRETE FLOOR.  How would we work out what we need and how much it would cost?  Quick offers from all round of expertise on cement, sand, gravel and even proportions.  How much?  We’d have to measure it, and we all get up and do so, using our own feet.  I’m afraid mine are the largest and they agree to use mine as standard.  That gives us the area.  There is some argument about thickness and cost, and recklessly we plump for the most expensive option.  And so on … the exercise is completed in a surprisingly short time.  At the end one of the two men asks what all this has got to do with multiplication, and I congratulate them on having licked it.  But the teacher and the area organiser ask if I couldn’t persuade the Ministry to put it into a textbook, and my first reaction is to say there’s no need.  Then I think back to the Scotland Road and all the Scotland Roads elsewhere and agree – but perhaps it should be in a book of suggestions for teachers, and maybe they shouldn’t be given that until after they’ve done it?

News and Events

ALM-8 Conference

28-29-30 June 2001

8th International Conference on Adults Learning Mathematics to be hosted in Denmark.

The ALM Conference in 2001 (ALM-8) will be locally hosted by the Centre for Research in Learning Mathematics at Roskilde University (near Copenhagen) Denmark.

The theme of the conference will be “Numeracy for Empowerment and Democracy?”

The local organising team are: Tine Wedege and Elin Emborg, Roskilde University, Lena Lindenskov, National University of Education, Lene Oestergaard Johansen, Aalborg University, and Eigil Peter Hansen, Adult Educational Centre. Information about the conference program will be available at the ALM website: http://www.alm-online.org where an initial call for papers will be posted in November. Deadline for submitting papers or poster proposals is 15th March 2001.

For further details, please contact:

Tine Wedege (content of the conference)       email: tiw@ruc.dk

Elin Emborg  (practical issues)           email: emborg@ruc.dk

Centre for Research in Learning Mathematics

Roskilde University

Box 260

4000 Roskilde

Denmark

Now available . . .

Adults’ Mathematical Thinking and Emotions: a study of numerate practices

by Dr. Jeff Evans

This book published by Falmer Press as one of the series of Studies in Mathematics Education edited by Paul Ernest, addresses several perpetual concerns around the teaching and learning of mathematics, and its use in work and everyday life, concerns that are reflected in the discussions at ALM each year.

Available from:  Falmer Press

Contact details:

11 New Fetter Lane

London EC4P 4EE

Tel. +44 (0)171 583 9855

Fax +44 (0)171 842 2298

E-mail: info@tandf.co.uk

or visit:

http://arakhne.tandf.co.uk/homepages/fphome.html

http://www.tandf.co.uk/journals/contacts.html

Publication date 3rd Nov. 2000
hb isbn 0750 709138 - price £55
pb isbn 0750 70912X - price £18.99

Perspectives on Adults Learning Mathematics, Research and Practice

edited by:
Diana Coben
University of Nottingham, UK
John O’Donoghue
University of Limerick, Ireland
Gail E. FitzSimons
Monash University, Victoria, Australia

Contents and Contributors

Acknowledgements. Preface. Introduction; D. Coben, et al. Review of Research on Adults Learning Mathematics; G.E. FitzSimons, G.L. Godden.

Section I: Perspectives on Research on Adults Learning Mathematics; D. Coben. Mathematics or Common Sense? Researching ‘Invisible’ Mathematics through Adults’ Mathematics Life Histories; D. Coben. Researching Adults’ Knowledge Through Piagetian Clinical Exploration – the case of domestic work; J.C. Llorente. Understanding their Thinking: the tension between the Cognitive and the Affective; J. Duffin, A. Simpson. Understanding their Thinking: the tension between the Cognitive and the Affective; J. Duffin, A. Simpson.

Section II: Adults, Mathematics, Culture and Society; J. O’Donoghue. Mathematics: Certainty in an Uncertain World? R. Benn. Ethnomathematics and Political Struggles; G. Knijnik. Statistical Literacy: Conceptual and Instructional issues; I. Gal. The roles of feelings and logic and their interaction in the solution of everyday problems; D. Colwell.

Section III: Adults, Mathematics and Work; G. FitzSimons. Women, Mathematics and Work; M. Harris. Technology, Competences and Mathematics; T. Wedege. Mathematics and the Vocational Education and Training System; G.E. FitzSimons.

Section IV: Perspectives in Teaching Adults Mathematics; J. O’Donoghue. Algebra for Adult Students: the Student Voices; K. Safford. Exploration and Modelling in a University Mathematics Course: Perceptions of Adult Students; B.J. Miller-Reilly. Assessing Numeracy; J. O’Donoghue. Adult Mathematics and Everyday Life: Building Bridges and Facilitating Learning ‘Transfer’; J. Evans. Teaching ‘not less than maths, but more’: an overview of recent developments in adult numeracy teacher development in England – with a sidelong glance at Australia; D. Coben, N. Chanda. Postscript: Some Thoughts on Paulo Freire’s Legacy for Adults Learning Mathematics; D. Coben. Index.

hardbound NLG 210.00 / GBP 69.00  

order email: orderdept@wkap.nl

in US: kluwer@wkap.com

more info: http://www.wkap.nl/

About ALM	Company No. 3901346  Charity No. 1079462
Adults Learning Maths – A Research Forum (ALM) ALM is an international research forum bringing together researchers and practitioners in adult mathematics/numeracy teaching and learning in order to promote the learning of mathematics by adults.

 

What is ALM?

ALM was formally established at the Inaugural Conference, ALM-1, in July 1994 as an international research forum with the aim to promote the learning of mathematics by adults through an international forum which brings together those engaged and interested in research and developments in the field of adult mathematics/numeracy teaching and learning.

ALM is a forum for experienced and first-time researchers to come together and share their ideas and their reflections on the process as well as the outcomes of research into hitherto neglected area of adults learning mathematics.  ALM puts people in touch with each other, providing a framework for collaboration and helping to stimulate and develop research plans.  We are especially keen to encourage practitioners to undertake research. 

Since 1994, ALM has gone from strength to strength and now has 140 members in 19 countries. In 2000, it was registered as a company and as a charity in England and Wales.

What does ALM offer?

ALM membership brings with it opportunities to:

•     contribute to an international forum of researchers and practitioners in the field

•     share concerns, insights and research at ALM annual conferences, and to attend at a reduced rate

•     receive ALM newsletter (free)

•     receive ALM conference proceedings (free of charge to conference delegates).  These proceedings constitute the most significant and authoritative collection of papers on adults learning mathematics available today

•     network, electronically and otherwise, with practitioners and researchers in the emerging field of adults learning mathematics.

ALM Officers

Chair: Prof. John O’Donoghue, University of Limerick

Secretary:      David Kaye, London

Treasurer:     Prof. Sylvia Johnson, Sheffield Hallam University

Membership Secretary: Sue Elliott, Sheffield Hallam University

Join ALM today!

ALM is actively seeking to expand its membership worldwide.  Membership is open to all individuals and institutions who subscribe to its aims.  For details contact Sue Elliott, Membership Secretary at the Centre for Mathematics Education, Sheffield Hallam University, 25 Broomsgrove Road, Sheffield S10 2NA, UK email:  S.Elliott@shu.ac.uk or your regional ALM membership agent:

ARGENTINA  Dr Juan Carlos Llorente, Fundacion PAIDEIA, Instituto de Investigacion Educativa, Mitre 862 (8332), Gral Roca, RN, Argentina.   Email: JCLlorente@paideia.edu.ar

AUSTRALIA  Dr Janet Taylor, OPACS, Uni. of Southern Queensland, Toowoomba, Australia. Email: taylorja@usq.edu.au

BRAZIL    Eliana Maria Guedes, Dept. of Architecture, Mathematics and Computing, UNITAU, University of Taubaté, Sao Paulo, Brazil.  Email:  emg@aquarius.com.br

DENMARK    Dr. Tine Wedege, IMFUFA, Roskilde Uni., PO Box 260, 4000 Roskilde, Denmark.  Email:  tiw@ruc.dk

NEW ZEALAND   Barbara Miller-Reilly, Student Learning Centre, The University of Auckland, Private Bag 92019, Auckland, N.Z.  Email:  Barbara@math.Auckland.ac.nz

REPUBLIC OF IRELAND   Prof. John O’Donoghue, Dept of Maths and Statistics, University of Limerick, Limerick, Ireland.  Email: John.ODonoghue@ul.ie

THE NETHERLANDS     Mieke van Groenestijn, Utrecht University of Professional Education, PO Box 14007, 3508 SB, Utrecht, The Netherlands.  Email:  Mieke.v.Groenestijn@feo.hvu.nl

UNITED KINGDOM   Sue Elliott, Centre for Mathematics Education, Sheffield Hallam University, 25 Broomsgrove Road, Sheffield S10 2NA, UK.  Email:  S.Elliott@shu.ac.uk

USA   Dr Katherine Safford, Saint Peter’s College, Kennedy Boulevard, Jersey City, NJ 07306, USA.  Email:  SAFFORD_K@spvxa.spc.edu

Membership fees

 

 

Editorial Committee

Mieke van Groenestijn        Utrecht University of Professional Education,  Netherlands

Dave Tout                          Language Australia

Tine Wedege                     Roskilde University, Denmark

For more information email: newsletter@alm-online.org

The views expressed in individual articles are those of the authors and do not necessarily represent the views of ALM or of the editorial committee.

We would like to encourage members to submit items to the newsletter. These should be sent to:
Mieke van Groenestijn, Faculty of Ed., Hogeschool van Utrecht, PO Box 14007, 3508 SB, Utrecht, The Netherlands.
Email: Mieke.v.Groenestijn@feo.hvu.nl

© ALM 2000