Abstracts

For many practitioners, the word "research" is not welcomed with open arms. Many practitioners feel inadequate and not a part of the research world. 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 Practitioner Research and Dissemination Network, I had these feelings about research. I would read an occasional abstract but rarely would it influence my teaching practice.

One of my duties as a state PDRN was to be involved in practitioner research around one of the NCSALL research projects. I was trained in the research process, supported in my endeavors, and best of all, became transformed by this process. I will share with you my journey into the "research world" and how it has affected my practice within and beyond my classroom walls. I will share my findings from my first research project on goal setting and persistence in a mathematics classroom and how it influenced my practice within the classroom. I will also share how this process went "beyond the classroom walls" by influencing my students, my program and other colleagues.

Questions to ponder: Is practitioner research a viable means to affect change in the adult education field? What other methods might also work to bring research findings into the practitioner arena?

Our schools and classrooms are intended to support students acquiring knowledge and skills that are "portable" to other institutions, including work. This portability beyond the classroom has generally been studied as learning transfer. The metaphor of transfer suggests that adults learn math in class, then carry the products of their learning to work where it is applied. The metaphor generates a tension in adult mathematics education--between learning "generic" math presumed to generalize to a variety of jobs precisely because they are generic, and learning math tailored to particular forms of work, also presumed to generalize, but because of their similarity to math on a particular job. The metaphor also promotes a view that adult math learning in the classroom is somehow sealed off from the possibility of future math learning at work. The logic of the metaphor suggests that transfer must occur continually in our daily lives if we are to function, but it is hard to find when we try to study it or support its happening.

I will present the concept of consequential transition as an alternative to the transfer metaphor. A transition is a change in the relation between the learner and the social practices she engages in, e.g. an adult successfully completing a course of study for his GED and entering a new job. Consequential transitions are often reflected on, struggled with, and involve changes in the learner's sense of self or social position, as well as changes in knowledge and skill. Studies of mathematical reasoning among high school students becoming shopkeepers, machinists adapting to technological change, and students working in a fast food restaurant will illustrate different aspects of the concept.

I will end the presentation with several possible arenas for discussion. What are the educational implications of viewing school-work transitions as opportunities for mathematics learning? What does it mean to move from classrooms organized around mathematical learning to work practices organized for production-- where math is part of the means of production, but workers often do not see themselves as "doing math"? How does the concept of consequential transition suggest some possible ways of reducing the tension between generic and job-targeted math, or at least afford thinking about it in some new ways.

Universidade do Vale do Rio dos Sinos, Programa de Pós-Gradução em Educação, Brazil

Gelsa Knijnik and Marilyn Frankenstein will discuss, using illustrations from their own work, how it is not possible to separate these two forms of 'reading' our world. They will argue that the attempt to split these ways of knowing underlies hierarchical divisions in educational institutions, and that these divisions undermine our work teaching adults math. Further, they propose that these divisions are part of forces which diminish our struggles for a just society.

ALM is an international research forum that brings together researchers and practitioners in order to promote the learning of mathematics of adults. This definition heads all the literature of ALM and is the banner under which many of us have met regularly for up to seven years. But the link between researcher and practitioner is not uncontentious, as earlier conference discussions have shown, so the topic of this year’s Conference is particularly welcome.

Having eavesdropped on this ‘conversation between researchers and practitioners,’ we will use this opportunity to pull together some of the threads and issues that have arisen during at the end of our time together the conference.

The use of the Internet in educational environments makes it easy to have contact with teachers and students in very different places. Especially for this conference we have made a task in English to show you the concept of our virtual collection of mathematical projects like the chair.

What is the weight of the chair?

In the workshop we will present problems like this and we will discuss the criteria for a good task for our students in adult and/or vocational education. Also we will present some examples of the work of our students. Furthermore we would like to hear about the use of the Internet as a communication instrument between students all over the world.

Parallel to the challenges of probability teaching and to the investigation of the comprehension of concepts in probability theory by adults, a question emerges: What do people believe Chance is? History and research have shown that a good performance on calculations of probabilities is not necessarily accompanied by normative probabilistic thinking. The objective of this research is to map conceptions and vocabulary of adult students concerning situations of chance.

This presentation will focus on a quantitative study that examined the delivery of mathematics instruction in General Education Development (GED) programs in Arkansas. The primary purpose of the study was to determine the current status of the delivery of mathematics instruction in GED programs in the state of Arkansas. Six sub-questions are centered around variables such as GED mathematics instructors' experience, education/background, current instructional practices, prior training related to teaching mathematics, awareness of the mathematics reform movement, and extent of support of the mathematics reform movement. The secondary purpose was to determine if there is a relationship between the GED instructors' experience/background and other selected variables.

The research involved 287 GED instructors at 55 Adult Education Centers throughout Arkansas. These centers are located in a variety of settings including technical schools, community colleges, and public schools. Each center has one or more instructors who can be housed at different sites within the program. The study was limited to GED instructors and did not include Adult Basic Education (ABE), workplace education, or literacy programs. In the State of Arkansas, ABE is considered to be below eighth grade, whereas GED is eighth grade and above. Data collection is nearing completion.

Quantitative analysis included a chi-square test of association to determine if variables are independent, or if there is some degree of association or correlation between them. The presenter will describe the study methodology, findings, and implications for practitioners. Audience participation will be encouraged through a Question and Answer session.

In this paper I want to pursue the work I presented at ALM5 and 6 on parents as adult learners of mathematics. My emphasis has been to establish a two-way dialogue through which while I engage the mothers in explorations about mathematics, we also collaboratively reflect on uses of mathematics in our everyday life and possible ways to establish connections between different forms of mathematics. Our research relies on the concept of ethnomathematics and on approaches to adult education grounded on critical pedagogy (Benn, 1997; Frankenstein & Powell, 1994; Harris, 1991; Knijnik, 1996).

In this presentation I want to focus on the process of establishing a two-way dialogue by looking at our experiences learning geometry. The geometry theme started through typical reform-based school mathematics tasks that allowed us to explore area and perimeter and their relationship (e.g., fixed perimeter, varying area). We then moved to a geometric exploration around the craft of "papel picado" (punched paper). This is a traditional Mexican craft that is quite typical in our local context. Using colorful paper one creates intricate designs by cutting out shapes in a careful and pre-planned fashion. This practice involves lots of opportunities for the exploration of symmetry, and can be pushed in other directions such as finding areas and perimeters of the shapes being cut out. In this project, the mothers taught me how to do "papel picado" and as we conversed through the practice, we brought up different mathematical questions to explore. I want to focus on the mathematical conversation around the table as we worked on the "papel picado" as constituting an arena in which we all had something to learn and something to teach.

Benn, R. (1997). Adults Count Too: Mathematics for Empowerment. Leicester, England: NIACE.

Frankenstein, M. & Powell, A. (1994). Toward liberatory mathematics: Paulo Freire's epistemology and ethnomathematics, in P. L McLaren & C. Lankshear (Eds.), Politics of liberation: Paths from Freire (pp. 74-99). New York, NY: Routledge.

Knijnik, G. (1996). Exclusão e resistência: Educaçáo matemática e legitimidade cultural. Porto Alegre, Brasil: Artes Médicas.

At present the dominant role of maths adult education can be seen as satisfying labour market and personal development needs. But there is arguably a third purpose: that of supporting adults in their roles as active citizens. This leads to the question as to what skills are required to support active citizenship. I will outline a draft list of ‘skills of citizenship’ and suggest that these can be seen as fundamental transferable skills. These could include the ability to identify problems, find information and locate issues in a political and social context; develop the sense of worth of the individual through both a knowledge that they have something worthwhile to say and the ability to speak in a way that will be heard; and be able to work effectively in groups to achieve common goals and to be able to deal with difference, diversity and, at times, conflict.

I will suggest that these skills can be learnt in the maths adult classroom. They will then be available to the learner to be utilised in other situations if considered by the learner to be desirable and/or appropriate. I will conclude by asserting that participatory democracy is learned through practice and therefore the adult maths education experience should itself be an experience of participatory democracy. This may help participants (and non- participants?) in maths classes to feel that citizenship and adult education are 'for us' and not just 'for other people'.

The workshop will explore this hypothesis through a series of questions that will draw on participants’ experiences.

There is ample evidence indicating that in Botswana, women are not well represented in occupations requiring mathematical competence. In 1995, the Government of Botswana’s Central Statistics Office reported that women occupy the majority of educational, retail, health, and private household employment, and men dominate construction, agriculture, mining, and business services. Gender imbalances exist in the formal educational institutions. In technical courses, the ratio of male to female can be up to 8:1.

With regard to attitudes about mathematical capacity, data is lacking in Botswana and is to be investigated in this study. It is assumed that women are believed not be good in mathematics and should not pursue careers in which mathematics plays an important role.

While women are under-represented in some professions, they are increasingly involved in small businesses in both the informal and formal private sector as owners. An area of investigation of importance is the need for financial training to be adequate and effective. In 1997, a study of the Government’s training policy for the informal sector has identified several major areas of concern: quality, access and relevance of training. Training is a significant consideration when taken in conjunction with the Government of Botswana’s several new policies regarding the importance of encouraging sustainable small businesses, intended to help create employment for its citizens and to promote economic diversity. The Government believes that smaller businesses can offer a better environment for creating new employment opportunities because of their flexibility, ability to specialise and their local nature.

This study will investigate the following questions with a focus on the urban, informal sector:

Suggestions as to how best to offer financial training for women in the urban, informal sector are planned as a result of the findings of the study.

Australia has been quite prolific in its development of materials and activities for teaching adult numeracy. The resources and activities are based upon the following approaches to teaching adult numeracy:

This hands-on workshop will enable participants to experience a number of such Australian activities suitable for classroom use. Mathematical topics covered will include whole numbers and decimals, data/statistics, and location and direction. Activities from different Australian resources will be used and copies of these and other Aussie resources will be available for teachers to look at.

The paper reports an experience developed in the south of Argentina with adult educators. We will concentrate on a series of workshops on math education. The workshops were part of a larger State project aiming at constructing a unified curriculum for adult basic education and vocational education. The workshops were seen as a tool of making explicit the actual teaching strategies in math education, and at the same time as a way of creating conditions for teachers from adult basic education and vocational education to work together.

The aim was to create conditions to make explicit and bring into reflection the teaching strategies used by teachers of adult basic education and vocational education. Teachers (with formal training) and teachers of vocational courses (without formal training) participated in a series of workshops where they were asked to designed a teaching situation on a particular content in the area of Mathematics.

We will present some examples of the situations designed during the workshops. Then, we will discuss the situations considering the limits and possibilities of the teaching strategies regarding the particular content involved. For the analysis we will follow the theory of G. Brousseau.

Finally we would like to discuss the potentialities of this kind of workshop as a tool for narrowing down the distance between prescription and practice, that is between normative curriculum and actual teaching or real curriculum.

An investigation into problems that emerge in the course of adults' everyday lives and how they are solved. Social relationships, tools and conventions, and working practices form the socio-cultural contexts of the adults' lives and the solutions to their problems are constructed within these contexts. As individuals, adults use both conscious and tacit knowledge to solve their problems and their emotions also often influence what they choose to do. I discuss how these individual and social factors relate to each other.

Teachers are better able to help their students succeed when they understand the brain's natural learning process and how to apply this understanding in the classroom.

A Review and Summary of Research on Adult Mathematics Education in the United States During the Period 1980-2000

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. There will be an extensive bibliography which the presenter will make available to attendees through some electronic medium, preferably a webpage at her home institution.

Royal Danish School of Educational Studies & Centre for Research in Learning Mathematics, Denmark

In a research project Lena Lindenskov interviewed learners and observed lessons given by Eigil Peter Hansen in a one-year adult basic mathematics course. The research project is comparing how different math-containing educational settings permit freedom of the adults expressing and getting fulfilled their own intentions, blockages, and fascinations.

As a brief introduction to the Danish context, we will give examples of the current Danish educational interpretation of "thematic mathematics" and "everyday maths."

The project brings forth two dilemmas. The first dilemma is how a teacher in his communication with the learners deals with their already established conception and acquired skills. Two examples will be discussed: one in percentages, one in area and volume.

The second dilemma concerns the power of the learners. According to Danish legal provision, the learners participate in the on-going planning of the course, but it seems highly difficult to provide them with adequate information on which to base their decisions. In our particular class two themes were democratically chosen: The first was art, the second was food. Although most of the adults imagined ‘food and mathematics’ the more relevant to their everyday life, at the end of the year they considered ‘art and mathematics’ as being the more relevant. This was confirmed a year later when we invited the adult students to discuss the outcome of their previous year's maths learning.

The symposium opens with contributions from two European countries. Mathematics in the workplace will then be discussed from the perspective of all the participants.

In Sweden the vocational programs are included in the upper secondary school, since 1994. In those programs all students have to study mathematics for approximately 100 hours. Nearly 50 % of those students fail in the national mathematical tests in this course (Course A). That is after already 900 hours in the compulsory school system. The content for this session is from a development project funded by The Swedish National Agency for Education. It has its main focus on studying the relationship between mathematics and the vocational subjects. Part of this is to improve and develop mathematical models that are relevant and applicable. The outcomes stress changing the approach of learning and teaching and assessing with focus in using integration and still keeping a door open for further education and the more formal side of the subject. Other foci to be discussed are obstacles in the local schools and benefits gained as an extra bonus out of this approach for the students and the teachers.

Since this project started the syllabus has changed in the same direction as this project which of course is of great importance for our future work.

In the Netherlands, there is a discussion about the organisation of the vocational education in the future. The Dutch Centre of Innovation of Education (the CINOP) and the Dutch Expert Centre for Mathematical Education, the Freudenthal Institute, have started a research project for the relation between key qualifications, vocational competencies, and mathematics. The background of this project is that the Dutch government wants to change the system of vocational education into a competency-based training. For the vocational training they want to use the central problems of the vocational practice. Mathematics will only play a part if it is very essential. In this seminar we will shortly describe this Dutch approach. Next we will explain the main differences between the traditional school mathematics and the workplace. We will give examples of our approach from a method of using mathematics for the vocational education. We hope that in this way we can discuss the best place for mathematics in vocational education.

3. How will the vocational education in your country be organised in the future? Will it be one broad education for many jobs, or just a lot of specific courses for every different job?

4. What are the differences/similarities between school mathematics and mathematics used in the workplace?

For our workshop the New York City Math Exchange Group, a voluntary staff development teacher collaborative, proposes to do the following:

This workshop will invite participants to explore current issues and develop future agendas for research and practice in the field of adults learning mathematics.

We aim to facilitate new research collaborations, especially of an international and comparative nature.

We shall draw on our experience in ALM and of editing the book Perspectives on Adults Learning Mathematics: Research and Practice (edited with Gail E. FitzSimons and published by Kluwer Academic Publishers in 2000).

Draft Proposal of the Los Angeles Unified School District Math Curriculum Workshop

The Division of Adult and Career Education of the Los Angeles Unified School District has a comprehensive adult high school program. The program titled Diploma Plus is a personalized, competency-based adult high school diploma program of instruction and assessment, designed to teach academic skills needed for job training and to develop life skills necessary for success in today’s world.

Students entering the program have a chance to improve reading, writing, and mathematics skills. About five years ago, the program saw a need to improve the overall effectiveness in which the math was being taught. A committee was formed and they looked at all of the latest research on math literacy as well as the NCTM math standards. Before the California State or the Los Angeles Unified School District at large had advocated standards, the committee felt it vital that standards be incorporated into the new curriculum. As a result, seven contracts were formed using an integrated approach that better served the educational goal of the adult student. The contracts use a spiraling approach that builds on skills from the previous course contract. The use of manipulatives, computers, and group work has greatly increased student’s retention and math literacy.

A Dialogic Approach to Adults Learning Mathematics: Maximum Efforts to Obtain Maximum Outcomes

This Research report tries to explain some of the findings that have been obtained through different research projects. CREA, as a Research Center, has a long and wide experience in the analysis of learning needs and competencies in Adults Learning Mathematics through which we have developed and implemented two assessment methods (ANAT& ACOT) as well as elaborated a new dialogic approach (Pedagogy of the Maximums). Some of this work has been developed in relation to workplace numeracy and vocational training for the unemployed. Our last work focuses on Adults Learning Mathematics targeted to adult inmates.

Contemporary theory in Social and Educational Sciences is taking a dialogic approach in which the intersubjective relations between people are put at the center of Social and Personal development (Freire, Habermas, Chomsky and Beck). In this way, most recent developments in Adult Learning are also framed within a communicative approach. All adults have Cultural Intelligence (CREA 1995-1998). That is a capacity for learning that includes the development practical academic and communicative competencies. It is thus necessary to develop a new understanding of Adult Learning and a pedagogy for adult learners, especially for those who are considered by society as unmotivated or unable to learn. We have denominated Pedagogy of the Maximums to this approach because it proposes to reach the maximum level of education for everybody, but especially for those who have traditionally been excluded from it. This innovative proposal leaves aside the beliefs that these persons are not able to succeed in their training and consequently have good job opportunities in order to overcome their marginalized situation. It has been demonstrated that it is necessary to start from positive expectations.

ANAT and ACOT are analytical tools that have been designed in order to analyze adult learning needs and competencies from this dialogic approach. Their main innovation consists in taking into account the competencies and skills that people already have. This is a very relevant point when we are talking about Adults Learning Mathematics, because of the importance of relating math to what is known from everyday life. The research we have done on Adults Learning Mathematics with minority population inmates has shown that these adults have many competencies directly linked to those required in the current Information Society.

Symposium: Developing a Theoretical Framework for Adults Learning Mathematics: ALM7

At the last three ALM conferences, a growing group of participants has engaged in an on-going exploration of the theoretical frameworks for adults learning mathematics. This session at the conference has always proved contentious, demanding and highly stimulating. We concluded at ALM6, that the question for each of us is not whether we each have a theory. It is more, which is your theory, and can you name it? Can you describe it and how does it affect your practice? We also agreed that learners each have their own theories concerning the nature of mathematics and learning mathematics. What are their theories and how do we as researchers and teachers respect and acknowledge these?

At ALM7, the aim of this topic group will be to add to the corpus of knowledge concerning adults learning mathematics. We invite you to join us in examining a "critical incident" through different theoretical frameworks and exploring the implications of these frameworks on our actual practice as adult educators and researchers.

This poster session will highlight the needs that led to the development of the parent math class, the kinds of problems that parents have found intriguing, the differences between "the old" and "the new" math as the parents see it, examples of the kinds of math leadership the participating parents have taken on, and the reactions of parents to what they are learning.

As education reform efforts in mathematics unfold, many parents feel bewildered by the lessons and assignments their children bring home. Adults who lack confidence in their own math abilities face special challenges, but also opportunities to discover new ways to approach math problem solving.

The Massachusetts Parent Involvement Project, a five year effort funded by the National Science Foundation and the MA Department of Education, works to increase parent involvement in math and science. The project focuses on parents and caretakers who avoid school settings and/or who experience language, cultural or educational gaps with teachers.

The project has developed activities to engage parents and children together in math and science. These include hands-on kits for use in public and community sites, "activity by mail" packets, and adult learner-generated materials for fellow parents. Samples will be on display.

An exhibition made by refugees, immigrants of twelve cultures, and Dutch students. Men, women, old and young. The works have been exhibited at school and the town hall.

In this exhibition you see pieces of work from our adult students, who have different needs for their educational or professional futures and daily lives. The aim of the exhibition is to integrate the social-cultural and religious backgrounds of the students in the basic math lesson, to make the students proud and to let them let each other know about their cultures. They used formal mathematics with a self-selected subject of their own culture.

During the poster session we want to discuss the use of key skills and the way mathematics is used in this project.

Departamento de Educação Cultura e Esportes- Prefeitura Municipal de Taubaté / DECE, Brazil

University of Taubaté / UNITAU, Departamento de Educação Cultura e Esportes- Prefeitura Municipal de Taubaté / DECE, Brazil

This poster will focus on the new standards-based reform curriculum in Brazil for Adult Education. An experience done with a group of students will be shown, having the teacher as a guide facilitating learning by providing each learner with the opportunity to develop a sense of how numbers relate to one another, to other areas of knowledge and to the real world. Some activities will be shown in which teacher and students are viewing themselves as mathematical thinkers when they work with meaningful social, economical, and financial Brazilian data. The results of how they learned, the investigations that involved the exploration of mathematical ideas, and the evaluation of the work gave the authors the opportunity to implement strategies which allowed students to feel as active participants in their study of mathematics and in Brazilian society.

Numeric Literacy in Two Hours: an Efficient Effective Method of Teaching Learners How to Read and Write Large Numbers

If you have learners who write "3,000417" for "three thousand four hundred and seventeen," they are in need of direct instruction in how to read and write larger numbers. After having researched the literature on the topic, the presenter developed an efficient language-symbol system for teaching these skills to adults in ESL, ABE, and GED settings. Many adults with math or language issues lack these skills, and place-value instruction is frequently ineffective. The system that the presenter offers requires only conventional classroom equipment and is appropriate to all age levels.

Congreso de Latinos Education Training and Employment Division: Aptitude Program, USA

My poster session will show how the measurement and geometry topics I teach in the APTitude program (Apprentice Prep for the Trades) are applied by the graduates during their apprenticeship as skilled craftspeople. I also hope to connect my class work with the Carpenter's Union curriculum. There will be photos, examples of class work, and quotes from APTitude graduates.

Harrie Sormani from CINOP (The Netherlands) asked us to work with him in a rediscovering Math project, paid by BVE, from emancipatory funds from Europe.

This project is for students who are afraid of math and/or think they cannot learn it. The project consists of five lessons which are given during a technical vocational training or educational course for adult students.

We combined the ideas of Professor Eliana Guedes from the University of Taubaté in Brazil about the use of origami in mathematics lessons with the ideas about "Structures" of "van Hiele." Each lesson our students work on the three levels of van Hiele; concrete, mental, abstract.

During the workshop we introduce our project with a theoretical framework and an exemplary session done by the participants. We also show an image of the lessons on videotape.

Tracking Ways of Knowing with the Role of Teachers and Peers: an Adult Mathematics Classroom

Women returning to study mathematics invariably hold the view that mathematics is absolute and infallible (Beesey, 1995) and perceive a need for procedural over relational understanding (FitzSimons, 1996). Coupled with mathematics anxiety (Carroll, 1994) this orientation is considered a major stumbling block in defining mathematics for these women.

Accounts of women returning to study mathematics commonly attribute success to the promotion of a collaborative environment and a teaching philosophy that incorporates the common-sense knowledge of women (e.g Feil, 1995; Isaacson; 1990). Broadly speaking, success stories do not address the issue of women’s beliefs about the nature, limits and certainty of knowledge (epistemological assumptions), and whether these beliefs shift during courses to promote more complex ways of mathematical knowing.

Two epistemological frameworks (Belenky, et al., 1986; Baxter Magolda, 1992) are adapted to track changing beliefs about mathematics during an adult course. An absolute orientation is to perceive only right or wrong, that knowledge is obtained from authorities and to not expect peers to play a significant role in learning. In classes where there is a focus on peer collaboration this may initiate an epistemological conflict. Using case studies evidence of shifts from an absolute towards a more relativist position is presented.

Do we teach mathematical skills or functional mathematics? How should learning outcomes in adult numeracy reflect this dichotomy?

Back in 1984, Alan Mortiboys warned against the extremes of teaching mathematical skills without a context or of adopting a purely functional approach with a variety of real life materials such as timetables, menus, advertisements and so on.

Tom Ciancone works in Ontario, Canada where learning outcomes for numeracy are being implemented based on traditional school math strands (number, measurement, space and shape, data, and algebra). They are essentially skill-based outcomes.

Dave Tout in Australia contributed to the development of numeracy learning outcomes which focus on the social purpose and use of mathematics within meaningful contexts. The outcomes include skills and knowledge in an organizational structure based on function.

In this workshop, Tom and Dave will use these two approaches to promote a discussion among the participants around the role of skills and function within an adult numeracy curriculum. In the first part of the workshop, participants will work in small groups to produce a demonstration of a learning outcome taken from the Ontario and Australian frameworks. In the second part, they will discuss their "experience" and draw conclusions regarding the merits of these two approaches.

I believe that for many adult students there is an unspoken social need that is integral to their return to study. Leaving the isolation of the home and mixing with others seems an important part of the new learning experience. This aspect of returning to study appears to be especially important for adult women students. If their classes are organized to include some time in which students mix purposefully in structured group and/or pair activities then they have opportunities to create social links. These links not only fulfil personal needs but also facilitate students collaborating with their mathematics. My own teaching with adults indicates that group activities which foster discussion through hands on activity can change students’ attitudes to the subject and make the classroom atmosphere lively, cooperative and enjoyable.

If, in addition, the group and pair activities are selected to encourage students to make meaningful connections between their lives, mental images and the symbols and formulae of mathematics, then the time is doubly well spent. This workshop offers a selection of group and pair activities designed to foster discussion, encourage visualization and estimation and facilitate the development of a sense of mathematical meaning beyond formulae and symbol manipulation.

In December 1996, ten ESOL, ABE, GED, or diploma preparation teachers from Connecticut, Maine, Massachusetts, Rhode Island, and Vermont initiated work on the Adult Multiple Intelligences (AMI) Study. This research project, a collaboration between Harvard Project Zero and the New England Literacy Resource Center (NELRC)/World Education under the auspices of the National Center for the Study of Adult Learning and Literacy (NCSALL) at the Harvard Graduate School of Education, lasted 18 months. During that time, the ten teacher/researchers explored the ways that Howard Gardner's Multiple Intelligences (MI) theory could support instruction in various adult learning contexts.

Two teachers who participated in the study, Meg Costanzo and Martha Jean, will report on their individual research projects and the broader themes that emerged during this study. They will also share a number of "student-tested and approved" math lessons and activities they developed during the course of their research. This will be an experiential workshop where participants will have the opportunity to learn about Gardner's theory while engaging in a variety of hands-on activities inspired by MI.

How can busy, working parents learn to do rich mathematical activities with their children? What happens when parents are given materials that explicitly describe ways to do math as part of family life? How do family mathematical interactions change?

In this session, we will report on our ongoing research on parents’ learning to infuse math into everyday life with their children. Typically, parents who initiate math activities with their children rely on the content and pedagogy that was at the core of their own school math experience: flash cards or computational drill. Our research, supported by the National Science Foundation, offers parents an alternative model. We have developed a set of family activities that build on the math of everyday situations, such as buying groceries, preparing meals, and cleaning up, and we are distributing these materials to parents at their workplaces. Working parents often have little spare time; the activities are designed to help them build math into the things they already do with their children. The activities are consistent with the emphases of US reform math, but are designed for all parents, no matter what their math background. Our presentation will include examples of our materials and a discussion of their impact on parents’ mathematical learning and on family mathematical interactions.

Communicating the Message: The Math Practitioner, the Numeracy Listserv, and the ANN Web Page

Words represent only 6% of communication. Deprived of the impact of the visual and tone in communication, a message carried only in words must be clear, concise, consistent in its form and dependable. The three communication vehicles of the Adult Numeracy Network—The Math Practitioner Newsletter, the Numeracy Listserv, and the ANN Web Page—all use the print medium alone to convey information. So we depend on high quality input from practitioners. But we want to expand our coverage of the message of reforming math practice to include activities from outside the US and more input from within the US. This poster session will offer examples of the "Best of the Math Practitioner" that conference participants can take with them, as well as opportunities to access the Numeracy Listserv and the ANN Web Page. Our purpose is to encourage contributions from the reluctant practitioners and researchers in attendance at the ALM7 Conference.

A select group of Massachusetts Adult Educators recently met for a pilot certification course focusing on collaborative efforts with learners to increase mathematics literacy. Through sharing experiences and best practices, and examining recent theories and studies of learning, the teachers developed curriculum units that focus on the needs of their learners.

The pictures shown here highlight the Massachusetts ABE standards in action: Mathematics as Communication, Problem Solving, Reasoning, and Connections. The learners are engaging in hands-on activities ranging from manipulatives to computer technology to increase their mathematical power. Real-life activities, such as planning a cookout, investing in the stock market, or using coupons, are the backdrop for concepts normally taught and reinforced as meaningless "drill and kill."

The success of this pilot course, developed by Esther Leonelli, Marilyn Moses, Barbara Goodridge, and MJ Schmitt, and coordinated through SABES and the Mass. DOE, will continue within the classrooms of theses learners and instructors as they explore ways to work together in learning and using Numeracy in their daily lives.

School of Communications Technology and Mathematical Sciences, University of North London, United Kingdom

Over the last twenty years the use of calculators and digital measuring equipment has to some extent replaced both mathematical mental/written activity and the use of analogue measure. This paper explores some aspects of number concept, reading the number line and estimation from scales. The students being considered are part of a foundation year in science/engineering/computing. The results obtained are compared with research undertaken in schools.

Further studies are undertaken to audit the measuring activities needed in professions such as architecture and sport's science. The results of the survey will be used to inform teaching of future foundation cohorts.

Year 2000 is Year of maths in the UK and as part of this initiative and alongside the Adult Learners Week (a national initiative to promote adult return to learning) we are involved in promoting numeracy in an inner city college in London.

The poster session will display a visual record of some of the activities, from supporting the phone-in line for information; using the BBC numeracy CD to encourage improvement in numeracy using IT; numeracy classes in college and in the community with refugee groups.

It has been said that "one can stretch a word to cover the world." Surely mathematics is such a word. To mention a few of this broad reach culled from numerous sources: Mathematics on the Playground (Mary-Margaret Shoaf); Mathematics in Political Decision Making (Deborah Hughes Hallet); Mathematics in Voting Systems (Donald Saari); Mathematics in Traditional Design (Dean E. and Susan C. Artanbright); Mathematics and Coincidences (Persi Diaconis); Mathematics and the Fear of Authority (Shandy Hauk and Mark K. Davis); Mathematics as Therapy. Mathematics for Seniors (Miriam L. Yevick), as well as a list of goals of quantitative literacy assembled by Olaf Steen.

It is becoming more necessary than ever that the citizenry at large be enabled to "figure" things out and advance solutions from below. Quantitative awareness opens up a new dimension of experiencing the world and so the possibility of basic changes in one's "cosmology" on a personal and communal level.

The suggestion is that we take to the road-- both literally and virtually-- to propagandize mathematics in the manner of the Fabians who disseminated simple tracts on social problems on street corners and public forums. We could distribute tracts expounding elementary quantitative tools (such as, say, powers of ten), with which to view budgets, national and local priorities, election expenditures, environmental problems, as well as illustrate their relevance to personal life experiences and observations. (A mathematics stall at street fairs and community celebrations would not be amiss.) Students and academics and other volunteers could participate in these exchanges, so creating a bond between the public and the "experts." "Each one teach two" can spread "the Mathematics Word."

TV411 is an innovative adult literacy and numeracy national television series which teaches reading, writing and math skills at the pre-GED level. It uses popular formats such as documentary, comedy, music video, cartoon, news broadcast and real life situations to teach mathematical concepts and their applications. Celebrities such as the Dallas Cowboys, the Atlanta Hawks and the Detroit Shock teach contextualized lessons in understanding fractions, calculating percentages and estimating distance. In this workshop, participants will have the opportunity to view these lessons and discuss how they might be embedded into a pre-existing lesson plan or program.

Recent studies have been conducted by the University of Michigan to assess TV411’s instructional and motivational impact on different populations of learners. The studies test the use of the materials with varying levels of support-- from groups working with a facilitator to individuals working alone, at home. The research results have broad implications for understanding how and in what formats adults learn best. The findings of these studies will be shared with workshop participants. Immediately following, there will be a discussion about the implications for pedagogy and practice that this type of instruction and research has on the education field.

The subject area of the didactics of mathematics is always already structured and delimited by the concrete forms of practice and knowledge that are currently regarded as mathematics teaching, learning, and knowing. The new research and practice area "adults and mathematics" is situated in the borderland between mathematics and adult education. At the fourth and fifth ALM conferences we had a debate about the characteristic features of the research area. Questions were formulated about "Adults Learning Mathematics" as a community of practice and research within the didactics of mathematics, a community where adult, learning, and numeracy are placed at the centre and where the answer to the so-called justification problem (Why teach mathematics?) is empowerment in social and working life.

Epistemological reconnaissances have given rise to my construction of the concept problematique for didactic activity in this field where interdisciplinary studies (mathematics, sociology, pedagogy) are necessary to bridge mathematics and adult education. Reconstruction of "math-containing qualification" as a didactic concept is given as an example of interdisciplinearity.

Mathematics Anxiety and the Adult Student: an Analysis of Successful Coping Strategies

Borough of Manhattan Community College of the City University of New York, USA

Mathematics anxiety is prevalent on college campuses. Scores of students dread taking their required mathematics courses and scores of faculty are at a loss when they encounter these students in the classroom. What precisely does the phrase "mathematics anxiety" mean? Why do some students experience it while others do not? What is the etiology of mathematics anxiety and perhaps most importantly, how can students and faculty cope with this phenomenon in an attempt to alleviate it? None of the above questions has a simple answer. The presenters of this session have conducted an extensive study of how approximately three hundred community college students cope with mathematics anxiety. The results of the study were used to design math anxiety workshops for college faculty which have already been conducted (at numerous conferences) according to the following format: the participants are split into small groups in order to complete an "experiential exercise" involving a comparison of math anxiety coping strategies. The workshop leaders serve as group facilitators. The entire audience then reconvenes to give each group the opportunity to share its experiences with all participants. Finally, the workshop leaders present the results of their own study so that the relationship between research and practice can be analyzed.

This interactive workshop is intended for all faculty, counselors, and administrators who desire to learn more about the practical uses of math anxiety research. Participants should leave the session with a heightened knowledge of and sensitivity to the mathematically anxious student. They will have been exposed to a repertoire of coping strategies that have been deemed successful in dealing with anxiety. Resource materials will be distributed and guidelines for presenting similar workshops on college campuses will be discussed.

Developing a National Framework for Adults' Mathematics Education in Ireland: a Pilot Study

The National Council for Vocational Education (NCVA) is the body in Ireland established to set, monitor and certify standards for vocational education and training programmes within the Further Education sector. Approximately 75% of learners are adults over 23 years of age who avail of services in a variety of educational settings - formal, informal and non-formal. The NCVA view collaboration and consultation with tutors and providers as an integral part of the development process.

The authors have been involved in the development of a national framework for adult mathematics education within the NCVA remit. This work has been reported at previous ALM conferences, most recently at ALM-6 (O'Donoghue, in press), where the proposal for a national framework was presented and discussed in a workshop. This work has continued under the aegis of the NCVA and elements of the national framework for adult mathematics education, namely, Mathematics, Level 2, were piloted during the academic year 1999/2000.

This paper reports on issues arising during the pilot study which was directed by the authors and is due to finish in May, 2000. These issues are discussed in the context of full implementation of Mathematics, Level 2, in September 2000.

Students are the ultimate arbiter of the quality of an adult education classroom. The adult education math instructor may be the most talented, creative and relevant teacher; but unless the students are convinced, she/he may as well be teaching to the mirror because the students will leave. Both teachers and students begin their conception of how math is taught by what they learned in school. Whether or not math is enjoyable or even basically relevant depends upon past math experiences. A teacher who has always done well in math can enthuse about beauty and emphasize practicality without conveying any more information than "I am good in math and can use it. You can’t." This workshop will share student surveys and focus groups and then encourage reflection among the participants about student outlooks, needs and wants. A suggested process for teaching math will be presented and participants will briefly walk through an example of this process including assessment, rule-making, hands-on activities, estimation, application, and multi-step problem-solving. The session will close with a discussion of experiences and problems of participants and presenter in facilitating student retention in math classes through shared communication and understanding on both sides.

Building on our earlier work, we have been developing collaborative ways of working which would be appropriate for research in schools, jointly involving teachers and teacher educators. We have addressed the fundamental questions concerning the role of the researcher and the researched raised by Day and Grundy and we have explored how new working relationships can address them in powerful ways.

To do this we have combined aspects of Wright's 'researching the other' and Skemp's 'role pairs' in order to establish our way of working as providing a model for developing and maintaining the kind of long term relationship necessary for truly collaborative work. In this presentation we will consider whether this way of working can be used to blend roles across three traditional boundaries in Adults Learning Mathematics: research/practitioner, practitioner/student and researcher/student. We suggest that such a blending of roles can give us access to understandings rendered invisible by traditional research work (which maintains the boundaries between roles) and can establish working relationships which can maximise outcomes.

Explore hands-on activities that develop adult learners’ number sense, mathematical reasoning, problem-solving skills, communication, and teamwork. Visual mathematics promotes the teaching of mathematics in ways that are respectful of adults, that prepare them for further learning and that help them achieve the mathematical literacy necessary for everyday life.

In the UK, prospective teachers are required from this year to pass a test of professional numeracy in order to gain qualified teacher status. In the year 2000 this will comprise a mental arithmetic test and a short written paper. This legislation has created much opposition, yet at the same time, those involved in teacher education acknowledge that it is desirable for teachers to be ‘numerate.’ Similarly, whilst not a legal requirement, pressure is being brought to bear on all academic degree courses in education to develop numeracy work with students.

This paper will look at some of the issues facing both prospective teachers and education degree students, as they attempt to tackle professional numeracy tasks, and will raise questions about the nature of professional numeracy for those employed within education, either as teachers or as other professionals-- administrators, governors etc.

As the education sector becomes more and more oriented towards performance measurement, we will examine what levels of numeracy are required to make sense of the emerging stream of performance data.

Does "Part-Whole Concept" Understanding Correlate with Success in Basic Math Classes?

For adults needing remediation in math, it is important to determine whether their difficulty is lack of skills in number manipulation or a more basic failure to grasp fundamental concepts of number relationships. Based on an analysis of the individual responses to the Test of Adult Basic Skills (TABE) from over 3,000 adult students possessing high school diplomas, it appears that many adults lack the part-whole concept, a transition concept from concrete to abstract thinking in math which is expected to occur by age 8. The concept's lack in adults appears on the TABE as an incorrect "multiple choice" response to problems which give the whole and one part and require finding the "missing part," such as:

A correlation will be reported between individual student responses to the "missing part" problems in the TABE and success in Basic Math classes among students at a 2-year post-secondary institution. The "success" will be measured in terms of class completion, final grade, and continuing with more math classes. This correlation will give insight into whether part-whole concept understanding plays a role in success in Basic Math classes.

Affective Research and the Mathematics Curriculum for Distance and Online Education

The affective domain has been the subject of much research over a number of years. This research has been incorporated into the teaching practice of many mathematics/numeracy teachers and course developers over a number of years. This paper describes the inclusion of the results of the research into the development of independence and confidence in mathematics into four mathematics units designed to prepare adult students for university study in Australia. The paper describes the development and evaluation of the curriculum initiative for students studying in the distance mode and using a CD-ROM. Implications for online delivery are discussed.

A mathematics which consists of timeless truths and value-free facts may be fundamentally inconsistent with one which develops through human endeavour within social contexts. (Fauvel, 1991:3)

It is our experience at Sheffield Hallam University that considering the history of mathematics through an activity based, problem solving approach has an impact on students’ mathematical epistemologies and their conceptions of mathematics. We argue for the need for an inclusive mathematics which respects connected knowing and person-relatedness and champions both the personal and the authority of the learner and claim that a mathematical curriculum which addresses such issues of social justice will be one which emphasises the historical roots and cultural locations of mathematics.

In this workshop I would like to share with you some of the activities that our students experience in our history of mathematics unit and some of their responses to the unit. Be prepared to take part in activities ranging from 2000BCE to 2000CE, from fractions to the four-colour map problem, and from Babylon to Boston!

Fauvel, J. (1991) ‘Using history in mathematics education’ in For the Learning of Mathematics, Vol 11, No 2, p3-6, June 1991

An international survey of the numeracy abilities of adults is to be part of the Adult Literacy and Lifeskills Project (ALL) planned for the year 2002. The conception of numeracy for the ALL is based on the premise 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. Thus far, the numeracy items which have been designed to be part of the project have undergone a feasibility test in two countries (US and Holland) to determine their suitability.

As part of the development process, the Numeracy Team designed a complexity scale which includes five factors that attempt to estimate, separately and in interaction, the difficulty level of the numeracy tasks. 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. The presenters will briefly illustrate the factors and their importance in the development of the numeracy assessment. In the ensuing discussion, participants will use the complexity scale to predict the difficulty of a few numeracy items, testing both the robustness of the scale and its predictive ability. Together, we will explore the implications of this scheme of complexity factors in teaching, assessment, and research.

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 was 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.

Moving from Fear and Loathing: the Development of Preservice and Inservice Teachers as Math Educators

How do new and aspiring elementary teachers think about their capacities to teach mathematics? Who or what has figured most prominently in their own memories of learning math, and how have those memories informed their view of teaching math to children? Is it possible to transform one's vision of what it means to teach math, and if so, how?

To explore these questions, I would like to discuss a qualitative, classroom-based investigation I am currently conducting at Emmanuel College with students of EDUC 2207, Math and Science Teaching Methods. During the course, students are required to: write and discuss their past mathematical learning in a math "memoir," participate in 30 hours of (pre-practicum) observation of instruction at the elementary level, conduct an analysis of the instructional strategies being used in that classroom, read texts and participate in classroom exercises using (primarily) constructivist techniques, revisit and reflect upon changes in their original stance toward teaching math, and consider what they need to continue to develop as math educators.

A preliminary analysis of the students' responses suggests a substantial shift, for the majority of students, from their original view of math as drill-based and unapproachable, to accessible, discovery-oriented, and something "I can do!".

Data for this project will mainly be based upon students' reflective, observational, and analytical writing, class discussions, and interviews. I envision this work as a first step in considering how teacher educators could better support the ongoing development of competence among teachers of mathematics at the elementary level.

According to teachers of adults, one of the reasons women return to study is to be able to help their children with their homework. One feminist view is that this is a worthy initial goal to encourage women to return to study, but that the ultimate aim is for women to develop their own separate intellectual space and direction.

Empirical studies demonstrate a large indirect relationship between home environment and mathematical achievement (Crane, 1996; Reynolds & Walberg, 1992) and these authors conclude that ways are needed to improve the home environment because the benefits for children’s mathematical achievements are potentially quite large. The more global benefits for children when their mothers return to tertiary study have been touched upon (Burns & Scott, 1997; Kelly, 1987). In this paper case studies illustrate the perceived benefits for children’s mathematical understanding and achievement when their mothers return to study mathematics in further education classes.

Using two feminist epistemological frameworks (Baxter Magolda 1992; Belenky et al. 1986) a theoretical position is proposed that the women’s own mathematical understanding is supported through the quality of the intellectual space that is created between them and their children. A parallel is drawn between the role of children as significant others with the role of peers in a collaborative mathematics classroom.

Burns, A, & Scott, C. (1997). Two-generation effects of maternal tertiary study. Journal of Family Studies, 3(2): 209-225.

Baxter Magolda (1992). Knowing and reasoning in College. Gender-related patterns in students' intellectual development. San Francisco: Jossey-Bass.

Belenky, M.F., Clinchy, B.M., Goldberger, N.R. & Tarule J.M (1997 [1986]). Women's ways of knowing: The development of self, voice, and mind. 2nd ed. USA: Basic Books.

Crane, J. (1996). Effects of home environment, SES, and maternal test scores on mathematics achievement. Journal of Educational Research, 89,5 305-314.

Kelly, S. (1987). The prize and the price: The changing world of women who return to study. Sudney: Methuen Hayes.

Reynolds, A.J. & Walberg, H.J. (1992). A process model of mathematics achievement and attitude. Journal for Research in Mathematics Education, 23,4, 306-328.

Testing adults in Adult Basic Education to assess their math skills is not easy, in particular when it regards not-native speakers, but it is a challenge to try to discover what adults really know and can do and what this means for math education in ABE.

In 1998 qualitative research was done into mathematical knowledge and skills of a group of not-native adults in ABE in the Netherlands. These adults came from twelve different countries. All of them got primary school education in their own countries and some of them also participated in low vocational courses.

Part of this research was content analyses of their results on a placement test for ABE, used in the Netherlands. The first purpose was to get insight in people's mathematical knowledge and skills when they enter ABE, in order to know what kind of math instruction they may need. A second purpose was to analyze the test itself. Does the test provide that information that it is supposed to test? What kind of problems do we encounter in a paper-and-pencil test? What is a good way of testing not-native speakers? Information based on these analyses should provide insight in ways of assessing not-native adults in order to improve math education in ABE.

In this presentation the first results of this research will be presented, followed by a discussion about criteria for math tests for not-native adults in ABE.

How Can They Belong if They Cannot Speak the Language? Enhancing Students’ Language Use in the Adult Mathematics Classroom

A sociocultural educational perspective sees learning as induction into ‘discourses’ or ‘communities of practice’ through interaction with more expert others. At the heart of any discourse are the language and symbols that carry its special meanings. To become a member of the discourse one must begin to learn its language. However, in traditional mathematics classrooms, the students, those who need to learn the language, usually have the least opportunity to speak it (Pimm, 1987).

This paper discusses a teaching experiment with an Australian adult numeracy class that used audio and video tapes to record students' talk during a range of mathematical learning activities. Included were group and pair tasks designed specifically to encourage meaning-making talk and to enhance students’ use of mathematical language. The ongoing, grounded analysis revealed two distinct aspects of language use in the mathematics classroom. The first was the ‘opportunity to speak’: the space, and invitation, given for students to articulate and modify their thoughts about mathematical tasks, through speech. The second identified aspect was the ‘means to speak’: students’ understanding of mathematical concepts, and their ability to use the mathematical terminology intrinsic to them. This paper will use qualitative data from the study to differentiate between these two aspects of language use and indicate advantages of attending to both within the context of adult mathematics learning.

Teaching Adult Students Mathematical Investigation (TASMI-6) is based on the continuing research work carried out for the last ten years of teaching on the Foundation Course in Mathematics at Goldsmiths University of London. Teaching Mathematical Investigation to adult students is a very challenging and often rewarding experience for adult educators as well as for the adult students.

The theme of the investigation is that adult students are asked to make ice-cream cones containing two scoops of two different flavors. First they are asked to decide the flavors, and then to make as many different combinations of two scoops of ice cream as possible, using each flavor only once.

The paper concludes that many adults already have a wealth of experience. Teaching methods such as "mathematical investigation" and discussion with adults can provide a bridge to new learning initiative for adult students. Clearly, the evidence in this investigation suggests that adult students gain more when they know what work they are personally accountable for and what to do what they have finished with the "AH HA!" experience.

Currently within the UK there is an increased need to support students throughout their Higher Education. This is due to the trend towards wider participation and employers increasing their demand for vocationally apt students.

Due to these trends and life long learning, students now enter the system with varied qualifications and experiences, hence the need for support.

The Student Learning Support Facility (SLSF), at the Robert Gordon University, was established to provide such support. The support is provided in terms of assistance with Writing and Communication Skills, IT applications and Mathematics.

The workshop will concentrate on the Mathematics thread, giving an indication of how the SLSF operates and the learning strategies adopted to help students.

All students entering first year undertake a mathematics diagnostic assessment. This allows us to identify students’ strengths and weaknesses needing addressing at a very early stage. This provides valuable information for both students and staff. Furthermore, it allows the SLSF to provide a tailored learning programme and guidance on resources available to help them, thus increasing student retention.

What enables parents to be effective facilitators of their elementary children’s math learning at home? Which aspects of parent-child math are you addressing in your research? What are your findings to date? What do you see as important questions to be addressed in future work in this area?

We invite everyone conducting research in parent-child math learning to join in this conversation. Current work in this area encompasses many different approaches; projects vary widely in which parents they try to reach, how they try to reach these parents, what messages about math they promote, and what kinds of parent-child math activities they involve and who is responsible for developing those activities.

In this informal discussion, we will collectively take stock of what we have learned in our research in this area, and will begin shaping an agenda for future research. Please come prepared to share the goals, methods, and findings of your research in parent-child math learning.

The Business Program at the Catholic University of Brasilia faces a challenge: the low level of quantitative literacy by its majors. The program includes the teaching of calculus and statistics. Nonetheless, students present difficulties in basic algebra and arithmetic. To help these students succeed in the quantitative disciplines of the program and become good professionals efforts have been made, since the first semester of 1999, to identify the specific difficulties students have, at the same time in which new approaches have been tried out to overcome them. In this workshop I am going to show some of the difficulties students have and what has been tried to remediate them. Feedback and suggestions by the audience will be welcome.

First we show how teaching numeracy in social contexts embedded within Australian numeracy frameworks and teaching practices, looking briefly at some of the guiding documents, but also questioning the purposes of accreditation, while highlighting a preference for ongoing assessment which is not separate from students' learning activities, as opposed to testing (regardless of which calculator you use).

This should give you an introduction to some of the approaches taken to numeracy teaching in Australia, particularly the emphasis there on the social contexts of what is learnt.