Teaching mathematics with adults using a dialogical teaching and learning approach

1. Teaching mathematics with adults using a dialogical teaching and learning approach Javier Díez-Palomar & María Padrós CREA - Center of Research in Theories and Practices that Overcome Inequalities crea@ub.edu

2. Teaching mathematics with adults using a dialogical teaching and learning approach CONTENTS • Introduction • Overview of adult learning in Spain • Overview of adult learning in Catalonia • Adult learning mathematics in Spain • Some features of adult learning mathematics • What type of mathematics • The dialogic learning approach • Some examples in adult learning mathematics • Next steps

3. Teaching mathematics with adults using a dialogical teaching and learning approach INTRODUCTION Information Age People who don’t have educational credentials are excluded of our society. APEL Policies in Europe Recognition of non-scholar knowledge Discussion about curriculum’s contents in mathematics (impact of last PISA) What is the impact of this situation on Adult Educational Systems? What about Mathematics?

4. Teaching mathematics with adults using a dialogical teaching and learning approach INTRODUCTION Participation in any learning activities (formal, non-formal, informal), by educational attainment, 2003 (% of population aged 25 to 64) Source: Eurostat yearbook, 2006-2007. (1) At most lower secondary education (ISCED 0 to 2). (2) Upper secondary and post-secondary non-tertiary education (ISCED 3 and 4). (3) Tertiary education (ISCED 5 and 6). (4) Informal learning is excluded

5. Teaching mathematics with adults using a dialogical teaching and learning approach INTRODUCTION Mathematics is embedded in our lives (Niss, 1995)

6. Teaching mathematics with adults using a dialogical teaching and learning approach OVERVIEW OF ADULT LEARNING IN SPAIN In Spain “adult education” is grounded on popular initiatives from the end of the XVIII Century. The ideas of “emancipation” and “critical transformation” are still embedded in adult education practices in Spain. Transformation Education Agency Labor Market Confidence Freedom practices Flecha, López, Saco (1988) & Tellado (2007)

7. Teaching mathematics with adults using a dialogical teaching and learning approach OVERVIEW OF ADULT LEARNING IN SPAIN Article 52. Objective. Permanent education offers lifelong learning to all members of the public in order to acquire, update, complete and extend their abilities and skills for their professional and personal development. To do this, the administration of education will collaborate with the civil service departments with competencies in terms of adult education, and especially in employment management. (...) Public administrations prioritizes all these people who have not completed their basic education, for various reasons. Also people over the age of 16 would be able to participate in adult education if they cannot attend a standard educational centre because of their job or other circumstances. (...) The administration of education will promote specific programs for the Spanish language, culture and other co-official languages in order to integrate the immigrant population. (Source: LOGSE – General Arrangement of the Educational System Law).

8. Teaching mathematics with adults using a dialogical teaching and learning approach OVERVIEW OF ADULT LEARNING IN SPAIN SCHOOL MODEL SOCIAL MODEL Meaningful education Teachers as facilitators Adults as participants Formal education Teacher conducted Adults as students Medina (1997)

9. Teaching mathematics with adults using a dialogical teaching and learning approach OVERVIEW OF ADULT LEARNING IN SPAIN • Basic Adult Education • Professional training • Courses to prepare for exams in order to access other levels of education • Spanish classes for the immigrant population • Non-regular courses

10. Teaching mathematics with adults using a dialogical teaching and learning approach OVERVIEW OF ADULT LEARNING IN SPAIN

11. Teaching mathematics with adults using a dialogical teaching and learning approach OVERVIEW OF ADULT LEARNING IN SPAIN In Spain every region (“comunidad autónoma”) is responsible about its educational system. The main government establishes the general features that every level of education have to reach. Then, each region manages its own educational system.

12. Teaching mathematics with adults using a dialogical teaching and learning approach OVERVIEW OF ADULT LEARNING IN CATALONIA Main levels

13. Teaching mathematics with adults using a dialogical teaching and learning approach ADULT LEARNING MATHEMATICS IN SPAIN Main objectives of adult learning mathematics in Spain • To update the educational background and to facilitate access to different educational levels to each person who may require it. • To develop programs and courses related to specific educational needs from excluded groups. • To improve professional qualifications and/or to acquire training in order to develop other professions. • To develop people's capacity to participate in social, cultural and political events.

14. Teaching mathematics with adults using a dialogical teaching and learning approach ADULT LEARNING MATHEMATICS IN SPAIN To… Incorporate the language and arguments typical of mathematical reasoning (numerical, graphical, geometrical, logical, algebraic, probabilistic) in order to be able to communicate in a precise and rigorous way. Use logical ways of thinking, to formulate and verify conjectures, to make inferences and deductions, and to organize and link information related to daily life and problem solving. Quantify real situations by virtue of data, measures and numbers while making the appropriate computations. (Alsina, 2001: 3-4).

15. Teaching mathematics with adults using a dialogical teaching and learning approach ADULT LEARNING MATHEMATICS IN SPAIN To… Elaborate personal strategies for analyzing concrete situations and for problem solving using various resources and instruments, analyzing the final results obtained. Use elementary techniques for collecting data to obtain information about phenomena and situations and to represent this information by means of numerical or graphical forms in order to evaluate it. Recognize the diversity of different situations and to see how different points of view can be used to explain it (deterministic / random, finite / infinite, exact / approximate). (Alsina, 2001: 3-4).

16. Teaching mathematics with adults using a dialogical teaching and learning approach ADULT LEARNING MATHEMATICS IN SPAIN To… Identify shapes and spatial relations present in reality, analyzing geometrical properties and relationships. Identify the mathematical elements (statistical data, graphics, maps, computations, etc.), which are present in news, pools, commercials, etc., critically analyzing their functions and possibilities for a better understanding of messages. Approach day-to-day situations and problem solving in a mathematical way (exploring alternatives, using a precise language, etc.). Know and value personal mathematical skills in order to deal with situations that require their use or in which one can enjoy the creative, manipulative, aesthetic or useful aspects of mathematics (Alsina, 2001: 3-4).

17. Teaching mathematics with adults using a dialogical teaching and learning approach ADULT LEARNING MATHEMATICS IN SPAIN Target in adult learning mathematics courses • They go to the adult school because they want • They feel interested / excited in doing / studying mathematics • They already have prior experiences with mathematical ideas

18. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS Difference between their prior experience with mathematics and current mathematics in the adult school Gloria: …of problems… We were dividing all day long! If the topic was division, then the whole year we did divisions; if it were division by decimal numbers, then the whole year we did divisions by decimal numbers… I mean, I remember… it was very monotonous, burdensome… very, I don’t know. Now I find them (mathematics) more pleasant, because they are more varied. Rosario: ...more varied… Gloria: yes, difficult… well, to do the operations and so, but… they are more enjoyable: with the computer, with, well, it is also a competition with your children who also know how to do that, and you too, and you still take things with more enthusiasm, and you really like them; you learn them. Now if you say “how hard mathematics is,” well…

19. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS Social image about mathematics Mathematics are so difficult! Mathematics is not for me. I like Mathematics, but it is very difficult to me. I’m not able to learn Mathematics

20. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS They feel more comfortable and safe using algorithms rather than solving problems. They are influenced by their memories from their previous schooling. For them “mathematics” = “make a lot of calculations” / “hacer muchas cuentas”.

21. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS They feel more comfortable with visual and concrete procedures to solve problems, rather than abstract procedures.

22. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS Insert clip#1

23. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS They prefer exact answers rather than estimations, nor rounding. For them “mathematics” = “exactitude”

24. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS There is no correspondence between “level of literacy” and “level of mathematical literacy / numeracy”.

25. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS There is a gap between scholar Mathematics and real Mathematics. Gloria: The kind of mathematics that we women do is not like the kind of mathematics that you do, as mathematicians. Because in order to solve each problem, we have to make huge jumps, I mean, that is... You, a woman who already knows how to use a computer, well, you do wonders, because... because it is a better mathematics than that one you know, the one that you use when you pay the bus, and you always pay the same amount, so you check if this month is the same fare as the last one, I mean, you check the bills, those bills that you have to pay when you run a house: the phone, the school for the kids, the...

26. Teaching mathematics with adults using a dialogical teaching and learning approach SOME FEATURES OF ADULT LEARNING MATHEMATICS There is no identification of the everyday life knowledge as being mathematics

27. Teaching mathematics with adults using a dialogical teaching and learning approach WHAT TYPE OF MATHEMATICS? So, what is Mathematics in terms of adult education and what kind of Mathematics should be included in the curriculum for Adults? How can we validate / legitimate adults’ knowledges (grounded on their experiences), that they bring in the classroom?

28. Teaching mathematics with adults using a dialogical teaching and learning approach THE DIALOGIC LEARNING APPROACH Egalitarian dialogue Cultural intelligence Instrumental learning Transformation Solidarity Creation of meaning Equality of differences Flecha (2000)

29. Teaching mathematics with adults using a dialogical teaching and learning approach SOME EXAMPLES IN ADULT LEARNING MATHEMATICS Valorization of different “types” of mathematics Mari Luz- Or by giving examples that touch what we are doing, because that way you get it more easily. If you give examples, well, as you do it sometimes, examples, then of course, it gives you a better idea. You understand better. To me, the most important point is that you get motivated. That’s me. Egalitarian dialogue & Equality of differences

30. Teaching mathematics with adults using a dialogical teaching and learning approach SOME EXAMPLES IN ADULT LEARNING MATHEMATICS Contextualization / Mathematization Insert clip#2 Creation of meaning & Instrumental learning

31. Teaching mathematics with adults using a dialogical teaching and learning approach SOME EXAMPLES IN ADULT LEARNING MATHEMATICS Contextualization / Mathematization Insert clip#3 Creation of meaning & Instrumental learning

32. Teaching mathematics with adults using a dialogical teaching and learning approach SOME EXAMPLES IN ADULT LEARNING MATHEMATICS Previous experience grounded on everyday practices Insert clip#4 Creation of meaning & Instrumental learning

33. Teaching mathematics with adults using a dialogical teaching and learning approach SOME EXAMPLES IN ADULT LEARNING MATHEMATICS Correlation between emotions and learning Alejandra: When I came to get the certificate, the first afternoon, I told Rosa: Look, I will sit here at a table, alone, because if the other women look at me, I will not write. And well, two days later I started working and now, now I have overcome that. Solidarity and transformation

34. Teaching mathematics with adults using a dialogical teaching and learning approach SOME EXAMPLES IN ADULT LEARNING MATHEMATICS Correlation between emotions and learning Mari Luz: That’s it, and being a strongpoint, and being with everyone, because some of us are clumsier, for example, as you said already, that I should keep trying, and so… Gloria: It is not that there are clumsier (people)… what happens is that that person, specifically the one from yesterday, she got nervous because she thought that he was going to smack her, because, because he had done it before. Well, no. I, look, I understood it this way: Lourdes explained it to me, and we try and I solved the problem correctly… (...) Gloria.- Then, it happens exactly the same with older people. We understood it by hammering it down… There were two or three ladies that did not understand it, so I completely ignored the teacher and I explained it to that lady… Solidarity and transformation

35. Teaching mathematics with adults using a dialogical teaching and learning approach SOME EXAMPLES IN ADULT LEARNING MATHEMATICS Mathematics as a critical practice Insert clip#5 Transformation

36. Teaching mathematics with adults using a dialogical teaching and learning approach NEXT STEPS In Spain a new line of research in adult learning mathematics is going to be open at the Autonoma University of Barcelona • PhD Graduate Program - UAB: line in adults learning mathematics • European Master in Mathematics Education: line in adult learning mathematics and dialogic learning

37. Teaching mathematics with adults using a dialogical teaching and learning approach NEXT STEPS We need more research… … to understand how the interactions work as “bridges” that mediate the learning process in a classroom with adults. We need to include adults’ voices from a non-deficit point of view. Some possible research questions could be: How do personal features impact on aspects such as participation? Do different types of participation promote learning? How to create challenging situations to problematize adults’ experiences (Freire, 1970, 1977, 1987) without provoking discouragement among them?

38. Teaching mathematics with adults using a dialogical teaching and learning approach THANK YOU!