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AND THE MATHEMATICS CLASSROOM
Silvanio de Andrade HYPERLINK "mailto:silvanioandrade@ig.com.br" silvanioandrade@ig.com.br or silvanio@usp.br
UEPB Universidade Estadual da Paraba, Campina Grande PB, Brazil
ABSTRACT
This work of inquiry, part of our doctorate research in finalization process, investigates the relationship between research and classroom in Mathematics Education with special attention to documenting processes related to the questions that fellow. What is the impact of Mathematics Education research in the classroom? How does research and researchers relate to the classroom? What do researchers have to say about the mathematics classroom, and what has it shown them? More specifically, we present this paper an introduction to the study object, theoretical underpinnings, methodology and data collection and some partial results in progress and conclusions. We will show that the relation between research and classroom in Mathematics Education is a very complex and of multiple look phenomenon.
INTRODUCTION
It seems to be a consensus among mathematics educators that, on one hand, the scholastic failure of students in mathematics and, on the other, the great importance of this discipline in the school curricula and in all the nations of the world have been the main reasons to originate the field of mathematical education - a study area that, in a direct or indirect form, has always been involved with the mathematics classroom. According to Kilpatrick (1992), "the mathematical education started to be developed as mathematicians and educators have turned their attention to how and what mathematics is, or might be, taught and learned in school". However, the research and the researchers of this area are not relating themselves in an efficient way to the mathematics classroom. These concerns have become stronger from the moment that we perceive that the data set disclosed in some research about the reality of the mathematics classroom indicates that there is a mismatch between research and academic literature and the mathematics classroom. That the research and the researchers have not related, in an efficient way to the mathematics classroom. So, a systematic study on the relation between research and classroom in Mathematics Education is necessary, in order to point out more effective ways to change the classroom and contribute towards a significant change in the relation between research and researchers and the classroom.
THEORETICAL UNDERPINNINGS
Theoretically, we have been working on this subject mostly with studies regarding to the theme research and practice and handbooks of Mathematics Education.
As an autonomous field of knowledge, Mathematics Education is recent and it is still being discussed, with frequency, what is Mathematics Education? What is the research in Mathematics Education? The expression "Mathematics Education" has still been strange for many Mathematics teachers in Brazil and perhaps around the world. A historical synthesis of the research in Mathematics Education was published by Kilpatrick (1992) and a study of the Mathematics Education, as a field of academic study, was edited by Sierpinska & Kilpatrick (1998): "Mathematics Education as a research domain: a search for identity ", that argues, in great depth, questions of the type: Is the Mathematics Education a science? Is it a discipline? In what way? What is its role inside the other domains of research and academic discipline? What is its specificity? In it, the Mathematics Education researcher will find a broad range of possible answers to these questions, a variety of analyses of the direction of the research in Mathematics Education in different countries and a set of visions for the future of Mathematics Education. More recent publications like the Second International Handbook of Mathematics Education (Bishop, A. J. et al., 2003), the Handbook of International Research in Mathematics Education (English, 2003) and the "Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) has also deepened such debate.
In the specific case of the researchers, there is also a concern over what is and how to do research in this area of knowledge. The objective of this is that the research in Mathematics Education reaches its own identity. Research in this area has been each and every time more molded by the research models in Education and in the Social Sciences.
But, facing all these discussions we, constantly, question ourselves: And the Mathematics classroom, how does it stand? How the research and the researchers have been communicating and relating to it? How have they been speaking of it? How have they been looking at it? How have they been facing its dilemmas? How have they gotten there? What have been the results of such relations for it? In what have the research and the researchers contributed to change it? What have been their concerns, discourses and actions about it? How can they make more effective changes in it? And what it has to say to the researchers?
These concerns became stronger when we came to realize that there is a misalignment between academic literature and the Mathematics classroom. That the research and the researchers have not been relating, in an efficient way, to the Mathematics classroom. Being, necessary a study on the relation between research practice and classroom practice.
For example, in our masters degree research (Andrade, 1998) and in Mathematics Education courses and lectures (from 1998 to 2007) that we have presented to Mathematics teachers in Brazil, specifically in the area of Problem Solving, we have verified that the academic literature on Problem Solving does not match what the teachers know and practice in the Mathematics classroom. While in the research in Mathematics Education, Problem Solving is conceived as a teaching methodology, in school practice it is not even perceived as content application, but simply as technique application (recipes, drills...). In content such as fraction, for instance, teachers teach - separately and without any connection to what has been previously given - all the operation rules before teaching problems with fractions. This attitude is in accordance with the banking concept of education, which is criticized by Paulo Freire (1987). Teachers do not even believe they can do otherwise. Only one out of seven teachers, with whom we worked with during our masters research in Rio Claro (SP), Brazil - a city with a tradition in Mathematics Education research-, showed some approximation/awareness between her theory/practice and the academic literature on Problem Solving. Another teacher was aware of the current trends in Problem Solving, but did not use them. She alleged that she could not apply in class what she had recently learned in college, consequently continuing in traditional teaching.
Regarding with a better approach between research and classroom has been emerging preoccupations in publications as Lessons learned from research (SOWDER 2002), Teachers engaged in research: inquiry into Mathematics classrooms (MEWBORN, 2006), The Challenge of linking research and practice (NCTM Research Committee, 2006) and in events as ICME 10 (2004), especially in the sessions ST1 (Survey Team 1): The relation between research and practice in Mathematics Education and DG2 (Discussion Group 2) - The relationship between research and practice in Mathematics Education. This last one also fellow this ICME 11.
METHODOLOGY AND DATA COLLECTION
The research methodology that have used this work has mainly been based on discourse analysis and studies from the standpoint of Michel Foucault (1996, 1999, 2004a, 2004b) that this way we seek to explain the fragile and strong points of the relationship between research practice and the classroom practice, type a topographical and geological summary. We take under consideration here that what in fact makes a difference in the methodology is the questioning that can be formulated within another way of conceiving the relations between subject, method, knowing and power. The method consists then of understanding that the things are not more than practical objectifications of specific practices, whose determination must be exposed to light, since consciousness does not conceive them. And, in this context, the movement of the relation research/classroom is perceived as practice that systematically forms the objects that are spoken of and the ideas and theories are taken as the keys of a toolbox.
We have also thought simultaneously with Foucault and, among others, Jacques Derrida. We have found fertile convergences between Derridas deconstruction (1974) and Foucaults splitting analytics that disturbs what was previously considered at a standstill; fragments what was considered amalgamated; shows the heterogeneity of what was imagined consistent with itself. Together, theses theories take on a provocative and irresistible energy (St. Pierre, 2004). This way, our research methodology would also be a deconstruction one, to keep things in process, to disrupt to keep the system in play, to set up procedures to continuously demystify the realities we create, to fight the tendency for our categories to congeal.
The survey of data/facts and their analysis include speeches of 71 Mathematics Education researchers (44 Brazilians and 27 from other countries), P01 to P71 - obtained through opened and discursive research questionnaire following:
Questionnaire - Questions (Dialogues) for Researchers in Mathematics Education
Subject: The Relation between Research and Classroom in Mathematics Education
1. There seems to be a consensus among educators that the main reasons for originating the field of mathematics educationwhich has always been involved directly or indirectly with the mathematics classroomwere, on the one hand, students failure in mathematics and, on the other hand, the importance of mathematics in the school curricula of every nation and in peoples everyday life. Still, according to Jeremy Kilpatrick (1992), mathematics education has developed . . . as mathematicians and educators have turned their attention to how and what mathematics is, or might be, taught and learned in school. What are your observations about these reflections?
2. From your point of view, what evidence is there of the impact in the classroom of research in mathematics education? And in relation to your research, do you perceive some evidence in this direction?
3. How in fact have research and researchers related to the mathematics classroom? What are your experiences, reflections, and suggestions in this direction?
4. How might we researchers contribute more effectively to changing the mathematics classroom?
5. What could the mathematics classroom say to us researchers?
6. In your opinion, what does globalization have to do with research in mathematics education, especially regarding the relation between research and classroom?
7. Besides the questions above, feel free to discuss other points you consider especially relevant regarding the relation between research and classroom.
8. If possible, say a little about yourself, about your practice as a researcher and teacher, your school background and academic trajectory, professional experiences that you consider significant, your trajectory in mathematics education or relation to it, and when and how you came to be introduced to it, among other things.
Such Survey also includes speeches of teachers of mathematics - selected of our Master Degree research and speeches of the works presented in the sessions ST1: The relation between research and practice in Mathematics Education and DG2: The relationship between research and practice in Mathematics Education, ICME 10 (2004).
SOME RESULTS AND CONCLUSION
Among the results, highlighted that in the speeches of most researchers, there is a strong defense for collaborative research and action research or similar, in the belief that these would have a better impact in the classroom than others. The declarations below, extracted of our data collection, from a Brazilian researcher (P24) and one from abroad (P49), are examples in this direction.
P24: The research is still very distant from the classroom. One of the reasons is that the school teachers do not understand the texts and the academic language do not identify themselves with the contexts being presented. During all this time of production in the area, the research has been about the teachers and for the school teachers. I believe that, only when there is a radical change and the research starts being produced with the teachers is that these will begin to produce the desired effect.
P24: In this sense, there are some innovative experiences that have been disclosing how much the teacher searches for processes of formation that mean something for him or her. The problem is that they rarely find them. In the last 10 years, several were the researches produced in the area of Mathematics Education that have been pointing to new alternatives of teacher education. These researches reveal that successful experiences are those carried through with the teachers, from their necessities, angst and search for solutions to the problems they find in their daily school life.
P49: One of the bigger successes I have had in research is working with schools and teachers ie the action-research-type model of research. This is a process where the teachers (and students) feel a commitment to the research and hence become active participants in the change, take ownership of the change/process and real outcomes can be achieved. The less successful model is that where the research is done on classrooms. This research tends to be less valued by the schools/teachers and less likely to have an impact. It does make for good research that is easier to publish and hence improve the career prospects of the researcher! The action research type research is less easy to publish as it does not conform with the general parameters of what constitutes good research in the field and hence more difficult to publish in high quality journals read by maths educators.
The research-action, collaborative and similar approaches as resources to bring research and classroom closer together represent only one of the several points discussed by the researchers, it does not represent the thinking of the whole group. There are also many other looks, some convergent, other divergent and another very singular. For example, there is researcher (P59) who attests that the impact between research and classroom happens in the theories and philosophies level.
In the transposition from research to practice, it is not research results that have the most recognizable impact but theories and philosophies. These are transformed into ideologies that are full of catchy phrases but are very vague in terms of concrete teaching practices and content matter. (P59).
There is researcher who looks research and practice as discursive activities, Sfard (2004); there is who attests that the research has to reach the makers of educational policies, Lester & Wiliam (2004) and so on.
Researcher P53 inquires if the researchers really are interested in doing the link between research and practice. I am not sure most researchers actually do want to do this. They are doing a job of work (P53). Researcher P03 states out that we, researchers, could contribute to a change in the classroom if we managed to institute new forms of relation with the knowledge. P26 places that it is necessary to go back to the classrooms and look closely at the student and discover who he or she is and then think how to give him or her support. P01 declares that there is some impact from the research in the classroom, but such impact has been to keep the status quo.
P03: The research objects are very "local" or very "broad", they do not reach the classroom directly, in the generic sense. This is not going to change. We, researchers, could contribute if we could institute new forms of relation with knowledge.
P26: It is necessary to go there, to the classrooms, and look at the student a lot. We have to disclose him, this student connected to the contradictions, vicissitudes, assets and benefits of the modern society.
P01: The Mathematics Education and the Education in general is the main strategy of the power structure [State, or Church, or Corporations] to maintain and to consolidate themselves. There is interest in "filtering" those that go through the educational system in order to be able to co-opt those convenient to the power structure. History teaches us this.
P01: There is some impact, as long as it allows the improvement of the strategy mentioned above. The great majority of the research is related to the models in practice [improvement of the same-old-same-old].
Skovsmose (2004) states in document presented at the ICME 10 (2004) that it is necessary that the research in Mathematics Education be focused in classrooms of the non model type, in classrooms at a poverty-stricken neighborhood, in classrooms of the 4th world. He questions the fact that a certain model classroom seems to dominate the field of research in Mathematics Education, that in many cases it seems to be selective regarding which practice to address. To him, the discourse in Mathematics Education has been dominated by the prototype of the model classroom. He suggests we defy the hegemony of the discourse bred around the model classrooms and, he adds that a non-standard classroom would have an enormous number of students, it would be located in a poverty-stricken neighborhood, it would be infected by violence. To him, research on the non standard Mathematics classroom can focus on many declarations: the violence, poverty, immigration and discrimination in general etc.
Speeches such as the teacher's below, subject 04, taken from our master dissertation (ANDRADE, 1998), also seems to point to the necessity of there also being research focusing on non-model classrooms.
Subject 04: Well, the school... it is kind of problematic today. I guess the teachers are with no incentive. We, in a general way, are. Another day, in a meeting, a teacher came and spoke so: look she does activities with newspapers in the Portuguese language class. And she makes the students bring news, because sometimes they do not have time to read. They read the news and later they explain to the class. Every week, one day is reserved to this. Imagine that there was a day, reading a newspaper about drugs, they got to talk, and she found out that in the class, most of them were all druggies, everyone was an addict. And she started to understand the behavior of the class. The adult education classroom is a classroom where I have no problems, but, the others do. Then, when I get to, if I get to, because I do not want to get to, in this case, the regular class, I do not know what to do. Because I never used drugs, I never had the problems that they have in life. What am I going to do with an adult about his or her problems? I said like this: my! Poor girl! What an awful situation! I have nothing to say to them. I won't know how to act with them, how to deal. The school today needs, not teachers, but yes, I am speaking about my school, a center where the students can be recovered, because what there is a lot of here are problems, students with problems. And they form a problematic classroom.
So, the discourses above indicate that the topic the relation between research and classroom in Mathematics Education is a very complex phenomenon and of multiple looks. Thus, the present study has been a brief look in search of a representative map of this complexity and multiplicity, in a deconstruction process that teaches us, on one hand, about the possibilities and impossibilities of impact of the research of Mathematics Education in the classroom, but, on the other hand, does not bring a key to the real impact. The different speeches of the researchers bring us then a deconstruction on the word impact, regarding the relation between research and classroom. Each speech/statement is transactional. They teach us something about the conditions of the production of making impact of the research in the classroom, but they do not give a key for the real impact. They teach us about the possibility and impossibility of such impact happening or not. They teach us something on essentialisms of being among the conditions of producing the doing, knowing, being, but they do not give a key to the real impact. For example, when the researcher P01 declares that the Mathematics Education and the Education in general are main strategies of the power structure, we then have impossibility for the real impact. But, there is another declaration of P01 in our data collection that points that we have to think about a Mathematics Education that can necessarily include Ethics:
Keeping on doing what we have been doing, that is, micro action. And, at the same time, to engage ourselves, politically, in an ample social transformation. In other terms, it is an illusion to think that we can change the mathematical education in the society as it is. The systems of values, the models of governance, that is, politics, economy, the moral imbued in religious and political groups, all of this constitutes the field in which education is located. The macro Mathematical Education is at the service of the power established from these factors. The political commitment that I mention is to incute, in our students, something beyond mathematical competence. It is necessary to incute ethics! Not to forget that our students today will be the adult citizens who will form society in 20 years. (P01).
Thus, we here have a possibility for the real impact but we havent a key for it.
Acknowledgements
I would like to thank to M. C. S. Domite (my Ph.D Advisor at University of So Paulo, Brazil) and Jeremy Kilpatrick (my Overseas Advisor at University of Georgia, USA). Thank you to UEPB and CAPES for the given financial support.
References
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