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White-paper #2 Learning
Edgardo José Avilés-Garay
C&I 430 Issues and Trends in Math Ed
Spring 1999
Dr. Kenneth J. Travers
Issue: Role of facilities in mathematics learning
Learning is one of the most essential and interesting dimensions of mathematics education. It is currently an important issue in the educational panorama. Educators, psychologists, and others experts have been dealing with questions about how students learn, which are the characteristics of learning, which factors have influences on it, is learning a behavioral reflect? Also, another questions are added to these previous ones, like, what is important in learning? How should be the learning of mathematics? This paper will serve as a discussion about mathematics learning and the influence that educational places have on it.
In its nationwide efforts to assure quality in mathematics education, the National Council of Teachers of Mathematics (NCTM) has published appropriate guidelines, in forms of standards, about how teaching and learning of mathematics should be developed in school settings. In one of its recent documents, Standards 2000, the NCTM has pointed out the role of learning in mathematics education. The learning principle in this document states that “mathematics instructional programs should enable students to understand and use mathematics” (NCTM, 1998, p. 33). Unfortunately, this principle does not widely discuss another current aspects related to mathematics learning, for example how mathematics should be learned keeping in mind the different learning styles of each student. Theorists, like Gardner, have pointed out that all students, including those with different kinds of intelligence need equal learning opportunities.
As this principle states, mathematics is still viewed as a set of rules to only memorize and procedures to follow rigorously in order to get a correct answer. I agree with the position introduced by this principle that mathematical ideas should be presented and reinforced across the school grades to assure an acceptable knowledge acquisition of these concepts (NCTM, 1998).
Until now, there are innumerable conceptions and ideas about learning in our mathematics education community. All of them, in one or another way, are based in learning and cognitive theories developed and showed years ago by Dewey, Piaget and Vygotsky, as Peterson (1994) said in her paper. As a sample of these multiple ideas, mathematics learning is considered as a “social and cultural activity” (Peterson, 1994, p. 6-5). In addition, the ideas of learning introduced by Mestre (1994) is closely related with the conception of learning supported by Dewey and his colleagues in the pragmatism philosophy movement. Going back to Peterson’s thoughts, her conception of learning is in all senses true because mathematics learning takes place and is developed in a real context keeping in mind the needs of the society and the culture’s characteristics.
Following this same line of discussion , Thomas J. Cooney from the University of Georgia in his most recent visit to campus, discussing issues in a lecture about mathematics teacher education, offered an interesting set of beliefs about learning mathematics. He argued that mathematics learning could be viewed, among others, as “cooking with a recipe, conducting and experiment, and building a house” (Cooney, 1999). All of them represent a brief description about how mathematics learning is being developed in schools. These beliefs have closest relationship with the view of mathematics as a set of rules and procedures, introduced above.
At statewide level, the corresponding education agencies have done efforts to also improve the learning and teaching of all school subjects, including mathematics. As an example, the Illinois State Board of Education has developed a set of standards, encouraged by the reform efforts conducted principally by the NCTM, to assure the quality of mathematics education at local schools. The general objective of this state educational initiative is centered in student learning. The criteria for these standards establish that they “should be specific enough to convey what students should learn, but broad enough to allow for a variety of approaches to teaching, curriculum, course design and assessment” (ISBE, 1997, p. vi). As the NCTM Standards, the Illinois Learning Standards are not representing rigorous laws to follow them carefully without alternative to change. Instead, these guidelines are plans that encourage students, teachers and administrators to incorporate new changes and ideas on them in order to improve student’s learning. The framework of this group of standards is based in particular components that promotes learning and knowledge acquisition, such as problem solving, communication, technology, team works, and connections with other related fields. In order to organize harmoniously the mathematics content knowledge, the standards have been divided and classified to improve the learning of essential mathematics concepts and terms, according to school level of each student.
Until now, our discussion has been around the concept of mathematics learning, the different beliefs about it, and over all, about the innumerable efforts that the mathematics community is doing to give excellence to education process. But, is also important another views of learning, sometimes not widely discussed, for example the facilities where mathematics learning takes place. Researchers have discussed different factors that have influence (sometimes positive or negative) on learning. Some of these factors come from the psychological view of learning, like attitudes, emotional dispositions and so on. In the following paragraphs I will discuss the relationship between physical facilities and mathematics learning.
As I discuss earlier, mathematics learning is a complex process. It needs another “external helps” to be appropriate in order to reach the established educational goals. Surely, a school with good facilities will encourage students’ learning acquisition. For example, if a school has technological facilities, like computer labs with instructional software available to students and staff, an extensive library resources, students will feel engage in their learning and in some way also responsible for it.
About this concern, the learning principle of Standards 2000 establish that “another view of learning mathematics is to see it as a process by which people gradually become members of a mathematical community (Lave, 1991; Sfard, 1998). The classroom is a community of mathematical inquiry and the students are participants in that community, striving toward mapping and understanding mathematical ideas, norms, and rules” (NCTM, 1998, p. 34). In this quote from the new set of standards, the NCTM is giving a primordial importance to classroom in the mathematics learning process. In classrooms, mathematics learning is acquired and developed, and overall shared by its participants. Also, classrooms could be viewed as a home of learning, where each student feel responsible and respect, free to ask questions, investigate, seek valid information and finally, make his or her own decisions about it.
Continuing in this way, Peterson (1994), argued that “each learner has a tool kit of conceptions and skills with which he or she must construct knowledge to solve problems presented by the environment” (p. 6-5). Also, she has pointed out the responsibility of the community in order to promote learning. The community has to provide appropriate settings, formulate the objectives and also give support and help to encourage mathematical knowledge acquisition. This settings that Peterson mentioned is precisely a classroom with a variety of learning resources.
Brown (1994) introduced an interesting and particular description of classrooms that gives an important point in this discussion. She used the term “multiple zone of proximal development” (Brown, 1994, p. 7) to describe the classroom’s environment. The wished classroom, supported by her ideas, should be a special place where students could be develop their potential and abilities helped by “tools and powerful artifacts”. Undoubtedly these tools and powerful artifacts, which Brown mentioned, are the incorporation of technology into the curriculum, and therefore on mathematics learning. In facilities and classrooms design, technology should have a predominant role, because today’s learning urgently needs these complements and tools in order to encourage and engage students in their own learning. Our changeable society everyday demands constant updates and revisions in the current issues in education – curriculum, teaching, learning, assessment and evaluation - especially in mathematics and sciences, without forget the learning facilities: classrooms and schools.
Pieces of research have demonstrated that school facilities have big influences on learning. As an example, based on reports from the Washington, D.C. Committee on Public Education (COPE, 1989), Berner (1995) argued that “a building in poor repair contributes to the attitude and discipline problems among students, which in turn contribute to poor performance in schools” (p. 86). Inadequate school facilities do not represent a well and attractive encouragement for students. Instead, this situation, which unfortunately is repeated in many schools through our country, promotes another problems that in any or another way affect negatively the learning process. Students with these kind of attitudes are not really interested in their learning because school become in only “a place to be” and share with their friends.
In another related research conducted by Berner (1995), she found that physical conditions of school buildings are statistically related to student’s academic achievement. In her study, school facilities were classified as poor, fair or excellent. Berner concluded that in standardized test, students scored better from one stage to another, like poor to excellence.
As final thought, school facilities have received their importance in mathematics learning process. Now, to reach our wished objectives is necessary that students, as well as, teachers and administrators work together toward the development of adequate learning facilities, keeping in mind also the different needs of the subject, society and students. All members of mathematics education community should share a healthy, free and democracy environments where them can growth as persons, fulfilling in this way the triple mission of education in each student: informative, formative and transforming.
References:
Berner, M. M. (1995). Buildings matter: The connections between school building conditions and student achievement in Washington, D.C. In A. Meek (Ed.), Designing places for learning (pp.85-87). Alexandria, VA: Association for Supervision and Curriculum Development.
Brown, A. L. (1994). The advancement of learning. Educational Researcher, 23 (8), 4-12.
Committee on Public Education. (1989). Our children, our future: Revitalizing the District of Columbia Public Schools. Washington, DC: District of Columbia Committee on Public Education.
Cooney, T. J. (1999, April). Considering the Paradoxes, Perils, and Purposes ofEducating Mathematics Teachers. Lecture presented at the Lecture Series in K-12 Mathematics Education, Champaign, IL.
Illinois State Board of Education. (1997). Illinois learning standards. Springfield, IL: Author.
Lave, J. (1991). Situated learning in communities of practice. In Resnick, L. B., Levine, J. M., & Teasley, S. D. (Eds.), Perspectives on socially shared cognition (pp. 63-82). Washington, DC: American Psychological Association.
Mestre, J. P. (1994). Cognitive aspects of learning and teaching science. In Fitzsimmons, S. J. & Kerpelman, L. C. (Eds.), Teacher enhancement for elementary and secondary science and mathematics: Status, issues, and problems (pp. 3.1-3.53). Washington, DC: National Science Foundation.
National Council of Teachers of Mathematics. (1998). Principles and standards for school mathematics: Discussion draft. Reston, VA: National Council of Teachers of Mathematics.
Norton, P. , & Wiburg, K. M. (1998). Designing learning environments. Teaching with technology (pp. 248-273). Fort Worth, TX: Harcourt Brace & Company.
Peterson, P. L. (1994). Learning and teaching mathematical sciences: Implications for in-service programs. In Fitzsimmons, S. J. & Kerpelman, L. C. (Eds.), Teacher enhancement for elementary and secondary science and mathematics: Status, issues, and problems (pp. 6.1-6.29). Washington, DC: National Science Foundation.
Sfard, A. (1998). Balancing the unbalanceable: The NCTM Standards in the light of theories of learning mathematics. Paper presented for the National Council of Teachers of Mathematics. Reston, VA: National Council of Teachers of Mathematics.