By Marsigit

Yogyakarta State University

Some students learn best when they see what is being taught, while others process information best auditorily. Many will prefer movement or touching to make the learning process complete. The best approach to learning styles is a multisensory approach. This type of environment allows for children, who are primarily kinesthetic or motor learners, to be able to learn through touch and movement; it allows the visual learner to see the concept being taught, and the auditory learner to hear and verbalize what is being taught. Ideally, the best learning takes place when the different types of processing abilities can be utilized. Constructivists have focused more on the individual learner’s understanding of mathematical tasks which they face (von Glasersfeld, 1995 in Brown, 1997).

Educationists use the terms 'traditional' and 'progressive' as a shorthand way of characterizing educational practices. The first is often associated with the terms 'classical/ whole class', 'direct', 'transmission', 'teacher-centred/subject-centred', 'conventional', or 'formal'; and the second is sometimes associated with the terms 'individual', 'autonomy', 'constructive', 'child-centred', 'modern', 'informal', and/or 'active learning'. The lack of any clear definition of what the terms mean is one of the sources of misleading rhetoric of the practices. Bennett (1976) found evidence that the loose terms 'traditional' and 'progressive' are symbolic of deep conflicts about some of the aims of education. The main sociological point is that the terms 'progressive' and 'traditional' are emotionally loaded but lack any consensual meaning among practitioners or researchers (Delamont, 1987). He found that, in the UK, ever since 1948 there has been a division between those exposing traditional and progressive ideals, and that feelings about these ideals are bitter and vehemently held. Then, since 1970, there have been some investigations on how the teachers' behaviors attributed by the term of 'traditional' or 'progressive'. The most persuasive prescriptive theory of teaching was that reflected in the Plowden Report (1967) which, influenced by the educational ideas of such theorists as Dewey and Froebel, posited a theory of teaching which distinguished between progressive and traditional teachers.

Specifically, Paul Ernest (1994) elaborated issues of mathematics education as follows:

a. Mathematical pedagogy - problem solving and investigational approaches to mathematics versus traditional, routine or expository approaches? Such oppositions go back, at least, to the controversies surrounding discovery methods in the 1960s.

b. Technology in mathematics teaching – should electronic calculators be permitted or do they interfere with the learning of number and the rules of computation? Should computers be used as electronic skills tutors or as the basis of open learning? Can computers replace teachers, as Seymour Papert has suggested?

c. Mathematics and symbolization – should mathematics be taught as a formal symbolic system or should emphasis be put on oral, mental and intuitive mathematics including child methods?

d. Mathematics and culture – should traditional mathematics with its formal tasks and problems be the basis of the curriculum, or should it be presented in realistic, authentic, or ethnomathematical contexts?”

The current and future challenges of (mathematics) education is how to innovate traditional teaching into innovative teaching; in which, traditional teaching is characterized as teacher centered, teacher delivering method, teachers' domination of initiation, direct teaching, strong controlled teaching. And progressive teaching is characterized as students' centered teaching in which the students will take over their role in learning.

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Ernest, P., 1994, Mathematics, Education and Philosophy: An International Perspective.The Falmer Press: London.

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Paul Ernest University of Exeter, United Kingdom. Retrieved

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