The Criteria of International Level of Educational Practice Adapted From Paul Ernest

Education exist since someone was borned in this world untill they die. Education can be done in school, family, and  environment (like the neighbours and friends). Talking about school education, there are some levels. Starting from the lowest level until the higest level like international level. It is same in mathematics education. It start from child and is processing as long as their life. May be some people hate mathematics because they think that mathematics is difficult. Actually mathematics is our daily life include in our society. It has moral values, they are good vs bad, pragmattism, hierarkhies paternalisitics, humanity, justice, and freedom.
Mathematics is viewed as set of truth and rules, unquestioned body of useful knowledge, body of structured pure knowledge, process view (personalized mathematics), and social constructivism in public educator thinking. Learning mathematics is not only learn about formulas, about numbers and also about symbols. There are some aims in mathematics teaching. They are:
a.        Mathematics as an essential element of communications
b.      Mathematics as a powerful tool
c.       Appreciation of the fascination of mathematics
d.      Awareness of the fascination of mathematics
e.       Imagination, initiative and flexibility of mind in mathematics
f.       Working in a systematic way
g.      Working independently
h.      Working cooperatively
i.        In-depth study of mathematics
j.        Pupils’ confidence in their mathematical abilities.
(Her Majesty’s inspectorate in The Philosophy of Mathematics Education)
If we talk about mathematical aims closer, in industrial trainer they think that mathematical aims back to basic (numeracy and social training in obedience. Then, in technological pragmatist, useful mathematics to appropriate level and certification (industry-centered). In old humanist is transmit body of mathematical knowledge (mathematics-centered). Creativity, self realization trough mathematics (child-centered) is in progressive educator. And then in public educator is critical awareness and democratic citizenship via mathematics.
There are some theories of learning that is shared by Ernest, they are based on industrial trainer are hard work, effort, practice, rote; in technological pragmatist are skill acquisition and practical experience; in old humanist are  understanding and application; in progressive educator are activity, play, and exploration; and in public educator are questioning, decision making, and negotiation.
It is not only theories of learning that is shared by Ernest but also about theories of teaching mathematics, they are authoritarian transmission, drill no “trills”; skill instructor, motivate trough work-relevance; explain, motivate pass on structure; facilitate personal exploration, prevent failure; discussion, conflict questioning of contents and pedagogy.
In technical mathematics teaching, there are technique to add students knowledge and also assessment to know how students ability in mathematics. Based on resources there are some point of view like before, they are chalk and talk only, no calculator; hands-on and microcomputer; visual aid to motivate; rich environment to explore; social relevant and authentic. In mathematics teaching, there is also an evaluation that consists of external test, porto-folio, assessment, porto-folio and social content. Theory of assessment in mathematics are external testing of simple basic; avoid cheating, external test and certification, skill profiting; skill examination based hierarchy; teacher led internal assessment, avoid failure; various modes, and use of various issues and content.
Not only talking about  mathematics teaching, Ernest is also talk about theory of social diversity because mathematics is our society. The theories are differentiated schooling by class, crypto-racist, monoculturslist; vary curriculum by ability only (mathematics neutral); humanist neutral, mathematics for all (use local culture); acomodation of social culturre, and diversity a necessaty.


Reference
Ernest, Paul. 1993. The Phylosophy of Mathematiocs Education. Basingstoke: Burgess Science Press.

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