Curriculum Design and Systemic Change
This chapter describes and comments on the large qualitative differences between curriculum intentions and outcomes, within and across countries. It is not a meta-analysis of research on international comparisons; rather the focus is the relationship betw
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Abstract This chapter describes and comments on the large qualitative differences between curriculum intentions and outcomes, within and across countries. It is not a meta-analysis of research on international comparisons; rather the focus is the relationship between what a government intends to happen in its society’s mathematics classrooms and what actually does. Is there a mismatch? In most countries there is. Why? This leads us into the dynamics of school systems, in a steady state and when change is intended—and, finally, to what might be done to bring classroom outcomes closer to policy intentions. Two areas are discussed in more detail: problem solving and modeling, and the roles of computer technology in mathematics classrooms. Keywords Curriculum change · Curriculum design · Curriculum goals · Curriculum implementation · Pushback · Modeling · Systemic change · Technology
“Curriculum” and Curriculum Change The term “curriculum” is used with many different meanings. In the US it often means a textbook series, in the UK the set of experiences a child has in school classrooms. Neither of these fits the purposes of this chapter, which is concerned with the interrelations and differences between the variant definitions set out, for example, by the Second International Mathematics Study (Travers and Westbury 1989). I want to distinguish and compare the: “intended curriculum”: that described in official documents carrying the status of policy;
H. Burkhardt (B) Shell Centre for Mathematical Education, University of Nottingham, Nottingham, NG8 1BB, UK e-mail: [email protected] H. Burkhardt University of California, Berkeley, USA Y. Li, G. Lappan (eds.), Mathematics Curriculum in School Education, Advances in Mathematics Education, DOI 10.1007/978-94-007-7560-2_2, © Springer Science+Business Media Dordrecht 2014
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“tested curriculum”: the range of performances covered by the official tests, particularly when the results have serious consequences for students’ or teachers’ future lives; “implemented curriculum”: what is actually taught in most classrooms. The “achieved curriculum”, what most students actually learn, would take us into much too large a field of research. Other chapters address this. Thus the focus in this paper is on the path from government intentions, usually set out in policy documents, to the actual pattern of teaching and learning activities in classrooms—some typical, some that are unusually innovative. As always, studying the steady state tells you little about causation. Accordingly, I look at two areas where there has long been general international agreement on the need for change in mathematics curricula: problem solving and modeling, and the roles of computer technology. I have benefited from special issues of the Zentralblatt für Didaktik der Mathematik, in which distinguished authors from around the world describe what has happened over recent decades to problem solving and to modeling in their own curricula.1
Curriculum Goals in Mathematics Around t
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