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Mathematical history, philosophy and education
, 2007
"... Abstract History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necess ..."
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Abstract History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and philosophy require generality and abstraction. The paper offers some methodological reflections about these matters together with two case studies from nineteenth century history of arithmetic and integration theory, respectively, which try to strike a balance between the directly opposed requirements.
Centre for Discrete Mathematics and Theoretical Computer ScienceSearching for Spanning kCaterpillars and kTrees
, 2008
"... We consider the problems of finding spanning kcaterpillars and ktrees in graphs. We first show that the problem of whether a graph has a spanning kcaterpillar is NPcomplete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1caterpillar in a graph with treewidth k. Also ..."
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We consider the problems of finding spanning kcaterpillars and ktrees in graphs. We first show that the problem of whether a graph has a spanning kcaterpillar is NPcomplete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1caterpillar in a graph with treewidth k. Also, as a generalized versions of the depthfirst search and the breadthfirst search algorithms, we introduce the ktree search (KTS) algorithm and we use it in a heuristic algorithm for finding a large kcaterpillar in a graph. 1
AN ANALYSIS OF MODAL AUXILIARIES IN TEACHER INTERROGATIVES ACROSS THE TEACHING OF FRACTIONS AND GEOMETRY
"... This manuscript has been reproducad frwn the mimfikii master. UMI films the text directly from the original or copy subrnitted. Thus, soma thesis and dissertation copies are in typewriter face, mile others may be from any type of cornputer pnnter. The quality of this reproduction is dependent upon t ..."
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This manuscript has been reproducad frwn the mimfikii master. UMI films the text directly from the original or copy subrnitted. Thus, soma thesis and dissertation copies are in typewriter face, mile others may be from any type of cornputer pnnter. The quality of this reproduction is dependent upon the quality of aie copy subrniîted. Broken or indistinct print. wlored or poor quality illustrations and photographs, print bleeâthrough, substandard margins, and improper alignment cari advenely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be rernoved, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, chafts) are reproduced by sedioning the original, beginning at the upper lefthand corner and continuhg from left to right in equal sedi*ons with small ovedaps. Photographs induded in Me original manuscript have been reproduœd xerographically in this copy. Higher quality 6 " x 9 " black and white photogaphic prints are availabla for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI dimcüy to order. Bell & Howell Information and Leaming
1 The Steiner TMEprogram of 1987:
"... Abstract: In this contribution we discuss the six theses presented by HansGeorg Steiner (1987), which were instrumental in the community becoming interested in theories and philosophies of mathematics education. We discuss overlooked aspects of this seminal paper particularly in light of recent d ..."
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Abstract: In this contribution we discuss the six theses presented by HansGeorg Steiner (1987), which were instrumental in the community becoming interested in theories and philosophies of mathematics education. We discuss overlooked aspects of this seminal paper particularly in light of recent developments in the field of mathematics education. Nearly twenty years later, we reflect on the development of Steiner’s program for theory development and examine if any progress has been made at all on the open questions that Steiner (1987) posed to the community.
SOME FACTS TO EXPLAIN THE CONTEXT OF THE QUOTATION IN THE TITLE
"... This talk presents some thoughts about the possible reasons of students ’ tendency to rely on teachers for the validity of their solutions and of their lack of sensitivity to contradictions in mathematics. Epistemological, cognitive, affective, didactic and institutional reasons are considered in tu ..."
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This talk presents some thoughts about the possible reasons of students ’ tendency to rely on teachers for the validity of their solutions and of their lack of sensitivity to contradictions in mathematics. Epistemological, cognitive, affective, didactic and institutional reasons are considered in turn.
DG Discussion
"... Aims and focus The aim of Discussion Group 4 was to explore the nature, role and state of Philosophy of Mathematics Education (PhoME) and particular themes focused on the perspective of PhoME. The group met three times. The initial part of the first session was dedicated to an orientation with an in ..."
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Aims and focus The aim of Discussion Group 4 was to explore the nature, role and state of Philosophy of Mathematics Education (PhoME) and particular themes focused on the perspective of PhoME. The group met three times. The initial part of the first session was dedicated to an orientation with an introductory overview “What is philosophy of mathematics educa tion? ” (see Ernest, 2004, for a written version). The second session, “Strands and issues for discussion within PhoME”, took place in smaller groups addressing different ques tions, followed by a synthesizing session. The prepared questions were: What are the conceptions of mathematics and mathematical knowledge underlying different learning theories? What roles do philosophies of mathematics play in the teaching and learning of mathematics? How do they relate to mathematics curriculum, teaching reforms and classroom practices? Different perspectives – a first metaphoric approach The group agreed on Paul Ernest’s suggestion to consider the PhoME not as one single