]> BibSonomy publications for /author/K%C3%BCchemann http://www.bibsonomy.org/burst/author/K%C3%BCchemann BibSonomy BuRST Feed for /author/K%C3%BCchemann 2008-07-20T23:41:06+02:00 Students understandings of logical implication http://www.bibsonomy.org/bibtex/2ea28caba038ad2d52c2c10fb9c7b7bba/yish yish 2008-04-27T20:07:24+02:00 argumentation bibtex-import deduction fetch implication it logic logical mythesis need proof read
Students understandings of logical implication
Celia Hoyles and Dietmar Küchemann Educational Studies in Mathematics 51 193--223 (2002)
to argumentation bibtex-import deduction fetch implication it logic logical mythesis need proof read by yish on 2008-04-27 20:07:24 ]]> Educational Studies in Mathematics193--223Students understandings of logical implication512002argumentation bibtex-import deduction fetch implication it logic logical mythesis need proof read 2008-04-27 20:07:24.0We report results from an analysis of responses to a written question in which high-attaining students in English schools, who formed part of a longitudinal nation-wide survey on proof conceptions, were asked to assess the equivalence of two statements about elementary number theory, one a logical implication and the other its converse, to evaluate the truth of the statements and to justify their conclusions. We present an overview of responses at the end of Year 8 (age 13 years) and an analysis of the approaches taken, and follow this with an analysis of the data collected from students who answered the question again in Year 9 (age 14 years) in order to distinguish learning trajectories. From these analyses, we distinguished three strategies, empirical, focussed-empirical and focussed-deductive, that represent shifts in attention from an inductive to a deductive approach. We noted some progress from Year 8 to Year 9 in the use of the focussed strategies but this was modest at best. The most marked progress was in recognition of the logical necessity of a conclusion of an implication when the antecedent was assumed to be true. Finally we present some theoretical categories to capture different types of meanings students assign to logical implication and the rationale underpinning these meanings. The categories distinguish responses where a statement of logical implication is (or is not) interpreted as equivalent to its converse, where the antecedent and consequent are (or are not) seen as interchangeable, and where conclusions are (or are not) influenced by specific data. Influences on Students' Mathematical Reasoning and Patterns in its Development: Insights from a Longitudinal Study with Particular Reference to Geometry http://www.bibsonomy.org/bibtex/2c56eb6c369335422546c4f949885e241/yish yish 2008-04-03T04:15:23+02:00 children geometry learning mathematics mythesis proof reasoning
Influences on Students' Mathematical Reasoning and Patterns in its Development: Insights from a Longitudinal Study with Particular Reference to Geometry
Dietmar Küchemann and Celia Hoyles International Journal of Science and Mathematics Education 4 581-608 (2006)
to children geometry learning mathematics mythesis proof reasoning by yish on 2008-04-03 04:15:23 ]]> International Journal of Science and Mathematics Education4581-608Influences on Students' Mathematical Reasoning and Patterns in its Development: Insights from a Longitudinal Study with Particular Reference to Geometry42006children geometry learning mathematics mythesis proof reasoning 2008-04-03 04:15:23.0We report some findings of the Longitudinal Proof Project, which investigated patterns in high-attaining students' mathematical reasoning in algebra and in geometry and development in their reasoning, by analyses of students' responses to three annual proof tests. The paper focuses on students' responses to one non-standard geometry item. It reports how the distribution of responses to this item changed over time with some moderate progress that suggests a cognitive shift from perceptual to geometrical reasoning. However, we also note that many students made little or no progress and some regressed. Extracts from student interviews indicate that the source of this variation from the overall trend stems from the shift over the three years of the study to a more formal approach in the school geometry curriculum for high-attaining students, and the effects of this shift on what students interpreted as the didactical demands of the item. Students’ Developing Knowledge in a Subject Discipline: Insights from Combining Quantitative and Qualitative Methods http://www.bibsonomy.org/bibtex/2f8d3b1d7eb50cab68bf833ef2741c351/yish yish 2007-07-21T18:09:28+02:00 geometry interviews learning mathematics methodology mythesis qualitative quantitative reasoning
Students’ Developing Knowledge in a Subject Discipline: Insights from Combining Quantitative and Qualitative Methods
Celia Hoyles and Dietmar Küchemann and Lulu Healy and Min Yang International Journal of Social Research Methodology 8 225-238 (2005)
to geometry interviews learning mathematics methodology mythesis qualitative quantitative reasoning by yish on 2007-07-21 18:09:28 ]]> International Journal of Social Research Methodology3225-238Students’ Developing Knowledge in a Subject Discipline: Insights from Combining Quantitative and Qualitative Methods82005geometry interviews learning mathematics methodology mythesis qualitative quantitative reasoning 2007-07-21 18:09:28.0In this paper, we describe research that combined quantitative and qualitative methods in order to investigate how students' mathematical explanations change over time and to identify factors underlying any changes. The quantitative methods used included tracing trends in hierarchically ordered categorical data, and multi-level analyses of student scores to identify significant predictors of students' progress. Qualitative methods used included interviews with selected students in schools identified from the multi-level modelling as those in which students performed significantly better than would be predicted. By reference to these analyses as applied to one geometrical item, the paper points to how the mixing of methods shed light on trends in patterns of student response as well as on unexpected results, and led to reflexive testing of some initial assumptions about the development of mathematical reasoning. Pupils' Awareness of Structure on Two Number / Algebra Questions http://www.bibsonomy.org/bibtex/26d6a270f6cbbbfd455c5a0a80d44b51e/yish yish 2006-05-09T19:17:39+02:00 as_conv divisibility factorial ijtme2006 mythesis sequences
Pupils' Awareness of Structure on Two Number / Algebra Questions
Dietmar Küchemann and Celia Hoyles The Fourth Conference of the European Society for Research in Mathematics Education (CERME 4) (2005)
to as_conv divisibility factorial ijtme2006 mythesis sequences by yish on 2006-05-09 19:17:39 ]]> SpainThe Fourth Conference of the European Society for Research in Mathematics Education (CERME 4)Pupils' Awareness of Structure on Two Number / Algebra Questions2005as_conv divisibility factorial ijtme2006 mythesis sequences 2006-05-09 19:17:39.0