Slide3 : Educational Design Patterns
in Mathematics Ambjörn Naeve
The Knowledge Management Research group
Centre for user-oriented IT Design (CID)
Numerical Analysis and Computer Science (NADA)
Royal Institute of Technology (KTH)
Stockholm / Sweden amb@nada.kth.se http://kmr.nada.kth.se
Slide4 : Structure of today’s math education system Closed layered architecture based on: • lack of subject understanding in the early layers. • minimization of teaching duties in the final layers. • life long teaching with: • curricular-oriented ”knowledge pushing”.
Slide5 : Problems with today’s math education It does not: • promote understanding. • support personalization. • integrate mathematics with human culture. • stimulate interest. • integrate abstractions with applications. • support transition between the different layers.
Slide6 : Possibilities for improving math education • visualizing the concepts. • interacting with the formulas. • using ICT to increase the ”cognitive contact” by: • personalizing the presentation. Promoting life-long learning based on interest by: • improving the narrative by: • showing before proving. • focusing on the evolutional history. • routing the questions to live resources. • proving only when the need is evident.
Slide7 : A traditional educational design pattern (Tenured Preacher / Learner Duty) Life-long teaching: Minimal learning efforts Doing time in return for a degree Agent 007 with a right to kill interest
Slide8 : An emerging educational design pattern (Requested Preacher / Learner Rights) Life-long learning: Developing your interests Requested teaching: You teach as long as somebody is learning
Slide9 : A Knowledge Manifold • is designed in a way that reflects a strong effort to comply with emerging international IT standards. • can be regarded as a Knowledge Patchwork, with a number of linked Knowledge Patches, each with its own Knowledge Gardener. • gives the users the opportunity to ask questions and search for live certified Knowledge Sources. • is a learner-centric educational architecture that supports question-based learning.
Slide10 : A Knowledge Manifold (cont.) • allows teachers to compose components and construct customized learning environments. • makes use of conceptual modeling to support the separation of content from context. • contains a conceptual exploration tool (concept browser) that supports these principles. • has access to distributed archives of
resource components.
Slide11 : The seven different Knowledge Roles of a KM • The knowledge cartographer • The knowledge composer • The knowledge librarian • The knowledge coach • The knowledge preacher • The knowledge plumber • The knowledge mentor • constructs context-maps. • fills the context-maps with content. • composes content components into learning modules. • cultivated questions. • provides live answers. • connects questions with appropriate preachers. • provides motivation and supports self-reflection.
Slide12 : QBL: the 3 performing knowledge roles ´ ´ ´
Slide13 : QBL: the 3 performing knowledge roles (cont)
Slide14 : Long term trend in mathematics education
Slide15 : Problem / Solution versus Problem / Elimination
Slide16 : Problem / Solution applied to Crime
Slide17 : isA because Problem/Solution applied to early math education
Slide18 : isA because Problem/Solution applied to late math education
Slide19 : Problem/Solution applied to calculator industry
Slide20 : no no no no no no no yes no yes yes yes yes yes yes yes
Slide21 : The digital view - from Pythagoras to Heisenberg
Slide26 : tid
Slide28 : References • Naeve, A., IT-baserade matematikverktyg på KTH, CID-49, NADA/KTH, 2001. These reports are available in pdf at http://kmr.nada.kth.se • Naeve, A., The Garden of Knowledge as a Knowledge Manifold - a conceptual framework for computer supported subjective education, CID-17, NADA/KTH, 1997. • Naeve, A., Conceptual Navigation and Multiple Scale Narration in a Knowledge Manifold, CID-52, NADA/KTH,1999. • Naeve, A., The Work of Ambjörn Naeve in the Field of Math. Educational Reform,CID-110, NADA/KTH, 2001. • Naeve, A., Begreppsmodellering och matematik, CID-109, NADA/KTH, 2001.