Interactive Presentation of Mathematics

50 %
50 %
Information about Interactive Presentation of Mathematics

Published on September 30, 2008

Author: aSGuest313


Interactive Presentations of Mathematics : Interactive Presentations of Mathematics Jeremy Gow & Paul Cairns Computer Science Middlesex University, London Overview : Overview Why interactive proofs? Polya-Lamport framework The IMP system Interactive topology course Theory presentation Future plans Mathematical Proof : Mathematical Proof Central to mathematics Mixture of prose and notation Deductive presentation Detail - incomplete, but convincing Context - extra-logical content Problems with Proof : Problems with Proof How much detail? Convincing Unintelligible and boring How much context? Helpful Justification Unnecessary and distracting You can’t please everyone Using Hypermedia : Using Hypermedia HTML, Java, XML, ... Reader controls proof presentation Aims Dynamic presentation of detail/context Easy to read/navigate Easy to write Polya’s Four Stages : Polya’s Four Stages Understand - terms, unknowns, diagrams Plan - abstract solution Execute - detailed solution Reflect - uses, alternatives, related theory Proof presentation format Argument vs. pre/post context Lamport’s Structured Proof : Lamport’s Structured Proof How To Write A Proof Labeled hierarchy Explicit argument structure Reader chooses own depth Manages complex detail Exposes errors Ideal for hypertext Polya-Lamport Framework : Polya-Lamport Framework Interactive proof format (with hyperlinks) Statement of theorem Understand - unknowns, terms, diagrams Plan/Execute - structured proof Reflect - uses, alternatives, related theory Demo The IMP System : The IMP System Authoring toolkit XML proof grammar In: Text proof file Explicit structure (XML) Maths notation (Latex) Out: Expandable proof (Java applet) Need unified tool Interactive Topology Course : Interactive Topology Course Elements of Euclidean & Metric Topology - Peter Collins Polya-Lamport framework Chapters, definitions, theorems Hand-coded HTML + IMP applet Demo ( User Evaluation : User Evaluation Seven topology students Tasks with course notes Questionnaires: background, SUS Interview Results SUS average 78%, range 63-88% Design feedback Theory Presentation : Theory Presentation Chapters/definitions/theorems frames Shallow structure Is there a deep structure? Dialectic maths - Lakatos Hard to write/present Is it worth it? Future Plans : Future Plans Evaluation feedback GUI for XML proofs Summarise sub-proofs Develop theory presentation Large evaluation Automate sub-proof expansion? Summary : Summary Dynamic proof detail/context Polya-Lamport framework IMP: XML to expandable proof Evaluated interactive course notes How to present theories?

Add a comment

Related presentations

Related pages

Interactive electronic mathematics presentations for the ...

making mathematics engaging and relevant for all students while ensuring its alignment with the National Council of Teacher of Mathematics (NCTM)
Read more

Presentation and Pedagogy: The Effective Use of ...

Miller, D., Glover, D. and Averis, D. (2005), ‘Presentation and pedagogy: the effective use of interactive whiteboards in mathematics lessons’, in D ...
Read more

Templates - Interactive Maths - The Interactive Way to ...

... and this interactive template is easily editable to create just the game you want. ... A set of fantastic mathematical matching games, ...
Read more

Interactive Mathematics Presentations | STEM

This collection of resources, produced by the University of Leicester, is designed for use by students preparing for or studying advanced level mathematics.
Read more

Math Interactives -

Exploring Surface Area, Volume, and Nets (Object Interactive) This interactive mathematics resource allows the user to explore the concepts of surface area ...
Read more

CiteSeerX — Interactive Presentations of Mathematics: A ...

BibTeX @MISC{Cairns_interactivepresentations, author = {Paul A. Cairns and Jeremy Gow}, title = {Interactive Presentations of Mathematics: A Position ...
Read more

Mathematics K-12 - FREE Presentations in PowerPoint format ...

Free Presentations in PowerPoint Format & Free Interactive Activities. Common Core Math. Counting, Numbers. Skip Counting. Telling Time. Money. Addition.
Read more

Interactive Presentations of Mathematics: A Position Paper

Interactive Presentations of Mathematics: A Position Paper on ResearchGate, the professional network for scientists.
Read more

Presentation "1 Interactive learning in mathematics ...

1 Interactive learning in mathematics education: Review of recent literature 指導教授: Chen, Ming-puu 報 告 者: Jheng, Cian-you 報告日期 ...
Read more