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Hands-on Mathematics for Hands-on Mathematics for Computer ScientistsComputer Scientists
Erica Melis, Martin HomikErica Melis, Martin Homik
Seminar Seminar WS 05/06WS 05/06
How to improve learning in math?How to improve learning in math?
Polya, Leron frameworkPolya, Leron framework Plan and structure your learningPlan and structure your learning Reflect on your learningReflect on your learning
Exercise structureExercise structure Concept mappingConcept mapping Erroneous examplesErroneous examples Learning logsLearning logs AssemblingAssembling
Exercise StructureExercise Structure
Concept MappingConcept Mapping
Erroneous ExamplesErroneous Examples
0=1
Book GenerationBook Generation
User Modeling and AdaptivityUser Modeling and Adaptivity
ePortfolio/Learning LogsePortfolio/Learning Logs
SloganSlogan
Be a coach!
Learn about “derivation”
What is ActiveMath?What is ActiveMath?
RepositoryCourse Generator
ChallengesChallenges
Reasoning about ContentReasoning about Content Reasoning about UserReasoning about User Tool SupportTool Support Adaptivity++, Interactivity, Adaptivity++, Interactivity,
Service ProvisionService Provision Pedagogical KnowledgePedagogical Knowledge
Repository
Learn about “derivation”
Course Generator
Repository
Repository
??
??
??
??
Examples for
“derivation”
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ActiveMath ArchitectureActiveMath Architecture
Demos
Organizational InformationOrganizational Information
When: Thursday 16:00- 18:00When: Thursday 16:00- 18:00 Where: Where:
Room 0.13, building 45Room 0.13, building 45 Room 1.03, building 45Room 1.03, building 45
Links:Links: http://http://www.activemath.org/teaching/www.activemath.org/teaching/mathSemWS0506/mathSemWS0506/ http://handson.activemath.org/http://handson.activemath.org/ http://handson-elgg.activemath.org/http://handson-elgg.activemath.org/
Organization ExercisesOrganization Exercises
Groups possible (at most 3 students)Groups possible (at most 3 students) We have */**/ *** exercises:We have */**/ *** exercises: Deliver 6 Exercises at least: Deliver 6 Exercises at least:
one *, one **, one *** one *, one **, one *** Remaining any-star exercisesRemaining any-star exercises At least 2 exercises per sectionAt least 2 exercises per section
Section:Section:1.1. October 20th -- November 24th October 20th -- November 24th 2.2. December 1st -- January 12th December 1st -- January 12th 3.3. January 19th -- February 16January 19th -- February 16thth
Maintain a regular ePortfolio (Elgg)Maintain a regular ePortfolio (Elgg)
Possible follow-up activitiesPossible follow-up activities
Educational Technologies Educational Technologies Bachelor/Master thesis Bachelor/Master thesis
Who is ActiveMath?Who is ActiveMath?
• Leader • Course Planning • Exercises • KR & Authoring
• Software engineer• ePortfolios • Style sheets • User modelling
… and many students!
Example ProblemExample Problem
Find the volume of the frustrum of a right Find the volume of the frustrum of a right
pyramid with a square base, given thepyramid with a square base, given the
altitude of the frustrum, the length of a altitude of the frustrum, the length of a
side of its upper base, and the length side of its upper base, and the length
of a side of its lower base.of a side of its lower base.
Step 1: Understand the problemStep 1: Understand the problem
What is given?What is given? AltitudeAltitude Length of the upper baseLength of the upper base Length of the lower baseLength of the lower base
What is unknown?What is unknown? Volume of the frustrumVolume of the frustrum
a
b
h
a = lower baseb = upper baseh = height
Step 2: Devise a planStep 2: Devise a plan
Is there a related problem?Is there a related problem? The volume of a right pyramid can be The volume of a right pyramid can be
obtained as follows:obtained as follows:
3
)Height()Base(Volume
2
Can you restate the problem?Can you restate the problem? Find the volume of the Find the volume of the
large pyramid minus the large pyramid minus the
volume of the small pyramidvolume of the small pyramid
Step 3: Carry out the plan Step 3: Carry out the plan
Calculate volume of large pyramidCalculate volume of large pyramid Calculate volume of small pyramidCalculate volume of small pyramid Subtract the second from the firstSubtract the second from the first
Step 4: Look backStep 4: Look back
This technique can be applied to other This technique can be applied to other problems such as: Find the area of a problems such as: Find the area of a donut, given the radius to the inside and donut, given the radius to the inside and outside.outside.
Don’t be cryptic!Don’t be cryptic!
332211 hGhG
V
hhh 21
2221 )(3
1hGhhGV
2
1
2
2
2
1
G
G
h
hh
h
h
1222 )( GhGhh
12222 GhGhGh
2122 GGhGh
12
22
GG
Ghh
First exercise for next weekFirst exercise for next week
Register for seminar if not yet doneRegister for seminar if not yet done Create an ActiveMath accountCreate an ActiveMath account
Input full nameInput full name Create an Elgg accountCreate an Elgg account
Comment the first session in your BlogComment the first session in your Blog Play with ActiveMath and ElggPlay with ActiveMath and Elgg Answer questionnaireAnswer questionnaire Sign declarationSign declaration
That’s it!
What is ActiveMath?What is ActiveMath?
Knowledge representationKnowledge representation User modelingUser modeling AdaptivityAdaptivity Exercise developmentExercise development Domain mappingDomain mapping Concept mappingConcept mapping Dictionary/SearchDictionary/Search
What is ActiveMath?What is ActiveMath?
eLearning environmenteLearning environment Bild der ArchitekturBild der Architektur Demo geben!Demo geben!