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

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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!