Hands-on Mathematics for Computer Scientists Erica Melis, Martin Homik Seminar WS 05/06

How to improve learning in math?  Polya, Leron framework  Plan and structure your learning  Reflect on your learning  Exercise structure  Concept mapping  Erroneous examples  Learning logs  Assembling

Exercise Structure

Concept Mapping

Erroneous Examples 0=1

Book Generation

User Modeling and Adaptivity

ePortfolio/Learning Logs

Slogan Be a coach!

Learn about “derivation” What is ActiveMath? Repository Course Generator

Challenges  Reasoning about Content  Reasoning about User  Tool Support  Adaptivity++, Interactivity, Service Provision  Pedagogical Knowledge Repository Learn about “derivation” Course Generator Repository ? ? ? ? Examples for “derivation” ?

ActiveMath Architecture

Demos

Organizational Information  When: Thursday 16:00- 18:00  Where:  Room 0.13, building 45  Room 1.03, building 45  Links:  mathSemWS0506/ mathSemWS0506/ mathSemWS0506/  

Organization Exercises  Groups possible (at most 3 students)  We have */**/ *** exercises:  Deliver 6 Exercises at least:  one *, one **, one ***  Remaining any-star exercises  At least 2 exercises per section  Section: 1.October 20th -- November 24th 2.December 1st -- January 12th 3.January 19th -- February 16 th  Maintain a regular ePortfolio (Elgg)

Possible follow-up activities  Educational Technologies  Bachelor/Master thesis

Who is ActiveMath? Leader Course Planning Exercises KR & Authoring Software engineer ePortfolios Style sheets User modelling … and many students!

Example Problem Find the volume of the frustrum of a right pyramid with a square base, given the altitude of the frustrum, the length of a side of its upper base, and the length of a side of its lower base.

Step 1: Understand the problem What is given?  Altitude  Length of the upper base  Length of the lower base What is unknown?  Volume of the frustrum a b h a = lower base b = upper base h = height

Step 2: Devise a plan Is there a related problem?  The volume of a right pyramid can be obtained as follows: Can you restate the problem?  Find the volume of the large pyramid minus the volume of the small pyramid

Step 3: Carry out the plan  Calculate volume of large pyramid  Calculate volume of small pyramid  Subtract the second from the first

Step 4: Look back  This technique can be applied to other problems such as: Find the area of a donut, given the radius to the inside and outside.

Don’t be cryptic!

First exercise for next week  Register for seminar if not yet done  Create an ActiveMath account  Input full name  Create an Elgg account  Comment the first session in your Blog  Play with ActiveMath and Elgg  Answer questionnaire  Sign declaration

That’s it!

What is ActiveMath?  Knowledge representation  User modeling  Adaptivity  Exercise development  Domain mapping  Concept mapping  Dictionary/Search

What is ActiveMath?  eLearning environment  Bild der Architektur  Demo geben!