creating interactive user feedback in dgs using the scripting interface of cinderella andreas fest...
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Creating interactive User Feedback in DGS using the Scripting Interface of Cinderella
Andreas FestUniversity of
Education Schwäbisch Gmünd
CADGME 2009RISC Linz
July 12th 2009
Overview
1.Feedback in interactive Learning Environments
2.Scripting in Dynamic Geometrie Software
3.An example from Discrete Mathematics
4.Feedback in interactive Geometry: Congruencies and Line Reflections
1. Feedback in interactive Learning EnvironmentsWhy? – And how?
•Students are free!Individual learning paths, solution strategies, tools, ...
•Teacher supports the student's learning process He attends the students, gives hints, stimuli and feedback
•Discovery Learning Method:Students develop own solutions on given mathematical problems
How we want to teach Math
•The teacher can not attend the whole learning process of each student!
•Our approach: interactive software with intelligent feedback system
But ...
•In mathematics: - innumerable amount of solution strategies- impossible to validate all automatically
•Most students - follow one of a few common solution strategies- make the same mistakes
Automated Feedback?
•Automatically detect those standard solution processes and
let the teacher analyse the exceptions!
Semi-automatic Analysis of individual Learning processes in Mathematics (SAiL-M*)[Bescherer, Kortenkamp, Müller, Schröder & Spannagel 2008]
Semi-Automatic Feedback!
* supported by BMBF, 2008-2011
•Timing [Cohen 1985]: immediatly – delayed – on demand – at the end
•Presentation:visual ⟷ acoustic
iconic/graphic ⟷ textual
static ⟷ animated
•Information content [Pridemore & Klein 1991]: verification ⟷ elaboration
Classification of Feedback
✔?✘
"Feedback on Demand"-Pattern:[Bescherer & Spannagel 2009]
•Students get feedback when they need it
•Feedback not only on the resultsbut also on the mathematical process
What do we want?
•Lecturer can identify interesting solutionsvia logging, Capture-&-Replay-Software, automatic analysis, ...
2. Scripting in Dynamic Geometrie Software
Zur Anzeige wird der QuickTime™ Dekompressor „MPEG-4 Video“
benötigt.
Modern DGS have many features but
not all things users want to do are possible! We need an easy to use interface for• executing (numerical) calculations • drawing functions• interacting with geometric objects• including algorithms • reducing information • implementing interactive visual feedback
Why scripting in DGS?
Our approach: CindyScriptScripting language requirements:• as simple as possible• syntax near by formal mathematical languageScripting in Cinderella 2:• functional programming language• direct access to all objects in the construction plane• event driven
Zur Anzeige wird der QuickTime™ Dekompressor „MPEG-4 Video“
benötigt.
More ...
•... this afternoon 14:00
3. An example from Discrete Mathematics
Minimum Spanning Trees
• Wanted: a spanning tree with minimum total weight
• Given: - a graph with nodes and edges - edge weights
•Construction of a road map
•Students develop solution strategies on paper
•Paper worksheet with exercise text
Exercise:
•Electronic worksheet as assistance
•The attention of the students gets more focused on the important aspects.
•The students had less problems in thinking structured and in verbalizing their solution strategies.
•The students were faster in developing good solutions.
Experience
4. Feedback in interactive Geometry: Congruencies and Line Reflections
Basic Idea:
Each congruency can be generated as composition of at most three line reflections
Line Reflections as Generators
•Collection of (until now) 6 laboratories -getting first ideas of congruencies
-getting a feeling for congruencies
-creating as combinations of line reflections
-constructing the corresponding axes
-reducing compositions of line reflections
•Objects are
Exploratory Laboratories
•Based on DGS Cinderella 2.1[Richter-Gebert & Kortenkamp]
•External interface written in HTML & JavaScript
•Using Cinderella's scripting engine for generating feedback
Technical realisation
•User interaction can be logged on a server via TCP connection
What do you like particularly when you learn using the computer as a tool?
•„fast feedback whether ,my‘ result is right“
Our Feedback on Demand
•„Ideas can quickly be implemented graphical ↳ rightness can be examined.“
Our Feedback on DemandHow did the automated feedback help you?•„Because there are different ,levels of rightness‘, solving the exercises gets easier.“•„When you don't know how to go on it is useful that the computer shows the next step.“•„When wrong, I could explain it myself after seeing the solution.“
•Automated feedback can help - the students to understand mathematics- the teacher to find interesting special solution approaches•Analysing the whole learning process •Benefits must be explored empirical
Work to be done
Conclusions•Scripting in DGS is an important tool to create adjusted learning environment with individual feedback
