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Creating interactive User Feedback in DGS using the Scripting Interface of Cinderella Andreas Fest University of Education Schwäbisch Gmünd CADGME 2009 RISC Linz July 12th 2009

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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

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1. Feedback in interactive Learning Environments Why?–And how?

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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

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The teacher can not attend the whole learning process of each student! Our approach: interactive software with intelligent feedback system But...

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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?

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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

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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 ?

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"Feedback on Demand"-Pattern: [Bescherer & Spannagel 2009] Students get feedback when they need it Feedback not only on the results but also on the mathematical process What do we want? Lecturer can identify interesting solutions via logging, Capture-&-Replay-Software, automatic analysis,...

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2. Scripting in Dynamic Geometrie Software

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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?

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Our approach: CindyScript Scripting language requirements: as simple as possible syntax near by formal mathematical language Scripting in Cinderella 2: functional programming language direct access to all objects in the construction plane event driven

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More...... this afternoon 14:00

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3. An example from Discrete Mathematics

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Minimum Spanning Trees Wanted: a spanning tree with minimum total weight Given: - a graph with nodes and edges - edge weights

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Construction of a road map Students develop solution strategies on paper Paper worksheet with exercise text Exercise: Electronic worksheet as assistance

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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

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4. Feedback in interactive Geometry: Congruencies and Line Reflections

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Basic Idea: Each congruency can be generated as composition of at most three line reflections Line Reflections as Generators

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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

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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

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Example: Reducing the axes

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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.

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Our Feedback on Demand How 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.

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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

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fest@sail-m.de

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