1. GeoSketch TITLE A Sketch-based Geometry Tutoring System Subtitle
Author T. Metin Sezgin
Affiliation: Koç University, Istanbul, Turkey
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Abstract
The recognition algorithm uses Image Deformation Model (IDM) features to train and an SVM classifier. The correct recognition rates for each class, obtained by leave-one-out cross-validation (LOOCV), are shown in Figure 2. The confusion matrix of the current recognition system is shown in Figure 3.
Pen is a natural interaction modality in education. Therefore, education is one of the areas that can benefit the most from the pen as a means of interaction in terms of providing a natural communication between the human and the machine. GeoSketch is a sketch-based geometry tutoring system that supports pen-based interaction.
GeoSketch allows students to annotate figures of the questions on a tablet PC as comfortable as they would on paper, while a machine learning algorithm enables the recognition of the annotations. This recognition phase is used in order to provide the students instant feedback according to the validation results of their input. The feedback aim to assist the students in their process of learning the geometry concepts, while guiding them towards the correct solution of the question.
Figure 3: Confusion matrix
User Interface
A snapshot of the resulting software can be seen in Figure 1. The area, where the figure of the question is located, can be annotated using a pen. The software starts to process the input if there has not been an interaction with the figure for longer than a second after the student started annotating. The software takes a text file that includes the questions’ rules for the session. This text file holds information on expected classes of the student’s input, figures and instructions that are to be shown to the student in the cases of the correct and incorrect input.
Figure 2: Recognition rates for each class
Related Work
There are some pen-based tutoring systems for statics [1], circuit analysis [2], geometry [3] and mathematics [4], which can be considered as private tutoring systems. There are also examples such as Classroom Learning Partner [5], which aims to make use of the sketch-based interaction in classes.[1] and [2] propose systems specific for subjects in physics, as we do for geometry. [3] inspect the case of free response questions, which we would like to enable in our system at some point. On the other hand, [4] discuss the user interface for a system that recognizes handwritten mathematics, which can be used in a geometry application.
Future Work
There are a number of possible improvements that can be implemented in order to increase the correct recognition rates. For example, we expect that using context information extracted from image patches in the neighborhood of ink annotations will improve recognition rates.
GeoSketch can also be improved further by deploying a more formal approach in terms of educational psychology while designing the questions.
Figure 1: A snapshot of the Geometry Assistant
Annotation Recognition
Current version of the GeoSketch recognizes 8 objects:
• 1 for denoting angles
• 2 for denoting equality of angles
• 2 for denoting equality of the length of lines
• 2 for denoting parallelism, and
• 1 for denoting perpendicularity
In order to form the dataset, samples for each class were collected in three different scales and two rotations with two repetitions from five participants. The final dataset consists of 30 samples per class for the angle and angle equality symbols and 60 samples per class for the other symbols, making a total of 390 samples.
References
[1] R. Silva, D. Bischel, W. Lee, E.J. Peterson, R.C. Calfee, and T. F. Stahovich Kirchhoff's Pen: a pen- based circuit analysis tutor. In Proceedings of the 4th Eurographics workshop on Sketch-based interfaces and modeling (SBIM '07)
[2] WeeSan Lee, Ruwanee de Silva, Eric J. Peterson, Robert C. Calfee, and Thomas F. Stahovich Newton's Pen: a pen-based tutoring system for statics. In Proceedings of the 4th Eurographics workshop on Sketch-based interfaces and modeling (SBIM '07)
[3] Kourtney Kebodeaux, Martin Field, and Tracy Hammond Defining precise measurements with sketched annotations. In Proceedings of the Eighth Eurographics Symposium on Sketch-Based Interfaces and Modeling (SBIM '11)
[4] Robert Zeleznik, Timothy Miller, and Chuanjun Li Designing UI techniques for handwritten mathematics. In Proceedings of the 4th Eurographics workshop on Sketch-based interfaces and modeling (SBIM '07)
[5] K. Koile, K. Chevalier, C. Low, S. Pal, A. Rogal, D. Singer, J. Sorensen, K. S.Tay, K. Wu Supporting Pen-Based Classroom Interaction: New Findings and Functionality for Classroom Learning Partner. First International Workshop on Pen-Based Learning Technologies (PLT ’07)
Acknowledgemets…