1. Geometry e-Learning System Valeri KRIVTSOV Institute for System Analysis Russian Academy of Sciences ICME-10, July 2004 1

2. TT2K’s General Functionality The prototype e-learning system is called TT2K. ICME-10, July 2004 2 The TT2K is capable of: treating any SCORM-compliant learning coursetreating any SCORM-compliant learning course forming an individual route through the courseforming an individual route through the course creating mini-courses on user demandcreating mini-courses on user demand storing and retrieving individual results of learningstoring and retrieving individual results of learning supporting other learning functions.supporting other learning functions. The TT2K is a distributed NG e-learning system supplied with advanced functionality reachable on the Internet.

3. Learning Geometry with TT2K The TT2K prototype is adjusted to teach school geometry. It handles an electronic version of the “Geometry 7” – the school manual by Igor Sharygin. ICME-10, July 2004 3 providing live geometrical sketches supportproviding live geometrical sketches support supporting real-time collaborations between student and teacher on the Internetsupporting real-time collaborations between student and teacher on the Internet supporting remote collaborative solving of geometrical problems on the Internet.supporting remote collaborative solving of geometrical problems on the Internet. In order to teach geometry the TT2K is supplied with advanced functionality:

4. Exclusive TT2K’s Functionality The TT2K possesses one exclusive feature: it supports real-time student-teacher complicated collaboration on the Internet. ICME-10, July 2004 4 Both “real-time” and “collaboration” are important here: most of students cannot concentrate their attention if response time exceeds a certain valuemost of students cannot concentrate their attention if response time exceeds a certain value valuable learning is impossible without collaboration, because computer can assist a teacher but cannot replace him completely.valuable learning is impossible without collaboration, because computer can assist a teacher but cannot replace him completely. To our best knowledge there are few systems that support the both functions, and no one system supports these two functions and any complicated e-learning feature simultaneously. To our best knowledge there are few systems that support the both functions, and no one system supports these two functions and any complicated e-learning feature simultaneously.

5. How To Compare e-Learning Systems? The TT2K is only a one of many e-learning systems. What for is it? Is it better then others? And how can we compare different e-Learning Systems? The answers to the above questions are of great importance for the entire e-learning community. Here are some thoughts on possible classification. ICME-10, July 2004 5 Let us consider three classification criteria: the response time of the Internet networkingthe response time of the Internet networking intensity of cooperationintensity of cooperation complexity of e-learning core functionality.complexity of e-learning core functionality.

6. The response time is an extremely important parameter of all e-learning systems. The “response time” classification criterion r depends on the mode of work on the Internet. We assume that it may take four integer values: 0,1,2,3. r=0 : r=1 : r=2 : r=3 : r=3 : Response Time Classification Criterion ICME-10, July 2004 6 {no Internet (simple PC, local network)} {off-line Internet (e-mail, FTP, …)} {on-line Internet (WWW, …)} {real-time Internet (GRIDs, CORBA, …)}. Example. In the case of solving construction problems with the TT2K, r=3.

7. The “collaboration intensity” c is the next criterion. It may take four integer values either: 0,1,2,3. c=0 : c=1 : c=2 : c=3 : Collaboration Intensity Classification Criterion ICME-10, July 2004 7 {one user (no collaboration)} {many parallel (independent) users} { static “one-to-one” or “one-to-many” collaborations} { dynamic “many-to-many” collaborations} Example. In the case of solving construction problems with the TT2K on the Internet, c=2.

8. We have not considered yet the e-learning functions themselves. The criterion f of “core functions” reflects approximately the level of complexity of the e-learning functions. It also takes four integer levels: 0,1,2,3. f=0 : f=1 : f=2 : f=3 : Core Functions Classification Criterion ICME-10, July 2004 8 {texts, drawings, sound, video, animation} {interactivity, Q & T, guided navigation, …} {adaptability, virtual laboratories,…} {intellectuality, proof checking, …} Example. In the case of solving problems with the TT2K on the Internet, f=2.

9. Every e-learning function can be represented by a fixed value tuple rcf consisting of the above three criteria. Applying rcf Model: Examples ICME-10, July 2004 9 Example 6. For instant messaging systems, rcf = (3,2,0). Example 4. For video conferences, rcf = (3,2,0). Example 2. For typical SCORM systems, rcf = (2,1,1). Example 3. For hypertext e-manuals, rcf = (2,1,0). Example 5. For the first generation distance e-learning systems, rcf = (1,2,0). Example 1. For live geometry sketchpad, rcf = (0,0,2).

10. Let us render all possible values of tuples to a 3- dimentional integer cube. Since every e-learning function has an unique rcf, all such functions may be mapped in this cube. Applying rcf Model: Example Rendering ICME-10, July 2004 10 cfr Live geometry sketchpads First generation DLSs Hypertext e-manuals Typical SCORM systems Video conferences Instant messaging systems

11. Results of applying the rcf model to the state-of-the-art analysis of the e-learning domain: 1. Few existing systems support functions satisfying the conditions r = 3, c = 2. 2. The TT2K is the single e-learning system satisfying the conditions r = 3, c = 2, f >= 1. 3. None of the existing systems supports any e-learning function satisfying the conditions c = 3 or f = 3. Applying rcf Model: SOA Analysis (1/2) ICME-10, July 2004 11

12. 4 (main SOA hypothesis). The entire set of e-learning functions provided by existing e-learning systems satisfies the condition r + c + f <= 6. Applying rcf Model: SOA Analysis (2/2) ICME-10, July 2004 12 Summary. All of the existing e-learning system functionalities are located within the region defined by the conditions r + c + f <= 6, c <= 2, f <= 2.

13. The resulting region looks as follows: The above listed conditions cut the classification cube in a special manner. Applying rcf Model: SOA Result Rendering 13 c r f ICME-10, July 2004

14. Every system that supports e-learning functions with r + c + f >= 7 or c=3 or f = 3, may be called NG e-learning system. Applying rcf Model: NG System Definition ICME-10, July 2004 14

15. Solving geometrical problems with the TT2K on the Internet possesses rcf = (3,2,2). So the TT2K is really an NG e-Learning System. Applying rcf Model: TT2K is NG ICME-10, July 2004 15

16. The main presentation concerns the next two TT2K’s functions (scenarios). Scenario 1. Learning school geometry for the 7 th form, rcf = (2,1,2). The learning course is made on the basis of the “Geometry 7-9” school manual by Igor Sharygin. Scenario 2. Collaborative solving of geometrical construction problems on the Internet, rcf = (3,2,2). TT2K Demonstration scenarios ICME-10, July 2004 16

17. 31 урок, связаны отношениями предшествования Примеры Пререквизиты урока 5: второй и четвертый Пререквизиты урока 2: первый Пререквизиты урока 4: третий Пререквизит урока 3: первый Scenario 1: Prerequisites ICME-10, July 2004 17

18. Скриншот со стрелками Scenario 1: Prerequisite Rendering ICME-10, July 2004 18

19. Скриншот Scenario 1: Mini-Course ICME-10, July 2004 19