Brief History of Math-Bridge and its Usage
- 1. Brief History of Math-Bridge and its Usage George Goguadze Leuphana Universität Lüneburg
- 2. Math-Bridge: short summary of features ▪ Tools for students: ▪ Static Courses ▪ Adaptive Course Generation ▪ Micro Course Generation ▪ Intelligent search ▪ Interactive exercises ▪ Student progress indicators ▪ What is the target audience? ▪ How do students work with the system? ▪ Which features are useful? ▪ Which pedagogical approaches are suitable?
- 3. Math-Bridge is a family of technologies made by a community of researchers ActiveMath-‐ EU Active Math Le-‐ ActiveM ath Math-‐ Bridge Math-‐Bridge+ MathCoach ATuF 2 2000 2004 Matheführer schein ATuF ALOE Mathe-‐ Brücke Math-‐Bridge final 2007 2009 2011 2013 ? eChalk
- 5. First Version of ActiveMath • Course Generation • User Model • Progress indicators • Multiple Choice Questions • CAS exercises
- 6. First Version of ActiveMath • Next Best Suggestion Engine • „Poor man‘s“ eye-‐ tracker „DFKeye“
- 7. Second Version of ActiveMath • Dashboard-‐style main screen • „better“ design • Open User Model
- 8. First Users of ActiveMath
- 9. Math-Bridge is a family of technologies made by a community of researchers ActiveMath-‐ EU Active Math Le-‐ ActiveM ath Math-‐ Bridge Math-‐Bridge+ MathCoach AtUF 2 2000 2004 Matheführer schein AtUF ALOE Mathe-‐ Brücke Math-‐Bridge final 2007 2009 2011 2013 ? eChalk
- 10. Matheführerschein (Driving License for Math) ▪ Matheführerschein Online helps preparing learners for college/ university ▪ It was initiated by FH Dortmund ▪ Content: wide range of school mathematics needed for University ▪ Fractions, Equations, Term Manipulation, Functions, Differentiation and Integration ▪ The pedagogical approach is constructivist, starting from complex real world problems ▪ ActiveMath interface was modified ▪ Specific strategy for interactive exercises was developed ▪ The ActiveMath possessed a library of terms with a novel structure (flavours and links to exercises) ! !
- 11. Matheführerschein • The system received positive reviews for its intuitive design and didactic approach • Matheführerschein is available online for wide public • Freshly enlisted students from FH Dortmund were recommended to use the system • Hundreds of Students tested their knowledge using the system • No records of learning effect !
- 12. Math-Bridge is a family of technologies made by a community of researchers ActiveMath-‐ EU Active Math Le-‐ ActiveM ath Math-‐ Bridge Math-‐Bridge+ MathCoach AtUF 2 2000 2004 Matheführer schein AtUF ALOE Mathe-‐ Brücke Math-‐Bridge final 2007 2009 2011 2013 ? eChalk
- 13. eChalk: Algebraic Geometry on a Smartboard ▪ This project connects three systems: ▪ ActiveMath ▪ Computer Algebra System Singular ▪ Smartboard technology eChalk ▪ A Course of Algebraic Geometry given by Prof. Schreyer ▪ Contents of a Course Book encoded in ActiveMath ▪ Handwriting recognition and Computer Algebra work together to help the lecturer manipulate interactive visualizations ▪ The Course was held at the Mathematics Faculty at Saarland University
- 14. Math-Bridge is a family of technologies made by a community of researchers ActiveMath-‐ EU Active Math Le-‐ ActiveM ath Math-‐ Bridge Math-‐Bridge+ MathCoach AtUF 2 2000 2004 Matheführer schein AtUF ALOE Mathe-‐ Brücke Math-‐Bridge final 2007 2009 2011 2013 ? eChalk
- 15. Le-ActiveMath: The next generation
- 16. Features of Le-ActiveMath • Tutorial Dialogue in exercises • Better design • Concept Mapping Tool • Elaborate pedagogical scenarios
- 17. Features of Le-ActiveMath • „Scrutable“ User Model
- 18. Example Usage of Le-ActiveMath Practical Calculus Course ! 238 Practical Calculus students, Edinburgh University, UK. Mean Age = 19 ! • 11 week course, 1 tutorial every fortnight. • Traditionally, tutorials and homework paper-‐ based. • Le Active Math used instead. • Content: University first year Calculus • Pre-‐recorded books authored for course and each homework/tutorial. à LeAM could be used in 3 homework/ tutorials. Source: Tim Smith
- 19. Tutorial Structure ▪ Before Tutorial ▪ Lecturer sets homework on LeActiveMath. ▪ Students complete exercises at home/computer lab. ▪ Answers automatically logged. ▪ Links in LeActiveMath between homework content and other content assist students. ▪ In preparation ▪ Admin Pages developed to allow tutors to view student progress. ▪ Reporting Tool produces reports on a group of user’s attempts at exercises. ▪ In Tutorial ▪ Students completed exercises and browsed the content if needed Source: Tim Smith
- 21. LeActiveMath Usage ▪ Expected regular usage ▪ Peak of usage prior to tutorials ▪ Increasing mean usage prior to exam. ▪ Observed very low usage. ▪ Most users were those recruited for in-depth tasks. ▪ Usage was mostly on exercises and searching for content. ▪ Advanced components rarely used. ! ▪ There were also some technical problems, so the usage statistics is not reliable Source: Tim Smith
- 22. ▪Users found navigation of the content easy. ▪Users liked the book metaphor, search tool, and hyperlinks. ▪But ▪ The content was often confusing, too scattered with jargon, and the difficulty level incorrect. ▪ They found the search tool too complicated e.g. they had to select too many options to find the content in a book. In-depth Evaluation: Summary Source: Tim Smith
- 23. In-depth Evaluation: Summary ▪Formula Editor ▪ Is seen as a useful tool ▪ But it is unintuitive, too particular in its syntax, and frustrates users. ▪Hints and feedback ▪ Learners find them useful ▪ But could have more levels of hints and always bottom out at solution. ▪Exercise Types ▪ Learners see the benefit of most types of exercises ▪ But prefer MCQ, SCQ, and computations without the input editor. Source: Tim Smith
- 24. Math-Bridge is a family of technologies made by a community of researchers ActiveMath-‐ EU Active Math Le-‐ ActiveM ath Math-‐ Bridge Math-‐Bridge+ MathCoach AtUF 2 2000 2004 Matheführer schein AtUF ALOE Mathe-‐ Brücke Math-‐Bridge final 2007 2009 2011 2013 ? eChalk
- 25. ActiveMath-EU: Dissemination and Exploitation of LeActiveMath
- 26. ActiveMath-EU: Using LeActiveMath in classroom ▪ ActiveMath usage for multilingual pre-service teachers ▪ In Charles University in Prague for pre-service teacher students learning math in Czech and English in parallel ▪ In Eötvös Lorand University in Budapest for pre-service teacher students learning math in Hungarian and German ▪ Other Sample Usage Scenarios ▪ Blended Learning in a classroom moderated by a teacher in Eötvös Lorand University Budapest ▪ Solving interactive Exercises in a secondary school in Germany ▪ Blended Learning and learning assignments with particular learning paths for pre- service teachers in Université Pierre Marie Curie, Paris 6 ▪ Blended-Learning with homework assignments at St. Michael College in the Netherlands (own content)
- 27. Math-Bridge is a family of technologies made by a community of researchers ActiveMath-‐ EU Active Math Le-‐ ActiveM ath Math-‐ Bridge Math-‐Bridge+ MathCoach ATuF 2 2000 2004 Matheführer schein ATuF ALOE Mathe-‐ Brücke Math-‐Bridge final 2007 2009 2011 2013 ? eChalk
- 28. ATuF and ALOE projects
- 29. ALOE Project • ALOE project investigated the Effects of erroneous examples in the domain of decimals • Several school experiments were conducted in Germany and U.S. • 6th grade, 7th grade, and 8th grade • Interactive exercises were solved in a classroom in teacher-‐ assisted exercise sessions • Pupils worked with fixed sequences of learning objects • General comments on the usage of the system • After just 1 hour of familiarization, pupils are able to cope with the system navigation and formula input • Intuitive user interfaces are important for school context • Good observations: • Students find and describe errors, but cannot correct ➢declarative vs. practical knowledge • Students solve similar exercises, but cannot correct errors ➢Memorized solution practice, but lack of deeper knowledge ! !
- 30. School Fraction Course and ATuF Project • A Fraction Course for School was authored in ActiveMath by a teacher (Mr. Kessler) • He used this course for teaching fractions in a secondary school in Saarbrücken for 2 Semesters • The Course was further reworked within the DFG Project ATuF (Adaptive Tutorial Feedback) • ATuF investigates various feedback strategies for interactive exercises, based on the feedback framework of Prof. S. Narciss • A structured user interface for solving interactive exercises in the domain of fractions was developed • Several feedback strategies have been tested with students • Lab experiments with about 200 students were conducted ! ! !
- 32. ALOE Users
- 33. Math-Bridge is a family of technologies made by a community of researchers ActiveMath-‐ EU Active Math Le-‐ ActiveM ath Math-‐ Bridge Math-‐Bridge+ MathCoach AtUF 2 2000 2004 Matheführer schein AtUF ALOE Mathe-‐ Brücke Math-‐Bridge final 2007 2009 2011 2013 ? eChalk
- 34. Math-Bridge
- 35. Math-Bridge: Intelligent Remedial Mathematics • The goal of the project was to create a European portal for mathematical bridging courses • The final product should be disseminated to the educational institutions and used for teaching • Project partners have used the system for teaching in their institutions, there is a community of associate partners • Leading Universities in Europe and Industrial Partners and Sub-‐ contractors have contributed to the project
- 36. Some Users of Math-Bridge ▪ Math-Bridge was used in bridging courses at Eötvös Lorand University for pre-service teachers ▪ HTW Saarland uses Math-Bridge in combination with Math-Coach System ▪ Universities of Kassel and Paderborn used Math-Bridge for Mathematics bridging courses for technical faculties ▪ University of Brandenburg used Math-Bridge for their Mathematics bridging course for Computer Scientists ▪ Math-Bridge is currently used at Leuphana University of Lüneburg in a Mathematics bridging course for economists.
- 37. Mathematics Bridging Course at Leuphana University Bridging-‐ course (7 Weeks) Pretest Posttest Blended-‐Learning Bridging Course (7 Weeks) Blended-‐Learning Bridging Course (4 Weeks) Lecture– Mathematics for Economics Exam Repeated Exam The first semester at Leuphana University (so-‐called Leuphana Semester) is divided into two halves: ! • The first half is devoted to introductory courses and bridging courses • In the second half some major Mathematics lectures build upon the introductory courses
- 38. Mathematics Bridging Course at Leuphana University Bridging-‐ course (7 Weeks) Pretest Posttest Blended-‐Learning Bridging Course (7 Weeks) Blended-‐Learning Bridging Course (4 Weeks) Lecture– Mathematics for Economics Exam Repeated Exam • Pretest determines the knowledge gaps • Bridging course in the first 7 weeks is using math-‐bridge and other technologies • Math-‐Bridge is used for information and training at home • Other teacher tools are used during the classes • Lecture materials are linked to Math-‐Bridge • Posttest shows the improvement for those who attended the first bridging course
- 39. Mathematics Bridging Course at Leuphana University Bridging-‐ course (7 Weeks) Pretest Posttest Blended-‐Learning Bridging Course (7 Weeks) Blended-‐Learning Bridging Course (4 Weeks) Lecture– Mathematics for Economics Exam Repeated Exam • A blended learning bridging course using Math-‐Bridge is given in the next 7 weeks • The main Mathematics lecture is running in parallel to the second bridging course, offering the students with difficulties to join right away and train with Math-‐Bridge system. • Another intensive blended-‐learning course using Math-‐Bridge is offered between two exams (duration 4 weeks)
- 40. How to teach it? Old and new Technologies for Mathematics Lecture 24.09.14 40 • Conflict: Blackboard vs. Computer & Projector • Blackboard: • Chalk supports arbitrary formula input and visualizations • Full freedom for improvisation with examples • Computer: • Power Point Slides: complex diagrams and animations • GeoGebra Animations: examples to touch • Intelligent Computer Algebra Systems • Commonly used solutions: • Use Smartboards to combine blackboard and computer • Use tablet computers connected to a projector
- 41. Our solution: E-Learning / E-Teaching Technologies ! ‣ Structured interfaces for teacher to interact with presented content ‣ Termania – tool for visualizing term manipulation ‣ GeoGebra ‣ Intelligent Learning Environment Math-Bridge ‣ VEMINT Portal Contents
- 42. First Bridging Course: Structure & Learning Materials 24.09.14 42 ! • Course: Bridging Course Mathematics for Economics • Number of students: max 250 • Lecture • Two times a week two hours each time • One book chapter per week (in total 6 Chapters) • Power Point Slides • Animations in the slides • External Animations • Learning materials • Book „Mathematics for Economics“ Chapters 1-‐6 • Slides including video recorded animations from the lecture • Additional materials in Math-‐Bridge • Animations in Youtube und GeoGebra portals as extra channels
- 43. Self-learning & Social Learning ▪ Micro-prelearning (Math-Bridge): ▪ Animated worked solutions (Math-Bridge, youtube) ▪ Training exercises with feedback (similar to homework exercises) ▪ Self-learning (Math-Bridge) ▪ Working with additional materials: ▪ Math-Bridge books, interactive exercises, (micro) course generation ▪ Social Browsing: ▪ Youtube channel of Math-Bridge ▪ One can browse related videos brought by youtube keyword matching ▪ Students can add own videos ▪ Browse GeoGebra Animation portal ▪ Animations from the lecture are uploaded and linked to ▪ Similar animations from GeoGebra portal can be browsed, they are automatically linked by common keywords 24.09.14 43
- 44. Math-Bridge Contents ▪ Each content book corresponds to a chapter of the course book ▪ The structure of each chapter is fixed and the students are suggested to follow particular learning paths, depending on their goals
- 45. 45 Interactive Power Point Slides =+b +a +b a+b=b+a a-b=a+(-b) +a -‐b -‐b +a a-(-b)+2a+b-a= a+b+2a+b-a= bereinigen +a +a +b = +2a +b -a +2a +2b
- 46. 46 Pascal´s Triangle 5 2 ! " # $ % & = 5! 2!3! = 4⋅5 2 =10 5 2 ! " # $ % & = 4 1 ! " # $ % &+ 5 2 ! " # $ % & = 4 + 6 =10
- 47. Term-manipulation- and Animation tool „Termania“
- 50. Geogebra Portal: Bridging Course Collection 24.09.14 50 Visualizations and animations of various concepts
- 51. Youtube channel: Math-Bridge Leuphana 24.09.14 51 Videos of Term-‐Manipulation
- 52. Blended-Learning Bridging Course (using Math-Bridge) running in parallel to the main Mathematics Lecture ! ▪ Number of Students: max 60 ▪ Course is given in a computer equipped seminar room ▪ Topics: ▪ Static and Personalized Courses in Math-Bridge corresponding the the contents of Chapters 1-6 of the reference book ▪ Visualizations and Examples ▪ Special examples for economists ▪ Animations (GeoGebra) ▪ Exercises: ▪ Demonstration of worked solutions ▪ interactive exercises in Math-Bridge 24.09.14 52
- 53. Blended-Learning Scenario: „Teach & Train“ ! ‣ Introduction to a lecture topic ‣ Definitions, interactive examples using Termania and GeoGebra ! ! ‣ Solving problems in Math-Bridge ‣ Interactive exercises with feedback and hints ‣ Self-assessment exercises solved on the paper and compared to the master solution in the system ‣ Multimedial exercises correct/wrong feedback
- 54. Students about using Math-Bridge ▪ Course Materials are easy to browse, intuitive and well structured ▪ However ▪ Most of the students did not notice that the search function exists ▪ Not all chapters of static books were structured in the same way, which introduced some confusion ▪ Most of the students did not use the micro course generation feature, even after explicitly introducing them to the feature ▪ Solving interactive exercises was too much effort for some students ▪ Formula editor is complex and slow means of entering formulas ▪ Many students prefer to write the solution of the paper and submit the final result into the system ▪ Multiple choice questions, graphical puzzles and one step exercises with simple input were more popular
- 55. Further Steps ! ‣ Automatic Generation of Termania Examples ‣ How? ‣ Use integrated domain reasoners to generate the annotated solutions ‣ Why do we need this? ‣ The teacher can generate on the fly a worked solution of an improvised example and show it right away ‣ Automatic Integration of the lecture slides in the system ‣ Generation of annotated e-Lectures ‣ Automatic annotation of parts of videos with links to corresponding concepts ‣ Evaluation of the learning effect of the „Teach & Train“ strategy and comparison to the classical lecture
- 56. Future?
- 57. 24.09.14 57 Classroom of the future (1969, Shōnen Sunday magazine) E-‐Lecture Working with Math-‐Bridge Flag Feedback
- 58. 24.09.14 58 Classroom of the future: the future is NOW!
- 59. Thanks! The Mathematical Bridge, Cambridge, England