Initial Design of Mathematics Assessment Grid

1. Initial Design of MathematicsAssessment Grid Wei Su, Guanyu Li, YanJuan Zhao, Lian Li School of Information Science and Engineering, Lanzhou University, China suwei@lzu.edu.cn http://iccm.lzu.edu.cn

2. Outline • Background • MAG (Mathematics Assessment Grid) • MAML • MAEdit

3. 1.Background

4. Introduction to WME WME: a Web-based Mathematics Education system WME is a modern distributed system on the Web for mathematics education. The WME system conforms to open standards, works with regular browsers, delivers integrated and complete lessons, enables easy customization, provides systematic access to client-side and server-side support, and allows these independently developed components to interoperate seamlessly.

5. The WME Concept

6. The WME Architecture WME : Web-based Mathematics Education MeML: Mathematics Education Markup Language MESP: Mathematics Education Service Protocol

7. The WME Pilot Project

8. Example

9. 2. The Concept of MAG Mathematics Assessment Grid（MAG）

10. Mathematics Assessment Grid(MAG) • MAG( Mathematics Assessment Grid) system aims to build a grid which can integrate the decentralized mathematics question resource databases into a very large virtual databases of Mathematics questions. Users can acquire their demanded assessment questions and createtheir test paper through MAG.

11. The MAG Concept User MAG Access Integration（Math Assessment ML） convert File data Database Web data Distributed Database Application Data MAML-based data

12. The main research • Build a very large, virtual Mathematics Assessment databases (convert) • Build a descriptive specification of mathematics assessment question and a xml-based Mathematics Assessment MarkupLanguage (MAML) • Research on and develop a web-based MAML Editor---MAEdit • Create a Mathematics Assessment Grid system

13. JavaScript Dom Web Browser SVG MathML The System Architecture MAML Pages MAG server HTTP Server MAG server MAML Interpreter convert Other Math Question resource MAG server MAG: Mathematics Assessment Grid MAML: Mathematics Assessment Markup Language

14. 1 MAG Server(S1) MAG Server (S6) … Math question provider 4 5 2 4 5 Resource manage Job manage Data manage User Interface 3 6 User Using MAG 1.Edit and deploy math question (MAML) 2.Register and publish the service resource (UDDI API) 3.Request for a test paper 4. schedule Job to the respective MAG resources for execution 5.Retrieve MAML data to Data Manager and produce a test paper 6.Return the result to user

15. 3.MAML Mathematics Assessment Markup language

16. Problem: How to search demanded question and produce a test paper? In MAG, we search questions and organize test paper according to the description of questions. a descriptive specification of mathematics assessment question

17. What is MAML MAML is an Xml application for describing mathematical assessment question. The goal of MAML is to enable mathematical assessment question to be served, received, and processed on the World Wide Web and MAG, as HTML has enabled this functionality for text.

18. Mathematics AssessmentMarkup Language • MAML aims to provide effective and expressive means for structuring and delivering mathematics assessment content on the Web. • MAML supports authoring, storing, processing, and exchanging mathematics assessment question in MAG system. • MAML is a XML-based language. It can embedMathML, SVG to process math notation and graph.

19. Mathematics Assessment Markup Language There are 23 Elements in MAML and about 100 Attributes.

20. Advantage of MAML • MAML provide expressive description information to an assessment question. MAG system can search test question from web based on question description • The system can retrieve test question from heterogeneous databasesand covert into MAML data.

21. Example • 如图，I是全集，M、P、S是I的3个子集，则阴影部分所表示的集合是（A）（M∩P〕∩S　　　　　　（B）（M∩P）∪S（C〕（M∩P）∩　　　　　　 （D〕（M∩P）∪

22. Example <question type=singlechoice> <qtopic>集合，集合的交，集合的并</qtopic> <qscope>高中一年级</qscope> <qauthor>王明</qauthor> <qdate>1/15/2005</qdate> <qanswer>C</qanswer> <qscore>2</qscore> <qdifficulty>1</qdifficulty> <qsource>91年高考</qsource> <qnote>理解集合、子集、补庥、交集、并集的概念</qnote> <qbody> <qobject type=text> 如图，I是全集，M、P、S是I的3个子集，则阴影部分所表示的集合是 </qobject> </qbody> <qchoice name=A caption=(A)> <mrow> <mo>(</mo> <mi>M</mi> <mo>&cap;</mo> <mi>P</mi> <mo>)</mo> </mrow> <mo>&cap;</mo> <mi>S</mi> </qchoice> <qchoice name=B caption=(B)> <mrow> <mo>(</mo> <mi>M</mi> <mo>&cap;</mo> <mi>P</mi> <mo>)</mo> </mrow> <mo>&cup;</mo> <mi>S</mi> </qchoice>

23. Example (cont) <qchoice name=C caption=(C)> <mrow> <mo>(</mo> <mi>M</mi> <mo>&cap;</mo> <mi>P</mi> <mo>)</mo> </mrow> <mo>&cup;</mo> <mover> <mi>S</mi> <mo>&OverBar;</mo> </mover> </qchoice> <qchoice name=D caption=(D)> <mrow> <mo>(</mo> <mi>M</mi> <mo>&cap;</mo> <mi>P</mi> <mo>)</mo> </mrow> <mo>&cup;</mo> <mover> <mi>S</mi> <mo>&OverBar;</mo> </mover> </qchoice>

24. Example (cont.) <qobject type=svg> <svg id="svg" width="400" height="300"> <ellipse style="fill:rgb(255,255,255);fill-opacity:1;stroke:rgb(0,0,0);stroke-opacity:1;" cx="154" cy="130.5" rx="40" ry="38.5" id="ellipse" transform="matrix(1,0,0,1,-9.24,-0.84)" /> <ellipse style="fill:rgb(255,255,255);fill-opacity:0;stroke:rgb(0,0,0);stroke-opacity:1;" cx="154" cy="130.5" rx="40" ry="38.5" id="ellipse2" transform="matrix(1,0,0,1,21.01,30.25)" /> <ellipse style="fill:rgb(255,255,255);fill-opacity:0;stroke:rgb(0,0,0);stroke-opacity:1;" cx="154" cy="130.5" rx="40" ry="38.5" id="ellipse1" transform="matrix(1,0,0,1,47.06,-2.52)" /> </svg> </qobject> </question>

25. 4. MAEdit ---A web-based question editor

26. 4.1 MAEdit—a web-based question editor • MAEdit is a web-based WYSIWYG Mathematics question editor. • MAEdit is also a GUI Editor of MAML

28. The main function of MAEdit MAEdit is a integrated question edit environment. Following is main function of MAEdit： • Question edit, defineformat of question • Mark question (question markup) • Create, insert and edit math graph • Insert and edit Math formula and notation • Add question description • Edit MAML • Edit test paper

29. MAML Design Preview Draw math graph QuestionMarkup Mark Question Insert and edit Math formula Switch to code, preview Question description

30. Advantage of MAEdit • web-based, online • presentationand content • provide math graph and equation • expressive typeset function • computer-based examination and written examination

31. 4.2 MathEditM • Problem: How to input and display mathematics formula and mathematics notation in computer and web?

32. MathEditM • MathML(mathematical markup language ) has become very important specification of showing Math equation on web • MathEdit ---A web-based MathML GUI Editor

33. MML or Blank DOM Parser MathEditM MML DOM Tree Command processor Layout Manager WYSIWYG User Interface Architecture of MathEditM

34. MathEditM

35. 4.3 GeoSVG • An SVG Based Tool for Plane Geometry • GeoSVG is designed as a totally Web-based DGS and implemented in SVG.

36. GeoSvg (cont.)

37. Conclusions • MAG is an open system, which integrates respective question resource and provides a very large resource databases. • MAMLis standard mathassessment markup language，which is better for transferring math question among different databases and displaying on web. • Web-based mathematics Editor—MAEdit provide typeset (include math graph and notation ) and online test • MAG can search Math question in MAML file on web and produce a test paper

38. WME Working Group • Prof. Paul S. Wang (ICM/Kent) • Prof. Li Lian(李廉，Lanzhou University, PRC) • Prof. Michael Mikusa (College of Education/Kent) • Mrs. Grace Dorene Ellis (Kimpton Middle School) • Mrs. Katie Jones (Lake Middle School) • Annie Jedick (College of Education/Kent) • Mr. David Chiu (ICM/Kent) • Mr. Xun Lai (ICM/Kent) • Dr. Xiao Zou (ICM/Kent) • Mr. Saleh Al-shomrani (ICM/Kent) • Mr. Kahraman Cem Karadeniz (Gem) (ICM/Kent) • Mr. Adnan Eshaque (ICM/Kent) • Mr. Su Wei （苏伟，Lanzhou University, PRC) • Mr. Li Guanyu （李冠宇，Lanzhou University, PRC) • Mrs. Zhao yanjuan (赵燕娟，Lanzhou University, PRC) • Mrs. Jing Ke (景珂，Lanzhou University, PRC)

39. Thank you！