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

Outline ¡ Background ¡ MAG (Mathematics Assessment Grid) ¡ MAML ¡ MAEdit Outline ¡ Background ¡ MAG (Mathematics Assessment Grid) ¡ MAML ¡ MAEdit

1. Background 1. Background

Introduction to WME: a Web-based Mathematics Education system WME is a modern distributed system Introduction to 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.

The WME Concept The WME Concept

The WME Architecture WME : Web-based Mathematics Education Me. ML: Mathematics Education Markup Language The WME Architecture WME : Web-based Mathematics Education Me. ML: Mathematics Education Markup Language MESP: Mathematics Education Service Protocol

The WME Pilot Project The WME Pilot Project

Example Example

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

Mathematics Assessment Grid(MAG) ¡ MAG( Mathematics Assessment Grid) system aims to build a grid 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 create their test paper through MAG.

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

The main research 1. Build a very large, virtual Mathematics Assessment databases (convert) 2. The main research 1. Build a very large, virtual Mathematics Assessment databases (convert) 2. Build a descriptive specification of mathematics assessment question and a xmlbased Mathematics Assessment Markup Language (MAML) 3. Research on and develop a web-based MAML Editor---MAEdit 4. Create a Mathematics Assessment Grid system

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

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

3. MAML Mathematics Assessment Markup language 3. MAML Mathematics Assessment Markup language

Problem: How to search demanded question and produce a test paper? In MAG, we 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

What is MAML is an Xml application for describing mathematical assessment question. The goal What is 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.

Mathematics Assessment Markup Language ¡ MAML aims to provide effective and expressive means for Mathematics Assessment Markup 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 embed Math. ML, SVG to process math notation and graph.

Mathematics Assessment Markup Language Category Elements Question Content questionset, question , qbody , qobject Mathematics Assessment Markup Language Category Elements Question Content questionset, question , qbody , qobject , qchoice , qanswerblank , qformula , qlocation，qhint Question Description qtopic , qscope , qdifficulty , qsource , qauthor, qdate , qanswer , qscore , qnote Test Paper paper , ptitle , pdifficulty , pscore , pnote , psection There are 23 Elements in MAML and about 100 Attributes.

Advantage of MAML ¡ ¡ MAML provide expressive description information to an assessment question. 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 databases and covert into MAML data.

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）∪ 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）∪

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 Example 集合，集合的交，集合的并 高中一年级 王明 1/15/2005 C 2 1 91年高考 理解集合、子集、补庥、交集、并集的概念 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 ( M ∩ P ) ∩ S ( M ∩ P ) ∪ S

Example (cont) <qchoice name=C caption=(C)> <mrow> <mo>(</mo> <mi>M</mi> <mo>∩ </mo> <mi>P</mi> <mo>)</mo> </mrow> <mo>∪ Example (cont) ( M ∩ P ) ∪ S &Over. Bar; ( M ∩ P ) ∪ S &Over. Bar;

Example (cont. )

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

4. 1 MAEdit—a web-based question editor u u MAEdit is a web-based WYSIWYG Mathematics 4. 1 MAEdit—a web-based question editor u u MAEdit is a web-based WYSIWYG Mathematics question editor. MAEdit is also a GUI Editor of MAML

presentation Typeset，holistic framework content Separated, per-question，store in database，online test presentation Typeset，holistic framework content Separated, per-question，store in database，online test

The main function of MAEdit is a integrated question edit environment. Following is main The main function of MAEdit is a integrated question edit environment. Following is main function of MAEdit： ¡ Question edit, define format 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

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

Advantage of MAEdit u web-based, online u presentation and content u provide math graph Advantage of MAEdit u web-based, online u presentation and content u provide math graph and equation u expressive typeset function u computer-based examination and written examination

4. 2 Math. Edit. M Problem: How to input and display mathematics formula and 4. 2 Math. Edit. M Problem: How to input and display mathematics formula and mathematics notation in computer and web? u

Math. Edit. M ¡ ¡ Math. ML( mathematical markup language ) has become very Math. Edit. M ¡ ¡ Math. ML( mathematical markup language ) has become very important specification of showing Math equation on web Math. Edit ---A web-based Math. ML GUI Editor

Architecture of Math. Edit. M MML or Blank Math. Edit. M DOM Parser DOM Architecture of Math. Edit. M MML or Blank Math. Edit. M DOM Parser DOM Tree Command processor MML Layout Manager WYSIWYG User Interface

Math. Edit. M Math. Edit. M

4. 3 Geo. SVG ¡ ¡ An SVG Based Tool for Plane Geometry Geo. 4. 3 Geo. SVG ¡ ¡ An SVG Based Tool for Plane Geometry Geo. SVG is designed as a totally Web-based DGS and implemented in SVG.

Geo. Svg (cont. ) Geo. Svg (cont. )

Conclusions ¡ MAG is an open system, which integrates respective question resource and provides Conclusions ¡ MAG is an open system, which integrates respective question resource and provides a very large resource databases. ¡ MAML is standard math assessment 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

WME Working Group ¡ ¡ ¡ ¡ Prof. Paul S. Wang (ICM/Kent) Prof. Li 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)

Thank you！ Thank you！