Theoretical Framework

Appendix B

Categories

Content: algebra

• 
  Multistep exercises, process feedback
  
• 
  Sound representations and operations (!!!): mathematical and cognitive fidelity
  
• 
  Possibility of using more than one representation;
  Multiple representations can help better understanding of concepts.
  
• 
  Randomization
  
• 
  Wysiwyg formulas and input editor
  
• 
  Integrated CAS
  
• 
  Level of competencies.
  
• 
  Gradual difficulty curve. Coherence and balance.
  

Technical: tool

• 
  Results and answers should be stored and accessible for both student and teacher.
  
• 
  Sharability and use of standards (questions and units)
  
• 
  Easy authoring for teachers (because teachers are often “neglected learners” (Sangwin & Grove, 2006))
  
• 
  Scoring as a game, for motivation.
  
• 
  Other tools available
  
• 
  Performance
  
• 
  Possibility of using multimedia
  
• 
  Ease of use
  
• 
  Customizability by teacher
  
• 
  Contexts.
  
• 
  Prerequisites server and client-side
  
• 
  Stability
  
• 
  Languages
  

Assessment

• 
  It should provide feedback at the right moment
  
• 
  Several "modes" ranging from diagnostics to exam. “Zoom” level. Several training modes (from practice to exam).
  
• 
  Enables a qualitative analysis of student work to reap the benefits of formative evaluation;
  
• 
  on a meta-level scoring should also be implemented to allow for quantitative data;
  
• 
  A student should be able to correct an answer. Possibility to correct an answer
  
• 
  The combination of elements from both summative and formative assessment should enable a teacher to adapt better to student's learning.
  
• 
  Go from feedback only to weak formative assessment or even moderate. This has a lot to do with the state of the art. (level of feedback)
  
• 
  The 11 conditions under which assessment might support student learning and improve chances of success.
  
• 
  Seven principles of good feedback practice.
  
• 
  Open questions providing an expressive environment
  
• 
  Halfopen/closed questions. Open/closed questions
  
• 
  Functional feedback on the answers
  Formative assessment
  
• 
  Feedback on the process`
  
• 
  Global feedback: mastery level within curriculum
  
• 
  Possibility of providing hints
  
• 
  One answer versus multiple steps
  
• 
  Storage of answers
  
• 
  Storage of the process
  
• 
  Question management
  
• 
  Adaptivity
  

General

• 
  Licenses
  
• 
  User base for content availability
  
• 
  Continuity
  

Appendix C

Minimal requirements

• 
  Webbased: we find it essential that using the tool can be anytime, anyplace, anywhere, using just a web browser.
  
• 
  Ease of authoring, configurable: it should be possible to add own content.
  
• 
  Actively developed: it is important that the tool is supported and has some sort of continuity.
  
• 
  Minimal math support: formulas should be displayed correctly and support basic mathematical operations.
  
• 
  Storage of progress: it should be possible to store results, so students can come back later, if necessary.
  

DITwis

Name	DITwis
Date	20080217
Version	DIT5
Key words	Too difficult too author. No multiple step solutions. No CAS in the background. Web-based javascript. SCORM possible. http://wiskunde.stmichaelcollege.nl/DITwis/
Screenshots
Doesn’t adher to minimal requirement	too difficult to author needed functionality

Algebra Tutor

Name	Algebra Tutor
Date	20080217
Version	Unknown
Key words	Interesting Eliza-type tutor. There seems to be no authoring option. Only algebra, no graphics. http//www.algebratutor.org
Screenshots
Doesn’t adher to minimal requirement	Not possible to add own questions

Math Xpert:

Name	Math Xpert
Date	20080217
Version	Unknown
Key words	Standalone windows. Not web-based. But with steps. 89.95 dollar per license for the three topics covered. This looks like a suitable program, but it’s not web-based. This would hinder the ‘anytime-anyplace’ criterium. http://mathware.stores.yahoo.net/mathpert.html
Screenshots
Doesn’t adher to minimal requirement	Not web-based.

Aplusix

Name	Aplusix
Date	20080217
Version	II
Key words	There are four modes: training, test, self-correction, observation. Two dimensional editor. Scores. 400 patterns of exercises. A disadvantage: it’s not web-based, so every students needs a copy of this software. Replay mode for looking at the process. http://aplusix.imag.fr/en/index.html Distributor is http://www.rhombus.be/index1.html . For 600 euro there is a sitewide license. As far as I can see then you need to pay 10 euro per student.
Screenshots
Doesn’t adher to minimal requirement	Not web-based

L’Algebrista

Name	L’Algebrista
Date	20080217
Version	Unknown
Key words	http://www-studenti.dm.unipi.it/~cerulli/LAlgebrista/index.php?lang=ita doesn’t work. http://telearn.noe-kaleidoscope.org/warehouse/Cerulli-M-Mariotti-M-2000-bis.pdf and http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG8/TG8_Cerulli_cerme3.pdf are papers about this program.
Screenshots
Doesn’t adher to minimal requirement	URL doesn’t work

webMathematica

Name	webMathematica
Date	20080217
Version	2
Key words	Only seems to provide a frontend for the mathematica program. There are some quizzes on algebra. I’m not impressed. There also is a license fee. http://www.wolfram.com/products/webmathematica/index.html
Screenshots
Doesn’t adher to minimal requirement	No assessment software, storage of results.

Wiris

Name	Wiris
Date	20080218
Version	2
Key words
Screenshots
Doesn’t adher to minimal requirement	No assessment software, storage of results.

AiM: Assessment in Mathematics

Name	AiM: Assessment in Mathematics
Date	20080217
Version	3.0
Key words	This open source program is a . Maple is running in the background. This is probably –Maplesoft has it’s Maple TA- why it has been discontinued. The developers wanted a similar program, based on open source CAS. See STACK and CABLE http://maths.york.ac.uk/aiminfo/
Screenshots
Doesn’t adher to minimal requirement	Software discontinued

CABLE

Name	CABLE
Date	20080217
Version	1.0
Key words	Similar to a very first version of STACK and following up on the AiM program. In the background the open source CAS axiom runs. http://www.cable.bham.ac.uk/
Screenshots
Doesn’t adher to minimal requirement	Software discontinued

Hot potatoes

Name	Hot Potatoes
Date	20080217
Version	6.2
Key words	Quiz software Unfortunately the mathematics support is quite bad. By using SCORM tracking scores within a VLE is possible. No support for a CAS. http://web.uvic.ca/hrd/halfbaked/
Screenshots
Doesn’t adher to minimal requirement	No good math support

Question Mark Perception

Name	Question Mark Perception
Date	20080217
Version	Unknown
Key words	Is assessment software with no particular support for CAS related questions. Use of MathML is possible. http://www.questionmark.com/. Example at http://www.questionmark.com/us/tryitout_k12.aspx
Screenshots
Doesn’t adher to minimal requirement	No good math support

Wintoets

Name	Wintoets
Date	20080217
Version	4.0 WEB
Key words	Is assessment software with no particular support for CAS related questions. Dutch. http://www.drp.nl/Producten/WinToets-40-WEB.html
Screenshots
Doesn’t adher to minimal requirement	No good math support

Moodle quiz module with extensions

Name	Moodle quiz module
Date	20080217
Version	All moodle versions
Key words	Limited question types but can be extended with STACK (see appendix C) http://www.moodle.org . Communication through the OPAQUE protocol: http://docs.moodle.org/en/Development:Open_protocol_for_accessing_question_engines As this technology actually uses STACK in the default installation, we will look at the possibilities. Moreover: Moodle is required for STACK.
Screenshots
Doesn’t adher to minimal requirement	No math support (CAS)

Wallis

Name	Wallis
Date	20080217
Version	Unknown
Key words	http://www.maths.ed.ac.uk/~wallis/
Screenshots
Doesn’t adher to minimal requirement	Software not maintained

WebWork

Name	WebWork
Date	20080217
Version	2.4.1
Key words	WeBWorK is a web-based interactive system designed to make homework in mathematics and the sciences more effective and efficient. It can be used with moodle. http://webwork.maa.org/moodle/
Screenshots
Doesn’t adher to minimal requirement	Difficult to install and use

Cognitive Tutor: http://www.carnegielearning.com/products.cfm

Screenshot: http://www.carnegielearning.com/products_algebraI.cfm

No authoring function.

 

Algebra Buster: http://www.algebra-online.com/Solving%20systems%20of%20equations.htm

Same: Algebrator > http://www.softmath.com/algebra-help/free-printable-linear-equation.html

 

Ti: http://www.t3ww.org/pdf/TII.pdf

http://education.ti.com/educationportal/sites/US/productDetail/us_ti_interactive.html

 

Maple TA: http://mapleta.can.nl/classes/kamminga/

http://www.mathmatch.nl/

GOSE VRAGEN OM TOEGANG

 

STACK: http://stack.bham.ac.uk/course/view.php?id=3

There is a lot of higher education material.

Appendix D

Maple TA

Name	Maple TA
Date
Version
Key words
Screenshots
Doesn’t adher to minimal requirement

TI interactive

Name	TI interactive
Date
Version
Key words
Screenshots
Doesn’t adher to minimal requirement

Digital Mathematical Environment

Name	Digital Mathematical Environment
Date
Version
Key words
Screenshots
Doesn’t adher to minimal requirement

Activemath

Name	Activemath
Date
Version
Key words
Screenshots
Doesn’t adher to minimal requirement

STACK

Name	STACK
Date
Version
Key words	In the new version 2.0 of STACK Moodle is required. Installing STACK is quite technical.
Screenshots
Doesn’t adher to minimal requirement

Wims

Name	WIMS
Date	20080217
Version	3.57 (3.62 released)
Key words	http://wims.unice.fr/ Exercises can be made by using Createxo. Power modules are also possible, but require more administrator rights. For dutch content: http://wims.math.leidenuniv.nl/wims -> studentenbereik -> Gestructureerde aanpak algebraische vaardigheden (administrator: Relinde Jurrius) username test, password gaav
Screenshots
Doesn’t adher to minimal requirement

Core-Plus Mathematics

Appendix E

Matrix

References

1 Information and Communication Technology. When use “tools” I mean “ICT tools”.

2 Digital Mathematical Environment, http://www.fi.uu.nl/dwo/en/

3 Wiskunde En Les Praktijk, dutch project that was aimed at using applets in an algebra curriculum