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
Not considered: WebLearn from RMIT Melbourne, mathxl from Addison-Wesley, Algebra Interactive, Core-Plus Mathematics
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
Calmaeth
Name
Calmaeth
Date
20080229
Version
Unknown
Key words
https://calmaeth.maths.uwa.edu.au/
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.
Because of the integration with moodle we included this in the matrix, even though one minimal requirement hadn’t been met.
http://www.mathsformore.com/
http://www.wirisonline.net/
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 not maintained
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/
