Theoretical Framework



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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

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
frame30

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.

frame31

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

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

frame32

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.

frame33

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

frame34

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



TI interactive


Name

TI interactive

Date

20080229

Version




Key words

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

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

Screenshots



Doesn’t adher to minimal requirement

No registration for assessment



Cognitive Tutor


Name

Cognitive Tutor

Date

20080229

Version

Unknown

Key words

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

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



Screenshots



Doesn’t adher to minimal requirement

No authoring function.




Algebra Buster


Name

Algebra Buster / Algebrator

Date

20080229

Version

Unknown

Key words

Looks nice.

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

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

Screenshots




Doesn’t adher to minimal requirement

Not web-based




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