[Maths-Education] Re: ICT in mathematics

[David H Kirshner]

I'm enjoying this thread. 

To be fair, Ken Koedinger, lead developer of the software, is a bona
fide cognitive scientist who has published a variety of academic papers
on the cognitive theory involved, in addition to publications on the
effectiveness of the tutor. And even the latter publications have been
in peer review academic journals. Still, it would be interesting to know
if "independent" evaluations of the effectiveness have been undertaken
and published. 

There is some software on the market now that seems to be effective in
raising students' test scores in comparison with standard classroom
instruction. For instance, at Northern Arizona University, the college
algebra course is taught through an online facility that 

"promote[s] active and collaborative learning, address the diverse range
of student learning styles and permit acceleration. It will use ALEKS, a
comprehensive instructional software and course management system that
individualizes assessment and learning. ALEKS is Web-based, allowing
students to access course materials at anytime from anyplace, and can be
customized to meet student and course needs. As a supplement to ALEKS,
NAU will also use Thinkwell, a video-based mathematics software program
that uses highlighted worked examples and video lectures for students
who learn better in this mode."
(http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm)

However, it is clear that the program's effectiveness primarily is
related to its effective provision of practice problems and immediate
feedback. In short, it promotes learning of skills through repetitive
practice in the behaviorist tradition.

I've looked at the Cognitive Tutor, and it's a more complex and
ambitious project. The Tutor functions through a multidimensional model
of expertise that it uses to update a student model, and thereby
determine what kinds of problems and assistance would best benefit the
student. It is not so straightforward an analysis as to whether what is
being promoted is skills through practice (in a sophisticated way), or
something more akin to what we would consider as mathematical concepts. 

The Cognitive Tutor is based on the ACT-series of acquisition models
developed by John Anderson and company at Carnegie Melon--in fact, Ken
was a student of his, and is now a frequent collaborator. The ambiguity
of the Tutor in terms of its learning modalities is reflected also in
the status of the ACT theories. Anderson (2005) would be a good source
to begin to answer those questions, and Anderson (2007) includes an
interesting discussion of the general issue of the kind of learning
addressed in the ACT theories. 

David Kirshner

Anderson, J. R. (2005). Human symbol manipulation within an integrated
cognitive architecture. Cognitive Science, 29, 313-341. [algebraic
symbol skills]
Anderson, J. R. (2007). How can the human mind occur in the physical
universe?. Oxford University Press.




-----Original Message-----
From: maths-education-bounces at lists.nottingham.ac.uk
[mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of
Alan Rogerson
Sent: Friday, March 04, 2011 10:10 AM
To: Mathematics Education discussion forum
Subject: [Maths-Education] Re: ICT in mathematics

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Dear Dylan,

What you say below does not in any way alter the fact that what you 
actually recommended to Sarah were reports on a webpage produced by a 
commercial company. That is the problem. You say something is "one of 
the best researched" but we need to know when and by whom? It is not the

quantity of research that counts, rather its quality.

Please note, I am not making any judgement about the actual research 
which you call "original" nor did I say that this research is some how 
invalidated by being used by a commercial company. Let's say for the 
sake of argument, that  all this research could be validated, and also 
note that some of the reports on the Carnegie.inc webpage were (as we 
know) from Carnegie Mellon University itself, and may have even 
pre-dated the formation of Carnegie.inc, I do hope you can see that this

does not change the problem? "Selective quotation" is still a real 
hazard, what company after all will quote research critical of its own 
products?

We know only too well the much bigger and much more serious debate going

on about so-called academic research being funded, or supported, (or of 
course suppressed!) by drug companies. Companies are in business to make

money, so we can hardly use them, or the reports they quote, as 
objective exemplars of "research". The contrast is between reports which

clearly have no such bias, and those which are at risk of being biassed.

Surely we cannot say "third party evaluations... would be better", 
surely you mean essential? We know from basic statistics that biassed 
evidence, when we can  not attach boundaries to the bias, , is, and must

be, useless (not second best). We all know the story of the millions of 
telephone calls surveyed  that failed to predict the next President of 
the USA....?

Please also note that there is absolutely no bias (or specific 
accusations) against Carnegie.inc in particular here, it is a purely 
general point that is being made.

The only remaining problem, and somewhat insoluble, is the one Douglas 
Butler has just mentioned.

C'est la vie, c'est la ICT.

Best wishes,
Alan




On 04/03/2011 15:52, dylanwiliam at mac.com wrote:
> Alan: Sarah asked specifically for studies that showed the impact of
ICT on attainment, and the Cognitive Tutor is one of the best researched
pieces of software for mathematics education.  While Carnegie Learning
is a commercial company that has taken over marketing and distribution
of the products generated by the people who developed the Cognitive
Tutor, the research itself is very solid (and much of it dates from
before Carnegie Learning became involved). I agree that third party
evaluations, such as those undertaken by Mathematica, would be better,
and of course educationalists should evaluate the merits of the studies,
but the fact that the research is now being used to support a commercial
enterprise does not invalidate the original findings.
>
> Dylan


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