[Maths-Education] Re: ICT in mathematics

[Sven Trenholm]

Re: NCAT
New to this thread...  I'm a PhD student at the Mathematics Education Center of Loughborough University (focused on mathematics e-learning in the higher education sector).  In 2010 I arrived "off the boat" from upstate NY where I taught for over 10 years at the American junior college level.

I've attended an NCAT workshop in the US and have followed their progress over the last decade.  They have a sizeable focus on introductory level mathematics courses.  Bill Gates recently put some of his money behind their work in "transforming" developmental mathematics offerings (which traditionally have failure rates around 40-60%).  I am very interested in what they are doing given, on the surface, it appears to be successful for the specific introductory level large enrollment mathematics course context.  Of course "success" may be well defined in terms of financial savings but not so well defined in terms of learning.  In any case the movement (if you can call it that) appears to be picking up momentum. 

My question is this.  After just over 10 years of work, the only peer-reviewed article, I am aware of, is a 2008 conference proceedings paper (citation below).  For those familiar with NCAT, how much do you think this may be attributable, as I believe NCAT would attest, to the "inherent conservatism" in higher education (and perhaps the disciplinary culture of mathematics, in particular)?  I don't necessarily believe that what they are doing is primarily instruction via repetitive practice...   

Sven

   
Greenberg, W., & Williams, M. (2008). New pedagogical models for instruction in mathematics. Mathematical Modeling, Simulation, Visualization and e-Learning, 4, 361-371. 

Also, for those interested...(think tank paper)
Miller, B. (2010). THE COURSE OF INNOVATION: Using technology to transform higher education.  Education Sector Reports




________________________________________
From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of David H Kirshner [dkirsh at lsu.edu]
Sent: Friday, March 04, 2011 4:57 PM
To: Mathematics Education discussion forum
Subject: [Maths-Education] Re: ICT in mathematics

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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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