=Paper=
{{Paper
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|storemode=property
|title=Crowdsourcing a Personalized Learning Environment for Mathematics
|pdfUrl=https://ceur-ws.org/Vol-709/paper02.pdf
|volume=Vol-709
|dblpUrl=https://dblp.org/rec/conf/ectel/Corneli10
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==Crowdsourcing a Personalized Learning Environment for Mathematics==
https://ceur-ws.org/Vol-709/paper02.pdf
Crowdsourcing a Personalized Learning
Environment for Mathematics
Joseph Corneli
Knowledge Media Institute, The Open University, Milton Keynes, UK,
j.a.corneli@open.ac.uk,
WWW home page: http://metameso.org/~joe
Abstract. Can we build a semantically adaptive personal learning envi-
ronment that helps people learn mathematics and that meets reasonable
criteria for sustainable growth and development? This is question that
applies at the interface between participatory social media and interac-
tive, adaptive, “knowledge media”. Ten years ago, no one had heard of
Wikipedia. Perhaps in another ten, P2PU will be as popular as my home
institution, The Open University. A wide range of stakeholders in educa-
tion are surely curious to know why, or why not, and what this may mean
for their careers. Aside from the possible social significance of the ques-
tion, I anticipate that the personal learning environment (PLE) approach
will provide an interesting stream of use data, including implicit and ex-
plicit information about how people learn mathematics. This opportu-
nity to look in detail at learning behaviour in open, online, participatory,
educational spaces is quite new. My project will combine socio-cultural
analysis, technical development work, and datamining techniques to help
support both individualized learning and ongoing system development.
Key words: crowdsourcing, personal learning environments, mathemat-
ics
1 Roadmap
How do people learn mathematics? What motivates people to learn in one way
or another, given that it’s not often easy? Here we recall Euclid’s warning: “there
is no Royal Road to geometry.” Even so, we can imagine a road to free math
(Figure 1)!
Just what does “free” mean in this context? I think it entails understanding
the ambitions of the people involved, as well as their frustrations. Learning math
may not be “easy”, but perhaps it can be free of unnecessary frustrations. My
approach aims to foster learner self-awareness and a realistic sense of what’s
possible. In the words of C. S. Pierce, “To know what we think, to be masters of
our own meaning, will make a solid foundation for great and weighty thought.”[1]
2 Review of Existing Research
As a sort of mantra, it is helpful to return to the view of personal learning en-
vironment put forward by the progenitors of the PLE concept: “Rather than
7
Fig. 1. The Road to Free Math
8
integrate tools within a single context, the system should focus instead on co-
ordinating connections between the user and a wide range of services offered by
organizations and other individuals.” (Wilson et al., 2006) [2].
The key idea here is that learning takes place in a complex “ecosystem”.
Rather than building monolithic, or even modular, educational structures, in
their fullest development, PLEs will support fully distributed, decentralized,
perhaps even “organic”, learning activities. With this vision in mind, it is still
useful to remember that all activities take place in some context (more on this
in Section 4).
Cormac Lawler’s research (e.g. [3], [4]) indicates some of the challenges in-
herent to collaboratively producing a given online space to support learning. In
particular, Lawler’s attention to the bottom-up nature of Wikiversity provides
an important contrast to the top-down nature of systems-engineering (a quality
that applies even to systems with significant distributed aspects).
Aaron Krowne’s master’s thesis [5] details his development of a system for
the collaborative production of digital libraries (such as the now-popular Plan-
etMath.org). In a subsequent collaboration with the present author, these ideas
of “commons-based peer production” are connected to various historical devel-
opments in hypertext [6]. The system’s usefulness in an instructional context is
discussed in Milson and Krowne [7], which incidentally also includes numerous
citations to earlier literature on collaborative and online learning.
So, what’s the hold-up? (If, indeed, there is a hold-up.) My sense is that
whether we are talking about engineered, democratic, or distributed solutions
(and we’re typically always talking about a combination of all of these), what
remains in very short supply is the multi-level, multi-scale adaptability that
could actually change a learning ecosystem. It is perhaps especially important
to overcome the “learner-centric” model that is so popular these days (and is
still clearly felt in the quote from Wilson et al. above). Or else, putting it another
way, to admit once and for all that we’re all learning – and that, as they say, we
all make mistakes.
Although there have been many academic and commercial projects that suc-
cessfully solve problems on behalf of learners, uptake or buy-in has often been
lacking (ActiveMath makes a particularly good example [8]), or else cost re-
mains prohibitive and major extensions are difficult or impossible to make (e.g.
Mathematica). These are the problems I aim to tackle in my work.
3 Research question
Can we build a semantically adaptive personal learning environment that helps
people learn mathematics and that meets reasonable criteria for sustainable
growth and development?
3.1 Development of the Research Question
Our aim is to build a lens for looking at mathematical learning behaviour in
detail. There are several criteria required for “success”.
9
1. It is essential that enough people are motivated to use the system.
2. It is essential that at least some of them learn mathematics while using the
system.
3. We will need to document how the semantic adaptivity and personalization
features, in specific, help people learn.
4. We will require evidence that the system will grow, not stagnate.
4 Specification of Research Approach
Building educational systems online, in the open, we hope to exploit both high-
intensity, high-cost contributions, and a long tail of smaller and less intensive
contributions. The process of assimilating many small contributions into re-
sources of high-quality – colloquially known as “crowdsourcing” – forms part
of a possible solution to the “sustainability problem”. But, like “open source”,
crowdsourcing is not a panacea. Section 4.1 presents two approaches that I think
can be applied to make crowdsourcing work well.
4.1 Situation relative to contemporary theory
In preparation for dealing with the issues I expect to come up in, I’ve been
developing some (interrelated) themes having to do with the ideas of shared
context in motion and sensemaking.
Nishida’s idea of shared context in motion, or basho [9], as filtered through
the the “SECI” framework of Nonaka and Toyama [10], can help us move from
stakeholder groups to a clearer picture of the roles of actual participants and on
to a detailed understanding of the activities which support these roles (e.g. a
student’s activities include going to class, collaborating on a class project, build-
ing a transcript, and ultimately gaining a skill). Activity theory seems to pick up
where SECI leaves off, as it provides another Nishida-like way to “understand
the unity of consciousness and activity” ([11], p. 7). These ideas will be used
on an ongoing basis to create increasingly detailed sketches of the activities we
would like to support.
Sensemaking is a methodology for finding and filling gaps. There is both
an extensive research literature (cf. [12]) and room for new and creative ideas
connecting to an interesting philosophical tradition (what does it mean for things
to “make sense”? cf. [13]). I hope to use sensemaking as a way to move back
and forth between high-level picture coming from SECI analysis and detailed
development issues, finding ways in which “various data elements fit together
in a coherent causal scheme”, helping understand how to actually support the
activities we’re interested in (see Klein et al., [14], [15]).
4.2 Summary of development goals
It is worth noting that the approaches described above work in a context where it
is assumed that that much of what happens happens elsewhere, i.e., where we do
10
not presume to be the only show in town. We will not aim to be all things to all
people, but to gather enough information to do useful research about what how
PLEs can help people learn mathematics. To do this well, we’ll want a system
should be compatible with various ways of learning and doing mathematics.
Planetary is the name of a system that is currently under development,
which meets these needs.1 Planetary began as a collaboration between myself,
Catalin David, Deyan Ginev, and Michael Kohlhase at Jacobs University, with
the goal of creating an easy-to-extend clone of PlanetMath’s software platform
“Noösphere”. We chose to base the system on the popular open source Vanilla
Forums2 , and the first set of extensions added mathematical writing and ren-
dering capabilities using LaTeXML3 . Subsequent extensions – all pure plugins
to Vanilla – have begun to integrate the “KWARC stack” of software tools for
working with mathematics with semantic markup.4
My development goals are to
A. finish the clone phase and port the legacy PlanetMath content to the new
platform as quickly as possible;
B. add tools for authoring and solving interactive exercises, so as to begin gath-
ering data and generating recommendations based on the learner’s perfor-
mance and prior knowledge;
C. add various other useful plugins that make the site useful and attractive
(e.g. integrating the SAGE computer algebra system, the Geogebra diagram-
creating system, and a maths-enabled version of Etherpad);
D. move in the direction of increased compatibility with other ways of inter-
acting with mathematics online (e.g. compatibility with Wikipedia, ArXiv,
Mizar).
5 Conclusion
The problem I’ve posed asks how to make large-scale computer-mediated learn-
ing system sustainable (something that has arguably not been done before, at
least apart from “the free/open source software movement” taken as a whole).
This is an ongoing challenge that I hope many people will help solve. A contri-
bution that I feel is more uniquely my own will be an improved understanding
of how people learn mathematics, discovered in patterns found via data mining,
and embodied in adaptive recommendation algorithms.
Acknowledgments
The author thanks the anonymous reviewers for their helpful comments. The
research work described in this paper is partially funded through the ROLE
1
http://trac.mathweb.org/planetary
2
http://vanillaforums.org
3
http://dlmf.nist.gov/LaTeXML/
4
http://kwarc.info
11
Integrated Project, part of the Seventh Framework Programme for Research
and Technological Development (FP7) of the European Union in Information
and Communication Technologies.
References
1. Charles S. Peirce: How to Make Our Ideas Clear. Popular Science Monthly 12 (Jan-
uary 1878), 286-302.
2. Wilson, S., Liber, O., Johnson, M., Beauvoir, P., Sharples, P., and Milligan, C.: Per-
sonal Learning Environments: Challenging The Dominant Design Of Educational
Systems. Proceedings of 2nd International Workshop on Learner-Oriented Knowl-
edge Management and KM-Oriented Learning, In Conjunction With ECTEL 06,
(2006) pp. 67-76
3. Cormac Lawler: Coconfiguring Expansive Learning and Action Research in Wikiver-
sity. Abstract submission: Mini-Conference on Medical Education, Learning Theo-
ries and Technology
4. Cormac Lawler: Action research as a congruent methodology for understand-
ing wikis: the case of Wikiversity. Journal of Interactive Media in Education.
http://jime.open.ac.uk/2008/06/
5. Aaron P. Krowne: An Architecture for Collaborative Math and
Science Digital Libraries. Master’s thesis, Virginia Tech (2003).
http://scholar.lib.vt.edu/theses/available/etd-09022003-150851/
6. Joseph A. Corneli and Aaron Krowne: A scholia-based document model for
commons-based peer production. In Martin Halbert, editor, Symposium on Free
Culture and the Digital Library (2005), pp. 241–254.
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In Martin Halbert, editor, Symposium on Free Culture and the Digital Library
(2005), pp. 255–272.
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Pollet, and C. Ullrich: A generic and adaptive Web-based learning environment.
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9. Masao Abe: Nishida’s Philosophy of ‘Place’. International Philosophical Quarterly
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Dynamic Knowledge Creation. Long Range Planning, 33(1), pp. 5-34 (2000).
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perspectives. IEEE Intelligent Systems, 21(4), (2006). 70-73.
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