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User:Arided/ParagogyPaper

Paragogy: Synergizing individual and organizational learning by Joseph Corneli and Charles Jeffrey Danoff

This paper describes a new theory of peer-to-peer learning and teaching that we call "paragogy". Paragogy's principles were developed by adapting the Knowles principles of andragogy to peer-based learning contexts. Paragogy addresses the challenge of peer-producing a useful and supportive context for self-directed learning.

The concept of paragogy can inform the design and application of learning analytics to enhance both individual and organization learning. In particular, we consider the role of learner profiles for goal-setting and self-monitoring, and the further role of analytics in designing enhanced peer tutoring systems.

=Introduction=

Jonathan Grudin identified several problems for computer supported collaborative work (CSCW), which apply a fortiori in computer supported collaborative learning (CSCL). The current paper tackles similar problems, from a human and social perspective, in which both individual and organizational learning are front and center.

Grudin's thematic problems are: (1) The disparity between the people who do the work to create and support the application, and the people who get the benefit; (2) The breakdown of intuitive decision-making whenever intuition comes from a different context; and (3) the ultimate difficulty of evaluating CSCW applications, precisely because they involve complex social dynamics.

In the peer-based context, Problem 1 is somewhat mitigated, but by no means completely gone. Specializations tend to develop within every group. Power laws appear to distribute work between a core of dedicated users or contributors and a peripheral "long tail" of persons who are less involved.

We encounter Problem 2 as a direct side-effect of novelty. However, peer-based learning itself can more accurately be thought of as "new-old" (see Eisen ). Eisen's peer-based learning principles of voluntary involvement, trust, mutuality, authenticity, non-hierarchical status, and duration and intensity leading to closeness, are ways to describe fundamentally human situations (and quite nice-sounding ones at that). Perhaps these features are not as prevalent as they should be in our educational cultures; still the fact remains that it is not peer-based learning that is new, but many of the technologies that can support it (we count analytical methods and pedagogies among these).

We feel that Problem 3 is generally best handled by asking the people involved. If they are satisfied with their experiences, the systems involved are probably working reasonably well. If, on the other hand, they can identify some way the system could be improved, there may well be a chance to improve the system in a subsequent iteration. User feedback or even observation can thus comprise a "light" form of end-user development. That said, this approach merely transposes the problem of understanding social dynamics into a new, "technology-enhanced", version of the same problem. In any case, this will be a key problem for the nascent field of learning analytics.

In Section, we will describe our new theory of the social dynamics of peer-based education. In Section, we will develop the ideas further, relative to more general forms of peer production. Our views on how this new theory can inform the development of learning analytics are presented in Section. Finally, in Section, we describe some of our own planned work in this area, and suggest some other possible lines for future investigation.

=Paragogy: a theory of peer-based teaching and learning=

The theory of paragogy was developed in the context of two online courses that we ran at Peer 2 Peer University (P2PU) in Autumn of 2010. One of the courses was called "DIY Math", and it was "designed to build independent study and peer-support skills for mathematics learners at all levels." http://p2pu.org/general/diy-math The other course was called "Collaborative Lesson Planning", and it was built around the question "Can publishing and collaboratively building lesson plans online make them better?" http://p2pu.org/general/collaborative-lesson-planning The first course (which was facilitated by the first author of the current paper) was not a resounding success as a course, but we learned a lot from it anyway, especially in a rich discussion about how it could be improved that took place in the second course (which was facilitated by the second author).

The key outcome was an outline of an analytical framework that applies to peer-to-peer or peer-based teaching-and-learning-between-equals. The difficulties with DIY Math pointed to possible improvements at the organizational level, such as developing a P2PU-wide "social contract", or only running courses when sufficient commitments had been "anted up". In light of this, Corneli's post-mortem analysis of DIY Math suggested that the concept of pedagogy is not sufficient in the peer-based learning context; he then introduced the etymologically more appropriate term, paragogy. http://groups.google.com/group/diy-math/browse_frm/thread/5fcb82598445cd54 He subsequently proposed five paragogical principles (see below), which were then improved and refined through a peer mentoring process in the Collaborative Lesson Planning course.

The fact that παραγωγή in is an existing word in Greek, meaning "generation" or "production", should not dissuade us from this new usage in English. Indeed, here we are precisely concerned with the activities that generate learning. And, vice versa, in the situated learning and communities of practice point of view, "learning was shown to be an inevitable aspect of all productive practices".

In any case, paragogy will be defined here in contradistinction to another neologism, andragogy, the teaching of adults, coined in Cf. . We found Blondy's "Evaluation and Application of Andragogical Assumptions to the Adult Online Learning Environment" to be quite useful. In succinct form, Knowles's five principles of andragogy are as follows: (1) that adult learners are self-directed; (2) that they bring a wealth of experience to the educational setting; (3) that they enter educational settings ready to learn; (4) that they are problem-centered in their learning; and (5) that they are best motivated by internal factors.

=Paragogical principles=

Each of these principles adjusts one of Knowles's five principles to the peer-based learning context, often by turning the original by 90°. This is not because we particularly disagree with Knowles about how to teach (see below), but because paragogy deals with a very different challenge, that of analyzing and co-creating the educational environment as a whole.

1. Context as a decentered center. "For learning design in a peer-to-peer context, understanding the learner's self-concept -- in particular, whether they see themselves as self-directed or not -- may be less important than understanding the concept of 'shared context in motion'." (See "Paragogy and basho", below.)

2. Meta-learning as a font of knowledge. "We all have a lot to learn about learning."

3. Peers are equals, but different. "The learner mustn't seek only to confirm what they already know, and must therefor confront and make sense of difference as part of the learning experience."

4. Learning is distributed and nonlinear. "Side-tracking is OK, but dissipation isn't likely to work. Part of paragogy is learning how to find one's way around a given social field."

5. Realize the dream, then wake up! "Paragogy is the art of fulfilling motivations when this is possible, and then going on to the next thing."

Paragogy compared with andragogy
Blondy points out both uses and challenges to each of Knowles principles of andragogy. For example, "Cheren stated that while learners may express a desire to be self-directed in their learning, most lack the required understanding of learning necessary to be self-directed and thus need guidance and encouragement in the learning process."

From our point of view, so much seems to depend on the way things are set up in the first place. For example, the most important initial condition in andragogy seems to be that an adult educator or facilitator is part of the picture. In a peer-based setting, that may not be the case: we can easily find examples of learning environments where there is no "teacher" in the "classroom"; where, for example, the task of facilitation is shared among all participants or even encoded in the learning materials or supportive technologies. Not that one way is more desirable than another: we simply mean to highlight the fact that the most basic features of a given learning environment will influence everything else.

In particular, it seems to us that a move to the more "horizontal" regime of paragogy can often occur within andragogy, e.g. when inviting participants to interact; and vice versa, a move to a more "vertical" regime of andragogy is possible within paragogy. For example, the second author fruitfully encouraged participation in his course via personal emails to those participants who had temporarily gone quiet.

In short, we agree with Blondy when she writes "Andragogy should be used as a starting point for approaching the adult online learning environment." We recommend paragogy as an additional starting point that sits on another dimension.

Paragogy and basho
The first paragogical principle stresses the importance of understanding the idea of shared context in motion. We will elaborate here.

The philosophical foundations of this notion, originally developed by Kitaro Nishida, and summarized in English by Masao Abe, describe the way in which events and objects arise from their larger contexts. In other words, the idea of basho ("shared context in motion") can help us think about how a context constrains or supports different types of (inter-)actions, and also about how we (re-)shape the contexts we find ourselves in.

Nonaka and Toyama take this idea and apply it to knowledge creation. They suggest that knowledge is created as people interact over time in a shared context, in a process that can be broken up into repeated phases they call Socialisation, Externalisation, Combination, and Internalisation (SECI). In simple terms, any given phase can be understood in terms of "what I do", "what we do", "how we do it", and "what it's all about".

The first paragogical principle says that instead of focusing on how learners see themselves (e.g. as "self-directed" or "dependent" or something else), we should be asking how the learning context shapes what learners are actually able to do. Note that this includes looking at ways in which learners can contribute to reshaping the learning context.

Instead of simply saying "so-and-so lacks the required understanding of learning, so I need to help them", a paragogue would also look for contextual features of the learning environment that are "blocking" self-directed learning. These may include features that block the ability of learners to make adjustments to the environment on their own behalf, or which limit their ability to ask for help.

=Paragogy and Peer Production=

The links between paragogy and peer production illuminate both. As Phillip Schmidt writes: "Upon closer inspection of commons-based peer production communities, we find learning at their core". Conversely, in the conclusion to "Education and Mind in the Knowledge Age", Carl Bereiter writes:

Schools are places where knowledge creation can go on, but where it does not have to be market driven or competitive. [...] Knowledge creation in schools is the creation of knowledge by students for their own use. [...] To the extent that knowledge created in schools has value beyond the classroom where it was created, it enters into a barter economy.

Context as a decentered center.
The idea that internal motivation is in conflict with goal-directedness (from Tennant, cited in Blondy) seems somewhat dubious if we consider the reciprocal effect of environment on character development described by Benkler and Nissenbaum.

Meta-learning as a font of knowledge.
Continuing this idea, gaining skills, employability, or a good reputation, seems to be a straightforward self-oriented way to enhance one's quality of life. But in fact, even these motivations come from somewhere. In a proper analytics of a learning or production landscape, we ought to ask: what learning? and why this learning?

Peers are equals, but different.
Benkler describes three necessary features for peer production: (1) the potential objects of peer production must be modular; (2) the modules must be small in size (noting that heterogeneous granularity will allow people with different levels of motivation to collaborate by contributing smaller or larger grained contributions); (3) the integration mechanism must run at a fairly low cost (either through automation or enforced social norms).

There are parallels in paragogy. The choice to work in a small closed group versus the choice to work as a group embedded within a larger commons has to do with the question: how much difference do you want to confront while engaging with the learning process?

Learning is distributed and nonlinear.
The view of fluid social contexts advanced by Engestrom as a move beyond the traditional "communities of practice" view is quite compatible with the most famous peer production virtue, freedom (cf. ), which is what allows people to function in a distributed and nonlinear fashion relative to a learning or production "ecosystem". Star and Griesemer, on whom Wenger drew heavily as he was developing the idea of community of practice, describe their view as "ecological". One key difference between Star/Wegner on the one hand and Engestrom on the other has to do with the nature of boundaries. In the community of practice view, boundary objects exist to effect translations or initiations. In Engestrom's view, attention is drawn to boundaries that remain in flux (via an ongoing process of co-configuration) or which are blurred (e.g. by a blurring of consumer and producer roles).

A closely related idea from Engestrom is that sociality revolves around concrete "shared objects", as opposed to e.g. abstract connections between people. Combining this with the idea of basho, we come to the at once intuitive and powerful idea of a context or environment as the largest shared object. An environment that is co-created by its inhabitants is likely to be a particularly meaningful and valued place.

Realize the dream, then wake up!
Blurred boundaries make it difficult to pinpoint a universally-applicable definition of "success". However, as Schmidt points out, measurable things like code commits can be used to make reasonably objective evaluations about participation in open source software projects, and we can expect to find other similar measurables related to modular contributions to other types of commons-based peer produced artifacts. It is may be in some ways more challenging to measure the (equally necessary) contributions to integration and coordination.

=Paragogy and Learning Analytics=

We now come to the paper's main application of paragogy, namely, to produce an outline that can give shape to the effectively infinite possibilities of learning analytics (henceforth, LA).

Context as a decentered center.
George Siemens defines learning analytics as "the use of intelligent data, learner-produced data, and analysis models to discover information and social connections, and to predict and advise on learning."

Measuring a student's progress in a given learning environment, whether it is centralized (Freshman to Senior) or decentralized (Padawan to Jedi), should suitably indicate the context of that student at each point. Progress may be defined relative to a context of the activities of other participants in the environment. In a straightforward case, LA will be established and maintained relative to a changing collection of goals that are defined by an instructor or facilitator. LA will themselves be a nontrivial part of any learning context that employs them, suggesting that transparency about the way they are used will be an important factor to consider.

Continuing, student and instructor LA will increase institutional effectiveness, one example being the project Paul J. Williams is working on, "to supply student and organisational `learner analytics' functionality to schools so that the decisions they make about the application of time and dollar resources amongst competing priorities can be better supported and justified. Institutions could see results for whether money invested in technology, teachers, facilities and more yields an improvement in learning for students, or not." http://groups.google.com/group/learninganalytics/msg/fbd3385b8a86785f

While applications of LA based on standardized tests is currently important, hopefully with more study the field will become more sophisticated and allow for a more holistic evaluation of learning than what is produced by standardized tests. In particular, this raises provocative question as to how best to measure school success.

Bereiter emphasizes developing a context that includes functional help for thinkers and learners, as opposed to applications of recieved wisdom about thinking or learning. He feels that thinking aloud research shows promise as a way to see just how people actually think (, p. 348). Paragogy suggests a broader view on thinking aloud: instead of traditional didactics, in a peer-based context, speech flows in a network, and thinking is done in an inherently social way.

Meta-learning as a font of knowledge.
Another definition given by EDUCAUSE's Next Generation learning initiative is "the use of data and models to predict student progress and performance, and the ability to act on that information". http://nextgenlearning.com/the-challenges/learning-analytics

In short, the meta-learning principle is the most obvious application of LA: the more effectively we can do LA, the more we learn about learning.

Peers are equals, but different.
Not only can LA be used to measure an individual student's successes, failures, and hours invested, they can be applied in relation to data about peers, including peer-facilitators or teachers (e.g. in connection with suggestions or critiques). LA could be used to pair up weaker students with more advanced ones, or to help learners with overlapping interests find each other in the crowd. Threshold values could be set to indicate when a student might be allowed or asked to move from a mentored to mentoring role. Measurements can also be made of how well students work with their peers, or how much they have individually contributed to the learning environment.

Data on how different learners appear to learn best could be combined with information on how certain tutors work to find the best pairing. Various other sorts of recommendations are part of the subject of a significant body of ongoing research.

Learning is distributed and nonlinear.
LA, especially attention metadata, can measure how much a student stays on topic, and give feedback on how these attentional investments pay off in the long-run. When logged into the class wiki, do they work for an entire hour on one page, or do they move around? Topics a student touches on but later abandons should be kept track of (for instance, because they may be useful later).

Students can show off their learning on things they may not have a degree in. For example, someone who majored in English in college who wants a career change can show an engineering firm school they independently completed "90 of the work towards a Journalism BA" to prove they have the skills and motivation for an entry-level job in public relations.

To get to point where a system can give feedback of this nature, goals need to be specified and agreed upon. Long-term goals would probably be easy enough, e.g. "I want to learn Japanese." It is harder to break a task into steps, and the first step is often the hardest. Corneli suggested to look for "the simplest step (that you can actually do) that gets you toward your goal." http://www.p2pu.org/general/node/5571/document/10225

Students can then share that step however small, and once achieved, can chose another one along the way. These patterns can be studied to find LA that will show a learner their percentage towards e.g. fluency in Japanese.

Realize the dream, then wake up!
We feel this is the key to combining LA and paragogy: a student should explicitly spell-out their motivations/goals and then keep track of their progress towards reaching them. LA will help students have a clear way to know how close they are to realizing their dreams, and to have a way to showcase their achievements to the rest of the world. In cases of trouble, LA should help identify how changes in behavior can help.

To think highlight here one possible large-scale application, we can imagine creating paragogical accreditation standards for learners, along the lines of those used for businesses by the Better Business Bureau. http://www.bbb.org/us/bbb-accreditation-standards/ This could come from a system to that would keep track of the kinds of courses people might like to take; and furthermore, courses could require people to ante up a certain level of commitment before the course would run. The degree to which people follow through on their commitments over time would determine their credibility rating.

=Conclusion=

We explored connections between paragogy and peer production, and paragogy and learning analytics, and showed how paragogy can intertwine with these to open new avenues for productivity, learning, and evaluation.

Next steps for the authors
We both plan to try running courses on Peer 2 Peer University again when the next round begins in January 2011. We will write syllabi that encourage paragogical activity while generating LA for evaluation. Another avenue we are exploring is creating our own learner profiles, as suggested by Siemens . http://en.wikiversity.org/wiki/User:Arided/Learner_Profile http://en.wikiversity.org/wiki/User:Charles_Jeffrey_Danoff/Learner_Profile Building on his framework, we will endeavor to maintain an outline our learning goals, steps to complete them, and criteria for evaluation. We will do what we can to encourage P2PU to support learner profiles across the board.

The ideas from Section will be further developed in an extensive case study by the first author on commons based peer-production in mathematics.

Implementing paragogy
We encourage the research community to test our ideas in practice of various forms. Some ideas for paragogical design include:

 * Establish a group consensus for expectations/goals/social contract of the course and how each of them should be evaluated at its conclusion.
 * Have learners designate learning goals that they then commit to stick with.
 * Formalize a process for assisting peers (e.g. responding to questions, giving feedback on publicly posted work).
 * Develop explicit pathways for learner feedback to translate into changes to the learning environment.

=Acknowledgments=

Joseph Corneli's work is partially funded through the ROLE Integrated Project, part of the Seventh Framework Programme for Research and Technological Development (FP7) of the European Union in Information and Communication Technologies.

We wish to thank Marisa Ponti, Alexander Mikroyannidis, Raymond Puzio, and Thomas Lynch for their help with ideas and references. Thanks also to everyone at P2PU. Finally, thanks to the organizers of Wikimania 2010, where the authors first met and exchanged the early inklings of the ideas developed here.

=References=

title: User:Arided/ParagogyPaper


license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: File:Fe1.s11.mtg9.djvu


text:
User:EGM6341.S11.team2.lee

=Problem 1.4=

Find
Plot f, g and find $$ {\left\| f \right\|_\infty } {\left\| g \right\|_\infty } {\left\| {f - g} \right\|_\infty }$$

Given
$$ f(x) = 3x + 5{x^3},x \in [0,1]; g(x) = \sinh x,x \in [0,1] $$

Solution
Because $$ {f^'}(x) = 3 + 15{x^2} > 0,\;\;x \in [0,1], {g^'}(x) = {(\sinh x)^'} = {(\frac{2})^'} = \frac{2} > 0,\;\;x \in [0,1] {\left( {f(x) - g(x)} \right)^'} = 3 + 15{x^2} - \cosh x > 0,\;\;x \in [0,1]$$

Which means that f(x) keeps increasing at [0,1], and g(x) and f(x)-g(x) as well

So $$ {\left\| f \right\|_\infty } = \max \left| {f(x)} \right| = {\left. {\left| {f(x)} \right|} \right|_{x = 1}} = 8 $$

$$ {\left\| g \right\|_\infty } = \max \left| {g(x)} \right| = {\left. {\left| {g(x)} \right|} \right|_{x = 1}} = \frac{1}{2}(e - \frac{1}{e}) \approx 1.71520 $$

$$ {\left\| {f - g} \right\|_\infty } = \max \left| {f(x) - g(x)} \right| = {\left. {\left| {f(x) - g(x)} \right|} \right|_{x = 1}} = 8 - \frac{1}{2}(e - \frac{1}{e}) \approx 6.82479  $$

Using the following Fortran code

program main real,allocatable::x,f,g integer::i,n real::e=2.71828 open (unit=10, file="input", status="old") read(10,*)n allocate(x(n+1),f(n+1),g(n+1)) do i=1,n+1 x(i)=-1.0+2.0/n*(i-1) f(i)=3.0*x(i)+5*x(i)**3 g(i)=0.5*(e**x(i)-e**(-1.0*x(i))) end do  open (unit=11, file="hw1.4.plt", status="replace") do i=1,n+1 write(11,"(3F12.4)") x(i),f(i),g(i) end do   end program main

We can easily get the image of f(x) and g(x) as following

title: User:EGM6341.S11.team2.lee


text:
Psycholinguistics/Language and Arithmetic

Introduction
At first it would appear that language and math are two completely separate entities; however, how different are they really? When analyzed, it is evident that both language and math are firmly rooted in a form of syntax. These set rules govern the way in which people can communicate both linguistically and arithmetically. Moreover, it would appear that language and arithmetic not only share governing rules, but also a set of cognitive resources. For instance, Spelke and Tsivkin examined the relationship between language and math in a study on bilingualism (2000). They studied Russian-English bilinguals in a series of arithmetic equations with a set of geographical facts, or historical facts that either did or did not contain numerical information. It was found that when participants were trained to perform a series of math questions, they performed those skills better in their native language. Moreover, information regarding non-numerical facts and numbers was similarly remembered in both languages. This suggests that language has an impact on the learning of exact numbers in an array of fields. While language and mathematics initially appear to be two starkly different subjects, they do hold some similarities. As these seemingly divergent subjects are examined closely, they become more complimentary to one another. On that basis, it would seem only natural to examine both language and arithmetic in context of one another. After all, aren't both language and arithmetic concerned with relationships, whether communicative or theoretical? Over the course of this chapter several elements of language and arithmetic will be examined, including brain systems and cognitive resources, the number sense, the development of numerosity, the importance of math and language in a social and cultural context, as well as contemporary research and its benefit to society.

Brain Systems and Cognitive Resources
Cognitive Neuroscience has given researchers the opportunity to study the specific brain systems that influence how humans operate. In this section, the neural pathways that coincide with language and arithmetic functions will be analyzed through an array of neuroimaging techniques. In analyzing these cognitive resources, the way in which math and language are both similar and different at a cognitive level will become evident.

Language
Language meaning in the brain is generally evenly distributed; however, there are some areas that are more known for their influence on language representation. As the major brain areas are covered in the textbook chapter “Language and the Brain,” this section will cover the main points regarding language localization and will act as a brief review before delving into the shared cognitive resources between language and arithmetic.

To begin with, most people have heard at some point about the notion that language is housed in the left hemisphere of the brain. While this idea for the most part holds true, language lateralization can vary within a population. In general, language does tend to be left lateralized, but some aspects, such as metaphor, prosody and language organization, are found in the right hemisphere (Lancker, 2000). Language functions thus seem to be bilateral, rather than strictly lateralized.

One of the primary brain areas involved in language is Broca’s area. Paul Broca was the first to qualify this area through an autopsy of one of his patients, Leborgne, a man who lost his ability to generate sentences, and could only say “Tan” and “Sacre nom de dieu!” (“Goddamnit!”) (1861). The postmortem analysis concluded that Leborgne had a deficit in the left frontal lobe, specifically in the area of the inferior frontal gyrus. Because of his research, Broca’s area is now the area of the brain known to have an effect on speech production. Another brain system related to language is Wernicke’s area, a region found in the angular gyrus (Wernicke, 1874). Lesions in this area of the left cerebral cortex cause deficits in speech comprehension.

While Broca and Wernicke’s areas are known as the 'language centres' in the brain, there are other neural systems that influence the way in which humans communicate linguistically. The Limbic system is one such area (Lamendella, 1979). This neocortical system tends to aid children with exchanges of language, while it plays a part in message interpretation in adults. The basal ganglia, an area that facilitates prosody production and comprehension, as well as automatic speech, also has a great effect on language (Lancker, 2000). The influence of the basal ganglia coincides with its other bodily functions, as it primarily deals with the motor system. One other area known for its role in language is the amygdala (Stuss & Alexander, 2000). Not only is the amygdala known for emotional awareness, but also for the integration of other information, such as language.

Arithmetic
Many studies and reviews have examined the relationship between arithmetic and neuropsychology through neuroimaging. Of these works, it has been found that one of the major brain areas involved with arithmetic is the horizontal segment of the of the bilateral intraparietal sulcus (HIPS) (Dehaene, Molko, Cohen, & Wilson, 2004). When Stanislas and colleagues reevaluated their theory of the number sense, they found through meta-analysis that the HIPS is the area of the brain that shows the most activity when processing numbers, as well as making judgments and comparisons on numbers. Moreover, Simon, Mangin, Cohen, Le Bihan, and Dehaene’s functional magnetic resonance imaging (fMRI) study found that once accounting for noise, the HIPS was the sole area of the brain active during calculation; thus, it appears to be the primary neural circuit active in regards to arithmetic (2002).

Another area of the brain that is highly involved in arithmetic is the angular gyrus (Dehaene, Spelke, Pinel, Stanescu, Tsivkin, & Science, 1999). In neuroimaging studies, it has been found that the angular gyrus shows the most activity when retrieving facts from working memory to use in arithmetic operations, such as multiplication. Further evidence for the impact of the angular gyrus is evident in Lee’s case study of a patient with a lesion in the angular gyrus that affected her ability to do simple multiplication tasks (2000). However, in another case study van Harskamp, Rudge, and Cipolotti analyzed the mathematical skills of another woman with similar damage to her angular gyrus (2002). In this case, the patient’s ability to subtract was impaired, while her ability to multiply and comprehend was intact. This recent study caused problems with the initial belief of the importance of the angular gyrus in arithmetic. As there is some debate on the function of the angular gyrus in arithmetic functions, it does not appear to have as concrete of a place in the mathematical brain system as the HIPS.

Moreover, meta-analysis of neuroimaging illustrates that the precentral sulcus and inferior frontal gyrus also appear to be triggered when managing a series of numbers in working memory (Stanislas et al., 2004). This seems to be specifically the case when completing arithmetic tasks, such as mental calculation.

In studying the meta-analysis of neuroimaging in terms of arithmetic, it becomes apparent that several areas of the brain are involved when processing mathematics. However, one must also consider the possibility that not all areas of the brain involved with math are used at once. Based on this idea, Rosenberg-Lee, Lovett and Anderson studied the specific brain loci activated when performing an array of math-related tasks (2009). They suggested that as individuals use different sets of strategies to solve math problems, there must also be different neural responses to correlate with the arithmetic functions. Their research illustrates that long multiplication calculations cause early activation in the posterior superior parietal lobule, and the posterior parietal cortex, but not in the HIPS, or lateral inferior prefrontal cortex. This suggests that areas, such as the HIPS that tend to be associated with calculation, may relate more to quantity processing and estimation than to certain arithmetic tasks, such as long division (Stanislas et al., 2004). This study illustrates that distinct areas of the brain devoted to mathematical calculation may be affected differently, depending on the manner in which the arithmetic is processed.

Communal Cognitive Resources
Although language and arithmetic appear to be different domains, they do share a set of cognitive recourses. Dehaen, Spelke, Pinel, Stanescu, Tsivkin, and Science explored the idea of communal neural pathways in a study that examined bilinguals and the role of language and visual representations on mathematics (1999). They found that visuo-spatial pathways were active during approximations (i.e. guesstimating), while language areas were affected with exact calculations (i.e. calculating 258 - 62). The fMRI scans showed activation in the left inferior frontal lobe, left cingulated gyrus, left precuneus, right parieto-occipital sulcus, left and right angular gyri, and middle temporal gyrus for exact calculations. Generally, all activation when doing exact calculations was left lateralized and coincided with language neural-pathways. While the study illustrates the need for multiple neural pathways when it comes to arithmetic, it also demonstrates a set of shared cognitive resources between language and arithmetic.

As Dehaen’s study illustrated, there is an apparent connection between neural responses responsible for language and those for arithmetic (Dehaen, et al., 1999). Of particular interest in his study is the interconnectedness of language and math through the angular gyrus. Indeed, the angular gyrus is not only activated with arithmetic tasks, but also with language tasks such as phoneme detection (Stanislas, Molko, Cohen, & Wilson, 2004). As the angular gyrus is often associated with arithmetic operations comparable to multiplication (if based on on the case study by Lee (2000)), then it would appear that there is some language-based retrieval dependency (similar to phoneme detection) for arithmetic operations. Moreover, Dehaen’s study suggests that operations, such as multiplication, are merely viewed as another type of fact to be retrieved at a neural level (Dehaen et al., 1999). It becomes apparent that even in retrieval from cognitive resources, arithmetic and language are not as different as one might imagine.

Communal Cognitive Resources for Math and Language

Despite the fact that previous studies have shown a relationship between the HIPS, quantity processing and arithmetic estimation, there is also association between the HIPS and linguistic syntax (Carreiras, Carr, Barber & Hernandez, 2010). Carreiras and colleagues illustrated such a correlation in their study on agreement violations. Participants were exposed to one of four different sets of word pairs, determinant-noun versus non-adjective pairs, and three disagreement conditions (word pair disagreements based on gender, number and baseline. i.e. "math affect language" would be a number disagrement). Words were shown one after the other and consisted of one of the word pairs and a disagreement. In the cases where there were issues with number agreement, the HIPS was activated; this suggests that the HIPS is not only affected by quantity in arithmetic, but in language as well. Moreover, when there was a violation in either gender of number, the left premotor and left interior frontal areas were activated. Once again, there is a distinct connection between math and language neural circuits.

The activation of brain areas when syntactic rules are violated

The Triple-Code Model
The number sense is one of the three components in Dehaen and Cowen’s triple-code model (1997). In order to understand the significance of the number sense and its importance in terms of arithmetic, one must first have some insight into Dehaen’s model. To begin with, the model states that digit identification, as well as quantitative representation, occurs in both the right and left hemispheres. As the triple-code model suggests bilateral properties for mathematic ability, it makes sense that the three codes that are used to judge various math functions come from an array of brain areas. The verbal area associated with math, found in the Broca’s area, facilitates the understanding and learning of arithmetic that is tied to language. For instance, the learning of one’s 'multiplication table" is attributed to the function of Broca’s area. This mathematic function correlates with the other roles of Broca’s area, that is, speech production and verbal working memory. The visual area, found in the inferior temporal cortex, aids in the understanding of written mathematics; thus it is the visual-symbolic code that makes it possible to read and understand an arithmetic problem written on a page. Finally, the quantity area, found in the parietal lobe (The HIPS), deals with the idea of basic math functions (i.e. counting), numerosity and making judgments regarding a number set. It is this quantity code that we will focus on in our explanation of the number sense.

The Number Sense and Numerosity
As previously mentioned, the number sense is interrelated with the quantity code in the triple-code model (Dehaen & Cowen, 1997). Essentially, numerosity is the ability to approximate and manipulate smaller math problems almost automatically, without the use of other cognitive resources, such as language devices (Binet, Simon & Kite, 1916). Thus, the skill of numerosity is the ability to identify and manipulate small number sets without having to count, as counting requires the use of language centers in the brain. As a result, the number sense and numerosity are mathematically defined as one’s ability to use intuition to approximate. This innate ability not only allows us to approximate a number of items almost automatically, as Jevons did in his study of iconic memory, but to estimate whether one group of items is larger than another group (Jevons, 1871). Furthermore, an individual’s capacity to quickly perform these tasks while making judgments is known as one’s ability to subitize (Kaufman, Lord, Reese, & Volkmann, 1949). This, of course, is related to numerosity, as it is the skill associated with the number sense.

Another property associated with the number sense is the linear representation of quantities in the human brain, also known as the number line (Binet, Simon & Kite, 1916). One interesting fact about the line is that it appears to be logarithmic, meaning that as the size of the numbers being examined increase, so must the difference between the two in order to successfully distinguish and approximate the numbers. In other words, the larger the difference between the two numbers, the faster the response time for quantity. This is an important aspect when factoring in the use of the number sense and its relation with the quantity code in the triple code model (Dehaen & Cowen, 1997).

Numerosity
While the development of math does not seem to be as innate as the development of language, some mathematical properties, such as numerosity, tend to appear earlier than language acquisition. In this case, children are more likely to subtize at a younger age than develop a sensitivity for phonemes (Binet, Simon & Kite, 1916). As numerosity appears to be an early function in the brain, its development at a young age seems to pave the way for the development of more complex functions later on in life.

Xu and Spelke conducted a series of experiments to examine the innateness of numerosity in five to six month-old infants (2000). Infants were placed in a situation in which they examined an array of dots that varied in set size from eight to sixteen objects. Infants were first habituated to the pattern of dots and then shown the second series of dots (a preferential looking design). In the cases where the two trials differed, infants spent a greater amount of time staring at the changed dot display. Conversely, participants did not spend a great deal of time looking at the second trial if it matched the first, as they were already habituated to the sight. Once all other factors were controlled for, it was found that children did, in fact, discriminate between the dot sets due to an innate approximation rather than independent representations of the objects. These findings were significant as the participants had not yet reached an age of phoneme acquisition and were not able to count. Effectively, Xu and Spelke illustrated that numerosity is one of the first skills developed by infants.

Subsequently, Xu and colleagues expanded on their research to see if discrimination depended on the ratio between items, and if it was dependent on large or small numerosity (Xu, Spelke &Goddard, 2005). As with their previous study, infant participants were tested with a preferential looking task. Four experiments were conducted to reexamine infants’ abilities to discriminate numbers. The results, once controlled for extenuating factors, illustrated that infants have the ability to subitize with larger sets, but have issues with smaller numerosities. These findings are congruent with the theory that there are separate brain systems that facilitate numerosity depending on size, as postulated by Binet, Simon and Kite (1916).

Social and Cultural Contexts
As with most aspects of life, societal context has an effect on the development of language and arithmetic. In a study on parental and teacher influence on mathematical development, it was found that social context had a large effect on student performance (Levpušček, & Zupančič, 2009). To study the impact that parents and teachers had on mathematic success, student participants were asked to fill out a questionnaire that documented their feelings on pressure, support, and help given by both adult groups. Indeed, parental pressures were correlated with poorer math results, while supportive teachers tended to have a positive effect on a child's arithmetic understanding. Moreover, it has been shown that other social factors, such as a lower socioeconomic status, residing in a disadvantaged neighbourhood, and race can have negative effects on academic achievement (Kohen, Leventhal, Dahinten, & McIntosh, 2008).

All of these social contexts have been shown to have a great effect on language development as well. One of the best, and most extreme, examples of the negative effects of parental upbringing and abuse is the case of Genie (Rymer, 1993). Genie, a small girl who had been abused for the first thirteen years of her life, was developmentally delayed both physically and linguistically due to her upbringing. Without any sort of social training or context, Genie did not develop a great understanding for language. Despite intensive therapy and years of effort, Genie still did not develop language in the way that a socially nourished child would. Such a case study illustrates the notion that language isn’t completely innate, but dependent on an array of social factors and context to help it flourish.

Cultural influences also affect the mathematical and linguistic worlds. For instance, just as there are universal governing rules of language, there are many aspects of arithmetic that are similar across cultures. In their review of Peter Gordon’s work on language nativism and the Pirahã tribe, Laurence and Margolis discuss issues that arise with cross-cultural studies (2008). Through Lawrence and Margolis’ review it is evident that while they believe there are issues in doing cross-cultural studies for language nativism, these studies could help demonstrate that numerosity is universal. While not all cultures and languages have the same number set or system, all humans seem to have a general understanding of size comparison and approximation. Moreover, the factors of the number line, including its logarithmic properties, seem to hold true cross-culturally. Studies such as these illustrate the fact that language and math are not only similar at neural, syntactic and social levels, but at cultural levels as well.

Math and Language Deficits
As math and language share similar neural circuits and syntactic properties, it would seem that there is a great chance that both subjects are severely impacted by specific learning disabilities. For instance, there are disorders, such as acalculia and dyscalculia that solely affect math skills and not language skills (Rosca, 2009). While these disorders seem fairly rudimentary, there are different grades of severities and arithmetic difficulties within each deficit. One such example is a case that Rosca examined in which the patient had acalculia with preserved functions in mathematic facts, but deficits in calculations. When examined, it was found that the patient had a lesion situated in the left parietal lobe, an area known to be involved in mathematic operations and language comprehension. Thus, when further analyzed, it is evident that while some disorders may typically highlight deficits in one field (i.e. math skills), other areas may be involved (i.e language comprehension).

Another disorder includes alexia, a problem in which individuals cannot read or multiply, but can add and subtract (Sakurai., Asami, & Mannen, 2010). Based on the type of disorder, one could pinpoint some of the communal cognitive areas of language and math that must be affected. For example, in the case of alexia, one could postulate that the left parietal lobe was affected, as individuals affected have difficulties with complex math calculations. Further empirical evidence on the relationship between language and math could aid in developing techniques to create programs to help individuals suffering from math and language difficulties.

Arithmetic and Phonology
One contemporary study that examines the influence of the angular gyrus was conducted by De medt, Taylor Archibald and Ansari (2010). This research team examined the relationship between phonology and arithmetic in grade-school children. The study found that poor phonological awareness and processing was related to issues with small-sized math problems. Moreover, the findings suggest that both difficulties in phonological awareness and math skills had to do with the retrieval of information.

Words and Numbers
In a study on the relationship between mathematic skills and poor comprehenders, Pimperton and Nation compared the mathematic abilities of typically developing readers and poor comprehenders (2010). Participants were tested in two areas of arithmetic, one that dealt primarily with simple calculation and another that dealt with complex mathematical reasoning. Poor comprehenders did show lower scores in mathematical reasoning than did their controls, as their verbal abilities and comprehension were lower than that of their peers.

What This Could Mean in Terms of Research
These contemporary studies are integral in understanding the ways in which a reading disability could affect math skills. Furthermore, the findings could extend to creating a clinical program that could increase phonological retrieval, comprehension, and thus math problem accuracy. As the relationship between phonology, poor comprehenders and math can be found in the angular gyrus, a plan that would focus on the stimulation of this brain’s functions could aid children falling behind in the school system.

Test Your Knowledge
Fill out this crossword to reinforce your understanding of studies and concepts before further applying and evaluating your knowledge in the next section.

Applying and Evaluating Your Knowledge: Thinking About Math and Language
These exercises are designed to solidify your understanding of the major concepts in the chapter and apply your knowledge to different situations.

1. If you were conducting an fMRI experiment on individuals with difficulties in phonological awareness, what areas of the brain would you expect to be activated? Moreover, what mathematical deficits would you expect to be present? Integrate this information with your understanding of the cognitive resources used in language and math to design a treatment to aid these individuals.

2. Identify and explain the major brain areas responsible for language and arithmetic. Imagine that the following image is a brain scan from someone performing both math and language tasks at the same time. Highlight the areas on the picture that affect both language and math.

3. Based on your understanding of the triple code model, design an experiment to illustrate that arithmetic development occurs before language acquisition.

4. Jodi is a 7 year old girl from a low socio-economic status family. Her parents each work two jobs, and as a result Jodi is often left unsupervised. Moreover, Jodi is a student in an inner city school that offers very few extra academic resources. While Jodi has always had some academic issues with reading, recently she's been having issued with simple mathematic calculations, such as addition and subtraction. Identify some possible solutions that will aid Jodi in achieving academic and arithmetic success (use examples and refer to social and cultural aspects of language and math).

5. Are there genetic components involved in mathematic and language abilities? If so, how could you test the biological nature of these two processes?

6. Design an experiment (unlike that of Spelke and Tsivkin) that illustrates the way in which language has an effect on math. Keep in mind some of the properties that are shared by both language and mathematics, such as syntax.

7. Look at the following image and try to rapidly and accurately judge the amount without counting. How many dots can you see? How are you able to do this? Describe this process (Think of one of the principles discussed in the development section). Is there a similar theory relating to language? Or, can you apply this theory to language processes?

8.Watch a portion of the following video. After watching part of the tutorial, would you qualify the type of math equation as simple or complex? Based on your answer, what area of the brain do you think would be active? Now, imagine that you suffer from dyslexia. Would you have normal mathematic abilities, still be able to only answer these kinds of math equation, or would you have issues with another form of mathematics?

9. Now let's do a bit of web surfing- find a website dedicated to math or language (i.e., a support group for individuals with dyscalculia). Learning from a first hand experience is often a great way to have a better understanding of a subject. What are some of the biggest concerns surrounding the disorder? How do individuals overcome these difficulties? Are there any treatment opportunities available that you were unaware of? Try to integrate this information with the knowledge you gained from this chapter.

10. Essay Question: How is language lateralized? Is it the same for everyone? What aspects can change the lateralization of language, and, if it isn't lateralized to one side which areas of the brain correspond to what language functions?

11. Group Discussion: Theories can be changed and disproved over time, and in order to fully understand a theory one must know both sides of the story. Choose one of the theories that are discussed in the chapter and look up a meta analysis on the subject. Has the theory changed, or added any new components to its reasoning? What are the current thoughts on the theory? Does everyone agree with the viewpoint? What are your thoughts on the subject.

12. Imaging that you are a researcher studying the language centers in the brain. While you are very interested in the subject, you do not have the funding for neuroimaging machines. Design a study that will allow you to test the language centers in the brain.

13. Debate: Break up into two groups and choose one of the controversial topics associated with language and arithmetic (such as new treatments, hemisphere activation, etc). One group should argue for the "for" side while the other group argues for the "against" side. Make sure to include empirical evidence in your argument.

14. Now that you've read the chapter and had a chance to solidify your understand on the topic, it's time to integrate this information together. Write a one minute thought paper on everything that you can remember about the chapter (including details). Have a friend time you and make sure that you write for the entire 60 seconds. Whatever you do, DO NOT remove your pen from the page and DO NOT stop writing. Even if you lose your train of thought just write down "I don't know what to write right now." You'll be impressed with how much information you've absorbed. Once you're done your thought paper, read it over and compare it with the information in the chapter. Were you able to remember the key points of the chapter? Were you stronger in some subjects than in others? This is a great way to find out just how much you've learned.


text:
User talk:Egm6341.spring-11.5.D

= Problem Homework 1 problem 4 Prove the Integral mean value theorem =

Given

 * {| style="width:100%" border="0" align="left"

\int _a^bf(x) w(x)dx=f(\zeta ) \int_a^b w(x) \, dx $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

where f(x) and w(x) are conitnous nonnegative functions $$\epsilon [a,b]$$

First, since w(x) is arbitrary and non negative we will set it equal to unity

$$ \int_a^b 1 f(x) \, dx=f(\zeta ) \int_a^b 1 \, dx $$

$$ \int_a^b f(x) \, dx=(b-a) f(\zeta ) $$

Next we will set constants at the extreme values of f(x)\epsilon [a,b]

 * $$\displaystyle

M=\max (f(x)),m=\min (f(x)) $$ Therefore, from the Extreme Value Theorem

$$\displaystyle \int_a^b m \, dx\leq \int_a^b f(x) \, dx\leq \int_a^b M \, dx $$ Evaluating and subsituting in from above

$$\displaystyle m (b-a)\leq (b-a) f(\zeta )\leq M (b-a) $$

$$\displaystyle \min (f(x))\leq f(\zeta )\leq \max (f(x)) $$ Egm6341.spring-11.5.D 02:42, 22 January 2011 (UTC)

title: User talk:Egm6341.spring-11.5.D


text:
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title: User talk:Isom.schmidtke


text:
Psycholinguistics/Acquisition of More than One Language

Introduction
When it comes to a person speaking more than one language in their life, there are different ways that learning this second language is affected. Some of the history in bilingualism and the effectiveness of how well the individual speaks, involves when they began to learn that particular language. . If the person learns more than one language at once, the chances of them being capable of doing this without a state of confusion is in fact highly probable. Findings suggest that children's early mixing of language does not necessarily reflect interlinguistic confusion. An example of this would be a child being born into a family where both parents have different native languages and would like their child to be fluent in both. One tactic that has been shown to work is when one parent primarily speaks one language to the child and the other parents speaks the remaining language, even if each parent both fluent in both. Alternatively, many people learn their second language at an older age, when they are already fluent in another language and start to learn a second. This is referred to as Second Language Acquisition (SLA). This page will go into much more detail about how SLA compares to learning a different language at a young age. Knowing more than one language can be seen as socially enhancing or on the other hand it can sometimes be restricting. However, due to the fact that language acquisition is a very complicated process there are certain things that predict how successful a person is going to be in their newest language and what is going to hold them back. People must remember that learning something new; especially something like another language takes time, concentration and dedication.

What is the difference between Bilingualism and Second Language Acquisition
The main difference between Bilingualism and Second Language Acquisition is that SLA is when a person has a language that they already speak fluently and they begin to learn an additional language. Whereas, childhood bilingualism involves the child learning two languages simultaneously. The success of mastering a second language is highly affected by the age at which the individual begins exposure to the new language. Older individuals will be able to learn the language itself more quickly than younger children; however, the older individual will be less likely to develop an accurate accent than the younger child.

Language Differentiation
Being able to differentiate between more than one language without getting the two languages mixed up is when a person (child or adult) has reached language differentiation. When looking at bilingualism, children who are learning two languages simultaneously are observed as oblivious to any differences between their two languages; this includes lexical and morphological elements. Children learning more than one language can be affected by many different things that are around the child at the time of learning, such as which parent has the dominant language (how easily it is to be learned), and the rate at which the parents mix the different languages for the child. When it comes to Second Language Acquisition, the learner already speaks one language fluently and has no problem differentiating between the one they already speak and the one they are beginning to learn. When learning a second language such as French, when the persons first language is English, conquering the grammatical parts of the language are much more difficult. The English language does not have the same types of feminine and masculine words the way that the French language does. Another issue could be spelling words. Consider the French/English example again, switching between these languages (called code switching - discussed below) may create spelling mistakes in words that are similar in both languages, such as “different” as ”differente”. This mistake reflects mental errors that occur when switching between two grammatical systems. Differentiating between more than one language is also related to code switching in which the person is capable moving back and forth between different languages.

Language systems and how speaking more than one language affects them
One of the skills that is slower to develp when learning a new language is the reaction time to process, access and voice the right combination of words.. Obviously, with much practice the person is more likely to have a very fast reaction time approaching that of a native speaker. Many people ask if people who speak more than one language are better or worse off than people who only speak one, in the sense that they will have more oppurtunities in the future. In childhood, being taught more than one language could have a variety of effects on children that could involve the child getting confused between the two languages, or even struggling to keeping up with their peers in school. However, once they have developed more than one language system and are able to use language differentiation to avoid getting mixed up, they are more likely to attain additive bilingualism. Being able to fluently speak and understand more than one language may also increase the chance for job opportunities for the individual.

Phonological Differentiation
Phonological differentiation is something that is most effective if the person has learned more than one language as a child. The fact that within different languages the accents cause words and phonemes to be pronounced differently causes people who do not speak the language to have a problem pronouncing certain sounds. For example, people who speak Korean do not hear a difference in the letters and/or sounds “R” and “L”, therefore it would be hard for a person who speaks this as a first language to be capable to learn another language where differentiating these sounds is important (i.e. English). Children however, do not necessarily exhibit confusion between two different phonological systems when they are learning more than one language in childhood. Many researchers wonder if the child is developing one language system or two, one meaning that they are incapable of differentiating between the different languages that they speak. When looking at the phonological differentiation between languages, researchers are looking to see if children exhibit confusion when trying to discriminate the phonological systems of two languages. There is also the question of whether or not the system could have started out as one system but diverged into two, because in this case it would not be a restriction for the children.

Lexical Differentiation
Most children learning more than one language at once generally are learning one language from one parent and the other language from the other parent, although this may vary due to the family structure (i.e. grandmother, other family members, etc.). There are arguments that say children are unable to develop both separate and undifferentiated systems of language, in the sense that they will not be able to differentiate between the words and meanings between the languages that they are attempting to learn. One way that researchers see if children are developing two systems is by asking them to find synonyms for words. An inability to perform such a task signifies that they are only developing one system.

Morphosyntactic Systems
This is the best way to determine whether a child is developing one or two systems for the languages that they are learning. Researchers will look at whether or not a child mixes up or gets confused with the grammatical aspects of the languages that they speak. A good example of this is when a person, usually new to the desired language, mixes up the order in which the words are supposed to appear. For a more in depth example: in the French language many of the adjectives come after the noun (“la maison rouge”) which would usually come before the noun in English (“the red house”). If the person that is speaking the two languages is unable to swtich the rules from one language than it is more than likely that the individual has only developed one system instead of two.

Issues in Bilingualism
Some of the main issues that people who are bilingual have, are the ones that involve social situations. As a child learning more than one language at a time this can be very difficult communicating with peers because many of their peers are not experiencing the same problem. For those learning a new language when at an older age, the problem shifts to being able to master the accent and pronunciation of certain things in the new language. There are some languages that include sounds that different languages would not even be able to notice. When a person is learning one of these new languages they need to be extra attentive to what is being said or how they are saying something.

Is there an Innate Component for learning a second Language?
One of the main questions relating to language is whether it is innate or learned due the fact that it is found everywhere. According to Noam Chomsky language potential was innate and innate to every humans mental capacity. He argued that there was no way a parent could be the sole factor in children developing language the way they do. Chomsky had the effect on scholars to the point where they began to define language as being universal and innate. Thus, the potential for language is innate, but whether or not it is practiced will determine the ability in using language (i.e. neglected children who are never taught the rules of language)

Psycholinguistics Competition Model
Also referred to as the competition model, this theory basically states that certain “cues” and rules from the previous language that speakers had learned will cross over to the new language that the person is attempting to learn. When speakers begin learning a new language, they are more likely to use techniques that facilitated their native language during that learning process. Other learners will use code switching as a way to learn a new language, because during code switching they can add in words for the opposite language when they are uncertain if a word suits a certain context. This model includes a contrastive analysis which is used to predict potential errors that a speaker will make switching from one language to a new one, by examining the different rules that are involved in the different languages. This competition model helps deepen our understanding of learning a second language and facilitates the process of developing a second language due to being made aware of the speed bumps of language

Socioculturists Approach
The socioculturist perspective focuses on whether or not learning a new language or being able to speak multiple languages will aid in making the person a more efficient and skilled individual in another culture. socioculturists look into how language performance is related to their personal identity and their identification in a different culture that speaks another language by examining factors such as ethnic pride, racism and prejudice in cultures.

Another aspect of the socioculturist perspective is that it helps language professionals with the issue between SLA and the cultural values. An example of this would be a family moving from another country into North America, and the child would desperately want to learn the new language so that they are not marked as a person who speaks a foreign language. A new language usually aids in cultural and personal experiences along with even helping the individual gain financial benefits. These factors generally cause the individual to become more motivated to learn the language to broaden their opportunities.

Bilingual Code-switching
Code-switching is something that is rather interesting in the study of how different languages effect a person and how the person functions in daily situations. Code-switching is recognized when an individual switches from speaking one language to randomly speaking in a completely different language.

Additive Bilingualism
Additive Bilingualism is act of acquiring a second language in addition to the mother tongue.

Subtractive Bilingualism
Subtractive Bilingualism is the act of replacing the mother tongue with the second language. This has negative effects in the self-image of the learner.

Biological/Emotional Consequences of Bilingualism
Being able to speak more than one language is an accomplishment in itself, but to be able to become more skilled in a particular language the speaker must be able to initiate contact with the desired language. This involves whether the speaker is keeping contact with the target language out of desire, necessity or both. It is very important to maintain and preserve the culture by staying involved. When it comes to SLA it has been shown that it is innate for humans to seek out others to interact with, in order to use our language.

The physiological structures involved in the motivation to learn a second language include:

 * The amygdala which involves the emotional perception and the production of language
 * The frontal cortex which has to do with ones decision making and risk assessment
 * Along with the body proper

Different languages affect a variety of cognitive process, including emotional responses.. The person’s native tongue is the emotional outlet when emotional schemas come into play. An example of this would be when someone is angry they are most likely to release their frustration in their mother tongue.

Another interesting point about an individual’s dominant language is that people are most likely to talk in their sleep using their dominant language rather than their second learned language. So it matter how fluent a person becomes in subsequent languages, there still appears to be a subconscious preference of superior ability in their native tongue.

Emotional Schemas
Emotional schemas are “mental frameworks” that are created and remembered due to an emotional response and/or experience in a social setting in which we keep to predict what we are likely to feel in future situations.

How Multiple Languages Effect the Brain
Learning multiple languages will obviously have some sort of effect on the human brain; no matter what age the individual begins to study the language. Kim and colleagues studied the native-language and foreign-language activation in accordance with when the language was learned. What they found was that a foreign language was spatially separated in the brain from ones native language when the foreign language was learned in adulthood. When the second language was learned in childhood it tends to be activated while overlapping within the Broca’s area, unlike Wernicke’s area where there was no separation of language that depended on age of acquisition.

Discussion
In conclusion, learning more than one language is underrated in the sense that many people do not consider it a big deal. Children who are learning more than one language at once most likely find it hard at times, but in the long run they are most likely going to become more advanced and have more opportunities than those who are not bilingual. Especially in Canada, where there are provinces that have more than just English as a native language; Quebec and New Brunswick both have French as a major language. It is a complicated task to learn a second language but for those of you who have accomplished the knowledge it is very rewarding. Many researchers are still looking into the studies that involve the brain when learning a second language and others are looking into the effects it has on the people who have obtained a second language.

Quiz

{Which form of language use has been shown to increase the odds of social success? + Additive Bilingualism. - Bilingual Codeswtiching. - Emotional Schema. - Lexical Differentiation.
 * type=""}

{When a bilingual person gets angry, they are more likely to revert back to the first language they learned. + True. - False.
 * type=""}

{The primary difference between bilingualism and second language acquisition (SLA) is: - Fluency. + Onset of learning. - Language individual is learning. - Pronunciation.
 * type=""}

{Noam Chomsky suggested that knowing more than one language is beneficial to a person's social and cultural adjustment. - True + False
 * type=""}

{Incorrectly applying the rules from one's native language during second language use is an error in which type of processing: - Lexical Differentiation. - Emotional Schemas. - Phonological Differentiation. + Morphosyntactic Systems.
 * type=""}

{ Motivation to learn a second language is governed in part by the _____________. { Amygdala }
 * type="{}"}

{Name one prominent factor that differs between children who are monolingual and children who are bilingual. - Bilingual children have funny accents. - Monolingual children have funny accents. + Bilingual children are likely to know certain words in one language but not the other. - Monolingual children will definitely try a second language later in life.
 * type=""}

{ According to _________________________________, people who are new to a language are more to likely to draw on techniques that previously facilitated their native fluency. { Psycholinguitics Compitetion Model }
 * type="{}"}

Critical Thinking
These questions and activities are to take you into a deeper and stronger perspective on the acquisition of multiple languages and to really get you thinking...

1. Explain the differences between Phonological differentiation, Lexical Differentiation and Morphosyntactic Systems.

2. When researchers use the term of people developing more than one system, what are they referring to?

3. Explain the differences between Additive Bilingualism and Subtractive Bilingualism.

4. What is Bilingual Code-Switching?

5. What are Emotional Schemas? Create a unique example of something you would consider to be one.

6. Maria is a 7 year old female who's mothers first language is French and her fathers first language is English. Maria understands what she is trying to say, but often knows words in one language but not the other... What is she having trouble differentiating? Is she dealing with one or two systems?

7. From the previous question, if Maria had been 17 years old instead of 7, and was having trouble converting between the languages that she spoke... what kind of effect would this have on her social facilitation? Would it have a positive or a negative effect?

8. Explain how Broca's and Wernicke's area respond differently to language as a function of age of acquisition.


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Summary
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User:Isom.schmidtke

Hello! I am Dr. Jennifer Isom Schmidtke and this is the beginning of a journey to develop online collaborative texts and resources for students in psychology at California State University, Fresno and Alliant International University, Fresno.

This semester (Spring 2011), classes will be creating three texts:

Topics in Personality

Behavioral Neuroscience

Topics in Social Psychology

title: User:Isom.schmidtke


text: User talk:Mikebogle

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User:EGM5241.S11.team5.cavalcanti/HW1

Problem 1 - L'Hôpital's Rule
Given: $$ f(x)=\frac{e^{x}-1}{x}\ $$. Find: 1. $$ lim_{x\rightarrow 0} f(x) $$. 2. Plot

Solution
According to L'Hôpital's Rule, if we have and the denominator is equal to 0, we evaluate the limit by  Therefore, $$\frac{\mathrm{d} (e^{x}-1)}{\mathrm{d} x}=e^{x}$$, and $$ \frac{\mathrm{d} (x)}{\mathrm{d} x}=1$$. By applying L'Hôpital's Rule, we get: $$ \lim_{x\rightarrow 0}\frac{e^{x}-1}{x}=\lim_{x\rightarrow 0}\frac{e^{x}}{1}=\frac{1}{1}=1 $$

Plot
The plot is shown on the domain [0,1]:

Octave Code
octave-3.2.4.exe:1> x=0:0.1:1; octave-3.2.4.exe:2> y=(exp(x)-1)/x; octave-3.2.4.exe:3> plot(x,y,"@13")

Problem 2: Taylor Series
Given: $$ f(x)=\frac{e^{x}-1}{x}$$. Find: $$ p(x)$$ and $$ R_{n+1}(x)$$.

$$p(x)$$
To find $$p(x)$$, we need to take the Taylor Series, as seen in Meeting 3. We start out by taking the Taylor Series of $$e^{x}$$, as shown: $$x_0=0$$ and $$ \frac{d e^{x}}{dx}=e^{x}$$. Therefore, the Taylor Series Expansion is: $$p(x)= 1+\frac{x}{1!}+\frac{x^{2}}{2!}+ ... +\frac{x^{n}}{n!}$$. Subtracting 1, we then get: $$p(x)= \frac{x}{1!}+\frac{x^{2}}{2!}+ ... +\frac{x^{n}}{n!}$$. Finally, dividing by x, we get the final answer: $$p(x)=1+\frac{x}{2!}+\frac{x^{2}}{3!}+ ... +\frac{x^{n-1}}{n!}$$

title: User:EGM5241.S11.team5.cavalcanti/HW1


text:
User:EGM6341.S11.team5.cavalcanti/Homeworks

HW 1 HW2 HW 3 HW 4 HW 5 HW 6


text:
User:Peterrawsthorne

I currently see myself as being hellbent to implement the ideas in and around pedagogy, new media, social networks and communities of practice. I see my success being measured by completed implementations. Oh, there is so much talk, I'd rather be measured by my project success! contact me

Open and Networked PhD (OnPhD)
The linked profile page was created in support of my work toward completing a Open and Networked PhD

Books
This is a list of books I am currently writing. They are both a work in progress with the intention to self publish. The content for these books will be created in a number of places, including;
 * My blog
 * My website(s)
 * Bowen Institute of Technology
 * Peter Rawsthorne for hire site

Mobile Web Applications
Related Courses: Topic:Three-Tier_Architecture

Badges Evidence
Evidence toward open badges earned from Wikiversity courses

title: User:Peterrawsthorne


text:
User:Eml5526.s11.team01/Hwk1

=Problem 1:= Obtain the dynamic partial differential equation of an elastic bar by doing balance of forces From Lecture Slide.

Given
An elastic bar of arbitrary cross section $$A\left( x \right)$$ with Young's modulus $$E\left( x \right)$$ under dynamic conditions, restricted to move in longitudinal $$x$$ direction only.

Find
The governing partial differential equation of the elastic bar under dynamic conditions.

Solution
In this document is deduced the differential equation of a bar made of linear elastic material, subject to small strain under dynamic conditions. Only strain in the longitudinal direction of the bar is considered.

Fig. 1.1 shows the bar which, in general, has variable cross-section $$A\left( x \right)$$. $$u\left( x,t \right)$$ is the displacement in the longitudinal direction. Fig. 1.2 shows the free body diagram of a small piece of the bar of length $$dx$$. On that fig. the stresses $$\sigma $$ acting over each face of the element are shown.

 * {| style="width:100%" border="0"

$$ -A\sigma\ + \left(\sigma\ + \frac{\partial \sigma}{\partial x}dx\right)\left(A + \frac{\partial A}{\partial x}dx\right) +fdx = dxA\rho\frac{\partial^2 u}{\partial t^2}$$
 * $$\displaystyle (Eq. 1.1) $$
 * }
 * }

In the latter equation, $$\rho $$ is the density (mass per unit of volume). Doing the indicated product we have:

 * {| style="width:100%" border="0"

$$ -A\sigma\ + A\sigma\ + A\frac{\partial \sigma}{\partial x}dx +\sigma\frac{\partial A}{\partial x}dx + \cancelto{0}\frac{\partial \sigma}{\partial x}\frac{\partial A}{\partial x}dxdx + fdx = dxA\rho\frac{\partial^2 u}{\partial t^2}$$
 * $$\displaystyle (Eq. 1.2) $$
 * }
 * }

Neglecting the second order factor, and dividing by $$dx$$ we have:

 * {| style="width:100%" border="0"

$$ A\frac{\partial \sigma}{\partial x} +\sigma\frac{\partial A}{\partial x} + f = A\rho\frac{\partial^2 u}{\partial t^2}$$
 * $$\displaystyle (Eq. 1.3) $$
 * }
 * }

Where, the product $$\rho A$$ has been replaced by $$m$$. The first two terms in the last equation are the derivative of a product, therefore:

 * {| style="width:100%" border="0"

$$ \frac{\partial A\sigma}{\partial x} + f = m\frac{\partial^2 u}{\partial t^2}$$
 * $$\displaystyle (Eq. 1.4) $$
 * }
 * }

Using the Hooke's law to replace the stress as function of the infinitesimal strain $$\varepsilon $$ we have:

 * {| style="width:100%" border="0"

$$ \frac{\partial AE\epsilon}{\partial x} + f = m\frac{\partial^2 u}{\partial t^2}$$
 * $$\displaystyle (Eq. 1.5) $$
 * }
 * }

The strain-displacement equation is obtained by applying the engineering definition of strain for an infinitesimal segment of the bar. The elongation of the segment is given by $$u\left( x + \Delta x \right) - u\left( x \right)$$ and the original length is $$\Delta x$$, therefore, the strain is given by:

 * {| style="width:100%" border="0"

$$\epsilon\left( x \right) = \frac{elongation}{original\ length} = \frac{u\left( x + \Delta x \right) - u\left( x \right)}{\Delta x}$$
 * $$\displaystyle (Eq. 1.6) $$
 * }
 * }

Taking the limit of the above as $$\Delta x \to 0$$, we recognize that the right-hand side is the deriative of u(x). Therefore, the strain-displacement equation is:

 * {| style="width:100%" border="0"

$$\epsilon\left( x \right) = \frac{\partial u}{\partial x}$$
 * $$\displaystyle (Eq. 1.7) $$
 * }
 * }

Replacing the infinitesimal deformation in terms of the displacement, we have:

 * {| style="width:100%" border="0"

$$ \frac{\partial AE\frac{\partial u}{\partial x}}{\partial x} + f = m\frac{\partial^2 u}{\partial t^2}$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 1.8) $$
 * style= |
 * }

=Problem 2:= Discuss the case in which the bar from problem 1 has rectangular cross section. From Lecture Slide.

Given
The crossection of the bar is given by:
 * {| style="width:100%" border="0"

$$ A = bh\left(x\right)$$
 * $$\displaystyle (Eq. 2.1) $$
 * }
 * }

Find
Discuss the case when the bar has constant width and variable height

Solution
Going back to Eq. 1.3 we can replace the area by using Eq. 2.1 to obtain:

 * {| style="width:100%" border="0"

$$ \frac{\partial \left(bh\left(x\right)\sigma\right)}{\partial x} + f = \frac{1}{2}\left(h\left(x\right)+h\left(x + dx\right)\right)\rho\left(x + dx\right)\frac{\partial^2 u}{\partial t^2}$$
 * $$\displaystyle (Eq. 2.2) $$
 * }
 * }

Where the factor $$\frac{1}{2}\left(h\left(x\right)+h\left(x + dx\right)\right)\rho\left(x + dx\right)$$ has been used to approximate the mass per unit length in the middle of the segment $$\left(x + \frac{dx}{2}\right)$$; the factor $$\frac{1}{2}\left(h\left(x\right)+h\left(x + dx\right)\right)$$ is the average height between the beginning and the end of the segment of length dx (Fig. 2) which is being used as an approximation of the height at the middle of the segment: $$h\left(x + \frac{dx}{2}\right)$$. But as the segment is small this height can be further approximated to the height at the beginning of the segment $$h\left(x\right)$$. Doing that approximation and considering that $$b$$ is constant and can be taken out of the derivative, Eq. 2.2 becomes:

 * {| style="width:100%" border="0"

$$b \frac{\partial \left(h\left(x\right)\sigma\right)}{\partial x} + f = h\rho\frac{\partial^2 u}{\partial t^2}$$
 * $$\displaystyle (Eq. 2.3) $$
 * }
 * }

Finally, replacing the stress $$\sigma$$ as function of strain by using Hooke's Law, and the strain as a function of the displacement by using Eq. 1.6 and Eq. 1.7 we have:

 * {| style="width:100%" border="0"

$$b \frac{\partial hE\frac{\partial u}{\partial x}}{\partial x} + f = h\rho\frac{\partial^2 u}{\partial t^2}$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\,(Eq. 2.4) $$
 * style= |
 * }

=Contributing Team Members=
 * James Roark
 * Harrison Sheffield
 * Abhijeet Bhalerao
 * Cedric Adam
 * Fernando Casanova
 * Yu Hao

title: User:Eml5526.s11.team01/Hwk1


text:
User:Peterrawsthorne/PhD

=Open and Networked PhD (#OnPhD) - candidacy= At the moment, I am accumulating works to prove my success. I see the review of all these works in combination with some effective publishing in a number of forms as giving credibility (and the opportunity for critical review) to my work. I will be open and public with my works through the;

 * 1) Use my blog (and related channels) for formative and summative notes and reflection.
 * 2) A whole lot of other artifacts, coming soon

What do I consider an Open and Networked PhD (ONPhD)?
It's the combination of putting in the time to become a master in an identified subject, advancing the body of knowledge in the chosen subject and doing it all in the open with transparency. Openness with transparency is publishing as much of the process as possible. This includes keeping a learning journal and publishing all writings without copyright.

What is being a master?
Mastery is being so familiar and comfortable with a subject that responding to questions / situations within the subject is done without hesitation or second guessing the response. Mastery is also knowing where the boundaries are within the subject and how to best approach investigating the boundaries. Mastery also includes be considered a master of a subject by others who are also masters of the subject.

What do I already consider myself a master?

 * 1) As an Educator with over 15 years facilitating learning at Colleges, Universities and a variety of online locations
 * 2) As a Solutions Architect where I have built complex (and not so complex) software systems for a whole plethora of organizations, from start-ups to huge enterprises.
 * 3) As a sailor, traveler and back-country explorer
 * 4) As a builder of Online Communities
 * 5) Gardener and home builder

What would I like to consider myself a master?

 * 1) Musician
 * 2) Folk Music Historian (with Focus on Morris Dancing)
 * 3) Master boat-builder
 * 4) Certified Enterprise Architect

Why am I doing this?
Because I am really worried that the education system isn't going to prepare my kids for the world they are entering. I believe that education needs to be much more self-directed and the credentials from antiquated and costly institutions are becoming meaningless. My thoughts regarding this issue is well articulated in my post on educational ROI.

My Learning History
This section has been written to fullfill the 'Describe your learning history' task for the P2Pu Open & Networked PhD Candidacy Challenge. https://p2pu.org/en/groups/onphd-candidacy/content/describe-your-academic-history/

25 years work experience in Information Technology

 * Numerous conversations about implementation of technology
 * Years of successful IT project completion
 * Invited speaker to numerous technology conferences
 * Reading, writing and blogging about Information Technology, Software Development and Solution Architecture
 * Many successful project across many different technology platforms within many different industries
 * Key Learning: I have a mastery of Information Technology (IT) that provides me a foundation to learn new IT very quickly. I also draw on this experience to bring complicated technology projects to completion, regardless of when I join the project.

15 years as teacher, facilitator, and mentor within educational realm

 * Numerous conversations about teaching and learning with other professional educators
 * Teachers are an amazing cohort who love to share and help people to fulfill their dreams
 * Development of many courses (traditional, online and blended)
 * Parenting children
 * Ongoing involvement with online learning communities
 * Reading, writing and blogging about Pedagogical approaches
 * Key Learning: People learn differently and this changes through time (as they age). The tools for online learning are brilliant and open a whole new world. In the end learning is iterative, personalized, community based and best done with love.

Lifetime of different roles within residential and commercial construction

 * Once the weather was good enough and I was able to follow instructions my parents had me working in the garden and on the house. My father was an engineer and we pretty much rebuilt the whole house over a 15 year period. I learned may things with this, most important was organizing things for project completion
 * I was a big boy growing up, I was quickly drafted into helping out on construction sites as the manual youthful labour. I learned a whole lot about how to build houses during my four summers as the assistant to everyone.
 * Many years as a residential and commercial painter. Mostly I learned about project completion, running a small business, simple accounting, running work teams, and contract negotiation.
 * Renovation of many houses since I have been an adult owning my own home. There is not a sub-trade role that I do not feel comfortable fulfilling.
 * Key Learning: Building things (particularly big things) requires thought and planning. Building projects need to be done in an orderly fashion, particularly if you want quality upon completion. All of the hands-on skills developed when building things brings a kinesthetic intelligence that transfers to other learning.

Many years playing outside in the mountains and on the ocean

 * Sailing is my passion
 * Backcountry skiing is the thrill I seek
 * Hiking, camping and time away from civilization grounds my spirit
 * Scouting and developing the skills to be successful in the outdoors taught me patience and an eye for opportunity
 * traveled to 32 different countries, so far...
 * Key Learning: Spending times in the outdoors forces you to become resourceful and to look for opportunity. It also teaches how to work as a team and care for every member of the team. It teaches about limits and how to push those limits (both individually and as a team). Being in the outdoors teaches you to pack light and share what you have. Travel allows you to experience different views and new perspectives.

Ongoing involvement as Performance Artist

 * Mostly as Morris dancer and accompanying folk musician (percussion)
 * http://criticaltechnology.blogspot.ca/search/label/morris
 * Key Learning: Performance art with a group of dancers and musicians is an amazing AND coordinated effort. It takes practice and a trust of all other performers. It is a highly creative endeavour. Learning an existing dance or creating something new can take time and all members learning processes need to be honoured.

Formal Learning

 *  Memorial University of Newfoundland (2005 – 2007)
 * Master of Education, Information Technology
 * Activities and Societies: Certified; Graduate Program for Teachers

 *  Justice Institute of British Columbia (1994 - 1997)
 * Certified, Conflict Resolution

 *  British Columbia Institute of Technology (1991 – 1996)
 * Bachelors of Technology, Database Management (with Honors)
 *  Capilano University (1984 – 1990)
 * Diploma, Computer Systems Management

 * Hillside Secondary School (1976 – 1981)

 * Professional Certifications
 * Microsoft Certified Professional + Site Building
 * Microsoft Certified Solutions Developer
 * Microsoft Certified Database Administrator
 * Microsoft Certified Trainer

Area of Study
My PhD will draw on both my two professional areas of expertise; Technology and Andragogy. And as my online profile states, "Hellbent to implement the ideas in and around pedagogy, new media, social networks and communities of practice." My focus of this will be toward the self-directed life-long learner, and in developing both technological and pedagogical approaches that will enable people to develop an advanced level of knowing without the restraints (financial and otherwise) of traditional institutions and approaches.

https://p2pu.org/en/groups/onphd-candidacy/content/identify-your-domain-of-study/

Technology Realm
Within this realm I aspire to create / add to the online body of knowledge focused on solution architecture. This solution architecture body of knowledge will focus upon the use of industry standard architectural frameworks and professional associations. With reference to these existing entities the focus will then be upon architecting solutions for the internet.
 * http://en.wikiversity.org/wiki/Solution_Architecture

Andragogical Realm
Within this realm I aspire to create / add to the online body of knowledge focused on life long learning and the online tools and approaches that facilitates this activity. My focus on life long learning will be through the role of the educational technologist. I do intend my focus to be upon life-long learning and related andragogical subjects. As I learn more I believe the focus will move into the heutagogical.

To do

 * 1) Research Heutagogy with enough depth to create dedicated concept map
 * 2) Add security related concepts to concept map

Reading List
List of references related to Heutagogy and autodidactism;

Folk Music and Dance Realm
I'm a Morris dancer and I love the music and dance that occurs within this realm. I intend this realm to be the anchor to all my pedagogical and technological studies and research.

Area of Research
Well... this keeps changing! I will settle on my research when I am further entrenched in the work of the OnPhD. My thinking to date includes;
 * 1) Building a Web2.0 based massively collaborative assessment system in PhP / MySQL. More on this later...
 * 2) An infrastructure (web portal) for clustering all the validated self-directed learning events
 * 3) A Personalized Instructional Design Methodology for the Heutogogue
 * 4) Learning practices of the Non-PhD holding honorary doctorates and global experts

Published book reviews since January 2011

 * 1) "A New Culture of Learning: Cultivating the Imagination for a World of Constant Change", (2011), Douglas Thomas and John Seely Brown. http://criticaltechnology.blogspot.com/2011/03/new-culture-of-learning.html
 * 2) "Programming Collective Intelligence; Building Smart Web 2.0 Applications", (2007), Toby Segaran. http://criticaltechnology.blogspot.com/2011/05/book-review-programming-collective.html
 * 3) "Talent is Overrated", (2008), Geoff Colvin. http://criticaltechnology.blogspot.com/2011/06/book-review-talent-is-overrated.html

Delicious tags
http://www.delicious.com/tags/prawstho

WikiEducator
http://wikieducator.org/User:Prawstho

During my time at WikiEducator I accumulated considerable amount of experience in furthering the 'cause' of OER. All this is best shown through my profile page.

School of Digital and Open Badges
The badge movement is growing. There are many aspects to digital and open badges and we are building a school to help people learn about this amazing addition to life-long learning.

Baselines
Doing a PhD in the open is also about publishing and having your work recognized. How better than using the social media to publish your works and increase the viewership of the work. Is this a peer review, I believe so... particularly through the endorsement of your work through accumulating followers, commenting and backtracks.

Twitter

 * 25 January 2011 = 425
 * 29 January 2012 = 543
 * 27 June 2013 = 715

LinkedIn

 * 26 January 2011 = 248
 * 29 January 2012 = 292
 * 27 June 2013 = 412

Google+

 * 27 June 2013 = 332

Slideshare

 * 26 January 2011 = 14
 * 27 June 2013 = 24

YouTube

 * 26 January 2011 = 4
 * 27 June 2013 = 19

Wikipedia Edits (As of July 2011)

 * 1) http://en.wikipedia.org/wiki/Data_dictionary

Wikiversity Edits (As of July 2011)

 * 1) http://en.wikiversity.org/wiki/Talk:Greater_Access_Choice_and_Flexibility:_Learning_at_University_of_Canberra

relevant subject areas

 * http://criticaltechnology.blogspot.com/search/label/openphd
 * http://criticaltechnology.blogspot.com/search/label/pipeandtabor
 * http://criticaltechnology.blogspot.com/search/label/nophd
 * http://criticaltechnology.blogspot.com/search/label/collective
 * http://criticaltechnology.blogspot.com/search/label/inspired
 * http://criticaltechnology.blogspot.com/search/label/fair-dealing

number of relevant comments (14)
I sometimes get involved in discussions related to pedagogy, technology and life-long learning. I will journal these discussion here.
 * 1) 3 August 2011
 * 2) Discussion about professional development for teachers and faculty; http://www.tonybates.ca/2011/08/01/why-the-current-professional-development-model-is-broken/
 * 3) 23 April 2011
 * 4) WSIS Platform of Communities: Should OER favour commercial use? http://www.wsis-community.org/pg/debates/group:14358/overview/251476
 * 5) 28 March 2011
 * 6) Paul Stacey from BCcampus: Open Education and Policy https://creativecommons.org/weblog/entry/26963
 * 7) How Can We Scale Educational Innovations? http://blogs.hbr.org/innovations-in-education/2011/03/how-can-we-scale-educational-i.html
 * 8) 15 March 2011 - Student as Narcissist
 * 9) http://keanewheeler.blogspot.com/2011/03/university-student-narcissism.html
 * 10) 23 February 2011 - interesting discussion around home bases and outposts within the legal publishing perspective.
 * 11) http://lawyerist.com/blogging-provides-publishing-platform-and-offers-control/#comments
 * 12) 26 January 2011 - bit of a flame war regarding #ds106. The real value was the discussion on branding within edu2.0 and working within academia. What later came from this "flame war" was how weak social media relationships can be. People I considered friends quickly turned on me... I think I was not a part of the "in" crowd so I wasn't allowed to play with them anymore ;)
 * 13) http://www.flickr.com/photos/97283472@N00/5389150753/
 * 14) http://bavatuesdays.com/a-little-confused/#comments

Slideshare

 * 1) as of 26 January 2011 = 9

Youtube

 * 1) as of 26 January 2011 = 12

title: User:Peterrawsthorne/PhD