What is knowledge?

I am now at Hong Kong University participating in a knowledge management workshop and offering seminars on educational technology and academic publishing. My contribution to the workshop was a presentation on assessing learning in complex domains – a topic with which I have wrestled for some ten years now. Several other presentations were more directly focused on knowledge building, knowledge management and knowledge visualization. The talks were all excellent and the technologies being developed quite exciting. However, at the end of the workshop, I found myself wondering about this concept called knowledge.

My immediate conclusion was that I was in a state of confusion. My first impulse was to look at how relevant words are used in ordinary language because I suspected some of my confusion was a result of differing uses of key words such as ‘know’ and ‘knowledge’. These remarks are a summary of where I have arrived after a few hours of deliberation – not very far from where I started, I regret to report.

In recalling several of the presentations, the words on which I focused were ‘believe’, ‘belief’, ‘know’, and ‘knowledge’. In each of these pairs there is a verb and a noun. The English language is full of verb-noun pairs, as are many other languages. An interesting exercise is to try to find a verb or noun for which there is no corresponding counterpart. Perhaps not so interesting after all, as nothing comes to mind – at least not to my limited mind. I expect a linguist to interject a comment at this point, but alas I am alone without a linguist to consult.

The next step is to notice that one can associate one and the same person with the noun and the verb, as in these phrases: “I believe that Columbus sailed the ocean blue in 1492,” “My belief is that Columbus sailed the ocean blue in 1492,” “I know that the cube root of 64 is 4” and “my knowledge includes the fact that the cube root of 64 is 4.” This line of reasoning led me to wonder about a number of things. First, is there always a subject associated with a verb – a believer to go with believing and a knower to go with knowing? Second, is there some essential difference in the objects associated with believing and knowing? I realize these are not particularly novel questions, and I have previously wondered about these matters myself, only to leave this logical landscape in pursuit of other seemingly more compelling matters.

I then tackled what I believed to be the simpler of these two questions – whether there was always a subject associated with a verb.  This is different than simply looking for a noun that pairs up with the verb; in this case I am looking for someone who performs or is associated with the action indicated by the verb. For example, consider the noun-verb pair rain-raining. Of course there is rain and when it is present we say it is raining. But is there someone who does the raining? Oops. Be careful not to slip on the wet pavement caused by all that rain.

With believing and knowing, however, we readily identify a subject: ‘I believe’ or ‘I know or perhaps he or she believes or knows something. Surely you believe and know many things. Individuals believe and know things. That analysis surely fits well with ordinary discourse.

Then I realized that the word ‘knowledge’ is used not only to refer to what an individual knows but to what a group of people know. This is more akin to its use in the phrase ‘knowledge management’. Many instances of such use can be found and are evident in such phrases as ‘scientific knowledge’, ‘common sense knowledge’, and ‘contribution to the knowledge base’. This dual use of knowledge to refer to individuals and to groups of individuals has the potential to introduce ambiguity and possibly confusion in discussions about learning, instruction and performance. While one can find uses of ‘belief’ associated with groups of people, this is much more rare than the ordinary use of ‘belief’ to refer to an individual’s cognitive state of affirmation with regard to a particular proposition or claim.

What ambiguity or confusion might result from the use of ‘knowledge’? Shall I step off this precipice? I shall. Constructivism is widely accepted by philosophers, psychologists, educational researchers and instructional technologists. The kernel idea in constructivism is that individuals actively construct and interpret experience. Constructivism can be traced at least as far back as the 18^th century and Immanuel Kant’s Critique of Pure Reason in which Kant postulates certain categories of the mind that a person brings to all experience – namely, the categories of space, time and causality. We structure our experiences according to those categories; part of the interpretation of experience involves space, time and causality. In subsequent centuries, much has been added to the notion of individual construction and interpretation of experience. In the 20^th century, Wittgenstein takes the notion much further. In the Tractatus Logico-Philosophicus, Wittgenstein observes that we picture facts to ourselves – we create internal representations of things we experience. Wittgenstein fails to mention that we also have the ability to picture things that are not facts to ourselves, but let us put that aside for the moment. In Philosophical Investigations, published after his death, Wittgenstein introduces the notion of language games, which involve a community sharing these internal representations with each other, implicitly following a set of conventions governing their discourse. Taken together, Wittgenstein’s two notions comprise what is often referred to as ‘socio-constructivism’. We create internal representations of things we experience – this is a descriptive claim about what people do in the process of making sense of their experiences and in coming to know about and understand things they experience. This ability to create internal representations is a remarkable aspect of cognition in and of itself – so remarkable that we hardly notice it at all. In addition, humans talk to each other about these internal representations – an equally remarkable ability that again goes largely unnoticed. Okay … enough history of philosophy already … I have now stepped off the precipice.

Wherein lies the ambiguity or confusion? There was that small matter that we set aside for the moment – namely that we also have the remarkable ability to create internal representations of things that are not factual. We can also picture non-facts to ourselves. By some form of twisted reasoning, I might arrive at the belief that the cube root of 1492 is 64 (of course it isn’t). I have created an internal representation of mathematics such that I am led to that erroneous belief. While this may seem outrageous, one can imagine other cases where a person legitimately creates an internal representation of an experience that is clearly false but also quite understandable (that exercise is left to the reader with an overactive imagination). Obviously people falsely believe things – that is to say, they sometimes sincerely believe things that are clearly not the case. We now arrive at an interesting juncture. Not all beliefs are true, which for now means only that some beliefs held by individuals would not be accepted as factual by a community who generally understand statements relevant to the domain in question. So, while the person holding the belief in question might say that “I know it to be so,” the larger community would not accept that alleged fact as knowledge. An individual belief represents an affirmative state of mind with regard to the matter in question. An individual belief may also be the basis for a knowledge claim on the part of that individual. However, to be considered knowledge, such claims require more than an individual’s affirmative state of mind. Typically, such claims require the affirmative states of mind of many individuals over a reasonably long period of time. While I believe that Columbus sailed the ocean blue in 1492, there are also many others who believe this as well, and their beliefs have been held by many people for a long time. Does that make the claim true? Perhaps not – perhaps he sailed the ocean blue in 1491 and the records of that voyage were off by a year. Perhaps the ocean was green. Perhaps he landed in Greenland instead of the Bahamas (not very likely). Anyway, claims that people have regarded as certainly true and legitimate knowledge have occasionally turned out to be wrong or mistaken. Nonetheless, it makes sense to hold knowledge claims to a higher standard than belief claims (if this is not obvious, then you are destined for a career in politics).

That excursion into the logical landscape surrounding beliefs and knowledge was a result of wondering about the person(s) associated with believing and knowing. While in each case one can associate a particular individual with believing or knowing, it is often the case with knowledge that we are referring to a set of beliefs accepted by a larger community as being particularly well established. All of this is probably obvious to most folks even though it took me a while to struggle to this interim and somewhat tentative conclusion. I am a very slow learner. In any case, I can now say to a person who wonders whether a child constructs knowledge or not, that surely a child does construct knowledge although what is constructed may not add anything to the knowledge base accepted by the relevant knowledge community. People are naturally constructing knowledge (beliefs that they accept as true based on their personal experience) all the time. It is what we do – we picture facts to ourselves and then we talk about those pictures to others. We cannot stop doing it, except perhaps when we are asleep. Creating internal representations of our experiences is a natural and ongoing process.

It is perhaps worth noting that a representation is by its very nature a simplification. Our internal representations do not and could not contain all of the details of the direct experience. Let us call these internal representations mental models. Models always simplify the thing modeled. This is a logical remark and not a factual claim, by the way. Models are simplifications. Mental models are simplifications. We simplify in order to understand. It is in our nature to simplify – it is in our nature to create internal representations of our experiences. On the other hand, when we engage in talking about these simplifications, we are engaging in an expansive enterprise. We are adding nuances and getting feedback and suggestions – in talking about our internal representations, we are adding complexity. Of course, this introduces the possibility for ambiguity and misinterpretation, but it may also enrich the original interpretation (mental model) and add to our understanding.

Well, not having arrived at anything especially insightful in exploring the first question, perhaps I should consider the second: Is there a significant difference in the things that are normally considered the objects of belief versus those that are normally considered the objects of knowledge? The two examples with which I embarked on this journey – ‘Columbus sailed the ocean blue in 1492’ and ‘the cube root of 64 is 4’ – suggest perhaps that there was an essential difference, which is surely the kind of answer that Plato would have provided. Objects of belief are subject to change and might turn out to be false whereas objects of knowledge are not subject to change and are eternally true. However, the first exploration of this territory suggests something different. What a community regards as knowledge are merely those beliefs that are widely held and which have been held for a period of time. I know that is vague and evasive – I should have been a politician. It is the case that claims in some domains lend themselves to being well-established and upheld for long periods of time. Mathematics is one of those domains. Nonetheless, it would seem excessively narrow-minded to restrict knowledge to mathematics and similar domains. From a practical perspective, we are problem solvers. What we seek is knowledge that will enable us to solve problems. Over time, the set of problems we want to solve grows in size and complexity, so we need to be expanding our knowledge base all the time. Otherwise we grow stagnant – or, some might say that we simply become comfortable with our existence as it is. Perhaps the job of an educator is to make one uncomfortable with one’s existence. That is a different path to follow perhaps on another day.

A Dozen Remarks on Academic Writing

These comments have been developed over a period of years to help graduate students develop an effective academic writing style. They are by no means comprehensive nor are they exhaustive. Rather, these twelve comments represent a few tips that may prove useful to a few who are in the process of improving their writing skills.

1.      Academic writing is quite different than writing fiction or essays for popular consumption. Academic writing typically involves the development and elaboration of a concept or the reporting of a study or series of studies aimed at exploring the efficacy of an intervention of some kind. The piece is about the concept or the study – it is not about you.

2.      Keep the intended audience in mind. Typically, readers will be professionals, scholars or researchers who want to know about the concept or intervention being presented. As a consequence, the scope and purpose of the piece should be made evident at the beginning of the paper – in the introduction and usually in the first paragraph or page.

3.      One can express complex ideas using short, descriptive sentences. Sentences that are long and that involve multiple dependent and independent clauses create a cognitive load on readers that is unnecessary and that is likely to detract from the purpose of the paper. As a general guideline, sentences should be relatively short – fewer than 30 or 35 words. It is generally desirable to express just one distinct thought in each sentence.

4.      It is all too easy to introduce unnecessary distracters and ambiguities in a paper. One source of ambiguity is the use of multiple terms to refer to the same thing. When a new term is introduced, the reader is inclined to believe that a new concept is being introduced. Minimize the use of what you may regard as synonyms for a term because the reader may not regard those terms as synonymous. You can clarify terminology early in the paper and mention that others use different terms to refer to the concept you are elaborating, but then use one term uniformly after the initial definition and elaboration of that term.

5.      Another source of ambiguity is the use of relative and personal pronouns such as ‘it’, ‘he’, ‘she’, and so on. In addition to creating potential ambiguity, relative and personal pronouns are a source of cognitive load as they create a need in the reader to construct the referent, which might not be as obvious as you think. Use a noun phrase to eliminate any possible misinterpretation and to minimize cognitive load in the reader. An exception might be the use of a relative or personal pronoun in a dependent clause in the same sentence.

6.      Avoid praising your own work. Simply describe what was done. Rather than claim that your intervention was highly creative and innovative, simply describe the intervention and let the reader make such judgments.

7.      Avoid exaggerations. Use of words like ‘all’, ‘always’, ‘never’, ‘impossible’, ‘proof’, ‘must’, and so on are difficult to defend. The reader is likely to start generating exceptions to such claims. Modest claims are typically more effective. Rather than claim that a study conclusively proves a point, a more likely conclusion is that a study suggests something of significance. Likewise, avoid multiple modifiers for a noun – rather than say, for example, “X was a highly articulate person” it is sufficient to say that “X was articulate.” 

8.      Cite the most credible and reliable sources for each of your major points. Rarely is it the case that one invents something altogether new. Rather, one may be building on the work of others to extend that work in some way. Failure to recognize the well known work of others will detract from the credibility of your own work. Moreover, while  you may think that a certain point is obvious, if that point has been argued effectively by an established scholar, give that scholar the credit when making the same point.

9.      Structure a paper so that it tells a story. Begin with the scope and purpose – tell the reader where you are headed. Then develop an organizational framework that builds up to the main point in a logical and coherent manner. Keep the focus on where you are headed, and remind the reader why you are covering specific topics along the way. Resist the temptation to tell everything you might know about related subjects – always stay focused on the major point(s) and resist telling the reader about everything you learned in the process of developing a concept or conducting a study.

10.  Be sure you are familiar with the requirements of the publication venue and with representative pieces previously published in that venue.

11.  Recognize that one cannot conduct a perfect study or a perfect conceptual framework. There are usually limitations and constraints. These should be recognized in the paper. Modesty and humility can be powerful allies in making your reasoning effective.

12.  Recognize that one cannot write a perfect paper. Once you have a draft, have a colleague read it and provide feedback. You do not want simple praise at this point – you want constructive criticism that will help improve the coherence and clarity of the paper.

Tensions between Educational Research and Practice

I recently participated in a meeting sponsored by the US Department of Education for project directors and evaluators award i3 (Investing In Innovation) grants. I am the lead evaluator on one of those 49 projects. It is clear that the overarching purpose of the i3 program is to improve educational practice (in terms of learning outcomes and quality of instruction) in America’s schools. It is also clear that the grantees are expected to have and implement very high quality research and evaluation plans to support claims about improved learning and instruction. There were many references to the What Works Clearinghouse and its standards (see http://ies.ed.gov/ncee/wwc/). If one does a search on the word ‘learning’ in the category of ‘evaluation reports’ one finds only one entry since January 1, 2009. Perhaps this is why some people refer to this site as the “Nothing Works Clearinghouse.”Entries in the Clearinghouse must meet specific standards set by the Institute for Education Sciences (IES; see http://ies.ed.gov/).

It occurs to me that there is some tension with regard to what IES and some educational researchers might regard as clear and convincing evidence that a particular intervention (instructional approach, strategy, technology, teacher training, etc.) works well with certain groups of students compared with what some educational practitioners would be inclined to accept as clear and convincing evidence. The stakes are different for these two groups. IES and its researchers are spending federal dollars – often quite a lot of money – to make systemic and systematic improvements in learning and instruction. They are accountable to congress and the nation who want to see a certain kind of evidence that investments have been used wisely. These people do not have to take the implications of findings back into classrooms.

On the other hand, educational practitioners do have to go into classrooms and their primary responsibility is doing their best, given many serious constraints and limitations, to improve the learning and instruction that occurs in our schools. Teachers are the ones who will put new instructional approaches, strategies and technologies into practice. Teachers are not trained in experimental design and advanced statistical analysis. Teachers are trained in implementing curricula appropriate for their students. While the experimental research may show that using an interactive whiteboard rather than a non-interactive whiteboard has no significant difference in terms of measured student outcomes, a teacher may believe that such use does gain and maintain the attention of students and result in a more well organized lesson, or something else that is not so easily measured. One can imagine other cases where the experimental research suggests no significant difference in X compared with Y but teachers believe that there are significant differences of some kind involved.

Should we simply disregard these teachers and only support the very few things that appear to have clear and convincing evidence of effectiveness as determined by IES standards? Should we expect teachers to understand the sophisticated statistical analysis that supports that kind of clear and convincing evidence? If so, then perhaps we ought to expect those making policy and funding decisions to understand the realities of teaching in a classroom for six or more hours every day. It strikes me that what is needed is research that can be practically implemented in classrooms that has reasonable evidence of effectiveness which can be understood by teachers. These teachers must be properly trained and supported in implementing innovations, which means their schools and school districts must understand both the value and likely impact of an innovation and the need to properly support such innovations.

This now comes full circle, since such innovations typically require funds, which means that parents and the community must then be convinced of the value of properly supporting education and electing officials who will provide the necessary local, state, and national support. What matters in the end is not the quality of educational research findings but the quality of professional teaching practice. I would like to see much less distance between [federally funded] educational research and [locally funded] educational practice. I would like to see research aimed at promoting teachers in achieving their widely held goals rather than research aimed at promoting the careers of researchers and program officials at federal agencies. It is clear that conducting rigorous randomized control trials and quasi-experimental studies in school settings presents serious challenges for those collecting and analyzing data – much more serious than that associated with similar kinds of studies in other sectors, such as medical care or computer science (which are admittedly complex and challenging areas for research). The variations in students, teachers, schools, communities, subject areas, and more make classroom practice a very tough research area. As a result, increasingly sophisticated analytical techniques are emerging which only a few researchers understand and can implement. The worry I am trying to express is that we may be closing the door on evidence that should be considered and might prove quite practical and effective in the classroom. We may be creating a research area that is closed to all except for an elite few who do not have to put findings into practice in the classroom. Is this an unfounded worry?

Teacher- and Learner-Centered Approaches

It has now been some time since I have made an entry in this blog. Perhaps no one is listening. No matter. I am writing mostly for myself – to try to become more clear in my thinking. Being snowed in for three days in Athens, Georgia has helped. Lately, I have been thinking about false dichotomies and misguided distinctions.

There is a legitimate distinction between teacher-centered and learning-centered approaches to instruction. However, this distinction is widely misunderstood and misrepresented. Teacher-centered approaches tend to emphasize the activities that a teacher will use to promote learning. Learner-centered approaches tend to emphasize the activities that will engage learners and result in desired outcomes. Stated in this way, the two approaches are not mutually exclusive nor are they necessarily incompatible. Because the goals of most teachers and instructional designers involve actions and activities that will result in improved learning and desired learning outcomes, a teacher-centered approach is likely to take into account those activities that are likely to be engaging and meaningful for learners. Moreover, once learner-centered activities are identified and elaborated, it is quite natural to consider how teachers can best support those activities. Considered this way, one can say that the difference has to do with emphasis and where one begins analysis and planning to support learning. The optimum end result is likely to include both learner-centered activities and teacher-centered support.

Imagine a Venn diagram (see the figure below) with a circle for teacher-centered approaches and an intersecting circle for learner-centered approaches. This results in four distinct areas: (1) teacher-centered without any learner centering (quite rare), (2) learner-centered without any teacher-centering (also quite rare), (3) both teacher- and learner-centered (highly desirable), and (4) neither teacher- or learner-centered (e.g., some museum environments). Associated with these two approaches is a continuum from structured, directed learning environments to unstructured, open-ended learning environments. Evidence suggests that the extreme ends of this continuum are not likely to be especially effective for a great many learners. Rather, some structure and directed learning blended with some open-ended activities are likely to engage many learners and result in desired learning outcomes, including a desire on the part of learners to pursue further study in the subject area.

A challenge for instructional designers is to determine for which learning tasks and learners it is appropriate to include more emphasis on structured learning or open-ended learning. A challenge for teachers is to realize that the roles and responsibilities are different depending on the nature of the particular learning activity. A challenge for learners is to realize the value of the particular approach and activity in which they are engaged – their roles and responsibilities are also somewhat in these different kinds of activities.

The question is not which approach to always use. The question is which kind of approach is likely to be successful for the particular goals, tasks, and learners involved. A thoughtful and reflective teacher or instructional designer will see value in both kinds of approaches. A thoughtful and reflective student is likely to succeed if the approach is clear and appropriate for that learner’s particular situation. This is not intended to be a middle-of-the road response to the debate about teacher-centered and learner-centered approached. It is intended to be a muddle-elimination response that recognizes the value of significant evidence in support of both approaches in different situations.

For example, a person who is not familiar with structural equation modeling is likely to desire and benefit from a structured, directed learning approach from a highly qualified expert with feedback on representative tasks that gradually build up competence and confidence. However, a person who is somewhat familiar with meta-analysis is likely to desire and benefit from a more open-ended approach with a highly qualified expert on hand to guide and suggest improvements in various learning tasks and activities. In summary, the two approaches are not mutually exclusive nor are they incompatible. In effective instruction, they are more likely to be blended together with both directed and open-ended learning activities.

http://dl.dropbox.com/u/4943446/teacher-learner-centered-figure.jpg 

Incantation on Constructivism

The world is wide and mysterious to the willing eye …

To a trained ear, sometimes loud and often off-key …

A wonderland of sensations for the child at play …

A lifetime of experience each and every day …

Where is the meaning in what we see and hear?

How to make sense of experiences that come our way?

What can be gathered from coincidence that will last?

Ludwig said that we picture facts to ourselves …

We create internal representations to make sense …

Ludwig noted that we talk about these pictures with others … we externalize …

Is it not amazing that we create internal representations to make sense of experience?

Is it not amazing that we engage in language games to make sense of those representations?

Well, that is what we do, it seems … there is no stopping it …

We are meaning makers … even when we are making mean …

An anti-meanness message embedded in an incantation on meaning …

The message here is simple … plain and unflavored …

We are constructors of meaning regardless of what is happening here and there …

We construct meaning regardless … that’s our nature … it’s what we do …

Construct this … a new movie … starring ... none other than … YOU!


J. Michael Spector (12 Nov 2010)

The Times They Are Changing

AECT 2010 has come and gone. Now I am the Immediate Past-President with new and different responsibilities, including finding folks to run for President-elect next year and serving as the AECT Board liaison to the ECT Foundation. The conference was a tremendous success, thanks to Barbara Lockee, Miriam Larson, Lois Freeland and Dalinda Bond. The organization is healthy with new collaborators and affiliates all around the world; there were 30 Indonesians at AECT 2010 and they added insight and diversity to a meeting already quite rich in terms of quality and multiple perspectives. AECT is now in the very capable hands of Barbara Lockee.

The American educational system, however, does not have such a bright outlook, especially with the November 2nd election looming large in the USA. I wish I could somehow magically transfer what I have learned working with Indonesians the last five years to the voters who decide how well to support their school districts and schools. I have seen how highly Indonesians value education, from remotely located multi-grade rural schools to the Ministry of Education. It is not just talk about how an education should be valued - the Indonesians are putting substance and meaning to such words. It seems like we used to do that in America, and I am sure it happens here and there ... but considered as a large-scale system, my sense is that American public education is faltering.

With my new found free time I wish I could think of something to do that would yield substantial and sustained improvement, but I just do not know what would really help. Please help me learn how to help improve our schools - I am a slow learner, but I am willing to learn.

Mike Spector