Evidence is good that students often get through many years of formal education without acquiring a sufficiently deep understanding of some of the fundamental concepts they have studied; they are not able to apply those concepts in new contexts.  Our ability to design educational policies and procedures that will ensure understanding is constrained by our limited knowledge of what it means to understand . . . The concept of understanding is a fundamental one for education . . . it deserves more attention than it has received.  (Nickerson, 1985, p. 235)

 Learning has been conceptualized by Marton, Dall'Alba and Beaty (Entwistle & Entwistle, 1992) as involving deep and surface elements.  The surface elements involve processes aimed at the "reproduction" of facts and information.  Deep elements involve "transformation" processes, one of which is understanding.  These authors feel that deep learning "involves an intention to develop personal understanding of the subject matter presented" (p. 1).

 Except for the ideas like those of Marton et al., the above notions of understanding, and the learning processes that lead to understanding, are limiting.  They suggest that a learner, when gaining an understanding, somehow learns that which has already been understood or fit together by others.  The notion of "transformation" potentially allows for the learner to be an active builder and for the learner's and society's amassed knowledge, theories, explanations, etc. to grow.  As educators, we should be regarding understanding as a form of learning which is different from, and better than, simply "knowing" or "comprehending".  We should view "understanding" as more than just "grasping" what someone else has already figured out or created.

 In education, understanding can be viewed as a process by which the student creates a personal meaning or representation of what is being experienced.  When it comes to content taught in school (and information gained elsewhere) the understanding the students create may be the same as the teacher's.  Here, learners may grasp and comprehend existing structured information as it was presented.  Alternatively, learners may personally create mental structures (understanding) possibly different from or even "deeper" than the teacher's.

 The gaining of understanding can be viewed as a process very much akin to that of theory building, an act that involves seeking labels and ways of organizing experiences as well as ways of explaining and predicting (Thomas, 1992).  Theory building according to Dance and Larson (1976) "is a very basic form of human activity" (p. 4).

 In education, where our task is to "empower" and "enable" children to do things and not simply to have them amass information (LeFrancois, 1991), a distinction between "comprehending" and "understanding" is important.  If one accepts John Dewey's (1910) notion that a well defined problem is halfway to being solved, students should be taken at least halfway to understanding and hopefully should be in a context in which they can go even further.  Teachers should emphasize those bits of information which are key to students developing an understanding.  More importantly, these key pieces should be presented in ways that allow students to discover known and perhaps new relationships between these bits.  Rather than just giving students information they can comprehend, teachers should expose students to information they can understand. 

 While information comes in many more forms then can be dealt with here, we can look at two of the common kinds of content that teachers ask their students to learn and ultimately understand.  One type of content takes form of discrete facts or what has been called "declarative knowledge" (Farnham-Diggory, 1992; Lesgold, 1988).  Students learning this material, in a sense, "apprehend" or "grab" hold of what is offered.  The other type involves organized information or knowledge.  This second type, like declarative knowledge, can be both grasped and also "comprehended".  This material is somewhat different as it is more integrated or structured and perhaps, though not necessarily, more complex.  It includes content such as: concepts, definitions, tables, formula, plot summaries and even theories.  What is being learned includes both facts and a structure which offers an organization to those facts.  In a sense this content might be considered as being "pre-understood".  Others, including the teacher, usually understand the content before passing it along.  Ausubel's idea of content that could be learned through "meaningful receptive learning" (Ausubel, Novak and Hanesian, 1978) or content that Farnham-Diggory (1992) would label "conceptual knowledge" would fit this category.  When "already organized" knowledge is learned, the learning resembles "understanding" as this content deals with both the discrete facts and the relationships between these bits and pieces.  In these instances we may be discussing "understanding" but, more often, are discussing what might better be labelled as "comprehension", something very similar to "understanding" but not exactly the same.

 As teachers we must describe (in test results and on report cards) the progress being made by our students.  Often based on Bloom's taxonomy (Bloom, Englehart, Furst, Hill & Krathwohl, 1956), we ask for simple factual answers and definitions of terms (knowledge).  We may ask slightly higher level questions which require students to describe (comprehension) and use (application) parts of these offered "pre-organized" chunks of information.  Such testing will not necessarily reflect "understanding", especially if the personal understanding students have created does not match well the organization or structure offered by the teacher.  When we try to see if students "know" facts or comprehend "pre-understood" knowledge, we may simply be testing detailed rote learned or memorized content.  This content can be given back to us in such a way that it can appear to be understood (Entwistle and Entwistle, 1992; Nickerson, 1985).  Situations can exist where learners, maybe by frequent repetition or rehearsal, have overlearned organized content and hence are able to give it back, perhaps in varied forms (which suggest understanding).  While we can test comprehension, we are less able to test personal understanding.

 When we look more closely at the various types of learning that we are fostering through our teaching we can readily identify classroom situations where the content we are offering is very new and very unfamiliar to our students.  Here we have a potentially quite difficult teaching task.  We may seek (i.e. in situations were all the content is unfamiliar or, as with a phone number, only appropriately memorized) to have our students rote learn what is deemed important through repetition or drill and practice.  Rote learning, while appropriate in a few specific instances, is very time consuming and, of course, can result in the learner not having useful or what was previously referred to as "enabling" knowledge (Lefrancois, 1991).  Often, students can only recite answers.  In another situation, confronted with teaching the same content, we may seek to have our students form associations between the "new facts".  Here, the content learned is not linked to any existing or known information.  What might be considered as relatively discrete chunks of associated facts are learned.  Mnemonic devices may come into play here.  An "imaging" strategy (like learning the items on a grocery list by creating a single mental picture including all the items on that list), for example, accomplishes this.  Such chunks, while containing linked facts, are not anchored into larger association nets or concepts.  Associated (chunked) content is more economical (in terms of how much is learned per unit of time) than rote learning (Solso, 1988; Good and Brophy, 1990).

 A third type of learning exists when students, usually with the help of a teacher, learn new content by experiencing it along with other, already familiar, perhaps previously rote or associatively learned, information.  To accomplish this, teachers might ask their classes to recall previous lessons or experiences outside of the classroom and then present the new content contiguous with the known and recalled content.  New facts, besides their being potentially linked with each other, are associated with "old" or already learned facts.  Learners are elaborating on what is already known (Benjafield, 1992).  These "teacher offered" and "student made" links very much help later recall or remembering of the information.  When there is a web or network of information (i.e. associated facts), there are many paths to finding a given fact in our memories and therefore many points to begin searching when we want or need to recall (Novak & Gowin, 1984).

 One might characterize the three types of learning discussed, so far, as existing in two dimensional space.  New facts can be learned in isolation (often by rote), by becoming connected with each other (simple association) or by being connected with other previously known facts (elaboration).  What is added by the learner is only the links or associations.  In the second and third cases the links formed are considered to be two dimensional in that no new information is created, only the links are added.  In all cases, the information simply rests "on a plane".  Very limited comprehension and probably no understanding are considered to be occurring in these situations.  No three-dimensional ("higher" or "deeper" level) structures are built.

 To this point, the kinds of teaching (and the assumed types of learning) often seen in classrooms have been portrayed.  What is described as taking place is indeed learning but not necessarily understanding as the term is being discussed.  While we can do many things to help students learn facts and knowledge (i.e. repeat information until it is overlearned, present it in sets or present it with recalled facts), we may not be adequately fostering "understanding".

 Many thinkers, including Piaget and Bruner, have told us that when students understand it is because of what they, themselves, do (Good and Brophy, 1990).  Learners create, often with our considerable help and support, their own understanding.  Experts on studying similarly state, for different reasons, that active learning is better than passive learning (Good & Brophy, 1990; Farnham-Diggory, 1992).  Interestingly, the products of active learning (namely insights or understandings) have been described as very positive, "aha" experiences (Wallas, 1921). Active, high level, learners create a set of superordinate links which hold the discrete or associated facts together.  These links are not just from point to point (as with associations). Instead, the links represent something, in a sense, added or created as an addition to the facts.  As suggested above, understanding thus can be viewed as a three-dimensional, association as a two-dimensional.

 An analogy can be offered to help us better appreciate (comprehend) information that is understood.  Consider "understood" facts as first being selected from among other bits and pieces of experience based on their having what learners (perhaps with the teacher's help) notice as being shared attributes, similarities or patterns of some type (Dance and Larson, 1976).  These facts, or more accurately, some simpler versions or models of the initial facts, perhaps, as a group, are "elevated" and placed together on what might be considered as a specially created "table" or "platform".  (Appreciate that some of these separate facts are already associated or "linked together" and that any existing links are not broken by these acts of selection and elevation.)  The selected information "on the platform", in a sense, has had some structure stood under it. This already associated (learned) content is now transformed (by having something added to it) and placed at a higher level by the active learner.  Obviously what is being described is akin to the creation of concrete concepts.

 A more complex and interrelated situation can be envisioned in which there are "tables" of transformed information standing on other "tables".  Here we have an instance of more complex "under standing".  A different analogy comes to mind when considering this more complex understanding, this one of a single circus acrobat, perhaps riding on a bicycle.  He/she is holding two or three others, each of whom may be carrying one or more other acrobats.  This image is something like an inverted pyramid.  While this image pushes still "higher" the notion of understanding, it does pose a conceptual problem.  The image of a tottering pile of tables or a heavily laden bicycle is too "unsteady".  The slightly more conventional notion of a normal pyramid with the facts at its base and the structures, created by the person who understands, built upon this base is preferred.  The greater the understanding (and hence the integration of the knowledge), the higher the structure.  Educators and researchers refer to, "higher levels learning" to describe situations being referred to by these analogies (Good and Brophy, 1990).

 Our every day language, reflecting the creativity and wisdom of our predecessors, utilizes the word "understand" to describe what it is that the learner, seeking some form of higher or deeper learning, does.  Learning in the broadest sense refers to facts being stored in our memories.  Not understood facts are learned at a low level.  Such "barely" learned facts are memorized, usually by rote (repetition). If they are "slightly better" learned, they are linked or interconnected (associated) with each other.  When new information is "moderately better" learned it is associated with previously known facts (elaboration).  If the new information is "well" learned, it is learned at a higher level.  Moderately high level learning might involve information that is comprehended or linked to an informational structure previously or concurrently internalized by the learner.  With understanding, much higher level learning occurs.  Here the learner creates a structure which supports the information by "standing under" it.  "Slightly" and "moderately" learned facts are "associated" or held together at a low level - in other words what takes placed is described as low level learning (Craik & Lockhart, 1972).

 Students, when they create their own higher level structures for linking information, are building the linking and conceptual structures that "stand under" that information.  Because of the conceptual limits of the label "understanding" and the concrete analogy it conjures up, it might be better to suggest that students be seen as building an "overstanding" for the facts they have learned.  Information that is integrated and structured by the learner is "over stood".

 Many of the ideas being discussed have their origins in explanations and the concrete examples tested by the author on his pre-service and graduate education students.  To help them understand differences between the various levels of learning they are encouraged to differentiate between contiguous associations occurring when one experiences information (from a book, lesson, or recollection) and the links that come about when one creates a concept or an understanding.  Two dimensional, contiguously made links are well depicted by the label "associations".  We lack a suitable label to describe the links between the specific facts and the superordinate ideas, the higher order links, we create to represent these facts.  The label suggested for these links is "props".  This label reflects the idea of structure being added to support or "prop" up something.  The label "prop" also has links to the idea of a "proposal" or a "proposition".  These terms identify a future (proposed) relationship or offer a suggestion about what might occur.  In the cognitive literature, Solso (1988) suggests a proposition is a small meaningful structure which represents knowledge.  Like an object on a theatrical stage, these props are not necessarily "real", they are a part of an idea.  All these aspects of the term "prop" are compatible with the concept of the creative acts carried out by a student seeking to understand.  The notion is also compatible with the position offered by Nickerson (1985) who pointed out that understanding is never complete.  Understanding, like any theory, is continuously being tested, revised, restructured and sometimes even replaced with a better creation or version.

 Students, who state they understand ("overstand") course materials, express confidence and have a feeling of "coherence and connectedness".  They say that having an understanding has "provided them with flexibility in adapting and applying ideas and information effectively" (Entwistle & Entwistle, 1992, p. 8).  Perhaps they are confident that their ideas are defensible!

 Hopefully, we as teachers are closer to our goal of fostering understanding by having actively considered the notion of "overstanding".  If we regard this small essay as an exercise, we will note that, along with adding additional meaning (associations and elaborations) to the term "understand", we may comprehend this complex notion better and even be more able to explain the concept and to foster the process in our students.  We may even have added onto (i.e. better understood) our own structured idea of how we understand in general and how we understand "understanding" in particular.  We, hopefully, are building a personal structure (an understanding or "overstanding") to organize the many current and past bits of information we have learned about how people learn.  We may better comprehend other people's understanding of the nature of learning and of the nature of understanding and use this learning to rebuild, for our selves, the "pre-understood" structures offered us.  In this latter case (when we rebuild) we may create an understanding matching that of our teachers.  It is even possible that we may come to develop our own, perhaps unique, ideas about the structure of learning and understanding.  Because of this exercise, we, hopefully, will be better convinced about the need to offer information that can be integrated (i.e. associated, comprehended and understood) and perhaps we will also be in a better position to allow our students the time to build these structures and the opportunity to test them personally by writing about them and by discussing and trying them out on relevant problems.  Hopefully we will all appreciate better (by seeing ourselves as examples of "structure builders") that our students can do the same thing we are doing if encouraged and allowed.

 Any personal and truly relevant structure is more easily built by our students if we, as teachers, support the building process.  If we simply expect students to get to learn previously built structures, too often the students will find these structures do not fit well with their knowledge.  Unfortunately, information that is not really integrated (understood) is not easily retrieved and used later, in an "enabling" way.  When we do not understand information, it is not ours, we have built no part of it.  We do not truly "own" the information.

 As teachers, by presenting ourselves as models always trying to build structures "over" the facts we encounter, we are encouraging students to do similarly (Bandura, 1977).  We thereby support their efforts to learn in more effective ways.  While we must continue to support some "fact learning", we must also offer the opportunity and time needed to encourage the building of understanding.  Now, and more so in the future, skills and a desire to build solid "overstandings" will be more important than the mere possession of "bricks". 

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