3 - What's Behind the Geodesic Learning Model

Problems, Contradictions and Instructional Switch-backs

in Education and Learning, As We Know It

It's not that we can't teach well or whether students don't learn enough. Rather, we have allowed ourselves to limit the way in which we view and understand the learning enterprise. It appears that, historically, learning has been seen as a lifelong, dynamic, and multi-dimensional exercise. For example:

"These Chinese characters represent the word 'learning'.
The first character means to study. It is composed of two parts: a symbol..."to accumulate knowledge," above a symbol for a child in a doorway.

The second character means to practice constantly, and it shows a bird developing the ability to leave the nest. The upper symbol represents flying; the lower symbol, youth...together, suggest that learning should mean: "mastery of the way of self-improvement." The roots of the English word for learning suggest that it once held a similar meaning...a noun meaning "track" or "furrow." To "learn" came to mean gaining experience by following a track - presumably for a lifetime."

Peter M. Senge, Art Kleiner, Charlotte Roberts,

Richard B. Ross, and Bryan J. Smith,

The Fifth Discipline Fieldbook, 1994

But, learning is more than a dynamic multi-dimensional exercise: Learning is a holistic self-assembling hyper-dimensional process.

Most would agree that modern learning theory accepts the multi-dimensional dynamism of learning, what David Jonassen describes as the "dialectic nature of learning". It is the hyper-dimensional aspects that frustrate us and confound our instructional efforts.

The goal of this document is to reveal the organizing geometry of learning and architecture of knowledge and demonstrate how it extends well beyond the dialectic, hierarchical nature of learning and knowledge, as we know it. To do this, the paper lays out some of fundamental problems and reconcile those frustrating contradictions with a different hypothetical principle and construct. In short, the Geometry of Learning and the Architecture Knowledge is ultimately holistic, geodesic, spherical (like a soccer ball), and hyper-dimensional .

A Paradoxical Impasse with our Tradition

Achievement-based & Standardized Learning and Testing

It may appear odd that the starting point for this project takes aim at the evaluation end of the formal, institutional, instructional and learning process: High Stakes Testing. Why? Because it epitomizes the "limited-headed" (vs. "wrong-headed") view we have of learning. We don't have a model that allows us to see the limits of specific learning strategies and technologies. Until now we haven't have a model that suggests that there is something more than what we know now. Thus, we are stuck, so to speak, trying to measure a mile with a tablespoon. To the mind of the author the recognition that there might be more to learning is the first step in 'thinking different' when it comes to learning and instruction. (See Section 2, The Geometry of Learning and the Architecture of Knowledge)

The "Y2K" presidential campaign and election served to bring to the forefront the American public's desire for better education. No definition here. Just "Fix it and make it better." Oh, and by the way, did anyone bother to ask just what education is, anyway? Most often the political candidates pointed at education's failure and called for more or better test scores. The logic? The higher the scores, the more effective the education, the better the learning. Paradoxically, their solution to the failure of today's education is simply to reinforce that which we all know is a failure for a majority of young people.

However, for some these declarations were just a bit too pat and really missed the point. In fact, they generated a whole raft of new questions: How much time are teachers and kids spending in arduous preparation for these tests? How much time is devoted to actual teaching? Just what and how much are kids learning? How much time is spent on actual learning? What is "better education"? What is "effective education"? Are we turning out kids who can actually think both critically and strategically, kids who can find and solve problems, and enjoy and benefit from the learning experience or just good/bad test-takers? Few if any candidates were brave or knowledgeable enough to ask the hard questions much less risk giving the even harder answers. In 2002, George W. Bush signed the No Child Left Behind (NCLB) legislation that, among other things mandated more high stakes tests . Now, nearly a decade later, NCLB appears to be leaving most if not all of our children in the dust.

The fact is, we are at a paradoxical impasse with our tradition. We want an educational elixir that will cure "traditional, if unproductive methods of teaching". Yet, we look to that very same tradition to remedy the problem. How? In very traditional ways using very predictable means. This is an example of faulty and circular logic (illogic?)

Just for giggles, let's take a group of people out on a boat, then throw them all overboard. This is what happens: a third of them, the natural swimmers, will make it to shore easily; another third, the "not so natural swimmers", will struggle, some desperately, make it to shore and save themselves; the last third, for whatever complex of reasons, apparently doesn't have the skill, will, ability or knowledge to even struggle, much less swim to safety.

Now let's repopulate this scenario. Let's call it "Students Overboard". Here we send kids to a traditional school. In this rendition, those students whose learning style matches the teaching style of their teachers succeed - they get As and B+s. Another set struggles and gets average grades - some get Bs but mostly Cs. The last set, a huge percentage of the students, essentially fail with a few Ds and and a lot of Fs. Even grade inflation won't float the last group to shore.

This phenomenon is reflected in a study by Sandra Rief [6] and goes a bit further providing both insights and hints to teaching and learning strategies.

Students retain:

• 10% of what they read
• 20% of what they hear
• 30% of what they see
• 50% of what they see and hear
• 70% of what they say
• 90% of what they say and do.

It would be fair to say that many if not most of our school systems and teachers emphasize only the first three or four of Rief's levels of student knowledge retention. Today's emphasis on high stakes achievement-based testing only mirrors this reality.

The author has scored several thousand of these achievement tests, from elementary through high school, in math, science and writing. His experience supports, anecdotally, both the "students overboard" illustration and Rief's description in terms of both the scoring process and the content.

For example, scoring 10th grade students in Los Angeles on a persuasive writing prompt, the two highest scoring rubrics, a 5 or 6, favor idea organization as a requisite for effective persuasion in addition to good writing skills. At the lower end of the rubrics, organization skills are specifically said and assumed to be in question or lacking and poor language and writing skills are all but assumed. This prevents the scorer from awarding kids for whom English is a second language a higher score even if the nature and organization of the persuasive exercise is top notch.

In another example, math for middle schoolers, a problem lays out a crude map to a box of treasure. The student, using a ruler, must follow the directions and determine the various distances from one place to another, eventually winding up to where the treasure is buried. While most students, and even the college educated scorers, looked at the prompt and followed it "correctly", quite a number of students saw the map differently and still followed the prompt and directions, but came up with entirely different measurements and still got the treasure. The prompt neither said that there was a particular way to look at the map nor did it give any indication that there was only one way to solve the problem. Yet, even though many kids solved the problem differently and, by definition (or the lack thereof), correctly, the scoring rubrics and answers failed to recognize this. These students had to be scored 2's at best and 0's otherwise, right along side those kids who flat out got the answers wrong or failed to grasp the nature of the problem.

The April 29, 2001 edition of Time Magazine featured a report by writer Wendy Cole, Feeling Crushed By Tests At Age 11, How a model North Carolina district struggles under state-exam pressures [7], which profiled what is declared a national model in school achievement. Parts of that story are bulleted here:

• In Roanoke Rapids, an industrial town of 17,000 just off I-95 near the Virginia border, many fifth graders spend about two weeks a year taking standardized tests - not counting practice and preparation.
• Using a complex formula, the state sets targets for each school to improve and doles out bonuses of as much as $1,500 to teachers at schools that meet those goals.
• The lowest-achieving schools face takeover by state-appointed turnaround teams.
• John Parker, an assistant superintendent for the Roanoke Rapids district: "You can teach poorly and get high test results." His schools... are sacrificing important lessons in science, social studies and foreign languages to focus on concepts that will be tested.
• Steffany LaBree, high school biology teacher: students no longer dissect frogs. "I can't spare two weeks for that..."
• A U.S. History teacher doesn't assign research papers because they don't help him prepare students for state-mandated tests.
• The town's educators say they don't oppose accountability. Many of them prefer the method adopted by states such as Vermont, in which independent reviewers assess portfolios of student work.

North Carolina's approach to student and school evaluation neither determines the extent of the knowledge a student has created and retained nor whether a student can actually use what "knowledge" he or she has accrued in a variety of contexts to solve problems. And, were it not so true as to be trite, what is life if not the process of identifying and solving problems?

In fact, the author contends that the only thing these tests measure is our unwitting inability and failure to enable knowledge transference and cognitive strategy integration as part of the general aim of education. Our notions and conception of the nature of learning are restricted and fail to fully recognize that learning is not only multi-dimensional but also hyper-dimensional. [8]

Its all a matter of Time... and Place: Well-structured vs. Ill-structured Instructional Domains

In education circles (I, for one, refer to them as squares), one often hears about well-structured vs. ill-structured problems or situations as vehicles and strategies for both instruction and learning. Studies support the notion that "... students who find themselves in ill-structured situations, that assume appropriate scaffolding [and, by the author's own extension, at times traditional directed, even transmissive instructional strategies], are more apt to become, over time, generative and self motivated learners". [9] Most would agree that if their students/children became generative and self-motivated learners parents, teachers, and schools would be proud of what they all have accomplished.

A New Domain

However, this ideal is confounded by contradictions that occur within what the author calls the "Well-Structured Instructional Domain"; that is the underlying instructional infrastructure, the application of fiscal, human and instructional resources and the use and structure of time and place as they apply to both the learning enterprise and the traditional "education community".

The "High rates of forgetting, low levels of applicability of knowledge and skills, insufficient of problem finding and problem solving, and aversion to school learning..." are the results of the traditional educational model. (Jonassen, University of Missouri, 2000, unpublished)

While a teacher might thrust students into student-centered ill-structured problems and situations that compel generative and self-motivated learning, the larger learning environment or instructional domain remains "well-structured". The author contends that this almost always guarantees a failure of hyper-dimensional knowledge transference and cognitive strategy integration. (Hyper-dimensionality will be explained a bit further on, but let it be said now that it is very desirable.)

Arguments against the Well-Structured Instructional Domain

The traditional school setting, the Time/Place/Space, is perhaps the best representation of what the author dubs a "well-structured instructional domain": many classrooms, some (but not enough) teachers, many students, a variety of discrete subjects disconnected from each other , all shoehorned into a strictly segmented 6 or 7-hour day. The author argues the following three points:

• The "real life" of traditional schools and schooling work to perplex even the best and most progressive of school systems, teachers and programs by virtue (vice?) of creating a meta-contradiction that works against the very things they are encouraging and supporting. This sort of Instructional Domain is a well-structured meta-learning environment, segmented and compartmentalized with social studies in this hour with that teacher, math and science in that hour with this teacher and, in still another hour, language arts or social studies with yet a different teacher. Perhaps a bit less confusing is the single teacher/single classroom format often found in elementary schools and which is gaining some favor in later grades. However, the argument applies: rarely is there a means, much less an attempt, to orchestrate the daily learning enterprise to overcome the compartmentalization that comes with teaching by time-place-and-subject. For the most part, the only continuity is on the dimension of time, i.e. first period, second period, etc. yet, by definition, it is segmented. All else is discontinuous: there is very little deliberate connection among any of the areas of study, temporal or otherwise.
• At the meta-level under these conditions, and with traditional instructive/ transmissive/passive methods of teaching, students at best gain what, in 1929, Alfred North Whitehead called "inert knowledge." Knowledge that, if not forgotten, serves no long-term purpose and is not readily available or accessible to the learner beyond the context or for the reason the student acquired the information in the first place. On the micro or classroom-level, Jonassen and Carr [10] describe this as the failure of students to apprehend and apply a "conceptual understanding of the problems and their underlying principles..." Kids stumble around without an appreciation of larger contexts, concepts, dynamics and strategies. The author argues that the way the schooling experience is structurally designed, and its use or misuse of time and space works against not only the learning enterprise, but against the students themselves. It fails to fertilize, nurture and enable the transference and cognitive integration of learning and problem-solving skills and strategies from one area or subject to another. The larger implication is that once out the school door, there is very little chance that any of what a student has "learned" will be accessible and applicable to his or her "real life". And, mores the pity.
• Neither traditional modes and styles of teaching and the reliance on a well-structured instruction domain nor newer modes based on current learning theory provide an even playing field for all or nearly all children. Traditional means of teaching and the traditional assumptions about learning actually separate many children from the learning enterprise and for many, make it all but inaccessible.

An Important Side Bar: Universal Design for Access and Learning

The Center for Applied Special Technology (CAST), on its opening WWW page, says of its goal for Universal Design in Access (UDA)

"Universal Design for Learning (UDL) is a framework for designing curricula that enable all individuals to gain knowledge, skills, and enthusiasm for learning. UDL provides rich supports for learning and reduces barriers to the curriculum while maintaining high achievement standards for all. (http://www.cast.org)

And,

"No two students learn the same way. Even within the normal range of performance and ability students vary greatly in their ability to see, hear, move, read, write, attend, organize, focus, engage and remember. Applying universal design to learning materials and activities can increase access for all learners, including those with disabilities. For example, history texts provided in standard print format present a barrier for students who are dyslexic or to students for whom English is a second language, and is completely inaccessible for blind students. The same material in a universally designed digital format can offer many options for these diverse learners. The material can be read aloud by a computer or screen reader, printed on a Braille printer, offered in spoken or written translation, and/or presented with highlighted main points and organizational supports." Http://cast.org/udl/UDforAccessLearning9.cfm

Combine this with CAST's Universal Design for Learning (UDL)
initiative:

"...A curriculum should include alternatives to make it accessible and appropriate for individuals with different backgrounds, learning styles, abilities, and disabilities in widely varied learning contexts. The "universal" in universal design does not imply one optimal solution for everyone. Rather, it reflects an awareness of the unique nature of each learner and the need to accommodate differences, creating learning experiences that suit the learner and maximize his or her ability to progress." Http://cast.org/udl/index.cfm?i=7

While current learning theories, as presented in such books as Theoretical Foundations of Learning Environments [11] and Computers as Mindtools for Schools [12], establish the case for the importance and efficacy of connective, constructive, situated and immersive learning environments and the creative use of new technologies in those environments, there are limits and drawbacks. This is most evident in technologies Jonassen dubbed MindTools, those computer-based technologies that promote critical thinking. These include data-bases, spreadsheets, Keynote and Powerpoint and a variety of "what if" design and computation and mind map applications. When applied blanket-like across the spectrum of learning, learning environments, instructional domains, teachers and students, they can and do thwart the learning enterprise for a goodly number of students; those who are not self-motivated, not constructive or connective learners or who are physically, cognitively or emotionally challenged in one way or another. Correcting this situation, making learning environments and technologies accessible to all students intellectually capable of learning is a "must do" situation.

OK, So What's an Ill-Structured Instructional Domain?

Ill-structured does not mean badly designed.

It simply means that the elements that comprise the instructional domain are arranged in such a way as to encourage a "real life" or "authentic" situation or representation. While, for example, one might need to ensure a student knows how to write "persuasively" and knows that it is different from writing "descriptively" (reasons for and rules governing), the ill-structured instructional domain might not separate these two forms of writing in time and space from other learning activities. The teacher or domain might present a real-time and real-life challenge, problem or situation where a student must learn or construct knowledge that discerns between the two, promotes effective accomplishment of both styles with real-time and real-life rewards and consequences.

One step further: the larger milieu or meta-environment might be one in which the subject of the writing deals with real-life mathematics, science or social studies. The obvious implication, here, is that the students are learning more than just a writing form. They are learning "subject content". It is here that the lowly word processor becomes a "TimeTool/MindTool", an application that can aid the student to think critically and strategically and creatively and render an artifact of his or her learning, of his or her constructed knowledge. For only in the "writing" environment, with a writing application can a student represent his skill at writing descriptively or persuasively.

Moreover, if this domain is designed to demand that students collaborate, reflect on and "represent" their knowledge and transmit it to others as an artifact of their experience in both the "real-present" (i.e., the classroom) and the "other-present" (i.e., another time, another place, another medium, another "audience") in a variety of ways and media, there is a better chance that students will actually construct viable learning strategies that apply across knowledge domains.

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