We excerpt from an article George wrote, "Conceptual
and Intellectual Skills Mastery" and add a commentary about how meditation
techniques can be used to augment the progress of learning new concepts
and acquiring the intellectual skills to work with them.
by George A. Boyd ©2003
Concept Mastery
"A concept is a tiny form or idea within the intellectual
stratum of the mind. It is a container of information. It may contain
information about
- Correct pronunciation of the word(s) for the concept
- Correct spelling of the word(s) for the concept
- Definition of the concept's meaning
- Derivation of the concept's meaning from word roots
- Synonyms for the concept, associating it to words
with similar meaning
- Antonyms for the concept, associating it to words
that have contrasting or opposite meaning
- Criteria for differentiating the concept from other
concepts
- The relationship of association of the concept to
other concepts
- Its place in an ordered category or schema, from
which it may be ranked with other concepts
- Its importance in a range of values, from which its
priority may be discerned
- Its size or number, from which its magnitude can
be compared with other concepts
- Correct use in language, when writing or speaking
the concept
- Its implications or consequences, or inferential
meaning
- Subjective meaning, identifying its symbolic, visual,
or mythological representations"
"Conceptual knowledge is primarily mediated through
the verbal quadrant of the intellect, but my also define and expand mathematical
concepts, axioms of logic, and symbolic representations."
We suggest that a technique of structured questioning
derived from meditation called process-style inquiry may be useful for
mastering concepts. This can be applied by asking the following questions
and finding the answers to:
What is the correct spelling and pronunciation of
this concept?
How is it correctly expressed in language [e.g.,
is it an adjective, noun, verb]?
What does this concept mean?
To what concepts is it related?
How does it contrast with its opposite concept?
Why is this important to what I am studying?
What are the implications and applications of this
concept?
Types of Intellectual Skills
Intellectual skills operate on an individual
concept or a conceptual matrix of interrelated concepts (model) by algorithmic
or heuristic methods.
An algorithmic method specifies a series
of steps to solve a problem. It tells you, if X condition exists,
you will do Y. Algorithms are used to develop flow charts, to perform
mathematical calculations, and to simplify routine decision-making.
It lays out a step-by-step procedure that you follow, like instructions
for a cookbook recipe.
A heuristic method sheds light upon a concept,
clarifies what the concept means, discovers its practical uses or
applications, and explores its implications. It allows you to contemplate
and appreciate the idea. In the heuristic method, you inquire and
explore what something means, and ask many questions to elicit new
perspectives and to uncover what something means.
Teaching a student is largely a heuristic process, which
sheds light on concepts, current and historical events. Testing is an
algorithmic method, which measures the acquisition of knowledge, as are
the problem solving exercises by which a student practices his or her
newly found skills.
To gain mastery of an intellectual skill requires the
combination of both heuristic and algorithmic methodsa heuristic
approach to promote understanding of the idea, and an algorithmic procedure
to practice or implement it.
Mastery of an intellectual skill proceeds through as
series of steps that may use algorithmic or heuristic methods.
Procedure
|
Method
|
Introduction, initial exposure to a concept
|
heuristic
|
Demonstration, teacher exemplifies, models or performs the task
successfully
|
algorithmic
|
Student practices the task on a simple problem
|
algorithmic
|
Student applies the skill on increasingly complex problems
|
algorithmic
|
The student discerns by the teacher's explanation and the application
of his or her own critical thinking the uses and limits of the method
|
heuristic
|
Demonstration of skill mastery through testing
|
algorithmic
|
Student integrates and owns the skill so it can be utilized whenever
appropriate. At this level of skill mastery, the student can explain
and teach the skill to others, and use it to solve real life problems.
|
heuristic
|
Meditation methods have heuristic value in that they
allow students to reflect upon and explore an idea to give greater understanding
of it. But this some approach can be applied to the larger scope of conceptual
knowledge embraced by a model.
This ability to explore concepts and models augments
the student's critical thinking ability. It permits the student to explore
all aspects of a conceptual model. The student can move up the conceptual
hierarchy from the facts that underpin it, to the concepts that organize
the facts, to the theories that tie together the concepts, to the model
that integrates the strands of explanatory theory into a coherent system.
The student's cognitive mastery of the entire system of knowledge presented
in a model leads to integration, the ability to apply the model to real
life problem solving, and to teach the model to others.
Levels of Application of the Two Methods
Algorithmic and heuristic methods have applications
both within and outside the purely conceptual domain of the academic classroom.
We can characterize three modes of demonstration: information gathering
(facts), organizing knowledge (concept/model), and utilization (integration
and application). The following levels of application of these two methods
can be identified:
Level
|
Content of this Level
|
Mode
|
Object
|
An object in the environment can be examined, weighed, measured,
etc.
|
Facts
|
Personal Interaction
|
A situation that involves an interaction between two or more people
|
Event
|
A historical event experienced by two or more people at a discrete
time
|
Concept and Model
|
Exploring and implementing an idea within its model
|
Concept/Model
|
Symbol
|
An abstract, symbolic representation of an idea appearing, for
example, in art, politics, mythology, or religion
|
Objective Application
|
Problem solving in the real world, for example in business, science,
or diplomacy.
|
Integration and Application
|
Subjective Application
|
Personal problem solving, for example, resolving a health concern
by seeing a physician, or a personal issue by seeing a psychotherapist.
|
Meditation best contributes to the heuristic exploration
of the dimensions of concept and model, symbol, and subjective application.
You can meditate upon a concept, a model, or a symbol, or work through
a personal issue. Meditation can also give rise to creative solutions
that can be utilized in the arena of objective applications, such as finding
a novel synthesis that breaks a deadlock in negotiations, though this
is less common than its conceptual and subjective applications.
In particular, reflective meditation methods have wide
applicability for these five dimensions. We suggest it would be valuable
for educators and students to learn them to augment the process of learning
and integrating knowledge and skills needed in career and family life,
and to function as an adult in our complex modern society.
For education to be effective, it must emphasize both
concept mastery and intellectual skills mastery. This will produce the
coveted high test scores that are so much in demand by school districts
across the country. It will further fulfill the presidential mandate that
no child shall leave the educational system without cognitive mastery
of the skills necessary for employment, to successfully raise a family,
to make a positive contribution to society, and discharge the civic duties
of citizenship.
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