Towards 3 Dimensional Education

Introduction

Disputes can usually be taken positively as a call to re-examine fundamentals.
  1. A's pointing out that we are patching the grades issue in the classical way of messing software --
  2. The surprising amount of concord that 3-d grading may work --
  3. Swami's demo that even for a `shallow' course like Programming-2 (programming tools and techniques), a 3-d syllabus is possible (appendix) --
prompts the following attempt to re-examine our grading questions from first principles.

The Situation Today

For centuries grades have been 'marks-out-of-hundred'. The complaints against this are
  1. The difference between 32-fail and 33-pass, 74-1st class and 75-distinction etc. is ridiculously fine.
  2. 33% with a tough paper may in fact be higher than 50% with an easy paper.
  3. Flattening out the infinite, multi-dimensional variety of human potential into a finite, linear actual loses information, usually vital information.
The letter grading scheme which has become popular in the last couple of decades solves (a) and (b) but not (c) which is exacerbated. It is possible to envisage that a student getting 77% may in fact understand less than one getting 74% but it is much more difficult to see that an O may -- for certain purposes -- be worse than an A.

How? Consider a paper with 5 questions of 10 marks each taken by two students X and Y. X does everything close to correct but nothing exceptionally -- 8 out of 10 in each, ie 40 marks or 80%. Y answers two questions brilliantly -- better answers than the instructor knew, new insights etc. He gets full marks 10, 10. The next two questions are done only partially, he gets 4 and 5. And the fifth is left unattempted. He gets only 29 marks, not even 60%.

The Issues

So the first question is: Does our grading scheme convey too much or too little information?

Clearly if we feel less is better, then a 5-point scheme is better than a 6-point scheme is better than a 100 mark scheme. It does not seem to me that this is the way any of us look at it. Even Swami who is asking for a 5-point scheme (remove O, divide by 5 not 6) is asking this to align our presentation with standard practices. In fact his other proposal -- a half-page, reco-like grade -- is in quite the opposite direction. In fact, it seems to me that:

we would all like to go towards more information rather than less.

The more fundamental question to ask is: What is it about our educational setup that is unsatisfactory?

This is the real question and -- as usual -- we dont ask it because we have only vague answers to it. As a first approximation to an answer let me suggest that

  1. The default norm of higher education is overspecialization
  2. The default intellectual state of students is boredom and confusion
  3. The default emotional state of not just students is anxiety and isolation
In other words modern education
  1. is linear and narrow where it used to be broad
  2. is flat and meaningless where it could have body and life
  3. is disconnected from the primal needs of the human being
In short, if we could look past the religious trappings , ancient or medieval education provided connections and a hope of fulfilment. Modern education creates disconnection whose hopeless conclusion is insanity.

The following proposal for curriculum design and grade assignment may seem to be a solution whose scale is disproportionately small as compared to the problem. Please read it as one small part of the solution and not the solution.

A Non-linear Proposal

It is emerging that a course -- if it is a coherent unit -- can be conceptualised, studied, evaluated, and therefore graded at 3 levels or dimensions. A 3-dimensional grading scheme gives a mid-point between a single mark or grade which loses too much information, and a detailed `reco-like' essay or report by the teacher on the student which is administratively infeasible due to lack of a summarising figure. What these dimensions are -- their names -- differ, and this is only natural considering that courses are vastly different not just in content but in orientation. However the separation of 3 almost orthogonal directions seems possible and worthwhile. In the following table are listed some of the many different possible names.

Notes:
  1. This table is not rigorous in any sense.
  2. The purpose of the table is to give a sense of the 3 dimensions. However running down a dimension column makes no sense. Please take it one row at a time with the left entry giving a feel for a human type or field whose three orientations would be as given.
  3. The first two rows (a,b) are the ones Swami and myself started off with .

3 Dimensional Education
Dimension 1 Dimension 2 Dimension 3
a.
Detail Principles Perspective
b.
Technology Science Philosophy
c. Focus Facts Laws Possibilities
d. Scientist Data Information Knowledge
e. Philosopher Information Knowledge Understanding
f. Source News-media Text-books Canonical texts (shastra)
g. Thinker Practice Theory Philosophy
h. Doer Philosophy Theory Practice
g1. Theory teacher Practice Philosophy Theory
h1. Practical teacher Theory Philosophy Practice
gh. Teacher Negative Neutral (reconciling) Positive
i. Engineering Analysis Design Paradigm
j. Theorem -- Name Statement Proof
k. Maths/Logic Theorem statement Theorem proof Area/Theory
l. Society myself my family my community
m. Humanity Individual Community World
n. Theology Self World God
o. Yoga psychology God Guru Self (jiva)
p. Vedantic psychology Body Psyche (antakarana) Self (atma)
q. Common psychology Perceptions Concepts Intuitions
r. Education
psychology		 Body-functions
(spine)		 Intellect
(cerebrum)		 Emotions
('heart')
s. Time focus The present Past and future The eternal Now
t. Curriculum Course contents Course Programme

Open Questions

  1. Syllabus: Swami has demonstrated a 3-d structure for P2 (Programming tools and techniques)-- a seemingly difficult candidate (Appendix). It is now just a question of working out the same for all courses.
  2. It is seemingly more work -- but how much more? Anyway, when we correct a paper having say 6 questions, we have to correct the 6 questions and then add up. The only thing that now changes is that the 'add-up' function becomes a 3-way addup. In fact it may be less work because many times we have to struggle to incorporate a vague impression in terms of marks. Now it just has to be recorded under a different head.
  3. How do we assign the relative weightage of the three dimensions? Some possibilities:
    1. Equal weightage. Administratively the simplest solution but not sensible considering the different types of courses.
    2. In view of the fact that we are a 'science' department we could have 1 for technology, 2 for science, 1 for philosophy. This may be fine as an overall representation of the department's flavour but would be inappropriate for individual courses.
    3. Pre-declared for every course: Make it part of the syllabus
    4. Late Binding: The instructor decides at the beginning of semester. Serves as a way out for those instructors that don't like or believe in the system. eg If the networks teacher believes there is no science or philosophy (or should not be any) in networks he may assign a weight of 0 for levels 2 and 3.