Category Archives: Education

The Educational Approach


Reference: Critical Thinking in Education


There are two distinct educational approaches.

  1. The Greek Academy System: This educational approach believes in the student learning to think rationally on his own.

  2. The Scholastic Model: This educational approach believes in forcefully impressing data.

The scholastic model uses an examination system to forcefully impress data. It raises the student’s anxieties of what might happen if he does not “pass” an exam. The student becomes confused and unable to think rationally. He resorts to memorizing data without understanding. The system passes him with good grades if he can regurgitate data verbatim.

Under the scholastic system, a good grade is supposed to be synonymous with a bright mind. However, it is no more than the ability to memorize and recall data impressed by others. Such forcefully impressed data conditions the mind. It reduces the ability to understand and analyze data rationally.

Education must avoid becoming a mode of conditioning if it is to produce effective human beings. The first vital principle in teaching is to do everything possible to keep the student alert and aware of the subject on a rational plane.

The alert mind is extroverted and analytical. Its essential mode is self-learning. It thrives best when it is least “molded.”


The Approach Needed

The approach needed in education today is to let the mind become alert, extroverted and able to self-learn. This is accomplished by resolving the existing confusions in the mind on major subjects.

In teaching a subject one should first check the key points of understanding, and clean up the confusion surrounding those points. For example, in mathematics, the key points of understanding in sequence are: (1) The purpose of learning mathematics, (2) reading and writing large numbers, (3) the operation of division, and (4) the use of fractions.

Besides mathematics, the other major subject is language and grammar.

The resolving of confusions in major subjects helps students become self-learners.

The students must learn to think rationally on their own.


Study Materials & Supervision


Reference: Critical Thinking in Education


The purpose of a Tutorial Class is to encourage students to self-learn directly from materials, and to strengthen that learning by students assisting other students.



The text material for a tutorial class must be written in a language that is easy to understand. It should be supported by dictionaries that consist of easy-to-understand definitions and pictures.

The tutorial class material must present how a subject came about, and the reason why one should study it. The materials should then provide an overview of the subject before diving into the details. The details should be presented starting from the earliest concepts on which that subject is based. The materials then gradually build up the subject on a gradient such that no gaps are created in the student’s understanding.



Given proper study material, the students should be able to self-learn. If a student is unable to focus, it is because the assigned materials do not address his basic confusions in that subject.

The job of the supervisor is to quickly isolate the student’s confusion and give him the right materials to study. Sometimes it may require a bit of troubleshooting in getting the student set up properly.

Here is an actual example of a troubleshooting session.

SUPERVISOR:     “Is there something in math you don’t feel quite comfortable with?”

STUDENT:            “Yes… multiplication.”

SUPERVISOR:     “Alright.  What does the word MULTIPLY mean?”

STUDENT:            “Umm…”

(The SUPERVISOR explained the process of multiplication as “repeated addition.”)

SUPERVISOR:     “I am going to check you out on the multiplication of two single-digit numbers.  What is ‘three times two’?”

STUDENT:            “Six.”

SUPERVISOR:     “What is ‘four times three’?”

STUDENT:            “Twelve.”

SUPERVISOR:     “What is ‘six times six’?”

STUDENT:            “Oh, that’s a big number.”

(The student could multiply with very small numbers, but got nervous when larger numbers were asked.)

SUPERVISOR:     “Six times six would be adding six to itself six times.  Can you do this addition and tell me the sum?”

STUDENT:            (Pause) “Oh! I don’t like adding either.”

(The SUPERVISOR then demonstrated the process of addition as “counting together.”)

SUPERVISOR:     “Adding is counting numbers together. Are you comfortable with counting?”

STUDENT:            “Yes, I can count.  One, two, three, …”

SUPERVISOR:     (Stops her at the count of twenty) “Very good.  Now count for me starting from eight hundred ninety five.”

STUDENT:            (Taken aback) “Oh! That is a big number… (thinking) eight hundred ninety-six, eight hundred ninety-seven, eight hundred ninety-eight, eight hundred ninety-nine (long pause) two hundred, two hundred one…”

The student did not know what number followed eight hundred ninety-nine.  By this time it was evident that the student was shaky in her understanding of the numbering system itself.  The student was then assigned appropriate materials to study. She was then able to focus and make rapid progress.



In the normal course the supervisor applies the principle of gradient to help the student overcome his difficulties. Here is an actual example of assisting a young child write numbers.

SUPERVISOR:     “Is it ok if I ask you to write some numbers for me?”

STUDENT:            “Yes.”

SUPERVISOR:     “Alright.  Can you write six thousand, seven hundred eighty-three?”

STUDENT:            “Umm…”

SUPERVISOR:     “That’s ok.  See if you can write seven hundred eighty-three?”

(The student thinks for a moment and writes “700 83”.  The SUPERVISOR noticed that she could write eighty-three correctly.)

SUPERVISOR:     “Ok.  Can you write eighty-three for me?”

(The student smiles and writes “83”.)

SUPERVISOR:     “Excellent.  Can you write one hundred?”

(The student writes “100” correctly.)

SUPERVISOR:     “Very good.  Now, can you write one hundred one?”

(The student writes “101” correctly.  The SUPERVISOR then asked the student to write “one hundred nine” and “one hundred ten”.  The student wrote them correctly.)

SUPERVISOR:     “Excellent.  Can you write one hundred eighty-three?”

(The student pauses then writes “183” correctly.)

SUPERVISOR:     “That is correct.  Now write seven hundred eighty-three for me?”

(The student feeling more confident writes “783”.)

And so on…

The general supervision is basically devoted to helping the students develop better study habits. The supervisor encourages the student not to go past any word he does not understand the meaning of. He must look up such words in a dictionary.

Usually a dictionary has many definitions for a word. The student selects the definition that fits the context. If the student cannot find the right definition then he must seek the help from the supervisor. But very soon he develops the skill of finding the right definition by himself.

Sometimes the student cannot understand a sentence even after he has looked up the words in that sentence for their definitions. In this case the student should make examples of the meaning of that sentence–how something is that way, or it is not that way—which then resolves the problem. Sometimes it is the wrong definition used for small simple words that causes the problem.



In a tutorial class, the student studies correct materials under proper supervision. He then practices to become a self-learner.

The students may be studying different lessons in the same tutorial class. However, a student must understand a lesson fully before moving on to the next lesson. The supervisor may go around quizzing the students verbally on the sections they have completed to make sure they are not going by concepts that they do not understand.

The supervisor may ask a student, who has completed a section on a lesson, to help another student who is still studying that section. The effort is to help the whole class move forward together as much as possible. When the whole class has completed a lesson, it is followed by a Q&A (Question & Answer) period in which questions from the students are answered by the supervisor. A diagnostic test may then follow to pick up anything that is still not fully understood.

The supervisor also teaches the students on how to help each other.


The Stages of Learning


Reference: Critical Thinking in Education


There are several stages of learning as follows:

  1. Being tutored on a one-on-one basis

  2. Self-learning under supervision in a tutorial classroom

  3. Tutoring under supervision in a tutorial classroom

  4. Practicing mindfulness, which is seeing things as they are with full awareness of all assumptions.



In the first stage of being tutored, the best place to start is with Mathematics. Mathematics means “tools for learning”. It helps the student build a sense of logic slowly and deliberately.

Mathematics starts with counting. This is a very simple activity, which involves the student in his environment.  Counting extroverts the student’s attention. Throughout the study of mathematics, the attention should be kept extroverted and on the mathematical rules as they apply to the environment.

The rules of mathematics should be learned in the sequence in which they come about naturally—numbers, digits, reading and writing numbers, large numbers, addition, subtraction, multiplication, division and so on.

These rules should be learned slowly and deliberately to understand their logic. The student should never go by something that he or she does not understand. Memory has its uses but memorization defeats the whole purpose of learning. Mathematics puts the student in a frame of mind to learn other subjects with understanding.



In the second stage, you get them to start studying materials by themselves. You check their understanding randomly as they go along. Correct their understanding per the materials as necessary. Teach them how to look up words in a dictionary to understand the lessons better.  So you train them how to self-learn given good materials.

Self-learning is an activity that a Tutorial class supervisor has to make sure that every student has it down pat. If a person is having difficulty with mathematics later then this skill in self-learning must be examined thoroughly.

It is a good understanding of the basics that makes a good self-learner. So, if the skill of self-learning is missing then the student should be thoroughly examined for his understanding of the basic concepts in mathematics.



In the third stage, an accomplished self-learner can start tutoring new students who need one-on-one tutoring. He puts them on the road to become self-learners.



In the fourth stage the person practices “seeing things as they are with full awareness of all assumptions”. This practice is called mindfulness.

In practicing mindfulness, a person learns to recognize anomalies and resolve them. Anomalies are discontinuities, disharmonies and inconsistencies in mental perception. Now he can learn anything that he wants to learn on his own by going to the Internet, or from experiences in life.


Self-Learning Diagnostic #2

Reference: Critical Thinking in Education


The above is the second “Self-Learning” Diagnostic Test for students in middle school and above

Can you find the illegible numbers represented by the *’s?

The purpose of this diagnostics is to assess the following:

  • Is the student able to move beyond patterned thinking?
  • Can the student think in novel ways to resolve problems?
  • Is the student’s mental math techniques up to par?

Calculators are very useful. They speed up the ability to calculate. But they should augment and not replace a person’s ability to calculate mentally and on paper with pencil. The person should not get so addicted to calculators that he loses his number sense and the gut feeling when computation go wrong.

This exercise may be timed. If the student can do this exercise rapidly and accurately then his attention and self-learning potential are in good shape. No remedy is needed at this level.

If the student is unable to move beyond patterned thinking then he should review the following documents to learn that different ways of thinking are possible.

Mental Math Techniques for Subtraction

Mental Math Techniques for Multiplication

This diagnostic helps locate and fill some of the early holes in the understanding of math. Filling of such holes in a subject restores student’s eagerness to learn.

With eagerness comes the ability to self-learn.


Self-Learning Diagnostic #1


Reference: Critical Thinking in Education


The above is the first “Self-Learning” Diagnostic Test for students in middle school and above

Can you compute the three addition problems above on paper with pencil?

The purpose of this diagnostics is to assess the following:

  • Is the student’s attention well focused?
  • Is the student confident of his/her answer?
  • Is the student’s mental addition techniques up to par?

In this diagnostics, the student

  1. Adds the numbers from top to bottom to get the sum.
  2. Adds the numbers from bottom to top to verify the sum.
  3. Checks his answers against those provided on the right.

This exercise may be timed. If the student can do this exercise rapidly and accurately then his attention and self-learning potential are in good shape. No remedy is needed at this level.

If the student’s focus and confidence in math needs improvement then he should practice mental addition on a gradient as follows.

  1. Practice adding two single-digit numbers.
  2. Practice adding a single-digit number to a double-digit number.
  3. Practice adding two double-digit numbers

It all boils down to knowing the sum of two single-digit numbers. And, for that, there are limited numbers of combinations. The rest is attention and technique.

The techniques for mental addition help develop basic number sense. The student is then able to rapidly add two numbers, while also verifying the sum at the same time. This skill is then carried forward to rest of the basic math operations. This builds up a confidence that is hard to shake.

This exercise develops the fundamental thinking skill on which subsequent math skills are built. It fills an early hole in the understanding of math.

The following document provides basic mental addition techniques and exercises. After learning these techniques, the student may develop his own techniques.

Mental Math Techniques for Addition

This diagnostic helps locate and fill one of the early holes in the understanding of math. Filling of such holes in a subject restores student’s eagerness to learn.

With eagerness comes the ability to self-learn.