Subject Clearing

Math

Reference: Critical Thinking in Education

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Since additional information on a subject may easily be accessed through Internet these days, the purpose of study is not to memorize but to improve one’s critical thinking.

The true purpose of study is to resolve inconsistencies (things that do not make sense) as you come across them in a subject. This develops clarity of mind and the ability to think fast on your feet.

When one is studying the basic postulates and fundamentals concepts of a subject it is very important to be able to detect hidden assumptions and subjective opinion. Such erroneous ideas can be very pervasive, and may even enter the definitions of words provided in dictionaries.

The following procedure helps one become aware of hidden assumptions and subjective opinions related to a subject.

1.    Make a list of key words in that subject.

Skim through the chapter that you are going to study, and make a list of key words. Put that list on an Excel worksheet. This list may grow as your studies get deeper into the subject.

Look up the broad concept and definitions for each key word, as described in Word Clearing, and note it down on the Excel worksheet.

2.    Gradually build upon each concept for that subject.

Study the materials of the subject one paragraph at a time. Reduce a paragraph to its main thought and note it down in an editable document on computer. Do this before proceeding to the next paragraph.

When it is difficult to reduce the paragraph then look for words that may not be clear in that context. If the difficulty persists then note down the confusion with the “main thought” in that paragraph. It may get clarified by something you read later.

Note down any additional conceptual understanding and questions next to the appropriate word on the Excel worksheet.

3.    Arrange the key words with their concepts in proper sequence.

The concepts in a subject always evolve in a sequence. This can easily be seen in Mathematics and Science.

In Excel, you may separate the key words on two different worksheets categorized as “fundamental concepts” and “derived concepts”. Then arrange the concepts in each worksheet in the order they evolved.

This sequence of the evolution of these concepts may not be linear but multi-dimensional . So, to look at the key words in different sequences, you may create “priority columns” in the worksheet with a number assigned to each key word. The whole idea is to arrange these words in different ways to examine the connections among them.

4.    Note any inconsistencies among the concepts and clarify them.

As the study of the subject progresses and better understanding comes about, rearrange the list of key words to examine consistency among the various concepts. You are looking for things that appear inconsistent and do not make sense. There may be holes among these concepts that need to be filled.

Deeper research may be required to discover such holes and fill them. First review your materials to clarify any inconsistency. If it does not clarify easily then note it down on the worksheet and research through other materials in the library or on Internet.

5.    Clarify the fundamentals of the subject as a priority.

The consistency of the fundamentals determines the consistency of the whole subject. Any inconsistency at the fundamental level must be handled as a priority. For example, a unified theory is desperately being looked for in the subject of Physics, which could bring the fundamentals of Newtonian Physics, the Theory of Relativity, and Quantum Mechanics in line.

There are likely to be many contributors to a subject who may use different words for the same concept. This is the case with religious knowledge from different cultures. Group such words together to discover inconsistencies among concepts.

Study of inconsistencies may lead to discovery of arbitrary assumptions that were made in the absence of knowledge, or you may find erroneous observation, or simply some ideas that are taken for granted. This may reveal gaps in the subject itself. Develop your own understanding by seeking consistency among these concepts.

6.    Make the subject as complete as possible.

There are many examples in the subject of religion where gaps in knowledge are hidden under assumptions and dubious explanations. This may be the case with any subject where inconsistencies abound. Follow up on inconsistencies, which may then reveal gaps in the subject. Real progress then becomes possible.

Fill gaps in the subject with wider research. Make the subject as complete as possible through direct experience and experimentation.

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