Factual Knowledge

Factual part & conceptual aspects of math knowledge are two levels in which math can be learnt. Both constitute knowledge in math that need to be “remembered & recalled”.

Factual knowledge can be considered the “final” form in which a deep concept is communicated to another person who has already understood the underlying concepts.

To take a simple example, conceptual knowledge is about “understanding” why a particular number is even. Factual knowledge is remembering a rule by which we can decide if a number is even. The important point is that one may now the rule but not why that rule works.

Conceptual knowledge is the deeper aspect. We will deal with this kind of knowledge in the next chapter.

Here are some statements in math that can be called factual knowledge.

1. 2, 3, 5, 7 are prime numbers less than 10.

a. The learner may not know what a prime number is Or

b. Whether 97 is a prime number

2. 8 X 7 = 56

a. The learner may not know the meaning of this statement

b. The learner may be unable to provide any real-life event which can justify it.

3. Odd + Odd = Even

a. The learner may know the meaning of the terms even & odd but may not know how to justify the above statement.

4. A Square is a quadrilateral with all its sides and angles equal.

a. The learner may know this definition without understanding the relation between a square and another quadrilateral like rectangle

5. A Right Angle equals 90 degrees

a. The learner may not understand the above statement at all.

b. The learner may not know the relation between a right angle & a complete angle

6. While evaluating an expression involving arithmetic operations, the multiplication & division operations have to be done before the addition & subtraction operations.

a. The learner may not know why such a rule is needed.

b. The learner may not know the meaning of a convention

Factual knowledge consists of (a) statements, (b) definitions & (c) conventions.

Statement (4) is a definition & statement (6) is a convention. The others are statements.

These statements are typical of the answers to some of the questions asked in math tests. They can be written as answers to questions.

What is important is that they can be answered, without understanding what they mean. We will explore the meaning of “understanding” when we deal with conceptual knowledge.

The statements themselves may or may not be mathematically correct. Their “validity” cannot be verified by a person who does not have conceptual understanding.

Typically, the Indian school curriculum emphasizes mostly on factual knowledge in contrast to conceptual knowledge.

Since factual knowledge consists of definitions, statements & conventions, which have not been really understood, the standard pedagogy is to memorize them.

Most school examinations contain questions which can be answered “correctly” without even understanding the meaning of either the question or the answer.

This is why you can have a student who scores very high marks in the school-leaving examinations but finds difficult to understand post-school math which is built on conceptual understanding expected to be developed in school.

Factual knowledge is the easiest aspect of math to be learnt.

This is one of the reasons, the curriculum and teachers focus on this aspect of knowledge in any subject.