Understanding the Deductive Method in Teaching Mathematics

The deductive method of teaching mathematics is a powerful approach where teaching moves from the general to the specific. In this method, a teacher starts with a general rule, formula, or principle and then applies it to specific examples or problems. This helps students understand how general mathematical concepts can be used to solve particular cases.

Analyzing Statement I: Using (a+b)\(^2\) Formula

Statement I describes a scenario where the general algebraic identity \((a+b)^2 = a^2 + b^2 + 2ab\) is used to calculate \((112)^2\). In this case, the general formula \((a+b)^2\) is applied to a specific number, \(112\). We can think of \(112\) as \(100 + 12\), so \(a=100\) and \(b=12\). By applying the general formula, we get:

\((112)^2 = (100 + 12)^2 = (100)^2 + (12)^2 + 2 \times 100 \times 12\)

This process clearly demonstrates moving from a general formula to a specific calculation, which is the core principle of the deductive method of teaching mathematics.

Analyzing Statement II: Using Law of Indices

Statement II describes using the law of indices \(\frac{a^m}{a^n} = a^{m-n}\) to find the value of \(\left(\frac{C^{10}}{C^2}\right)\). Here, the general rule for dividing powers with the same base \(\left(\frac{a^m}{a^n} = a^{m-n}\right)\) is applied to a specific expression involving powers of \(C\). Applying the law, we get:

\(\frac{C^{10}}{C^2} = C^{10-2} = C^8\)

Again, this is an application of a general rule (law of indices) to a specific mathematical problem, which is characteristic of the deductive method of teaching mathematics.

Conclusion

Both statement I and statement II show instances where a general mathematical rule or formula is applied to solve a specific problem. This aligns perfectly with the definition and application of the deductive method in teaching mathematics. Therefore, both statements are examples of the deductive method of teaching mathematics.