Memorizing basic formulas: easy investment with great return

As a college STEM instructor, I often encounter students who question the necessity of memorizing basic math formulas. In an age where technology provides instant access to information, it’s a fair question. However, there are several compelling reasons why committing these formulas to memory remains crucial for students, particularly those in STEM fields.

1. Foundation for Advanced Learning

Basic math formulas are the building blocks of more complex mathematical concepts. Understanding and memorizing these formulas allows students to grasp advanced topics more easily. For instance, knowing the quadratic formula

$$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$

by heart enables students to solve quadratic equations efficiently, which is essential for higher-level algebra, calculus, and beyond.

2. Enhanced Problem-Solving Skills

Memorizing formulas enhances problem-solving skills by allowing students to focus on the application rather than the derivation of formulas. When students don’t have to pause to look up a formula, they can spend more time analyzing the problem and developing a solution strategy. For example, the Pythagorean theorem

$$a^2 + b^2 = c^2$$

is frequently used in geometry to find the length of a side in a right triangle.

3. Improved Mathematical Intuition

Familiarity with basic formulas fosters a deeper understanding of mathematical relationships and patterns. This intuition helps students recognize which formulas are applicable in various contexts, leading to more effective and efficient problem-solving. For example, recognizing the relationship between the area of a circle:

$$A = \pi r^2$$

and circumference of a circle:

$$C = 2\pi r$$

can provide insights into geometry and trigonometry problems.

As a quick test, how many of you can momorize the formula for the volume of a sphere? a cylinder? a parallelepiped?

4. Increased Confidence

Confidence in mathematics often comes from a solid grasp of fundamental concepts. When students have key formulas memorized, they approach problems with greater assurance. This confidence can reduce math anxiety and encourage a more positive attitude towards learning and applying mathematics.

5. Practical Applications

Many real-world problems require quick and accurate mathematical calculations. Engineers, scientists, and other professionals frequently rely on basic math formulas in their work. Memorizing these formulas ensures that they can perform necessary calculations efficiently, without the need for constant reference to external sources. For example, the formula for calculating compound interest

$$A = P(1 + \frac{r}{n})^{nt}$$

is essential in finance and economics.

6. Preparation for Tests

Standardized tests, such as the SAT, ACT, GRE, and professional certification exams, often require quick recall of basic math formulas. The same goes to a chapter exam, midterm, or final in your courses. Students who have these formulas memorized are better prepared to tackle these tests with confidence and accuracy, leading to improved performance.

Conclusion

While technology has made it easier to access information, the importance of memorizing basic math formulas cannot be overstated. These formulas are the foundation of mathematical understanding, enhance problem-solving skills, improve intuition, boost confidence, and have practical applications in both academic and professional settings. By committing these formulas to memory, students equip themselves with the tools necessary for success in their mathematical endeavors and beyond.

I once had a student wrote me a comment like “I feel I was tested on memorizing stuff instead of my creativity”, only because I emphasized the importance of memorizing basic formulas. Well, if one does not know basic stuff, I’m not sure how creative they can be.