Order of Operations: Why Even Teachers Get It Wrong

In the world of mathematics, the order of operations is a fundamental concept that dictates the sequence in which calculations should be performed. It’s a set of rules that ensures consistency and clarity in solving mathematical expressions. While the order of operations seems straightforward, it’s surprising how often even experienced educators get it wrong. This article delves into this common misconception and highlights the importance of understanding and applying the correct order of operations.

The Order of Operations: PEMDAS/BODMAS

The acronym PEMDAS or BODMAS is often used to remember the order of operations:

• Parentheses (or Brackets)
• Exponents (or Orders)
• Multiplication and Division (done from left to right)
• Addition and Subtraction (done from left to right)

This means that when evaluating an expression, you should first solve what’s inside parentheses or brackets, then exponents or orders, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

The Misconception

A study published in the Journal of Mathematical Behavior found that a significant percentage of prospective teachers incorrectly applied the order of operations. This highlights a widespread misconception that needs to be addressed. Many people tend to perform operations in the order they appear in the expression, without considering the priority of different operations.

Why It Matters

Understanding the order of operations is crucial for several reasons:

• Accurate Calculations: Applying the correct order ensures that mathematical expressions are evaluated correctly, leading to accurate results.
• Consistent Results: Following the order of operations guarantees that everyone gets the same answer for the same expression, eliminating ambiguity and confusion.
• Foundation for Higher Mathematics: The order of operations is a foundational concept that forms the basis for more complex mathematical concepts and procedures.

Examples

Let’s look at a few examples to illustrate the importance of the order of operations:

1. Example 1: 10 + 5 × 2

Incorrect Solution: 10 + 5 × 2 = 15 × 2 = 30

Correct Solution: 10 + 5 × 2 = 10 + 10 = 20

2. Example 2: (4 + 2)²

Incorrect Solution: (4 + 2)² = 4² + 2² = 16 + 4 = 20

Correct Solution: (4 + 2)² = 6² = 36

Conclusion

The order of operations is a fundamental concept in mathematics that ensures consistency and accuracy in calculations. While the rules seem simple, it’s important to remember that even experienced educators can make mistakes. By emphasizing the importance of PEMDAS/BODMAS and providing clear explanations and examples, we can help students develop a strong understanding of this crucial mathematical concept. It’s essential to address this misconception and promote a deeper understanding of the order of operations for accurate and consistent mathematical problem-solving.