Order of Operations, Equals Signs, and the Math Myths We Teach

Some things taught in elementary are simplifications that later become obstacles. These five are worth getting right the first time, because the true version is no harder.

Myth 1: The Equals Sign Means "The Answer Comes Next"

The most consequential one.

Ask a 2nd grader to fill in 8 + 4 = __ + 5 and a large share write 12. They read the equals sign as an instruction: do the thing on the left, write the result.

What it actually means: both sides have the same value. It is a statement of balance, not a command.

Why it matters: a child who reads it as an instruction hits a wall in algebra, where 3x + 2 = 14 requires the balance reading and makes no sense under the other one.

What to do: use balance language from the start. "Is this side the same as that side?" Write true or false statements: 7 + 3 = 10, 6 + 2 = 9, 5 = 5, 10 = 6 + 4. That last form, answer on the left, is startling to children and worth doing often.

Myth 2: Multiplication Makes Things Bigger

True for whole numbers above one. False the moment fractions arrive.

12 x 1/2 = 6. A child holding the rule as universal concludes they have made a mistake.

What to do: avoid stating it as a rule. When children notice the pattern, agree carefully: "with the numbers we're using now, yes. That changes later, and we'll see why."

Same for "division makes things smaller" and "you can't subtract a bigger number from a smaller one".

Myth 3: PEMDAS Is a Six-Step Queue

The acronym implies multiplication before division, and addition before subtraction. Neither is right.

Multiplication and division rank equally, worked left to right. Same for addition and subtraction.

12 ÷ 3 x 2 is 8, not 2. A child following PEMDAS as a strict order does the multiplication first and gets 2.

What to do: teach it as three tiers, not six steps: brackets, then multiply-and-divide left to right, then add-and-subtract left to right. Same effort, correct.

Myth 4: You Always Start From the Right

Column methods start from the right, so children generalise it as a rule about maths.

Then mental arithmetic, estimation, and most efficient strategies start from the left. 48 + 26 is easier as "40 and 20 is 60, 8 and 6 is 14, so 74".

What to do: be explicit that the written column method starts from the right, and that mental methods often do not. Number talks surface the left-to-right strategies naturally.

Myth 5: There Is One Right Method

The method a child is taught becomes, in their mind, the method, and other approaches feel like cheating.

What to do: ask "did anyone do it a different way?" routinely, and ask which was more efficient for these particular numbers. Efficiency depends on the numbers, which is itself an important idea.

Why This Is Worth the Care

None of the true versions are harder to teach. They just require not reaching for the convenient simplification.

Something unlearned in 6th grade costs far more than something taught correctly in 2nd. And the practice should reinforce the true version: balance-style equations, mixed operations, and problems where the efficient method varies. Worksheets sorted by grade and skill cover those forms alongside standard practice.

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