Why Smart Kids Still Get PEMDAS Wrong

MATH · STUDY SKILLS

Outstanding difficulties from actual tutoring sessions — the same order-of-operations slip showed up across students years apart in level.

Why Smart Kids Still Get PEMDAS Wrong

Ask a student to state the order of operations and they'll rattle it off without hesitation: parentheses, exponents, multiplication and division, addition and subtraction. Ask them to actually solve 35 + 7 × 5, though, and a surprising number will add first, out of habit, and land on 210 instead of 70.

This isn't a knowledge gap. It's a reading-direction gap. Students learn PEMDAS as a list of words, but under time pressure their eyes move left to right and their hands just do the next operation they see — not the next operation in priority order. We saw this exact error pattern in three separate sessions this week, from a Grade 4 student working on multi-digit arithmetic to a Grade 8 student solving 96 ÷ 8 × 7 + 5 and dividing and multiplying in the wrong sequence.

The fix isn't more repetition — it's a physical habit

Telling a student “remember PEMDAS” one more time rarely works, because the mistake doesn't happen at the knowledge level. It happens at the execution level, in the half-second before pencil hits paper. What actually closes the gap:

• Circle before you calculate. Before doing any arithmetic, have the student physically circle every multiplication and division operation in the expression first, in the order they'll do them — then go back and handle addition/subtraction.

• Say the plan out loud. “First I multiply 7 and 5, then I add 35” — said before writing anything. Verbalizing the plan catches the error before it's on paper, where it's harder to unsee and easier to defend.

• Practice with ugly numbers on purpose. Clean numbers let students get the right answer by accident. Deliberately mixed expressions (e.g., 18 − 4 × 3 + 21) force the sequencing skill instead of letting number sense paper over it.

The pattern shows up again later in a more dangerous form: solving inequalities. When a student multiplies or divides both sides of an inequality by a negative number, the same left-to-right autopilot causes them to forget to flip the sign — turning a correct method into a wrong final answer. It's the same underlying habit, just with higher stakes on a test.

Order-of-operations errors rarely show up as “I don't understand math.” They show up as “I understood it in class but got it wrong on the test” — which is exactly why they're so frustrating for parents and so fixable with the right kind of practice.

The Class Tutor works one-on-one with students to close exactly these kinds of gaps — the small, fixable habits that quietly cost marks. Get in touch at support@theclasstutor.com to talk about a session.