Math on the Page: Misaligned Columns and Misread Signs

By Laura Lurns · Reviewed by Philip Weaver · Last reviewed 2026-10-07

What column and sign mistakes cannot tell you

Columns that drift and mixed-up signs are mistakes on the page. The mistakes alone do not tell you why.

Nothing on this page rules anything in or out, and we are not able to.

Our rule is to describe patterns on these pages. We do not put a name on a child.

What one study found

Raghubar and colleagues (2009) studied 291 children in grades 3 and 4. Each child did 12 written problems, all with numbers of two or more digits. Some were adding and some were taking away.

The authors grouped three kinds of mistake together. Digits slipped out of their column. Numbers were misread. Or the work was crowded together.

Column and misreading mistakes went with weaker reading, whatever the child's math. So did crowded work.

These are findings about groups of children. They are not a checklist for one child.

Younger children made more column and misreading mistakes

In the same study, younger children made more column, misreading and crowding mistakes. Those findings are about groups of children, not a promise about yours. They are not a reason to wait and see. No study we have tests wait-and-see as a plan for a learning difficulty. So we would not tell you to wait.

Mixed-up plus and minus signs

Sometimes a child adds when the sign says to take away. The study counted that as a sign mix-up.

In the same study, sign mix-ups were not shown to go with weaker math. Nor were they shown to go with weaker reading.

These are findings about groups of children. They are not a checklist for one child.

Children without learning trouble make column mistakes too

The authors wrote that children without learning trouble make column and misreading mistakes too. They wrote that this had not been studied with care.

An older idea was that those mistakes mark math trouble. This study tested that idea. It did not back it. It was one short task, in two grades.

What you can try

We read no study of a way to fix column or sign mistakes. So the tips below are teaching advice, not findings.

Here is one tip, as our teaching advice. Turn lined paper sideways. The lines then give each digit its own column.

Here is another tip, also our teaching advice. Before each problem, your child can say the sign out loud.

We cannot promise either tip will change the mistakes.

The eyes are worth checking too

In our view, an eye exam is worth doing early. Some children avoid close work, rub their eyes or lose their place. In our view, that is a reason for a full eye exam. Ask for one that includes near vision.

If an exam finds an eye problem, that problem needs its own care.

If your child has lost a skill

Some children could do something and now cannot. That is different from a child who has not built the skill yet. Our position is that a lost skill goes to a doctor first, not a tutor.

When to ask for help

Each of these is a reason to ask for help on its own.

• Little change, even with steady practice and good teaching.
• Schoolwork well below what school expects.
• A teacher who raises a concern about learning.
• Extreme upset about schoolwork.
• Complete avoidance of school or learning.
• Hopelessness about learning.
• Sadness or worry that lasts.
• Significant delays in speech, language or motor development.
• A skill that was there and has gone. Our position is that a lost skill goes to a doctor first, not a tutor.

If no skill has gone, start with the teacher. Say what you are seeing at home, and what you have tried. Beyond the teacher, the right person depends on what it turns out to be about. If the work is too hard, someone who works on that school skill. If worry or mood is the thing, someone who works with children's mental health. In our view, delays in speech, language or movement are worth raising with your child's doctor. In our view, if you are worried enough to ask, a professional evaluation is worth asking about.

Any talk of hurting themselves is a same-day call to your doctor or a crisis line.