Child Doesn't Understand Math? Pitfalls in Grades 1-4

A parent describes on Reddit a ten-year-old for whom math used to be the favorite subject: "Now he sits down, stares at his worksheet for 30 seconds, and completely shuts down."

If you know afternoons like that, you are not alone. In the IQB Bildungstrend 2021 (in German), around 22 percent of fourth graders in Germany missed the minimum standard in math, meaning requirements that everyone should reach. In the TIMSS 2023 (in German) study, 25.1 percent of fourth graders were on the two lowest competence levels. So difficulties in math are no isolated case in elementary school. But what helps you most is the question of where exactly your child gets stuck.

When your child doesn't understand math: find the pitfall first

Elementary math is like a staircase. The Saxon curriculum (in German), for example, provides that in grade 4 children carry their knowledge of the operations over to numbers up to one million. That only works if the lower steps hold. A child who still counts 7 + 8 finger by finger has to count on the side at every digit in 47 + 38 and later in written calculation. The math project PIKAS at TU Dortmund writes in an information sheet for parents (in German): if children keep counting the individual fingers from the beginning, that is "also very laborious and error-prone later when calculating with large numbers."

So "my child can't do math" is too big a verdict. The more helpful question is: with what kind of problem does your child become unsure? Look at the last pages in the notebook and watch for three things:

• Does your child still count on their fingers one by one for simple addition and subtraction?
• Do they mix up tens and ones, when writing numbers or when subtracting?
• Do they calculate confidently as long as the problem is written as numbers, and only fail at the text?

With the answers you can find the best-fitting pitfall in the table below.

Pitfalls in grades 1, 2, 3 and 4

Which topic comes up in which grade is set by each German state (Bundesland) in its curriculum. Bavaria and Saxony, for example, combine grades 1 and 2 in one shared section (LehrplanPLUS Bayern (in German), Lehrplan Sachsen). The grade levels below are therefore only a rough guide. We built the error examples ourselves; they do not come from real worksheets.

Pitfalls at a glance (our own compilation)

Grade 1: from counting to calculating

Counting on fingers is no reason to worry at first. The guideline on arithmetic disorder (in German), whose recommendations were adopted by 20 professional societies, calls it "a normal aid for building factual knowledge and learning efficient calculation strategies." It treats only long-lasting finger counting as a sign of problems, especially with easy, often practiced problems.

The next big step is adding across 10, that is, problems like 7 + 9 whose result goes past 10. The Saxon curriculum shows the way via the 10: 7 + 9 = 7 + 3 + 6. For this your child needs the ways to split 10 (1 + 9, 2 + 8, 3 + 7 and so on). In its first parent letter on the basic addition facts (in German), PIKAS lists these "split problems for the number 10" among the problems children should learn by heart.

Try this: Lay out eight counters and ask: "How many are missing to get to 10?" If the answer comes confidently, add two counters so that ten are lying there. Then the remaining three are added. This way your child sees 8 + 5 as 8 + 2 + 3, without counting. What else children learn in first grade is covered in What does my child learn in first grade?.

Grade 2: tens, ones and the multiplication tables

With numbers like 47, we say the ones first in German: seven-and-forty. But when writing, the 4 comes first. The Saxon curriculum therefore lists the point "paying attention to the direction of writing and speaking" on its own, and the guideline on arithmetic disorder names difficulties with the place value system and with converting between number words and digits as possible signs. A single swapped digit says little about this. According to the guideline, what matters is not the calculation errors themselves, but "their variety, stability and frequency."

In subtraction, shaky place value shows up like this, for example: in 45 − 28, the child takes the bigger minus the smaller digit at both places and gets 23 instead of 17. The Bavarian curriculum for grades 1 and 2 requires that children translate numbers back and forth between notation, number word and materials such as ones cubes and ten-rods. At home you can do this with coins: lay out 45 cents as four ten-cent coins and five one-cent coins, then take away 28 cents. Your child notices that they have to exchange one ten for ten ones.

For the multiplication tables, the Bavarian curriculum provides a clear path: first the core problems should be secure, that is, the tables of 1, 2, 5 and 10 and the square problems like 7 · 7. Children derive the remaining problems from them, in the curriculum's example 9 · 8 = 10 · 8 − 8. If your child recites the whole table of sevens for 6 · 7, try deriving the problem from 5 · 7 together. Ask: "Which easy problem do you know that looks almost like this?" 5 · 7 = 35, plus one more 7. Then have your child explain why this works. An overview of the whole school year with a checklist is in Second grade math: what does my child need to know?.

Grade 3: large number range and written calculation

In the Saxon curriculum, the number range grows to 1,000 in grade 3, and the written methods are added: addition and subtraction "also with carrying," multiplication by a single-digit number, plus division with remainder. In addition, children there are supposed to solve the multiplication problems automatically in grade 3. More on grade 3 with examples and a checklist: Third grade math: what does my child need to know?.

Zeros get tricky: in 403 − 158, your child has to fetch a ten where there is none on top. The Saxon curriculum provides for explaining the methods with materials and a place value chart and making the unbundling visible. That is exactly what helps at home too: lay out hundreds, tens and ones and exchange one hundred for ten tens.

There are also different methods (in German) for written subtraction, and your child may learn a different one than you did back then. More on this further down.

Grade 4: million, written division, estimating

In grade 4, the Saxon curriculum extends the number range to 1,000,000, and adds written multiplication with a second factor of up to three digits and an introduction to written division with a single-digit divisor. It also explicitly lists the "meaning of zero." That fits this error: 824 : 4 = 26, because the zero in the result is forgotten.

A good habit against this is estimating, which the Saxon curriculum provides for as a check from grade 3 on: 824 : 4 is about 800 : 4 = 200. So a result of 26 cannot be right. If your child asks themselves this question, they can find such errors on their own.

Word problems run through all four years. If your child can do the calculation but fails at the text, the article Child doesn't understand word problems helps with a method in five steps.

Not understood or not practiced?

Two children can make the same error and still need different things. One has not understood what happens in the problem. The other has understood it but still calculates slowly and hesitantly because they need more practice. In its parent letter on the basic addition facts, PIKAS advises: if your child counts all the fingers one by one while practicing, "it is still too early for memorizing." Then they should first lay out the problems with materials.

What this can look like is described by someone who sometimes does homework with children, in the forum r/Eltern (in German), using an example from 2nd grade: asked what 23 minus 5 is, a child answers "35....?". When asked how they calculated it: "All that comes back is silence again." If your child cannot describe their way of calculating, try materials and explaining first, before you practice for speed.

The 5-minute check (our own compilation)

Take a problem your child has just failed at and go through these questions in order. The check is an aid for conversation, not a diagnosis: it shows you what you can continue with.

If your child cannot show or explain the problem: Go back to materials, pictures and talking. According to PIKAS, it is "very important that your child may learn with concrete materials, that is, in the widest sense with their hands, until they can imagine numbers and calculations in their head." Take counters, coins or an abacus and let your child tell out loud what they are doing.

If the way works, but slowly: Practice briefly and regularly. The PIKAS parent letter on the basic addition facts recommends "ideally 5 to 10 minutes every day. No longer!" Problems that are already secure can take a few days' break. If the gap is big and you don't have the time to practice, tutoring can be an option. What it costs and what to look out for is in Tutoring in elementary school.

Helping with math homework without solving it for them

Solving the problem for them is tempting, especially in the evening. Then the result is in the notebook, but your child has not taken the step themselves. In the information sheet "Mathe in den Kopf?!", PIKAS gives parents a simple rule: "Stick to your child's way of calculating and ask what they were thinking!"

You can ask these five questions in order:

1. "Read the problem to me. What are you supposed to do here?"
2. "Which problem do you already know that looks almost like this?"
3. "Can you lay it out or draw it?"
4. "What did you calculate first?"
5. "Could the result be about right?"

If even the wording of the task is unclear, Child doesn't understand the instructions helps.

Be careful with sentences like "That's easy" or "Can't you do that in your head?" PIKAS warns: if a child cannot yet imagine the numbers in their head, "then they can be very unsettled by what you say." So don't take materials away too early either.

And what if every math afternoon ends in an argument? PIKAS has advice for this too: sometimes it is better not to practice at all for a while or to let someone else practice, because "practicing is useless if your child feels uncomfortable and under pressure while practicing." Then discuss the situation with the teacher.

New ways of calculating that you don't know

You may come across ways of calculating in the homework that you never learned yourself: the number line, helper problems, a different method for written subtraction. The Saxon curriculum requires, for example, that children record their solution paths on the number line, and explicitly mentions "avoiding any premature standardization of solution paths and notations."

For you this means: don't show your own way before you know the school's way. PIKAS explains this in the information sheet for parents like this: if ways of calculating are explained at home in a "completely different" way than in class, "this can lead to great confusion for your child!" Flip back in the notebook to the last similar problem, have your child explain the way to you, and if neither helps, ask the teacher which method the class is currently practicing. Why school calculates this way today is explained in the article Elementary math: why it works differently than it used to. You will find more help with understanding tasks in the guide Understanding tasks. How Gennady checks your child's answers is on the page Checking answers.

When an evaluation makes sense

Not every child who gets stuck in math has an arithmetic disorder (dyscalculia). According to the guideline in the Deutsches Ärzteblatt, it affects 3 to 7 percent of all children, adolescents and adults. Those affected have "pronounced and persistent problems" with the basic operations and the multiplication tables, which do not result solely from an intellectual disability or inadequate schooling.

The guideline names these signs, among others:

• Number and quantity do not match: the child does not reliably connect the 2 with two objects.
• Difficulties with counting, comparing numbers, place value and converting between number words and digits.
• No transition from counting-based calculation to ways of calculating without counting.
• The multiplication tables cannot be recalled from memory but are worked out anew every time.
• The difficulties grow as the problems get more complex: larger number range, written calculation, word problems.

The guideline also names other reasons why children can be weak in math, such as undetected vision or hearing problems, frequent changes of teacher or canceled lessons, long absences due to illness, and fear of school.

According to the guideline, a diagnosis should only be made if a standardized math test shows below-average performance and the history and examination fit. Support should begin early in elementary school age, with trained specialists and in one-to-one sessions.

What to do if you are unsure:

1. For two or three weeks, write down which problems your child gets stuck on and how long they take.
2. Talk to the teacher. They see your child in comparison to the class.
3. Have the pediatrician check vision and hearing if that has not happened in a while.
4. If the difficulties remain despite practice, ask the teacher or pediatrician about a professional evaluation.

This article does not replace diagnostic assessment or advice from a teacher, pediatrician or learning therapist.

Frequently asked questions

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Sources

• Institut zur Qualitätsentwicklung im Bildungswesen (IQB): IQB-Bildungstrend 2021 (2022). iqb.hu-berlin.de
• Kultusministerkonferenz: press release on TIMSS 2023 (2024). kmk.org
• Deutsches Ärzteblatt: Haberstroh, S., Schulte-Körne, G.: Diagnostik und Behandlung der Rechenstörung, clinical guideline (2019). PDF at aerzteblatt.de
• Staatsinstitut für Schulqualität und Bildungsforschung München: LehrplanPLUS Grundschule, subject curriculum Mathematics 1/2 (as of September 2026). lehrplanplus.bayern.de
• Sächsisches Staatsministerium für Kultus: Lehrplan Grundschule Mathematik, revision 2026 (as of September 2026). schulportal.sachsen.de
• PIKAS, TU Dortmund: information sheet for parents "Mathe in den Kopf?!" (2012). PDF at pikas.dzlm.de
• PIKAS, TU Dortmund: parent letter 1 "Das kleine 1 + 1 richtig üben" (2010). PDF at pikas.dzlm.de
• PIKAS, TU Dortmund: Elterninfos, overview (as of September 2026). pikas.dzlm.de
• Reddit, r/Parenting: post of May 16, 2026 (third-party quote, English). reddit.com
• Reddit, r/Eltern: post of May 16, 2025 (third-party quote). reddit.com