Maths support in lessons without creating extra material
How teachers can support children in maths during regular lessons without making their own material, with examples for grades 2 and 3 and ready-made aids.
In brief: Support in everyday maths lessons works through short, regular practice phases, through taking up a misconception in a targeted class discussion and through material that is already in the classroom, such as the twenty frame, hundred square or place value chart. Ready-made diagnostic and support materials are available, for example, from PIKAS and from a further project of the German Centre for Mathematics Teacher Education (DZLM). In Mazio Math, a support card explains the class’s misconception, lists steps for the lesson and suggests matching content, which the teacher puts on the board with one tap.
This article is for teachers in grades 2 and 3 who want to support children with gaps in their own lessons, without creating worksheets in the afternoon. It describes building blocks of support in regular lessons, two examples and then how Mazio Math helps. First indications of dyscalculia are the subject of the article Early signs in grades 1 and 2 and when a specialist assessment is needed.
Building blocks of support in regular lessons
| Building block | What it looks like | What you prepare |
|---|---|---|
| Short daily practice | Ten minutes at the start of the lesson on a basic topic, such as partitioning numbers or making up to 10. | A sequence of tasks on the board |
| Discussing an error together | A typical wrong answer is shown anonymously and the class looks for the error in thinking. | An example from the children’s exercise books |
| Existing material | Twenty frame, bead frame, hundred square, place value chart, play money. | Nothing new, the material is already in the room |
| Children explain to each other | Partners explain a calculation method to each other and check it with material. | Fixed partners and a guiding question |
| Ready-made support materials | Baseline assessments and support tasks from ready-made collections. | Select and print |
| Adaptive practice on a device | A programme adjusts the difficulty and evaluates the answers. | Choose a piece of content |
Two German-language sources of ready-made materials are PIKAS, a service of the German Centre for Mathematics Teacher Education (DZLM) with research-based materials tested in practice, including baseline assessments, and a second DZLM project on basic maths skills with diagnostic and support materials for securing basic mathematical skills in grades 3 and 4 of primary school.
First find out which idea lies behind an error, then work specifically on that idea. Ten minutes at the right point can help more than a long practice phase with mixed tasks.
Grade 2 example: counting when bridging ten
The error. For 8 + 5, several children say 12. They count on and include the 8 in their count: “8, 9, 10, 11, 12”.
In the lesson. For one week, every lesson starts with ten minutes at the twenty frame. The children place 8, fill up to 10 and add the rest: 8 + 2 + 3. After that, the task is only shown briefly and solved mentally. The question “How many more to make 10?” becomes a routine.
Follow-up questions. “How did you work it out?” shows whether a child is still counting. Children who count work with the material; children who partition carry on without it. There is more on the topic on the page Bridging ten in primary school (in German).
Grade 3 example: smaller from larger
The error. For 52 − 27, several children get 35. In each place they subtract the smaller digit from the larger: 5 − 2 and 7 − 2.
In the lesson. Using tens rods and unit cubes, the children make 52 and are asked to take away 27. There are not enough ones, so one ten is exchanged for ten ones. Then they calculate step by step: 52 − 20 − 7. An estimate (50 − 30 = 20) and the inverse calculation 35 + 27 = 62 show that 35 cannot be right. More on this in the article Subtracting the smaller digit from the larger.
Follow-up questions. “What happened to the 7 ones?” and “Check your answer with the inverse calculation” show whether the child has understood the exchange.
How Mazio Math helps with support in lessons
Mazio Math is a learning platform for primary maths lessons. While the children practise, Mazio Math evaluates every answer; the diagnostics are rule-based and traceable. No additional testing time is needed.
The class’s misconception. Once a week, Mazio Math checks whether the class’s wrong answers show a widespread misconception, for example “The carry is forgotten when bridging ten”, or that in subtraction with regrouping the smaller digit is subtracted from the larger.
The support card step by step.
- Under “Results”, tap the flag under “Misconceptions in the class”. The support card opens, and “Next flag” moves on to the next one.
- You read the example and the background. Under “In lessons” you find steps you can take with the class yourself.
- You tap “Matching content for the board”. Units and Knobelbox tasks are suggested.
- You select content and put it on the class board. Whether you take up the flag is your decision.
On the home page, “Misconceptions” collects the flags from all your classes. “Matching suggestion” moves the content that matches the error to the top of the stack. For reference, the library collects common misconceptions by content area.
Practice that adapts. The Basiscamp builds up calculation skills step by step, for grade 2 for example with sections such as “Tens and ones” and “Across ten”. It records for each child which task types they have mastered; an exercise only counts as completed when several tasks in a row are solved at the first attempt and without help. Under “Results”, “Back on the board” suggests the sub-worlds that are not yet secure. When a child makes a mistake, the learning assistant Mazio helps directly in the task, with a question, with markings in the picture and, if needed, with a given partial step. He does not give the solution.
Ready-made lesson ideas. On the shelf under “Collection” there are lesson ideas with a goal, a sequence of phases and matching material, from 10 minutes to a double lesson, filterable by grade and duration. “Everything on the board” puts all the material for an idea on the board at once. Once a week you also receive an email with a summary of your classes and suggestions for the following week.
An example from grade 3. On Monday, the support card shows a flag on subtraction with regrouping. You go through the steps under “In lessons” with the class in two short phases at the start of lessons and then put one of the suggested units on the board as compulsory, with the note “Check with the inverse calculation”. The children who are already confident get through it quickly.
A teacher from the scientific study writes: “I am currently working with two parallel classes on Mazio Math and am amazed at how accurately the diagnostics reflect the classes. I appreciate the suggestions for catching up or going deeper. It makes the work easier.”
Next step. The page Taking up a misconception in the class shows how this looks in everyday teaching, and background is given in the article How Mazio Math evaluates the class’s errors in thinking. Create an account under register for free. Using Mazio Math with a class is currently available to schools in Germany. If your school is in another country, registration records your interest and we will let you know as soon as Mazio Math is available there.
Frequently asked questions
How much time do I need for support in lessons?
Ten minutes at the start of the lesson over one to two weeks are often enough if they target exactly the idea that causes the error. More important than the duration is that the practice takes place regularly and that the material shows the structure.
Where can I find ready-made support material for primary maths?
For example from PIKAS, a project of the German Centre for Mathematics Teacher Education (DZLM), and from the DZLM project on securing basic maths skills. PIKAS provides research-based materials for primary maths lessons, and the second project provides diagnostic and support materials for grades 3 and 4. Check the terms of use of each provider.
What does Mazio Math show me after a practice phase?
Under “Results” you see the evaluation for each unit and level, how many Basiscamp tasks were solved at the first attempt and where the class stands in the five content areas. If a misconception shows up, tapping the flag opens the support card with steps for the lesson.