How many levels are there in the abacus

The right tricks when practicing arithmetic

You are right here if:

  • you would like to practice arithmetic with your child at home
  • arithmetic doesn't really want to work out
  • your child is unmotivated
  • your child just doesn't want to understand how this works
  • your child uses their fingers to do arithmetic more often

Do you sometimes miss them sparkling ideahow you can optimally support your child with arithmetic? Do you know which ones Computational strategies your child should really know?

If these are also questions that occupy you, then you've come to the right place. Feel free to read the following articles or watch my video on YouTube.

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That's why it doesn't work

When calculating at home, the picture often looks like this. Maybe you know it too. Your child brings home a worksheet or a given page in the workbook that needs to be worked on. Filled with a wide variety of easy and difficult tasks. With some tasks you may ask yourself what to do.

It is possible that your child is completely unmotivated even before the start and it is difficult for you to even start with the tasks.

Then you sit there and you torments you from task to task. What happened that had to come to this? At what point has your child lost the pleasure in arithmetic or was never allowed to really discover it and what can you do to make your child (re) discover this pleasure?

What you should know about this, I would like to share with you here.

Basis for successful arithmetic

The fact is and you shouldn't neglect that (unfortunately too many teachers do that) so that the arithmetic can work, your child needs a strong understanding of quantities. Without this understanding, arithmetic cannot succeed. This is THE main problem for children who solve problems by counting.

Let's take exercise 8 + 6 as an example

How does your child approach this problem when solving the problem (I don't mean what result your child will come up with), what strategy does he use to solve the problem?

If necessary, it takes the 8 and from there continues to count 6 individually -> 8, 9, 10, 11, ....

Then your child still lacks the right strategic approach. But that's no problem. That's why you're here. If you read the following lines, you will gain more clarity about what you can do.

So that your child can learn arithmetic in the long term, you absolutely have to know these three levels of representation. Don't worry, you don't have to be able to remember the formal terms, but what is behind them and what your child needs for them.

There are three levels of representation

  • Enactive representation
  • Iconic representation
  • Symbolic illustration

If you are practicing with your child at home, you will likely have the tasks in front of you in symbolic form. That is the form of the pure arithmetic problem. Exercise 8 + 6 is written in numbers in front of your child and he or she should now solve it.

On the one hand, your child needs arithmetic strategies (more on that later) and, on the other hand, your child must have fully penetrated the task on the enactive and iconic level. Unfortunately, this is often not the case. I'll show you how to do it here.

The active display level means that the Task with specific material is solved and not counting, but as a quantity.

What does that mean in our specific case 8 + 6? The abacus (calculating machine) is a suitable material for loosening. These are available with 20 and 100 pearls. The color changes after every 5 pearls.

In order for your child to be able to understand the process of solving a task, it must be able to "grasp" the numbers in the direct sense. It has to treat the number as a quantity to be aware of its size.

Unfortunately, this is often not done at all (even at school). No material - no time - with lasting consequences. Children need that. Not all children, probably yours already, otherwise you probably wouldn't have read this far.

Enactive display level

If your child now solves problem 8 + 6 with the abacus, that means Not (please be careful) that the pearls are counted individually.

The Number is seen as a quantity. That means, first I move 8 pearls to the other side - that's 5 of one color and 3 of the other. In addition there are now 6 pearls. To do this, I break the 6 into 2 and 4. First I add 2, then I already have 10 and then add 4 to it and thus get 14. Your child is not allowed to count them. It has to know the magic 5 that appears when the color changes 5 - 10 - 15 and orientate itself on it.

Pretty difficult. That is why the calculation strategies are so important. Only when your child has grasped active action on the enactive level can they move on to the iconic level.

Note: children with a Arithmetic weakness do not manage (depending on the degree of expression) to exceed the enactive level. That's okay then. In the disadvantage compensation you can specify that the abacus can be used at any time to help. Your child should not use it as a counting aid.

Iconic display level

After your child has tasks of the respective type (here in our example it is a task from the number range up to 20 with the tens transition) you switch from the active to iconic display plane. Iconic means that I now see what I have just depicted with the pearls as a picture.

I see 8 points as a set. Your child does not count these individually, but recognizes there are 5 and then 3 again makes 8. Now 6 are added to the 8. First, the full ten is added, i.e. another 2 is added. Then 4. are missing. Now we can see a full tens and 4 ones. That's 14.

Symbolic representation level

At the iconic level, your child can still see the action, even if it is not actually carried out. After a certain amount of practice (and each child takes a very different amount of time) they will be able to do this Automatically evoke the image in the inner eye. Then your child is ready to solve tasks in this number range exclusively on the symbolic level.

What can you do now

Ask your child the task 8 + 6 and let them explain to you exactly how they solve the task. Does it solve the task by counting? Or does it not find a solution at all? Then this is a sign for you to use an abacus and show your child how to "grasp" the task. If your child can safely solve the task, you are ready for the second important major area.

In the previous part, I told you how important it is to have a good understanding of quantities. Once your child has formed this understanding of quantities, they need arithmetic strategies in order to solve tasks strategically.

Here in our example 8 + 6 we have already used a calculation strategy. It was that Calculation strategy of the numbers in love. Numbers in love? Two numbers are in love when they add up to 10. So your child adds 2 to the 8 for the 8 + 6 task, because the 2 is in love with the 8. To do this, your child has broken down the 6 - into 2 and 4. Your child has already added 2 to the 8. Now 4 are missing. So 8 + 6 = 14.

Another strategy is that Computational strategies for giant and dwarf problems. Take e.g. B. Exercise 14 + 3. That is a huge exercise. This can be seen from the tens at the 14. To calculate this problem, I first solve the dwarf problem 4 + 3. So I first hide the tens. 4 + 3 = 7. From this I can conclude that the huge problem must result in 17.

In addition to these two calculation strategies, there are others. It is very important that your child has the calculation strategies and can use them appropriately depending on the task. It is not that easy and it doesn’t happen straight away. But if you take enough time with your child for exactly this in the first two years of school, they will benefit in the long term. I can promise you that.

Always go step by step. You can also use my virtual classroom for this. There you have the material, tutorial videos and explanations to learn with your child at home with ease.