Articles for parents

How does Kumon encourage children to think for themselves?

Oct 2023

For many children, their favourite part of studying maths and English comes from developing an understanding of a topic that had been difficult for them. Learning new methods and techniques to solve questions can be a bit part of a child's enjoyment of studying maths and English and can help them to develop confidence and pride in their learning, which can carry through to other aspects of life.

In order to develop confidence early in a student's Kumon journey, we make sure that we set them work that is manageable at their current level. It is important that the child gets to experience satisfaction with their own success during the learning process. No matter how advanced or lacking in confidence a child is when they come to Kumon, we aim for them to feel supported in making use of their new knowledge. Learning how to use the worksheets as a guide to learn from is a big part of developing that confidence.

At the start of their Kumon journey

When your child initially starts studying with Kumon, the Instructor spends time with them as they complete the diagnostic test, and then - after analysing their observations and findings - discusses a study plan with you. As well as gauging exactly what your child is capable in order to set work that is at the ‘just right’ level for them, the Instructor is looking to develop your child’s study skills such as working with pace, focus and concentration. The Instructor shows the child how to use the guidance in the worksheets to work out the solutions, rather than expecting to be ‘taught’ in the traditional manner. Commonly, a child is not used to working in this way and they are quick to raise their hands in class when they get ‘stuck’, or perhaps they seek a lot of reassurance from the Instructor. That’s why this new experience is so valuable to them in their journey to become an independent learner.

How can Kumon worksheets actually teach children?

We want children to gain the ability and confidence to be able to think for themselves, and to form and try out hypotheses based on their existing knowledge. They will learn to make judgements based on their own logical deductions, and we believe every child, regardless of age or school year, will be able to do this with practice. Additionally, we look to develop children’s other abilities, such as curiosity, noticing hints and clues, and to show them that if they pause and think deeply, they can work out the answers themselves. Learning in this way is powerful, memorable and more rewarding than simply being taught the process of how to answer a question.

When introducing worksheets that have new concepts, the Instructor may assign these so that your child works on them in class, to ensure that your child is supported and can be guided. The worksheets show example answers, clues and hints to help students work out the correct process independently. They can then apply this learning to other similar questions in the worksheets that they do afterwards at home.

Working it out for themselves

A key principle of learning with Kumon is for the child to discover new concepts for him or herself. In the Kumon Maths Programme, the worksheets introduce the concept sum-by-sum and page-by-page, gradually allowing them to reason out the answers for themselves.

For example, the earlier part of Level C is multiplication of single-digit numbers, e.g.; 3×3=9, 4×4=16. Students repeatedly practise their single-digit multiplications so that they become confident and can complete pages of worksheets very quickly and fluently. They come to a point where they know their times tables so well, they do it without having to think consciously, they just ‘know it’. They can rely on this knowledge as they move forward in their learning.

When they reach Level C 51a, where the concept of two-digit × one-digit multiplication is introduced for the very first time, how will they feel about tackling this?

The first example on the page is 43×2= and has the box 86 already completed. Because of their fluency with single-digit multiplication, the child may look and understand that the right-hand column shows 3×2=6 and reason that this must be correct. But what about the answer box showing 8? Where did this 8 come from? A child that is already familiar with single-digit multiplication will see the pattern between an eight, a four and a two, and can accept the answer as 86 and start to work out why it is correct. Because of their experience in completing Kumon worksheets and looking at everything on the page, they will also find the note at the bottom of the page, which shows that there are two solutions for 43×2=86, achieved either through addition or through multiplication.

The worksheet then shows another example, 34×2=6, this time with only partial completion of the left-hand box and by thinking about it, they work out that they will need to complete the second box. They may find this straight-forward as it’s single-digit multiplication which they are already confident in.

Powerful learning

The worksheets continue in this manner, giving enough practice in each concept to gently support the student. Within a few pages, the example leads the student to hypothesise what happens when there are numbers greater than nine and whether carries are also used in multiplication as well, as they already know from having learned double-digit addition. Once they work this out, they’re away and doing it for themselves! This thrill can be very motivational and, as there is an emotional response, it means it is likely to be more memorable. They also feel reassured that they worked it out before and they can do it again.

The Instructor and the worksheets 

The worksheets are carefully constructed so there is only one conclusion that can be reached. It is very hard for the student to misunderstand where the example answers came from, and in this way, they can hypothesise about the reasons and can be creative with their knowledge. The Kumon Instructor’s careful observation of your child and their expertise in the setting of the ‘just right’ level of worksheet then ensures that they have enough practice to be able to complete the calculations in their head with speed. They work with each child to build upon their knowledge and help them feel fluent in the topic. The Kumon worksheet-based study programmes have developed and evolved over the course of 60 years from working with students of all abilities, and the Instructor uses them to develop all aspects of the child’s study skills.

The real expertise of the Instructor comes from enabling a student to work something out for him or herself so that overcoming the challenge becomes a thrill and therefore a deeper learning moment too.