"I believe Kumon is the reason why my maths has improved, and without it I wouldn't have achieved an A in my GCSE maths and wouldn't have even attempted A-level!"
Support with column addition
Q: I'm having trouble helping my child with the workings out of column addition and subtraction in level B, as it is different to that in school. In particular, how do I help my child not to write carries and borrows in their work?
A: Level B is the culmination of the adding and subtracting work students have completed in the previous levels. By the end of level A, students should have a high level of mental calculation ability. They should be able to see a problem such as 14 - 11 or 15 + 10 and automatically provide a response. Students who possess such a high level of mental calculation have little difficulty in understanding the process of carrying across the columns in vertical addition and subtraction.
The first set in level B and set B 101 are review sets of work completed in level A - the vertical addition and subtraction sums are introduced after these. If a student cannot proceed by themselves on sets B 11 or B 121, simply explain that they have seen the same numbers but in a different layout in level A. When a student starts completing sets B 21 and onwards (addition of pairs of two digit numbers) and B 131 and onwards (subtraction of pairs of two digit numbers), if they seem to be struggling, ask them to read the whole sum aloud, for instance, "15 + 15 = 30".
Hearing a sum helps the student to think about whether their answers are reasonable. If they are still having difficulty, encourage them to start from the right hand side of the sum, working out what number the sum ends with and then calculating what it starts with. On certain pages there is a correlation between the questions in the left hand column and the questions in the right hand column, for example on B 22b question 11 is 26 + 9 and question 16 is 26 + 19. Or likewise on B 125a question 1 is 13 - 5 and question 6 is 23 - 5. This encourages the students to think for themselves about the answer by relating it to those that came before.
Every question on a Kumon paper has been put in a specific order for students to develop the skills they need at an optimum rate. It is important to observe that they are not cherry picking the answers by completing the "easy" ones first. This is also the first maths level since 3 A where an example is printed to help students. I have found, in many instances, that the main error is that the student uses the borrows/carries inappropriately leading to a high number of the same type of mistake, so help your child analyse and think about where the mistake occurred. Suddenly, once that one error of process has been rectified, their accuracy will improve greatly.
Parents are often concerned that Kumon is demanding too much by expecting students to do these sums in their head, but I am sure you would not expect your child to need a piece of paper to write carries and borrows if they were buying a couple of items at a shop, for instance, to work out how much money to tender or how much they were due to receive in change. The skills they are learning here in level B are no different to that. The more a student can develop with their calculation and self study skills on this level, the easier later levels will become as they will be developing a smooth flow of thought and be able to complete questions without the need for numerous side calculations. They will also have learnt to follow the questions in order, looking and thinking about how each one is introduced and linking them with previous questions.
The National Numeracy Strategy in England and Wales has put an increased emphasis on pupils being able to learn basic arithmetic skills with speed and accuracy and a stated aim is to learn to add or subtract any pair of two digit numbers using mental (rather than written) calculation. The overall aim of Kumon and schools is the same: to achieve a high level of mental calculation skills and then to learn the formal written methods of addition and subtraction. Sometimes students will be at different stages of maths at school and at Kumon and it is recommended that students use school methods at school and Kumon methods at Kumon.
