Children need to have many opportunities to problem solve using mental strategies before they are exposed to more rigid, procedural strategies. We want our children to approach each Mathematical task creatively and critically.
Welcome to my third and final blog in the series “Teaching Mathematics to young children”. In this blog I aim to educate parents on the effective strategies that children need to learn to solve addition and subtraction problems. I also want to highlight the negative effect algorithms have on young children. (An algorithm is the strategy of using a set of rules and set procedure to solve a problem)
In my experience, most parents tend to focus on one strategy to help their child work out an answer to an addition or subtraction problem. It is usually the “Algorithm Method” as this is how they were taught to solve these problems when they went to school. Unfortunately teaching this to a child too early does more harm than good.
Why we do not teach an algorithm to a child under 10 years old?
I have coached many different types of sports for a long time and I always encounter the same problem as a coach no matter what sport it is. Children want to work on a harder aspect of the game before they are ready to. In basketball, the children all want to shoot a “three pointer” when they first start. In order to do this, they do not use the correct shooting technique. They just throw the ball and hope for the best. This incorrect technique will need to be “unlearnt” in order for them to develop their shooting skills in the future. This is harder than learning it the correct way from the beginning.
While teaching students addition and subtraction, I encounter the same problem. Students have constantly been exposed to algorithms as a method of solving problems without understanding the concepts behind the algorithm. They have learnt how to solve the problems as a procedure instead of what is logical and what makes sense.
Teaching a child how to use an algorithm too early will encourage your child to learn a procedure by rote learning (learning something off by heart) instead of understanding what they are doing.
Now let’s look at the addition and subtraction strategies that will benefit your young child. I like to think of these as tools for your child’s problem solving toolbox. Each tool has a different purpose and when used correctly can help a child solve a number problem successfully.
Strategy 1 – Split strategy
A child “splits” up a number into their place value to add or subtract quickly. For example 45 + 23 = . The child would be encouraged to add the larger place value numbers first as this is the logical way that our minds work. In their mind they would add 40 and 20, which would equal 60 and then add 5 and 3 together to make 8. The final step would be to add the two totals together. 60 + 8 = 68
Strategy 2 – Jump strategy
A child “jumps” from the stated number forwards or backwards depending if the problem involves addition or subtraction. For example 45 + 23 = . The child would be encouraged to put the 45 in their head. They would then jump 2 tens forwards to make the number 65 and then jump another 3 forward to make the number 68.
Strategy 3 – Compensation strategy
A child rounds a number to make it easier to calculate. They then adjust the answer to compensate for the original rounding. For example 97 + 63 =. A child would round the 97 to 100 in their head. They would then add 100 and 63 together to equal 163. Then they take away 3 to compensate for the addition of 3 at the beginning of the problem solving. The answer would be 160.
Children need to have a solid understanding of addition and subtraction strategies before they use algorithms to solve problems. Introducing children to algorithms after they have this solid understanding will allow them to develop their number sense, make fewer errors, have strong mental computation (mental problem solving) and require less “reteaching” of concepts. As parents and educators, we need to encourage children to explain how they solved a problem mentally. This will enable a deeper understanding of the concept to occur.
Many parents inform me how much they disliked Mathematics when they went to school. They always throw around terms like “borrow and pay back”, and “a number doesn’t go into another number”. What do these terms actually mean? We need to be clearer in our own understanding of Mathematics before we start assisting our children. We need to make sure that our children have a positive experience of Mathematics. We can do this by teaching them for understanding and not just learning procedures like many of us were taught. These procedures have a place in solving problems but it should not be used as strategy for young children until they have a solid understanding of the concept of addition and subtraction which comes around 10 years of age.
I hope you have enjoyed reading this blog. We have loved writing our series “Teaching Mathematics to young children”. Our next series will be available next week. The three part series will be titled “How to make the new school year successful for your child” It will provide a lot of tips for parents to enable you to provide the best learning environment possible for your child.
Until next time …