Editor’s note: This is an updated version of a blog post published on July 03, 2018
Multiplication is a tricky concept to master and it’s up to you to make sure learners don’t fall behind. Here’s how to overcome three of the most common obstacles facing struggling learners.
After two weeks of teaching multiplication to children aged five to six, we gained some insights into how children develop an understanding of multiplication. Because children with different attainment levels face different challenges, we realised we had to reflect and differentiate our teaching in order to facilitate their learning.
Here are some of the most common problems we saw when we taught multiplication, and the strategies we used to keep struggling learners on the right track.
Obstacle 1: Struggling to understand grouping
Children should understand the concept of multiplication as the process of creating groups of equal size. But that’s easier said than done. In our classroom, some children didn’t understand what the term ‘groups’ meant. They weren’t making the connection between how the objects were shown and how we grouped them.
For example, one problem showed 4 trays of 5 fizzy drinks. All the children could see that the drinks were arranged on 4 trays. However, struggling learners got confused when we asked them how many groups of fizzy drinks there were. This lack of understanding prevented the children from moving forward with the problem because they couldn’t progress beyond initially counting the way the objects were organised.
The teaching strategy
To overcome this problem we began with peer explanation to see if this helped struggling learners. We reinforced the idea of what a group is by always saying, “we have three bunches of bananas, we have three groups of bananas”.
Finally, we took our struggling learners for an afternoon intervention where we asked them to group different objects that they were already familiar with. Exposing them to the concept of a group meant they were then able to move forward in their understanding of multiplication.
And speaking of the concept of grouping — once you move on to teaching division, this blog post about equal sharing and equal grouping in division is a handy resource.
Obstacle 2: Poor working memory
Some struggling learners also had poor working memories. When faced with a mathematical problem asking them to record both the number of groups and the number of objects in each group, they got confused.
At first they were able to count the number of groups and then the amount in each. However, once they had moved on to counting the amount in each group, they were unable to recall their first step (how many groups they had counted).
Multiplication involves remembering different numbers that mean different things, and this is a struggle for children with poor working memory.
The teaching strategy
To overcome this barrier we made sure the children always had access to concrete resources. We encouraged them to use resources to show the problem. Having a physical representation in front of them meant they could always refer back to how many groups there were.
It also helped them internalise the problem as they physically made the groups. We encouraged the children to write down how many groups they had or gave them number cards so they could select the amount of groups and then how many objects in each group.
This took a lot of pressure off the children, letting them focus on solving the problem.
Obstacle 3: Weak mental maths skills
Once the children had progressed in their understanding, we found they were still unable to complete the workbooks and activities independently using multiplication. This was because their mental maths skills were weak.
They were unable to count in 2s, 5s or 10s with confidence. This was interesting as the children were able to say “I have 5 groups of 2” but solved the problem by counting in 1s.
This was even clearer when we looked at doubling, as again the children came to understand that doubling meant having two 5s but had to count all the counters to realise this made 10.
The teaching strategy
This is a problem that we weren’t able to immediately tackle and solve. Instead, we’ve started including counting in 2s, 5s, and 10s on a more regular basis throughout the day. We’ve also encouraged these children to count at home whenever possible.
Overall, we found it challenging to teach multiplication to our struggling mathematicians.
But there was a silver lining. By working to increase learners’ exposure to the concepts along with the use of concrete resources, our struggling learners began to understand the ideas being taught.
There’s no quick fix to teaching this tricky concept. Through observation and timely intervention we will ensure that every learner masters multiplication.