# Do we ‘Place Value’ on our understanding of Mathematics?

During my time on placement, the aim of one of my group lessons was to teach the children who were ‘struggling’ all they needed to know about place value in one 30-minute slot.

Simple right?…

Armed with white boards and place value blocks we headed to the group study area where I could begin my teaching. To start the lesson off I explained to the children that we had both ‘tens’ and ‘units’ blocks and that when you have ten ‘units’ you swap them for a ‘tens’ block. To get a general feeling of understanding within the group, I stated some random numbers both below and above ten to see if the children could represent them correctly with the blocks . Having felt the children understood, I explained that we do the same when we are doing ‘chimney sums’ and that we would write down how many ‘tens’ blocks we had in the ‘tens’ column and do the same with the units. Feeling as if the children had an idea of what I meant, I handed out the white boards and done a few examples with the children and then left them to do some without my help.

The picture shows the work of three pupils, of which all had very contrasting results. The pupils work which can be seen on the top got all the answers correct, carrying the ‘tens’ over and having the correct units. The child on the bottom left did not grasp the idea of ‘carrying over’ and therefore just wrote out the whole answer, completely disregarding the ‘tens’ and ‘units’. The child on the bottom right made an educated guess at the answer hoping it was correct, without trying to work it out in ‘tens’ and ‘units’ at all.

Within the group, the majority of children either got the wrong answer, or completely misunderstood the whole concept of what I had ‘taught’ that lesson. Taking this in to consideration, I have to question what extent the children who got the answers correct understood place value and in turn, which were just able to follow the ‘formula’ I had given them.

Why is this important?

The lecture on Place Value with Eddie Valentine made me reflect on my own understanding of profound mathematics alongside my profession practice.  Did any of the children actually benefit from my lesson or had I just fed into ‘teaching children how to pass tests’. This made me appreciate the importance of having a profound understanding of mathematics as a teacher in a way I had not during my placement. How can I teach children to understand mathematical concepts if I do not know them in depth myself? As the children progress through school, each year they will build on what they already know in each area of maths. This further shows that a profound understanding is vital as it provides a solid foundation which ensures the children do not switch off next time they revisit this topic. The children who did not understand first time will switch off when the area is revisited which causes maths anxiety later down the line, again highlighting the importance of a good understanding.

Overall, the most important thing is what I do with what I have learned from this experience and reflection respectively. First of all, before going back on placement I will make sure I have a profound understanding of the areas of mathematics I will be teaching as this has a direct effect on the quality of learning the children receive. Furthermore, taking time to teach certain areas of maths across a longer period of time. A simple video like the one linked above can get the children engaged and wanting to learn more which reduces the chances of children getting bored and guessing the answer as we have seen in the examples and if they remember the song they may be able to sing it to remember the rule. Further, exploring different base systems with the children may help them appreciate how the base 10 system we use works, which allows them to understand both what they are doing and why rather than just follow a formula.

References:

NUMBEROCK (2016) Place Value Song For Kids | Ones, Tens and Hundreds | 1stGrade, 2ndGrade, 3rdGrade. Available at https://www.youtube.com/watch?v=a4FXl4zb3E4 (Accessed 21October 2018)