# 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.

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# Removing the ‘bucks’ from Starbucks?

Having recently got a job in Starbucks I noticed there are many transferable skills which I need to use every shift. One of the skills that I needed, as highlighted to me in my interview, was to be able to work effectively with money when on the till in order to make sure the customers got the correct change. However, whilst on the drive through window on one of my shifts I realised that I was handling less money than I expected because everyone was using their card.

As a teacher, one of our most important roles is to teach children the value and importance of numbers as a whole, and more specifically of money. Therefore, this made me question whether people’s skills in handling money have decreased or if it was just a matter of convenience and that contactless required less effort than counting the change in their pocket, or even having to type in their pin.

The first issue this raises is that the Curriculum for Excellence suggests that teachers should make learning relevant to the children in the class. However, by the time the children of today are finished school and looking for a job will money still be physical and require thought or will contactless become the norm? Further, does this mean we should change the curriculum to keep up with the changes in society or does this make the teachers job of providing the children with a profound understanding of money even more important?

With these questions in mind, on a different occasion someone offered to ‘give me the extra 20p’ if it made giving the change easier – which it didn’t, but they gave me it anyway. As I had already typed in the change they had given me, the balance on screen was incorrect as they had given me extra and so I had to work out how much they were to get back. Although maths was not my strong point, my profound understanding of numbers allowed me to give back the correct change.

This begs the question, so what?

Providing the children in your class a profound understanding of basic mathematics will not only help them throughout their lives but may also have a wider impact. Before considering how this may help them in the workplace, we have to explore applying for the job. With it becoming harder and harder to get a job, a basic understanding of maths is vital in being considered for any role therefor, not having a fundamental understanding may give someone less of a chance than someone else. More importantly, if the children have a profound understanding of maths, for example in the situation of handling change, they will be better equipped as they will have multiple perspectives. This is true as someone who understands money and numbers may be able to give £1 change in a varieties of ways, 5 x 20p, 10 x 10p, or even as far as 2 x 20p 1 x 50p and 2 x 5p. Someone who does not have a deep understanding may be able to do the simpler calculations but when the till is running low on certain coins may struggle.

The importance of this can be further shown when thinking about the impact of giving the wrong change which can have a detrimental effect. Working for a company which revolves around the customer, giving the customer the wrong change can result in complaints which reflects badly on the company. Another aspect of giving the wrong change multiple times would result in the company losing money which over time could add up to a big over loss.

Overall, I believe that despite the changes that are happening before our very eyes in terms of money, the curriculum should stay the same or even further incorporate money skills rather than shaping it around more electrical ways of using money. To me, teaching children about newer ways of using money would be like learning to drive an automatic car, if you learn in an automatic you are restricted to only these where as a manual allows you to drive both. Similarly, giving children a profound understanding of the value of money would allow them to then further apply this knowledge when things inevitably change in the future. Finally, if everything money related moves over to card and online, giving children a profound understanding will allow them to be able to manage and track their money and finances effectively regardless of its physical status which would be harder without this foundation.