1 Prof. Values & Personal Commitment | Jack Harris' Eportfolio

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 | 1^stGrade, 2^ndGrade, 3^rdGrade. Available at https://www.youtube.com/watch?v=a4FXl4zb3E4 (Accessed 21October 2018)

Derek commenced the task by numbering each table from 1-5 and giving each group an envelope. Each group were allocated the same task and were requested to produce an item which could assist a new student in their first week at university using only the resources contained within the envelope.

My group was at table one and our envelope contained a significant number of resources such as coloured paper, coloured pens/pencils, envelopes, rulers etc. The envelope contained enough materials that each member of our table was able to create a different item to go in to the pack. The table created a campus map, a blank time table, useful tips on cards, a kitchen manual and from the remaining items managed to also produce a make-shift pencil case made out of an envelope filled with most of the resources which had not been used.

Throughout the process, Derek continually provided us with praise, commenting on how well we were working together as a team and telling us how productive we were all being. This boosted team morale and the whole team brimmed with confidence and constantly kept turning to each other and saying “we are really good at this aren’t we” with big smiles on our faces. The offering of a biscuit from Derek during the work also supported this view more and relaxed the team and made us so comfortable that we were unaware of what was really happening around us.

Each of the groups then took turn to present their final product. Our group were unaware at this stage as to what had happened and within our group we were still praising ourselves and commenting on how well we had done compared to the other groups.

Derek started off by appearing extremely interested by our presentation but as each group presented he demonstrated less and less interest in what was being shown. By the time the last group were presenting he appeared to be more distracted by his phone than what the final group had to say. Our group again remained oblivious to the connection being made.

Following the presentation by the final group, Derek asked everyone in the room “So, who noticed what was really happening there?”. The majority of those present noted they had identified the trick being played out and made the connection with his actions and reactions, whilst those in group one remained confused and wondering what had just occurred and what everyone else had became aware of that we did not.

Derek then informed all that each group had been provided with different envelopes containing differing amounts of resources and were all being tasked independently to produce items depending on what resources we had available. Group one had no awareness of this and were shocked that this had taken place without any of our group realising until this point.

I feel this exercise has provided me with a significant lesson to ensure that I now give everything my full attention and has opened my eyes to see how easy it is to miss very important, yet very small, details in the classroom. The exercise demonstrated that there is no space for bias in schools and although every child will have a different background, each and every one has to be treated equally, fairly, and in a consistent and professional way.

In summary this also highlighted how providing praise and encouragement in a positive manner also promotes confidence and goes a long way, the more Derek complimented us the more confident we became and so in turn the more effort we became willing to put in. Again this demonstrates that the attention/praise/encouragement we can provide to pupils has positive outcomes and should also be given during group work to each pupil to promote team work.

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

Resource Allocation Task