Monday - 1st Year Teachers (Middle Years Group)In order kick off the morning the quote below was put up on the screen for people to think about. "Good mathematics is not about how many answers you know... it's about how you behave when you don't know" - Author Unknown Kristin then handed out an executive function summary and were ask to reflect on the quote in relation to that summary. The discussion continued in relation to ELL not just aimed at improving subject knowledge or executive functions, it is aimed at improving both, using one to build the other. From here we started talking about about the lesson that would be presented, it was a lesson that would introduce fractions with the class, they had done fractions in previous years but this was the first time that had done it this year. The lesson started by asking students to fill out a post it note using the following prompt "When I hear the word fractions I feel ____________________ because _____________________________________" This was to help them start thinking about their past experience with fractions but also was an opportunity to write those feelings down. Writing down your feelings about an activity or bit of content is particularly effective in helping to reduce the effects of maths anxiety. The post it notes were separated into postive feelings and negative feelings and it was noted that there were more positve than negative responses, mainly because they felt confident as they had done it before.
In the next task the students were asked to make up a diamond diagram. This diagram is a way in which students can represent the different ways of thinking about a mathematics problem. How to make one of these is shown in the video below and a copy of one a little closer up is shown in the image. In this activity students were asked to pick a card out of a pile, the card had two fractions on it, they were asked to write these two fractions in the centre diamond as that represents the problem to be solved. Their task was to determine which of the two fractions were bigger. Some of the strategies used by them to do this are as follows - e.g 3/8 or 5/8**More parts** Students generally found this situation the easiest to deal with as the size of the parts (the denominator) was the same, so they were able to talk about 5/8 as it had more parts than 3/8.- e.g 5/4 or 7/8**Close to 0, 1/2 or 1** The close to argument was also used quite commonly with confidence and was attempted by comparing the two fractions to the benchmarks of 0, 1 and 1/2 to see which one was closer. For the example of 5/4 or 7/8. Some said 7/8 was bigger as they were comparing the size of the numbers that make up the fraction rather than the relationship of the numerator to the denominator. Most were able to talk about both of the fractions being close to 1, but the 5/4 is more than 1 and the 7/8 is less than 1 so the 5/4 is bigger- e.g 1/8 or 1/5**Larger parts** The larger parts argument was the least used but it did come up in circumstances such as this one where the parts are not the same size and they are both close to the same number, in this case they are both close to 0. In this case they approached it in relation to the size of the parts. The biggest misconception here was that 1/8 was bigger than 1/5 as 8 is larger than 5. Some were able to talk about the whole being divided into less parts with 1/5 so those parts are bigger. This also became particularly useful at the other end where it is close to 1, for example 4/5 or 7/8. because they are both 1 part away from the whole and fifths are bigger than eighths then 4/5 must be further away and therefore smaller than 7/8.
From here the rest of the day was spent on some further discussions and some planning for what they will try before the next session Thursday - ELL Site Based LeadersIn the morning the teachers worked on a problem called the "fold and cut theorem" which essentially states that any shape with straight sides can be cut out with just 1 straight cut if you are willing to fold the paper first, a video on this theorem is below. Teachers were first asked to cut a square out of the centre of a peice of paper using only one straight cut and were then asked to look at the other shapes and rank them from easiest to hardest to cut out. They then had a go at a few from different levels to see if they could do them. The shapes given are available from the file below.
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