Young Mathmaticians 5-7

I think I have mentioned this before, but the fourth and fifth grade classrooms I tutor in are currently working through fractions right now too so it has been interesting for me to think about what I am seeing them struggle with compared to some of the examples raised in the texts. One thing that I think creates struggles for students with fractions is that it seems like the classrooms I observe usually go over one way to add or multiply fractions and it remains a very abstract idea for students. I have seen things like the double number line like they talked about in chapter 5, but this text just demonstrates how many ways you can approach looking at fractions. I looked at the array for quite awhile- I remember being first introduced to it in math 201- and while I can understand the answer I'm not sure I can really make sense of it for myself. I could easily plug the numbers in and make an array but I just can't relate it to anything else. Fractions are difficult for me just because I feel like I always think about them in abstract ways. It is hard for me to really make sense of dealing with complex fraction problems- I can do it- I just feel like I don't always understand exactly Why I'm doing what I'm doing. For some reason with the array in chapter 6 when they put a short story problem with the array it seemed to make more sense to me. I could kind of picture what was happening instead of just seeing tiles shaded in for no real apparant reason. Based on my own experience, making fractions as realistic to students as possible is an important part of teaching multiplying fractions. In chapter 7 I also thought it was advantageous for the teacher to have students work with ideas of multiplying (in this case groups of dots) before she introduced the idea of looking at it as fractions of the whole. Students already explored some math around the problem and found the whole before they started thinking about fractions. This also helps connect what students already know about multiplying and dividing whole numbers. I have heard of strategies like using the clock and money before because it is something very concrete to students. I am looking forward to talking more about this topic just because I feel like it is something I am weak in.