Berger- Week 6

         This week we were working on adding and subtracting mixed fractions. This proved to be a very difficult concept with our students. We have been working with fractions for the past two weeks and began mixed numbers at the beginning of this week. Monday we taught a very scaffolded lesson, demonstrating first and then guiding them through problems on the board. Eventually we released the responsibility to the students and they worked on problems on their own. They seemed to be getting the hang of the subtraction of mixed numbers when either the first number had a fraction and the second did not, and even when the second number had a fraction and the first didn't, meaning they had to borrow from the whole number. When we introduced two mixed numbers, with like denominators they were also doing well, until the first mixed number had a smaller fraction than the second. This would mean that the students have to borrow from the whole number again so they have a new whole number and the fraction (that equals a whole) as well as the fraction that they began with. What most of the students were doing was forgetting to carry the initial fraction over so if the problem was 4 2/8 - 2 3/8 the students would pretty much understand that the 4 becomes a 3 & 8/8. But what they were then doing was subtracting 2 3/8 from 3 8/8 instead of adding that initial 2/8 which would make 4 10/8 - 3 8/8. To follow that, once we introduced mixed numbers with unlike denominators, they seemed to forget everything. I do understand this is a very hard concept but they completely shut down. A problem like 3 1/2 - 1 5/9, the students would realize that they had to find common denominators, so they would come up with 3 9/18 - 1 10/18. Now, instead of realizing that they need to borrow like they were before, when there was no prior step, the students would simply write the answer as 2 1/18. And this was not just a few students thinking the 9-10=1, this was about half of the class that didn't realize they needed to borrow. In the past few days many students have even answered problems that they knew last week about subtracting fractions (not mixed numbers) incorrectly. They went from knowing that for 5/7 - 1/2, you would need to find a common denominator, to just subtracting the numerators and denominators and coming up with 5/4. It is a lot to handle in 2 weeks and although they have seen it before, it was most likely never taught in depth so they lost most of their prior knowledge. It's difficult not to become frustrated when you have seen the students do a similar process correctly last week and then 7 days later they claim they have no idea how to do it and come up with an incorrect way to perform the function. So today what we did was go over the homework and work out about 5 problems with the students on the board. We went slowly and clarified any questions that the students asked. We asked the students a few times if they had any further questions and no one spoke up. At the end of the class the students took a quiz with 8 subtraction and addition problems with mixed numbers. Over half of the students not only failed but only got maybe 1 problem correct. Needless to say both my mentor and I were shocked because the day before we had clarified and the students did well on the exit slip. Then today they students claimed they did very well on the homework and were no longer confused. After keeping the students and explaining a few important steps, the class period was over. My mentor teacher and I chatted and decided we needed to do something different for the second class so that this would not happen again. We went over the homework again in a similar fashion, asking the students for specific steps and if there were any confusions. After we went over the homework, we had the students work in their table groups of 3 or 4 on one subtraction problem that we assigned them. Their job was to figure out how to solve the problem as a group and explain it to everyone in the group so that if anyone was called, they could come up to the board and explain all of the steps as they performed the problem in front of the class. This put some responsibility on the students because no one wants to be put on the spot and not know the answer. The students worked really well together and took turns explaining the problem to one another. After all of the groups were done we called one student from each group to do and explain the problem on the dry-erase board. Each of the students that we called was able to do the problem and explain it correctly. We went through this process one more time and again all but 1 group got the correct answer. My teacher and I were thrilled and thought that this really helped them because not only did they want to learn for themselves, they wanted to learn so they could help their group and explain it to the class. Then we gave the exit slip and again half of them seemed as confused as before the class.

It is definitely important to go through these topics slowly and carefully. Also students learn in many different ways so one thing we can do instead of attempting to drill the process into the students heads is to provide alternate ways to do these problems. We could potentially use illustrations and visuals if it will help the students understand better. It's important to realize that the students are not understanding these concepts and not to just move on, but to take longer to explain and figure out the misunderstandings that the students are having. It is also important not to get frustrated and show frustration to the students because that is not motivating to them, in fact it's the opposite and just makes them want to give up and forget about this part of math. We need to figure out a way for this to be clear and hopefully fun, so they don't hate working with fractions in the future. I can understand what's happening here because there are certain things that I don't understand and then when more things are added to that topic, it just seems like you're drowning in an endless pool and there is no getting out. This is where we need to go back to the beginning, which unfortunately takes a lot of time and is limited in the schooldays, and see where the misunderstandings are happening. We need to slowly clear up the small aspects of the topic so that when they are all brought together, the students don't go blank, but can recognize all of the steps they have previously learned and take it step by step to figure out the problem.