Fourth Lesson- March 28, 2008

Today went really well for both me and Lauren. We decided that the class was very split in terms of who understood the material and who didn't. With this in our minds, we decided to split the class into two, ability based groups and we could each work with a group to help implement the strategies one more time. Lauren took the lower ability group and I took the group that seemed to understand it a little bit more. The problem with this, in my group, was that because of behavioral issues, we weren't able to completely split them by ability. We initially did it by ability but then had to trade people around so it presented a little bit of a problem in my group. I had one student who was doing the typical algorithm and could complete problems within 30 seconds and I had others who still had trouble splitting up the number 78 into a tens and ones column. I also had some people in my group still working with manipulatives because they were still not able to visualize the situation. I would say that out of my group of 7, 4 began to really understand it and the other three were straggling behind. I could see why it would be beneficial for teachers to split groups up based on their ability because I saw how it could be frustrating when you are working in a small group with students of different abilities. I was fortunate in the fact that the one student who understood it the most was sitting right next to me, so I would continue to give him additional problems to do on his white board while I was guiding other students through other problems. The boy sitting next to me was even able to add numbers with regrouping that went into the hundreds place so I started giving him more challenging examples to deal with. I think that overall, the two different groups are beneficial but as I had stated before, it posed a problem for me because I still ended up with a VERY mixed group. I did find the groups rewarding though because for some of the struggling students, you could really see where their confusion was kicking in and I was able to address that whereas if I were doing a whole group instruction, I might not have been able to pinpoint that one portion. Additionally, I found the groups to work out well because students had the chance to help each other out as well. I noticed that some of my more advance students would help some of the struggling students when they were done with their problem. This was helpful because I could only focus on one student at a time so it was nice to see them helping each other.

Third Lesson- March 27, 2008

Today was another good day in the classroom. Today we decided to introduce regrouping in addition to them and see how they could handle this one. Additionally, we decided that we wanted them to explore different strategies and really get a feel for who is comfortable doing what. We decided to review place value with them one more time and to represent the number 17 in different ways so that there wouldn't be any confusion when it came time to discussing regrouping. We showed the numeral 17 and they were able to tell us that the 1 was in the tens place and 7 was in the ones place. From there, we showed them the numeral with manipulatives and showed them that when you have more than ten ones, you could take them out of the ones column and trade them in for a tens rod. Some of them caught on immediately while others were still a little confused. We decided to continue with more examples using the manipulatives because we knew that most of them strongly benefited from visuals so we kept the base blocks out for the entire lesson. From here we introduced them to an addition problem involving regrouping. We went through the entire problem with them so they would be able to see the process that you should take when you want to regroup. We had them show the first addend using their manipulatives. We then had them represent the second addend with manipulatives making sure that they understand that when we add, we put things together so they wouldn't want to get rid of the first number they represented. We then had them push the two sets together so they would see that adding is combining two numbers. Once they had both numbers represented and then pushed together, we asked them to count the amount of ones represented. When they realized that in our problem, there was 13 in the ones place, we asked them if it was alright to write the number 13 in the ones place, then add whats in the tens place and get a number in the hundreds place. They knew this was wrong but some of them couldn't initially come up with how we could rectify our errors. From here we showed them how ten individual ones make up a tens rod and they realized that we could "trade them in". While the students were using the manipulatives they began to understand. Some of the time, it would get a bit frustrating because some of them would understand one problem, but when you give them another one, it was like they had forgot everything they said 2 seconds ago. We continued to do more examples with the manipulatives to get them to practice as much as possible. At the end of the lesson it seemed like they understood the concept but definitely still needed more practice.

Second Lesson- March 26, 2008

Today went so much better!!! Lauren and I went home after yesterday's lesson and completely changed around everything we wanted to do. We decided that if we wanted them to understand the strategy, we would have to reintroduce the Hundreds Chart and make them familiar with the patterns and arrangement. We had noticed yesterday that some of the students didn't notice that the numbers were in order because when we asked them to find a certain number they were wondering around aimlessly until the number caught their eye. Additionally, we had noticed that when we were trying to get them to skip down by 10, they could comprehend that you go down but we didn't feel confident that they understood WHY so that was another thing that we considered while planning the lesson. We began this lesson by first reviewing place value since that was definitely a weakness that we had encountered. After doing this, we began to show them with manipulatives that when you go down a column on the Hundreds Chart, you don't change the ones place, only the tens place changes which allowed them to make the connection that when you move down, you are adding ten. Additionally, we showed them that when you go across a row, the tens place stays the same and the one places is the one that changes. This made them realize that when you want to add by one, you move to the right. Within this process, they were able to understand that the upper left portion of the chart had the lowest number and the lower right corner had the highest number and all the numbers in between were in numerical order. We then introduced a Hundreds Chart that only had the first row (1-10) and the last column (10-100) written and we were asking them how we might be able to find a certain number. Here we were really able to analyze and evaluate whether or not they had a good understanding of the Hundreds Chart. They understood that in the first row, whatever was in the ones place had to be the same throughout their column so that was good! The only thing they had trouble with was that at the end of the row, if the row ended in 70, they thought that everything before that would be 70 too when in reality, all the 70s are actually on the next row. I learned a lot from this experience and most of it was carried over from our previous one. I learned that modifying a lesson can be extremely beneficial and if you realize that your students aren't at a certain level that you expected them to be at, then it can be EXTREMELY beneficial to them to back track a little bit. Although I was extremely frustrated yesterday, I think it was a great learning experience on many levels.

First Lesson- March 25, 2008

Today was our first Math lesson in this lower level class. We decided to focus our unit on different strategies for solving addition problems. Ms. C suggested that we show them how to solve addition problems using the Hundreds Chart, so we prepared our lesson based off of this. She had told us that the students already understand place value and can do easier addition problems. With this in mind, we began by demonstrating how when adding two, two-digit numbers, you can help solve it on the hundreds chart when drawing or using manipulatives may be too lengthy. We showed them that you can jump down by tens since each row represents 10. We had a BINGO game planned and we had tons of guided practice as well as time for individual practice. We were very confident about this lesson until we got into the classroom. This was probably the most frustrating teaching experience I have had to date. When we got in the classroom and began to teach, we realized that not only did they not want to accept any form of skipping by tens, but they didn't know place value at all. Additionally, they were not clear that there were two numbers that you added together to find the sum. This completely took me by surprise. I realized that we would not only have to change our lesson on the spot, but that our entire unit plan would have to be seriously modified. Lauren and I began to back track during our lesson to try and go over the initial fundamentals that we thought might help them learn the strategies we were proposing to them. I thought we did a really good job at trying to simplify everything for them to understand but I think by the time we tried to simplify things, they were already unfocused. Some of them were catching on but it was only a smaller portion of the group. If I could do it again, I would have included place value on our preassessment to see if they understood place value but for whatever reason, I didn't even think that place value would play as important of a role as it did when we used the Hundreds Chart. So I would say that one thing I learned for sure would be to thoroughly check all aspects of your lesson and make sure they are covered in your preassessment before you attempt to plan the lesson. The other thing I learned from this situation was that as a teacher, you might have to completely abandon what you have planned to make sure that they have a concrete understanding. If you continue with the lesson you have planned, it might end up hurting them in the end. Lastly, I learned that when you are frustrated as a teacher, chances are good that the students are too so it is important to take a step back and start to reform your initial plan to gain their confidence again.