We are starting to settle in to a routine and get everything figured out. I think our students are starting to get a good understanding of what they need to do to graduate and its starting to show in their work ethic throughout the day. This seems to make my day a whole lot easier even though there is still a lot to work out.
Today in my math classes, in my efforts to get my students to gain confidence in working with numbers in different ways, we worked on addition of two and three digits numbers without using the standard algorithm. For example, I asked what 4981 + 3759 is. Rather than stacking one on top of the other and adding each digit and carrying the “extra” numbers we talked about making one of numbers “nice” so that it become easy to add without the algorithm. For this example we talked about how 4981 is close to 5000. So then what could we take from 3759 and give to 4981 to make 5000. If we add 19 to 4981 we get 5000 and then our problem becomes 5000 + 3740. This becomes a simple addition problem and we end up with a final answer of 8740. As I went through this with both of my classes there became some clear and interesting differences between the two classes.
At the beginning of the discussion I asked everyone if the standard algorithm makes sense when you carry the numbers you need. In this class it was near unanimous that it made no sense. We worked through and students seemed to understand what they have been doing for years with addition. If there is one thing that I learned in this class is that I have to be very careful how long we carry on a class discussion. I always try to keep it short but today we went a little longer than I usually do and starting to lose the class fast. Going forward I am definitely going to keep this in mind. Today also seemed to be a sort of break through with one of my students. She has been pushing back on our activities and has been one of the students who gives up very easily. I gave students a worksheet with problems to practices working through this “new” method and asked that they just do what they could before they left. She didn’t finish but took it with her a brought it back later finished. Before she left for the day she asked for a couple more worksheets to practice so she would do well in the class. I’ll admit worksheets aren’t my favorite but the fact she wants to work after school on math is awesome!
This time things went just about as opposite as they did the first time around. Students were convinced that it made sense why they carried numbers using the algorithm. However, when I asked them to explain why it made sense to do that I couldn’t get anything more than because thats the way that it worked. We continued through our discussion but it was evident that this group really struggled moving away from the traditional way. I was surprised with some of the students who struggled to even follow what I was doing. The students who seemed to struggle the most have been the ones who have been striving in activities I would have classified as more difficult. I will give it up to this group of students they work very hard a diligently trying to understand what we are doing.
After today I have decided to change my sequencing in my plans. Initially I had planned on working through the number sense activities like the one today for a couple weeks as a review. After today I think it may be a bit overwhelming to do this and I would hate to have them shut down. I think now we are going to work on reviewing algebraic concepts they need to be successful and work this number sense into class as smaller chunks spread out throughout the year. I am glad I was able to see some of the differences between classes today. I think by finally seeing this I will be able to plan more effectively for each class.