Math Blog #3: Understanding a Student’s Number Sense

• Today, I worked with Michael and Luis (referred to as Student A and B) during centers. We played this game called "Crazy Mixed Up Numbers." I gave both students a ten-frame and took them from the classroom and into the 1st and 2nd grade pod. The counters were already on the table and both students instantly began playing with the counters.

Mrs. Sanders had told me that Student A was very low in mathematics; whereas, Student B is quiet but she thinks he's got it going on in mathematics. I did not know what to expect when working with these students for I haven't really worked with them one-on-one before; however, I had assumed that the students would not have any difficulty working with the lower numbers and representing them on the ten-frame. Numbers above six or so, I imagined they would have difficulties.

Both students have seen ten-frames before, and they are accustomed to seeing them in their math books and on the Landmark and Benchmark tests. Therefore, I didn't feel that this activity would be too foreign for them to fully comprehend.

I began the activity by asking them if they had ever seen a ten-frame before. Student A said yes, but B didn't say anything at all. I explained that when we use ten-frames, we begin on the top left and count all the way to five and then back to the bottom left and begin with six. They seemed to comprehend the set up of the ten-frame.

The first number I said was four. The boys responded by putting a marker on the fourth box, not filling it in or anything. The next number I stated was six. Again, the students merely put one marker on the corresponding box. When I looked down, each student had two markers (one in the "4" box and the other in the "6" box) on their ten-frame. I do not know if this case was due to the fact that they didn't understand what I was asking of them or if they just didn't grasp the concept yet. I asked them how many I needed from four to get to six. Both had to count each square in the ten-frame to know that six is two more than four.

I then decided that I should demonstrate what my ten-frame would look like if our number was seven. I asked them to do the same. Student A began looking over at my ten-frame, as well as Student B's. He seemed baffled by the idea that either of us would fully fill in our ten-frames to represent a number, rather than just placing a counter on the said box.

I asked the students to show me what fourteen would look like on a ten-frame. At that point, Student A wiped off his board and then counted out all fourteen markers and dumped them on his ten-frame. Student B began where he left off (at seven) and counted on to fourteen. Rather than dumping the rest that didn't have a box on the ten-frame onto the table, Student B scooted four counters over in the last four boxes and made room for each counter. The last four boxes contained two counters each. I asked Student B why he decided to represent it in such a way and he just shrugged and said, "There wasn't enough room. I had to make room." I also participated in this ten-frame and showed them my way of doing it. I told them that they were correct in counting out all fourteen counters; however, I asked them how many boxes were in a ten-frame. Both students cleared off their boards and began to count each square until they answered 10. With that, I asked them how many fourteen was away from ten. Both students stared at me. I asked them to pull out fourteen counters again and fill each square and count the counters they have left over. Student B stated that he had four more than ten. Student A still tried putting all the counters on the one ten-frame I had given him.

The students surprised me in many ways, but I did learn a lot about number sense in the first grade.

• Student A, throughout the lesson, tried to speak for Student B. Honestly, he kept playing with the counters and trying to stand on his chair. I didn't realize that he had such a difficult time focusing on one activity. Often times, I noticed that he would begin counting, look over at Student B's ten-frame, and then seem to forget what he was doing. I continually had to ask him what number he was trying to represent because he just kept putting the counters all over the ten-frame. Student A needs help with basic number sense because he can count correctly, but he has a tendency to rush things and mess up. There were a few times that I had to slow him down and ask him specifically how many markers did he have on the ten-frame. To count one and two more, Student A had recognize where the first number ended on the ten-frame and compare it to where the second one ended on the ten-frame. This was extremely difficult for him to do because he couldn't remember what the first number was once I asked him to represent a new number to me.

• Student B, with some prodding, can do this. He is a smart student, but both my CT and I believe that he has some learning difficulties. Student B has the ability to count on and he has a basic number sense. He can correctly identify more than, but struggles with the concept of "less than." (However, both students did.) When I asked the students to represent six and then three, both students had to wipe off the boards completely and then count on three from zero. Seeing that made me realize that subtraction is difficult for both boys. Student B did not understand that six minus three is three. His number sense is magnificent with adding, yet deficient in subtracting. With more practice, Student B can correctly work with ten-frames. Student B merely needs more one-on-one attention throughout the school day. He is struggling in other subject areas, and there 17 other students my CT is monitoring.

Student B also needs some practice with oral activities. He can correctly represent numbers on the ten-frame, but was hesitant to orally explain how he came up with his answer. When I would ask him questions, he would squirm in his seat or look to Student A for help--Student A would then try to speak for him. I am suspicious that this has been happening for a while now for Student B. Maybe he is not confident in his speech or explanations and then lets other students speak for him.

• Why is it that in the beginning of the activity, the students both only placed one marker on the corresponding ten-frame place? Did I explain the activity correctly? Do they struggle with number sense? I find it interesting they did this because once they continued on with the activity, both students seemed to better represent numbers on the ten-frame.

Although they have seen the ten-frames on tests and the like, both students need a better understanding of a ten-frame. On a test the class took, the question asked, "How many are there?" and it showed two ten-frames put together and the students had to circle the answer with the correct number represented. I found this to be very easy for the students, simply because they merely counted the squares with markers in them. Aside from that, the students need exposure to ten-frames.

I think it's important to remember that the ten-frame is a tool that can be used to think about and do mathematics. We have certain conventions when it comes to using ten-frames. One of those is representing a number by filling up all of the squares necessary. For conventions such as these, it's okay to directly instruct students ("we'll start by representing 6. This is how we use the ten-frame to represent 6.") The way the students initially represented 6 was not wrong (in fact, it's similar to how we often show 6 on a number line), but it doesn't allow for students to gain the most from the activity.

ReplyDelete