It was the first week back from Christmas break and I was so excited to see the students and begin working with all of them in math again. On Tuesday Morgan and I asked Mrs. Peterson if she had any specific goals in mind that we can work towards achieving when working with the students. She said that with the new quarter beginning, one of the new assessments has to do with incorporating dominos. Morgan and I decided to use the dominos on Tuesday as way of helping the students practice number recognition in a pattern. There are still a number of students who are not able to identify how many dots are being represented in the pattern unless they count the dots. We decided to work one on one with the students who were still struggling to look at a pattern and recognize the number. The activity I decided to do included the dominos. First the student and I would like at every pattern on the dominos (1-6) and see if they could first recognize how many dots are on the domino. The majority of the students that I worked with could recognize patterns with dots 1, 2, and 3, but any pattern after 3 dots students would count the dots on the dominos. This helped me see that the students still were unsure of number recognition when looking at patterns. After going through the patterns on the dominos. The student and I would line up the dominos with the ones that matched. Since there were two patterns on the dominos, students would match the first half of the pattern with a matching pattern and continue the process until all the dominos were in one straight line. The students and I said that they could only connect if the patterns matched. Every time the students would connect the dominos they had to say the number on the dots. During this process I asked the student, “why did you connect those two dominos?” The students would respond, “…because they have the same amount of dots and are matches.” Not all students used the dominos, because some students in the class are able to look at the pattern and recognize the numbers higher than 6 dots. For those students I used the IPad app, pattern sets. The students really liked this app and I am able to adjust the settings so that if students need more time to look at the pattern they are able to do so. The goal is for all students to be able to look at a pattern and be able to say how many dots are in the pattern without having to count the dots every single time. What I am currently seeing with the students is that they are scared of being wrong and second guess the answers and count the dots anyway. There are also times when students will count the dots on a pattern and when they get that same pattern again (two or three patterns latter) they do not recognize the pattern they just counted and recount the dots again. This happened multiple times with the students I was working with and I am wondering how can I get the students to recognize not only the pattern and amount of dots in the pattern, but also recognize the patterns they just worked with? I wonder, how do the students see the dot arrangement? For instance, when working with the pattern of 2 dots the students would not have to count the dots; they could easily recognize 2 as the amount being shown on the domino. However, when working with 4 dot patterns students would have to count the dots. They could not recognize the 2 dots on the left and the 2 dots on the right for a total of four. The students would always have to count the pattern when more than 3 dots were being shown. This brought me to the question how do students view the pattern and how can I continue working with the students, so that they are making progress at recognizing the amount of dots in the pattern. This will be something that I work towards with group of students who still need more guidance in pattern recognition.
When I returned from the holiday break, I was curious to see whether the students I had been working with the past 5 weeks would retain the information. After working with the kindergarten students this past week, I discovered that the students not only remembered the content and skills previously taught, but also developed further levels of comprehension associated with number sense skills. This development can be seen in several students who I have worked with. One student had a difficult time including the number 13 during rote counting exercises. Before break, we worked together and discussed where the number 13 lies in the number line, what the number 13 means, and how to represent the number 13. The first day back from break, this student was able to count higher than before and included the number 13 as well. A few students who had difficulty recognizing shapes and defining shapes with the correct terminology were able to do so. Skills in rote counting and shape recognition have progressed since the holiday break. One skill that needed to be addressed this week was counting by tens. Many of the students I work with cannot count by tens and therefore cannot count very high during rote counting exercises. This week, I tried a different approach to counting by tens. Instead of iPad applications, I explained how to count by tens with a dry erase board. I told the students that if they can count to ten, they can count to anything because the pattern simply repeats. I wrote the numbers 1-10 on the dry erase board and then had the students count as high as they could for me by tens. For each “ten” said, I added a 0 to the corresponding first digit. Once a student was stuck, I explained the pattern of counting by tens through the process of adding a zero to the end of the first digit. The students caught on quickly and were able to count by tens after the end of this math session. The following session, we addressed rote counting development. I approached this skill the same way I approached counting by tens. Many students are stuck on numbers such as 29 and 39. I then reviewed that the pattern repeats. We reviewed what “ten” came next and then discussed that we simply repeat the pattern by counting how we count by ones (30, 31, 32, etc.). The students caught on quickly and were able to count to 100 with some assistance. I am hoping that these fundamental skills stuck with the students over the weekend and they will hopefully be able to count to 100 (or close to it) on their own. I am so proud of the progress the students are making after 5 short weeks and I cannot wait to see how they further develop the remaining of the school year! Hope everyone had a wonderful holiday
This week was a very productive week for Courtney and I with students in Mrs. Peterson’s class. Mrs. Peterson had asked us to work with the majority of the lower students to try and catch them up with the rest of the class as best we can. This is counting up to 20, recognizing quantities of numbers up to 10, and recognizing number symbols up to 20. There are several students that are almost there, but not quite. So those were the students that we worked with primarily on Tuesday. I did an iPad app with them where we traced numbers 1-20 with their fingers, and then we counting objects that were provided and picked the number symbol that went with how many objects we counted. I found this app to be very successful and enjoyable for these students. I surprisingly did not have any issues with the students having troubles with using their finger on the iPad.
Since returning from a two week long break, the students are filled with enthusiasm and energy. It seemed that the break was beneficial to some and may serve as a step backwards for others. Many students who were struggling returned from break refreshed and ready to learn whereas some of the students who were excelling seemed to have lost some of their momentum. There were several students who were working with simple addition and are now struggling to recognize the number symbols.
Thursday was a much more productive day with the students, perhaps because they were re-settling into their routine again. This week my partner and I decide to continue to work with the students using the dice patterns and addition strategies. One student, who I have struggled to connect with since the beginning of this project, had a break through and began hinting at seeing 5 on the dice as 2+1+2. She did not fully grasp the task at hand but by simply trying she has made some progress! I worked with another student who is typically very shy and reserved and today she really came out of her shell. When working with the dice patterns she was able to take the 6 on the dice (which is portrayed by two columns of three dots) and make several different equations. She drew out the dice pattern on a white board and then took the second white board to write out the different equations that she saw. She first saw 6 as 3+3 and indicated this by first circling the columns and then writing the equation. When asked if she saw it any other ways she simply nodded and continued on to discover that 4+2, 2+2+2, and 5+1 all equal 6. It was especially exciting to see her circle the different dot patterns because it is similar to steps the students may take when learning multiplication.
It is incredibly exciting and rewarding to see the students make the connections that we have been hoping they would make. I am excited to see if we can apply this concept to working with the hard to distinguish teen numbers. I am also hoping to find a way to integrate the concept of rolling the dice into a more interactive game in order to keep the students engaged.
As we are getting back into the swing of things after our winter break, the students seemed to have all of this energy that was preventing them from sitting at a desk and studying shapes, number configurations, etc. Students, who were excelling in areas before break, seemed to have lost some of the previous material they had been working with. Some students who were once able to count up to the 50-100 range began to skip numbers and forget the order of their multiples of ten.
This week we focused more on assessments than anything. Each of the students had to be assessed on a certain number of tasks, such as shape recognition, orally counting, pattern recognition, and much more. Since the teachers at Longfellow were required to conduct these assessments, this what we spent the majority of our week doing. In addition to the required assessment, we also gave our sticker assessment (orally counting) on Friday. Throughout these assessments the children really impressed us. Nearly all of the students made progress on how high they could count and we even had a few that exceeded their initial goals. One student in particular counted up to the 40s and when we reassessed her on Friday, she was able to count up to 75 (and only mixed up a few numbers after that). She was extremely excited to come count for us and had a smile on her face the whole time. In fact, this student was so thrilled about counting and reaching her goal that she counted all the way up to 100 (even though a few areas were incorrect). Since starting the assessments and giving out rewards to the students when they achieve their goals, students have seemed more willing to participate in counting and even find it enjoyable. It really makes me excited to see students really getting pumped to learn. I think this result is also attributed to our goal cards that we sent home with the students. I feel the parents are more informed and can therefore help their child practice while at home. After working with half of the students I asked them how they were able to count as high as they did and most of them commented that they had either been practicing or practicing at home. With these kinds of results, I think the goal cards are a way to go! I will definitely be implementing this tactic in the future.
The past week we have been assessing the student’s number sense skills with a very long, tedious standard assessment. While testing the students on their ability to preform various math goals that we have been working with this term, we noticed a few pleasing progressing and a couple confusing regressing reports. Read more…
This week we worked a lot on assessing the students for their end of quarter grades. So on Friday, we kept things fairly simple and just had the students count for us and be able to add stickers to their charts if they had made progress. We now have a total of five students who have counted to 100 by 1′s and now by 10′s. One of those students was able to count to 100 by 5′s and is moving on to counting by 2′s. Three of our students are still struggling with getting through the teens without skipping a number. Several of the students made gains in their counting, previously they were stuck on getting to 25 and this week they were able to reach that goal. One of our students in particular surprised us. As of the middle of last week she could successfully count to 10 without any mistakes. After 10 she would skip numbers and put them in random orders until she got to 20 and then she would stop. We thought at first that it might have been a language barrier, however she made the same mistakes when counting in Spanish. This week, she had to hold herself back from running down the hallway she was so excited to count with us. She sat down in the chair and started counting before I had sat down. She not only reached her goal of 25, but she went all the way to 50 without missing a number! She seemed like she could have gone farther, but the rest of the class was coming back from the library and she got distracted and then could not get back to where she was counting. She was extremely proud of herself and was very excited that she got to put the special stickers on the chart for reaching markers of 25 and 50.
On Monday of week four my partner and I started using a sticker chart to track the students progress in rote counting. We pulled the students one at a time and took them into the library where it was quiet and where there were minimal distractions. We explained to the students that we wanted them to count as high as they could, and the higher they got the more stickers they got to put on their chart. The students counted and when they made a mistake we explained to them where their mistake was and wrote we down the highest number they were able to count up to. Then we showed the student where their name was on our chart and let them place the correct number of stickers next to their name. Then as I walked a student back to class I would stress how important it is that they practice at home too so that they can get better and add more stickers to their chart. Being able to count seems like such an easy skill to adults, but some kindergartners or students really struggle with counting when there are no physical objects in front of them. The only way they are going to get better is if they practice. That is why every time I work with a student I say “I know I ask you to do this every time I work with you, but I need you to count as high as you can for me”. Also, at one of our weekly Number Sense meetings my teacher/advisor Randy Hengst said that repetition, movement, and songs may help the students improve their rote counting skills. I have a video that shows the teen numbers and has a rap to go along with it that seems to be effective so I guess I could try to find a way to include movement. My only concern is that I do not want the students to become dependant on that movement in the future when they are counting. I have a song that I can sing in my head when I am trying to figure out what months have 30 or 31 days, but if I were to clap every time when I was counting and could not count without clapping that may become a problem. Anyways, the whole point of the sticker chart is to create incentive to practicing rote counting. We send a note home to the parents at the end of the week letting them know how high their student was able to count for us, and asking that the parents help encourage students to practice counting at home. The goal for the students right now is to be able to count up to 50. If they reach 50 they receive a small eraser as a prize and if they reach 100 they receive a bigger eraser as a prize. I am not saying I agree with giving prizes or rewards such as erasers to students, but I will not go into that here.
At the beginning of this past week, I had a bit of a breakthrough with a student. Although this was not math related, it did help the student to open up and therefore work be more willing to work and participate in the math activities that Markaye and I conducted. For the first couple of times I worked with one of the students in the classroom I noticed that she was very shy and did not speak up very often, letting the other students answer the questions, even when I would direct them towards her. I also realized that when it was just the student and I for individual working time (whether it was seeing how far she could count orally by herself) that she seemed to have a language barrier. This student would occasionally respond in Spanish and even count some of the numbers in Spanish as well. With this realization, I knew what I had to do; I put my Golden Apple classes (great teaching scholarship program) to use and asked her what she was called at home and if her parents called her by something different than she is called at school. Slowly she nodded and then responded with this name. It was much different than the name she was being called at school by all the students and teachers. I then asked this student’s permission to call her this in school and she responded with an excited nod. Surprisingly, from that point on I have seen much improvement in this student, not only through participation, but also through her number sense skills.
In my Golden Apple class I was taught that sometimes there is a disconnect created between school and home when kids have to change their names for the people at school to be able to pronounce them. Ultimately, this makes the learning experience less personal to the student and can even cause them to drawback from learning.
I shared this new name change with my partner and have been calling this student by this name ever since, and like I said, she has improved greatly because of it in both participation and number sense skills (order of irrelevance, counting up, etc).