This week has been a really great week working with the kindergarteners. Several of the students that I have been working with have experienced “breakthroughs” where the information we have been learning and practicing has finally sunk in and they understand the hows and whys of some of the math concepts. Several of the students I work with have been having a lot of difficulty counting by 5s to 100. However, once I wrote down 5-100 by 5s for the students they were able to get it. It was one of those moments when I overlooked the simplest solution. It was great to watch their faces light up once they were able to complete this task. I had another student who had been struggling to identify shapes earlier in the year but when I prompted her by saying , “can you draw an shape with four sides for me?” she drew and identified a trapezoid!
This week was full of exciting developments for each of the students I work with! It seemed as if some of the things that we have been working on for the past15 weeks have just “clicked” for them and they are able to understand it now. One student, when we first began working together could only count to 11, counted all the way to 42 and remember the number 13! This is something that we have worked on every time we are together and 13 would get skipped time and time again so it was very exciting for the student and I when she was able to remember to count 13. Another student who I work with was able to count to 35 when just the week before she would not count past 22!
This week, the fourth quarter goals were the main focus. We have a sheet that identifies which students need extra instruction for given math tasks. While working on these objectives, I was able to incorporate the domino and scenerio aspect of my research. With the new domino application, the students “roll” a domino and show the number on the domino by placing counter peices a ten frame box. The objective of this application is for the students to see the top half of the domino as one color counter and the bottom half of the domino as a second color counter. I observed that many students create a pattern out of the colored counters instead of corresponding each color to the number of dots on the domino. I also incorporated a scenerio for my research question. During the winter months, I provided the students with a sledding scenerio where the students would tell me how many people can ride the sled and how many people have to wait. This week, I created a scenerio about cookies. I provided the context of the scenerio by stating that a student in the class had a birthday today and brought in cookies for a snack. I gave the students counter chips to represent the cookies. The students would then count the number of chips. I would then draw two columns on the dry-erase board: one with my name on it and one with the students. I explained to the student that the cookies in his or her hand are left over after everyone in the class has received one. The student who brought the cookies in said that the student and myself can have the remainder of the cookies. The students would then sort the chips into the two columns in different groups. Interestingly, many students I worked with believed that both myself and the student had to receive the same number of cookies, even if I informed them that one of us could have more. For the most part, the students were able to come up with at least a few ways of representing the number of chips. The groups were less than with the sledding scenerio and the dice task though. I will think of a different scenerio this week to see if the students can create more groups to show how they see a given number.
The first week back was exciting. The students were ready to begin math again and ready to play the math games! I received a list of skills the students should master by the fourth quarter. All of the students I have worked with had made substantial improvement. The largest areas of improvement were seen in problem solving, ten-frame, and rote counting. It’s great to see the planning and effort that the students put into each math session having a positive effect on the mathematical performace. Tuesday was simply getting the students back into the routine. I didn’t get as much completed as I wanted to because the students couldn’t wait to tell me about their spring breaks. We simply worked on previous skills such as shapes, rote counting, 1 more/1 less and writing numbers. I also introduced a domino application this week. Since the dice pattern is similiar to the pattern on dominos, I was interested to see how students would perform on such tasks. One of the domino games had the students find equal dominos. The students had a difficult time with recognizing the set of dominos that had the same pattern and had to recount, making the task longer. One task had the students finish equations by filling in the missing addend with the correct domino piece. This task was too hard for the students and caused frustration. Interestingly, the students called the domino application math, while other applications such as Math Monsters and Butterfly math were considered games. On Thursday, the students worked on problem solving skills. I found several new applications that met the students interest and wanted to try them out. Math Monster is a game of bingo that provides the students with unlimited time to solve the problems. The students really liked this application because there was not a time limit, so they had plently of time to work out the problems without feeling the need to “beat the clock”. Butterfly math is an application that has the students solve the addition problem by placing the correct sum of butterflies in the cage. I used this activity with the girls and found it successful. Students found it easier to place each addend individually and then count the total number of butterflies to find the sum. AUM Addition was the third application introduced this week. The students solve simple addition problems to unlock puzzle pieces to complete the puzzle. The students were able to play this application twice. The second time, all of the students increased addition speed! I am hoping that the problem-solving applications will enhance the students’ ability to complete the domino application which requires the students to fill in the missing addend next week. The domino application also has some adjustments made to it. It will be interesting to see how the students respond to the application next week!
Over spring break my partner and I spent a lot of time developing our research question and doing our literature review. A lot of the information we found directly correlated to what we had been working on with the kindergarteners. A big breakthrough we had was when we discovered our work had an academic term for it: subitizing. Once we discovered this term a whole different set of academic journals, activity ideas, and iPad apps became available to us.
On Tuesday and Thursday of this past week Morgan and I worked together with one student at a time to assess their understanding of questions that used specific math vocabulary. We continued to focus on before, after, greater than, less than, and more vs. less, but instead of using the number line app on the IPad, Morgan and I used counter chips to see how quantity may change a students answers. While I filmed the students on the IPad this week Morgan lead the assessment with questions that we planned to use before bringing a student out of the classroom to work with us. Some of the questions we asked the students were, can you give me three more chips and then asked students how many more chips do I have than you? We asked students who had the greatest amount and who had the least amount. Then we changed the chip count and asked the student who has more and who has less. We wanted to see how students answered the question, if you were given one more chip how many chips would you have and the question, what number comes after the amount of chips they currently had in front of them? We did this in reverse order by asking if we took one chip away and what number of comes before the amount of chips they have.
Interestingly enough a lot of students were able to correctly identify who had more and less and who had the greatest amount and least amount of chips. What the majority of the students were having difficulty with was the questions how many more chips do I have than you and the before and after concept. When students were asked what number comes after 13 the student would say 14. When we asked what comes before 13 they would say 15. This was interesting to us, because one we asked them how many chips do you have if we take one chip away from your pile of 13 chips, how many would you have? The students were able to know that the answer was 12, because 13 comes after 12 or 12 comes before 13. Not all students were able to understand the concept of one more/one less. Morgan and I knew that if the students were unable to understand one more/one less, then they would not be able to answer the questions correctly in our mini assessment that looked at students understanding of before and after. After asking a variety of questions with the chips, Morgan and I had the student imagine that we were getting in line to go somewhere. We had the student stand in between us and Morgan would ask who is standing before you? The majority of the students were pointing to the person standing behind them (Morgan). When Morgan asked so who is standing after you, they would point to either Morgan again or point to the person standing before them in line. We did this assessment to see how word choice can affect a students understanding of math concepts if the words are unfamiliar to the student.
The assessment we conducted on Tuesday and Thursday raised many questions about how students are making connections to the various questions that are being asked to them. For instance, if the student was able to give Morgan 3 more chips after asking the student “can you give Miss Olsen 3 more chips” and successfully do that task we would think that when ask the next questions, “how many more chips does Miss Olsen have than you?” the student would be able to answer the question correctly. What we noticed was students were not making the connection between giving 3 more and how that relates to having 3 more chips. When we asked the student, “how many more…” the student would respond with the total amount of chips that Morgan, which they were correct about in the total amount but no in terms of the question being asked of them. Morgan and I are working towards trying to understand why students are unable to make that connection. We plan to take the time over our spring break to research strategies that looked at word choice in math vocabulary and apply that the math work we do with the kindergartners at Longfellow Elementary School.
This was the last week working with the kindergarten students before we head off for spring break. This week, we worked on how the students saw a given number, but different than before. Instead of rolling the dice amd creating groups that way, we gave the students a scenario based on the math morning routine. We informed the students that the tiles represented people that wanted to ride a sled. Some people got to ride the sled first and some had to wait for a turn. The students were asked to create groups based on a number of tiles riding the sled and a number that had to wait. Interestingly, the students who have been struggling with coming up with different groups were able to complete this task with ease. One student who has not been able to complete the dice problem was able to come up with all of the combinations to see the number 10. She even started with the number 10 and said 10 people can ride the sled and 0 people had to wait and worked her way down to 0. I also encountered one student who was able to see various ways of creating a number through the dicep problem, but only could come up with one combination for the sled problem. We will need to collect more data after break. Over break, we will continue finding literature research based on this concept as well.
This was our last week at Longfellow before finals and break. It is a bittersweet feeling; more bitter than sweet seeing as I do not want to leave my students for three whole weeks, especially when we had such an exciting and progressive week! This week for our weekly focus goals we remained focused on 11-20 ten frames but for problem solving we focused on the make a number concept. With this concept, I would give the students a set number of tiles (example: 12) and we would construct a problem (12 kids were sledding, some went on the sled and some stayed behind). The students would then take the tiles and construct number sentences showing me all the different ways they could make the number 12. The most exciting thing I noticed with this activity is that students who we had been working with to do a variation of the same thing with dice patterns were able to grasp this concept. In fact, a student who had not been grasping the dice concept that we have been pushing took this new way to “make a number” and ran with it. I prompted her to show me one way to make 12 and instead she showed me four ways! I was absolutely blown away! It was very exciting to see this substantial leap forward after weeks of struggling to make a connection.
Another big breakthrough I had this week with my group was the ability to look at a full ten frame and recognize that as the number ten without having to count each dot. Last week I mentioned that many of my students were on the cusp of understanding this concept. This week, they were able to not only understand this idea but also apply it! Many of my students when given ten frames representing numbers 11-20 would simply tell me the number without counting each of the dots. When I asked them how they did that without counting each student told me: “Well I know a full thing is ten and then there is 1 (or two, three, etc.) so it is 11. I was so impressed and excited to see the students move forward. With all of these exciting breakthroughs I cannot wait to return after break and pick up where we left off!
Last week Courtney and I were really trying to focus in on just one question rather than the two that we were juggling with. Because we had been working with a group of 10 students the past two weeks really trying to get some interesting information to work off, we decided to keep with that same group, but take a different approach. One question was looking at the idea of more, less, and the same. When brainstorming, we wanted to try a different angle with the same idea. We came up with playing “Line Em Up” with the iPad, and video recording each student while Courtney and I both asked questions and worked rather than each of us working one-on-one. I thought having both of us work with the students allowed us at the teachers to bounce ideas off each other to ensure we were getting the information we wanted. So while playing “Line Em Up” we wanted to use vocabulary that goes along with more, less, and the same such as before and after, as well as greater than and less than. We decided this because we felt that we used this vocabulary with the students (on accident) interchangeably while WE knew the meaning behind each term but it was clear that our students didn’t. For example, a student could tell us what numbers came before and after a number that we chose, but they could not do one more or one less. This difference in learning vocabulary and meaning sparked an interest because we wanted to see which terms came easier to the students to understand than others.
For now, we noticed that across the board, most students really struggled with the concept of “Less”-before, less than, one less. It was much easier for students to count up and count on than it was for them to go backwards and think in reverse. This makes sense because the students are used to the patterns of counting up in their head and out loud, and not the pattern of counting backwards. We also thought it was interesting that some students had a good grasp on the concepts of “greater than and less than” while others had never heard of those concepts before.
Overall, I would say this was a successful week for us because we were able to zoom in just a little bit closer on not only picking one question, but gearing that question towards the idea of vocabulary use in mathematics and how students learn those vocabulary terms with different means or at different times as if some are harder to understand than others even though essentially they are talking about the same concepts. Getting the students to wrap their head around this will be fun and enjoyable to have them connect the dots and come full circle…hopefully! Assuming everything will go as planned, but that is never the case, Hah!
This week we worked on various skills with our students. With our four students who understand the most basic math concepts, we started some work on addition. We found that three of the four already have a pretty solid grasp of how to make ten with numbers. All three of them were able to quickly tell us what number they would need to make ten given another number. The fourth student is really shy and she often lets someone else answer for her, so she may know the answer, but we have some more assessing to do with her.