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.
Each week I am impressed by the visible amount of growth in the students. This week Markaye and I continued to strengthen and assess number recognition with the majority of our students. We have chosen to implement the Randomize-er Game every time we work with the students so that we have a constant factor in our activities. This way we can use the Randomize-er Game to assess their progress. By using this game, we hope that students will not only be able to recognize their numbers, but also be able to apply this pattern to counting in the teens.
Using the Randomize-er Game, we saw substantial growth in the three students we have been working with on number recognition. One of the students, after playing the Randomize-er Game and participating in the other activities we had planned for that day was able to count up to 50 with some help from us. Only the week before had she been able to count up to 30 and prior to that she had struggled with 27 and 28. This was a huge success for this student. However, we have discovered that this student in particular has a certain inconsistency to her skill set. Some days we do not know what to expect. This being said, she was able to count to 30 without help once again, but struggled with what came after 30 (she kept on saying 40 or 41). I find this very interesting since this does not follow any particular pattern (except for counting by 10s-10,20,30,40). Our hope is that with some more work and practice with counting orally, the student will be able to count to 50 all by herself. In addition to this achievement, this student has been consistently playing the number game with my partner and me. When the Randomize-er Game is played we usually include a number line at the top of the paper to help the students along (to figure out what number they are circling by counting the numbers in the number line). This student was able to do the game without the presence of the number line on Friday of this week! Not too long ago, she would constantly have problems with 7, 8, and 9 and relied heavily on the number line to help verify the number she was circling. My partner and I were both very proud of this achievement!
In addition to this student, we also had another student making progress in his number recognition. Because this student is one of our easily distracted students, we have broken up each session with different activities that revolve around number sense, but give the student a break from the regular routine. Thus far, adding more (small) activities has proved beneficial for this student and kept him more on task than he usually is throughout the session (there were even other kids around and he was focused!). One of the games we played with the students was a matching game. This matching game had number symbols that the students had to match with the correct number of objects (block pile) in front of them. Without any help or prompting this student correctly matched all the block piles to the correct number symbol and put the numbers in order (like the number line)-this last task was not asked of the student, but was done on his own accord! I could not help but smile during this session. The particular student I am speaking of has struggled in both number recognition and counting the teens, so it was exciting to see this progress unfold right before my eyes.
This week was full of exciting growth for the students. Every student I work with is now able to count to 100 by ten and most can count to 100 by five! I am blown away to see how fast they absorb and learn. This week we focused on the same skill set as last: 11-20 ten frames and number recognition, shape recognition, problem solving, comparing, and subtraction. The students liked working through subtraction problems with iPad games like “Math Bingo” and “Math Puppy”. I personally prefer using Math Bingo because there are fewer extra distractions to the game and it keeps the students focused on their subtraction skills. I was excited to work on the 11-20 ten frames because my partner and I see a connection between making ten frames and our dice patterns. Only a couple of my students are able to recognize that a full ten frame represents ten (and they told me so without being prompted!), while most are still counting all of the dots. I am hopeful that after going over this skill a few more times they become more comfortable with making that connection. We are also continuing to collect data on our research question. My partner and I are trying to focus on how students see numbers. We have the students roll one or two dice (depending on their math skills and comfort level) and count the number of dots. They have the option of drawing the dots or counting out the number with a manipulative. I then prompt the students to arrange the tiles or draw the dots in the way that they view them. The students then at that point will begin talking themselves through it or including me in the thought process. One of my students was able to recognize that you could “flip” the numbers it would be the same. When I asked what she meant she said: “See, right now it’s like 4+2 but if I do this, its 2+4 but it still equals 6!” It is pretty exciting to see the students make these connections and I look forward to what comes up next week!
My partner and I have begun our research on when technology should be used as a supplement for Kindergarteners. We have begun pulling students aside to assess their success with the skill of balancing numbers on an iPad application and with a balancing scale that has a bucket on each side. Each student was able to successfully complete the physical lesson with manipulatives while the iPad proved to be difficult for a few students, which was our assumption in the beginning. As we have been working with our students, some have become frustrated or distracted using the iPad. We believe iPads may be too abstract for some of the students to work with. If a student has yet to master a skill, iPads and other technological supplements may impair them from gaining a proper understanding. It seems that once the students have mastered a skill, they can effectively practice their math with an iPad.
This week, the students made substantial progress. All of the students I work with can count to 100 by tens! Many of them can count to 100 with limited assistance, if any. It’s amazing to see the growth in such a short time period. This week, we worked on similiar skills seen in the sessions last week. The students worked on identifying shapes by drawing and defining the proper name of various solid and two-dimensional shapes. We also worked on solving subtraction problems. The students love the application entitled “Math Puppy”. They love solving the problems correctly to get a puppy on the board! We also worked on ten frames. Most of the students I work with can recognize that a full ten frame represents ten objects. However, some still need to count to be reassured. I’m hoping after a few more lessons with the ten frames, the remainder of the students can recognize that a full ten frame represents ten objects. We also worked on my research question. My partner and I are interested to see how kindergarten students view numbers. The students roll two dice and either draw the number of circles or select the appropriate number of colored tiles that matches the number on the dice. The students then inform me of how they see the number. One student today included subtraction within his ways of seeing a given number! The students also really enjoy this activity. I am interested to see if students who are struggling with seeing various ways a number can be created also struggle recognizing patterns. I have not collected enough data with this category yet to have a conclusive answer. We will just have to wait and see what next week has in store!