This week at Longfellow was quite eventful (and messy!) After the long holiday weekend, we picked up right where we left of with our Kindergarten students. At this point in the number sense project, we have been creating activities based on the abilities of two groups – students who have mastered number recognition, and those who have not. Therefore, Julie and I wanted to create an activity that would maximize the learning experience for the students who are still struggling to identify numbers one through twenty. We decided that the most important factor at this point was repetition for these students. Thus, Julie and I took the time to make a set of individualized flashcards (containing numbers one through twenty-four) for each student. We then spent roughly 20 minutes with each group reviewing flashcards. We also marked which numbers the students got right and which they did not in order to monitor students’ progress.
After reviewing our notes and reflecting on our past lessons, Lisa and I discussed how we should proceed. We decided that we would continue focusing on number recognition for numbers 1-20 with the students that meet with us twice a week and that we would move on to missing numbers or counting on with the students we meet with once a week.
Because of the Thanksgiving holiday break, Julie and I only worked with the Kindergarten students on Tuesday of this week. Mrs. Arnold and Mrs. Carmack provided us with instructions and materials to lead a turkey finger counting activity with the students. Because we would not be seeing the students again on Thursday, we adjusted the times that we would be working with each group in order to ensure that all students from both classes would be able to create the turkey counter manipulative and spend an adequate amount of time utilizing it to practice their number sense skills.
Because of Thanksgiving break, we only met with our students one day this week. Therefore, we adjusted our plans in a way that would allow every student to be seen and complete the activity given to us by Ms. Arnold and Ms. Carmack. Though the students did not receive an ample amount of time, they were still able to create the Thanksgiving craft and use it as a counting tool or a resource to help solve several math problems.
Lisa and I began our Number Sense experience this week. Though we were a little nervous to embark on this long journey, our nerves were quickly settled after meeting our students. Prior to our instructional delivery we met with both Ms. Carmack and Ms. Arnold to discuss their expectations and goals. We were told that we would see some students two times a week, while others would only see on either Tuesdays or Thursdays. Ms. Carmack and Ms. Arnold were able to collect evidence based off the ESGI assessment that some students had only a foundational understanding of early number sense. Thus, these students would be meeting with us both days because the teachers felt they needed additional attention. We were also given a packet of activities and lesson plans that the teachers received at professional conference. Lisa and I reviewed the packet and agreed it would serve as a good resource in planning future lessons.
This week Julie and I took on our first day of Number Sense. On Tuesday, we arrived early in the morning to meet with Mrs. Arnold and Mrs. Carmack to discuss the process and expectations for the next few months. After conversing with the Kindergarten teachers at Longfellow, we were excited about the opportunities that would be presenting themselves while interacting with the students. Mrs. Arnold and Mrs. Carmack had recently attended a professional conference workshop, where they received a packet containing a copious amount of activities, ranging from number recognition activities to counting and base-ten activities, which can be used later in the term as students begin to develop a stronger number sense. Because we had agreed with our cooperating teachers that Julie and I would be taking the reign when it comes to planning lessons each week, we plan on using this packet as a reference when planning number sense activities for the students. We will be using the same ability grouping that we used during EDUC360 with Dr. Egan this past fall. On Tuesday, we wanted to begin with an activity that would allow for an initial assessment of all of our students. Thus, we began with a number recognition bingo activity. We were confident that the students would enjoy this fun game for their first day, but it also provided us with a lot of feedback regarding the students’ current understanding of number sense. The students in groups A-F struggled to recognize numbers beyond ten, where as the higher ability students provided us with evidence that they have mastered number recognition for numbers 1 through 20. However, many students who struggled with number recognition began to pick up on the pattern of teens. For example, students began to grasp the concept that a one and six is 16. However, this pattern became problematic for numbers such as 12, as some students would guess “two teen”. After we completed the bingo activity with each group, we had the students complete a Join – Result Unknown word problem. Julie and I decided that we would be doing one word problem a day with the students. Each week, we will add the new word problem pages to the students’ preceding pages, creating a book for each student. On Thursday, we did a number recognition activity with the students who have not yet provided evidence of mastering number recognition. These students rolled a large die, stated the number, and then colored in the corresponding symbolic number on a sheet. Again, we continued to see similar observations that we had seen on Tuesday. Many of the students were unable to recognize most numbers beyond ten, particularly numbers ten, eleven, twelve, and thirteen. The students who had demonstrated mastery of number recognition completed a base ten-frame worksheet. The students filled out ten frames, demonstrating their understanding that a given number eleven through nineteen is one group of ten plus “x” ones. The majority of the students showed a strong understanding of the value of a number through the ten-frame activity. I was astonished by the performance of one particular student, student I.E. After filling in nineteen dots on the ten-frame, I asked this student “If I were to add 1 more dot, how many would we have?” She answered 20. She was then able to tell me that twenty would be 2 groups of ten. While not all of our students have developed the profound number sense knowledge that student I.E. has, this experience sparked my excitement for the remainder of the number sense experience. Julie and I both look forward to helping these students practice their mathematical skills and develop a stronger number sense over the next two terms.
This week with Mrs. Carmack’s students we proctored this quarter’s acuity assessment on the iPads. As this is what my research has been focused on and leading up to, I was interested to see the new test as well as how the students would score. I asked the other two teacher candidates to complete learning notes for each of the students they sat with for the assessment, this way I would be able to gain a larger amount of data from a wide range of students and skill sets. As well as I was able to get others insights on the process of completing learning notes in the classroom. While working with my students personally I saw some of the same mistakes that I had seen last quarter, but one source of the errors was eliminated by the aid who usually gives the assessments told us to have the students tell us which answer to pick. By having us click the answer, the amounts of errors were somewhat diminished, but not completely gone. For example some of the wording in the questions lead to confusion for the students. Also the layout of the test lead to misunderstanding based on the students. One of the questions asked students to select the cone shape, but the answer options were letters that corresponded to the shapes in the question. Other problems that arose during the assessment was the fact that these tests are completed on the iPad. The program did not always work the right way, would kick out the student multiple times, or take a while to load, all of which could have an effect on the students performance. One aspect that I ad a multiple students comment about was the size and layout of the questions. Students would want to zoom in on the options to better see, but then would not be able to see the question and would lead to frustration or guessing. By completing this new assessment I was able to gain a better understanding of the benefits for learning notes, and the sufficient need for them during the assessment process in the lower grades. I am glad this week was the time the students needed to complete the test. I also gained confidence that my student’s hard work one on one with me has been helping their number sense:)
This week we were finally able to get back into the swing of things and have work with both classes on their correct day. My plan for this week was to take another question from the standardized assessment that the students took earlier in the year and approach it in a more hands on approach. The question we worked on this week had to do with a ten frame. That original question asked students to look at a partially filled ten frame and figure out how many more counters they need to completely fill the ten frame. From working with the student I found that many of them did not even know the name of the ten frame. When simply asking the students how many more they would need the students struggled to visualize what they were being asked to do. One thing that I found to help students in the completion of the task was to tell students that they needed to fill all the boxes not “complete the frame”. Once students had the different terminology and access to manipulatives they were more successful. One interesting thing that occurred this week was not in regards to the assessment questions I was recreating. Randy has created a new app that Has a string of beads that can be moved and counted. Another portion allows the app is a random number of the beads are hidden and the user is asked to identify the number hidden. One of the students that I worked with figured out that her figure was equal to the width of the bead and then placed her figure over the hidden bar to decide how many beads were actually hidden. Granted she wasn’t vert precise, but the thinking and logic were impressive.
Our main goal this week was to transition the students who were still using counting-all strategies to begin using counting-on. In order to accomplish this, we once again started by presenting students with addition problems and observing how they solved them. Some students began solving the problems by using their fingers, others preferred to draw dots, and some even had the sums of a few addition problems memorized. For those that were using their fingers or drawing dots, the challenge was to have them realize that they didn’t have to count both of the addends. We had a student working on the problem 5+3 and she began by putting five fingers up on her left hand and three up on her right. After she told us that the answer was eight we asked her why she had to count all of her fingers starting at one. She seemed perplexed so we then asked her how many fingers she had on her left hand. She responded that she had five, so we then offered a suggestion. “If you know that you have five fingers on your left hand do you really need to count them all starting at one?” The student responded by saying no. Then we prompted her by saying, “Okay, so do you know what number comes after five?” She told us that six comes next and then we showed her how she could just count-up three from five instead of counting all of the addends. After demonstrating a few times the student was able to use counting-on on her own.
In the kindergarten classrooms this week, Jackie and I have been continuing work with our students on counting on strategies. We are continuing practice for students who do not yet utilize the strategy of counting on for addition, and for those who have been using the strategy we are practicing the strategy with the goal of helping the students discover that it is more efficient to count on from the larger addend.
This week, we had two new sets of materials to help us work with the students. One of the materials was a container which held three dice, two of which were numbers 1-6 and the other was either an addition or subtraction sign. We also had a set of addition and subtraction flash cards which had numbers on one side and dots on the other.
We used the dice with students who did not have their addition facts for addends 1-6 memorized. The students would shake the container and then read the math problem that resulted. We had white boards for the students to write the problem out, and we then asked them how they would solve their problem. Many students said that they wanted to draw dots on the white board or use their fingers in order to represent the addition problem. Since most of the sums that resulted from the problems were less than 10, we found that many of the students would want to hold up both addends on their fingers and then count all in order to solve the problem. If they chose to draw dots, they would represent both addends and then count all in order to solve. We let the students solve the problems counting all the first time if this was the strategy they chose, but the next time they began using counting all as a strategy we would prompt them by questioning whether they needed to count the first addend or if they already knew how many they had. A good visual seemed to be when the first addend was five and the students chose to use their fingers. The students already know that holding one hand represented five without having to count each finger, so they did not need to count the first addend. We even heard students thinking out loud, saying “I already know that I have “x”…” when referring to the first addend. For these students, we focused on counting on from the first addend instead of counting on from the larger.
For students who could have performed the dice addition in their heads, we used the addition and subtraction flash cards. Since the cards had dots on the back, we started by having the first addend represented by a number card and the second represented by dots, hoping to prompt students to start at the first number and then count up the number of dots to find the sum. After students were demonstrating this, we flipped the second addends over so the number side was showing for both addends. At this time, we started placing the larger addend second. If students did not choose the larger addend to count on from, we would ask the students if the reverse of the addition problem gave them the same answer. We then modeled by counting on from the larger addend, and asked if this seemed easier or took less time. Many of the students would note other students in the group using the counting on from the larger strategy and would then use this same reasoning when solving their own problems. It will be interesting to see if the practice with the strategies in both situations will result in a change in strategy when we work with the students next week.