This week we had the opportunity to work with the students in Mrs. Carmack’s class. My goal for these one-on-one sessions with the students was to determine which of the students in my group demonstrated the counting-on strategy. Out of the five students that I worked with, only one of them utilized counting-on to solve an addition problem. This particular student used the strategy without being prompted by me or by being shown the strategy on the Number Line App. Also, her use of the strategy was consistent, and she employed the strategy to solve all of the addition problems I gave her. When I asked her how she learned the strategy, she told me that it was the fastest way to add and that’s why she did it that way. From all of the problems that I gave her, she always started with the first addend and counted-on starting with that number. She may not have been introduced to the idea of working with the bigger of the two addends. In future work with her, I will be sure to ask her why she always starts with the first addend, and if she thinks it would be easier to do it another way.
This week we worked with Mrs. Carmack’s class on both days this week. During my time with the students I individually pulled students out and asked them to all complete the same task. I asked each student to draw three shapes on the white boards. After they drew the shapes and we talked about the differences between each of the three shapes, I wrote the three words that corresponded to the shapes on the white board and asked each student to point to the word as i said it. I was surprised that all of the students were able to correctly draw the shapes that i requested as well as explain the differences and characteristics of those shapes to me verbally. When it came time to students selecting the words of the shapes that they just drew, only two students from the other math groups were able to be successful in this task and correctly point to each of the words. I decided to have students recreate this problem that was asked on the standardized assessment that they needed to complete for their quarterly grades. When I gave the standardized assessment I thought that some of the students did not know their shapes due to their answers to this questions, but when I started to asked what worked they were looking for on the answer key I realized they did know the answer, they just couldn’t find the correct option. With my research on Learning Notes, I realized that the student would benefit from implementing something similar when completing standardized assessments to show a more accurate picture of what the students actually understand. I am excited to see where my research continues to take me and the kindergarteners understandings!
This week I had the opportunity to work with the students in Mrs. Carmack’s room and gather data related to counting on. The schedule this week was adjusted a bit, and I was not able to work with all of the students in my group, but of the students I was able to work with I saw the students fitting into groups similar to the ones I had seen in Mrs. Peterson’s class.
One of the goals of finding out if students can count on, is seeing if different situations seem to encourage counting on. In Mrs. Carmack’s class this week one student, E, demonstrated the strategy of counting on in multiple situations where the first addend was 10. For all of the problems, the sum was greater than 10 to discourage the use of counting all on fingers, but when the addend was anything other than 10, E did not use counting on.
One other student I observed, T, attempted to utilize counting on after it had been modeled on the Number Line app. When she did so, however, she would place her finger on the first addend on the number line, but then would count up the number of the first addend instead of the second. I wonder if reinforcing the fact that we start at the first addend because we already know that we have that many without needing to count, will help T to understand the strategy of counting on.
All of these findings will be interesting to take a closer look at now that I have started to identify students who are counting on.
We are finally back into the swing of things after what felts like months without working with the kindergarten students. This week was my first chance to start focusing on my research topic and see what i can find out. My topic is focused on examining multiple forms of assessments and trying to conclude a sound method for assessing kindergarteners rather than standardized tests. On tuesday we did not have the chance to work with many students one on one due to Mrs. Carmack being absent. I was able to talk to the new student in the class during math when I saw something interesting on her paper. The students were working on counting cartoon bugs and then graphing how many there were of each. I saw that in the new student’s tally section she had drawn four vertical tallies, then the fifth was horizontal across the four. I asked her why she did her tallies that way, and she told me ‘because there are five and its easy to see’. I was IMPRESSED! Connecting this to my research, on the standardized assessments, there would not be an opportunity to ask why the student completed the question in such a manner, but only make judgements. On Thursday I was able to work one on one with the students from Mrs. Peterson’s class. To start to gain information linked to my research topic i asked the students to complete multiple different types of questions that overlapped content. Then I specially took a question similar to one of the Acuity questions to recreate and observe what was happening. For this question I asked students to draw me three shapes on a dry erase board, a square, triangle, and circle. One student was unable to draw a square, so I asked her to draw a rectangle for her third shape. After each student drew the three given shapes, I erased the board, wrote the words of the three shapes they drew, and then asked them to pick the word as I called them out. There was only a few (3-4) that were able to get one right. Many of the students told me they couldn’t read the words, or went in the order they were written. I was not surprised to see this happen, but I was glad to see that the students did know their shapes just not their names. This evidence was different than what would have be given from the standardized assessment. I am excited to what the next weeks bring in both my research findings and the student’s number sense understandings:)
Our work with the kindergarteners has resumed and I’m extremely excited to start diving into our research topics! Jess and I have chosen to focus on counting-on, and more specifically we would like to identify what subskills are needed in order to count-on and what strategies teachers can utilize to reinforce the addition strategy. The first step to begin our investigation was to identify which of the students in our groups were able to count-on. Once we establish this, we can begin to teach the students who were unable to count-on using the strategies that we found during our research, and we can ask the students who know how to count-on how they learned it.
After what felt like forever, we finally got back in the kindergarten classroom! Over the students’ Spring Break we have been working on writing literature reviews over the research we’ve done to try to answer the questions we are investigating while working with the kids. Jackie and I have chosen to research the same topic, which is the development of counting-on as a strategy for addition. Our research is focusing on the general background numeracy skills that are necessary before counting-on can be addressed, the specific subskills that are directly related to counting-on, and different methods for teaching students to count on.
This week, I focused on identifying students who were already demonstrating the strategy of counting on when given an addition problem. This week we only pulled students out of the room in one class, because the other class had a substitute teacher. So, after one session this week, I have identified three groups of students based on the skills they were demonstrating. One group is comprised of the students who utilized counting on. Only one student demonstrated counting on in the first addition problem he was presented. This student had been using the Number Line app, and was first presented the problem 8+7. After solving the problem I asked him to show me what he did first, and he told me he started at 8, then 9 is 1, 10 is 2, etc. I then asked him to show me the next addition problem using his fingers instead of the number line. To demonstrate a problem where the first addend was 10, the student held 10 fingers up at once, stated that he had 10, then held up the second addend and counted on from 10 one finger at a time. This leads me to conclude that he understands that he has “10,” but does not need to count out 10 in order to determine this. In coming weeks, I plan to see if students who fall into this group demonstrate all the subskills that our research has stated are directly related to counting on.
The second group of students I identified were those who sporadically utilized the strategy of counting on and needed modeling of the strategy before doing so. The Number Line app has an option which underlines the first addend for the students and then shows an arrow counting-on the amount of the second addend. After this modeling, a handful of students began to count on. One item of confusion that arose was when one student had the problem 6+7 and started at 6 but then only counted up to 7 instead of counting 7 more. One other student demonstrated counting on in some situations, and knew that 2+6 was 8 because “6 and 2 more was 8.” With this group in the coming weeks, I plan on working together on the different subskills related to counting on and seeing if the students then utilize counting on without seeing it modeled first.
The final group of students that I identified were those who I felt needed continued work on numeracy skills before counting-on could be addressed. If students could not identify and set up an addition problem without prompting on which two numbers to add together and how to count both parts in order to find the whole, I did not model counting-on. Counting-all is a strategy that should be in place before counting-on can be introduced or conceptualized.
This week was our first week back from our own Spring break, and also the last week the students would be in school before their Spring break began. Coming off end of the quarter testing and having gone weeks without seeing us, the students were all excited to be taken out of the classroom and eager to tell us all about what they plan on doing over break. On Tuesday in Mrs. Peterson’s room, I used Dominos to work on addition and subtraction with my students. For students who had demonstrated that they could formulate and solve addition problems without scaffolding, I started with subtraction, and for students who still occasionally needed scaffolding while performing addition, we worked solely on addition. Across the board, the students all expressed excitement when they saw the Domino box. This interest really helped keep the students on task and many wanted to keep practicing addition and subtraction until all the Dominos in the box had been drawn. When the students drew the Domino, they either had to add or subtract the dots on both ends. All of the students working on addition chose to count each dot one-by-one in order to determine the total. Since my research focus is on the acquisition of the counting on strategy for addition, I gave the students who were working on subtraction one Domino to add. I had the students identify the number of dots on each end before adding them together, and in this particular instance one of the two students in the group demonstrated the counting on strategy.
In Mrs. Carmack’s class on Thursday, I worked on the addition and subtraction story problem app with the students. All of the students were able to add or subtract based on what the problems asked for, some requiring scaffolding and others determining if they needed to add or subtract without assistance. With students who were repeatedly solving the problems without consistent scaffolding, I had them start identifying whether the problem was an addition or a subtraction problem before they began solving. It helped to discuss key words such as “take away” or demonstrate the action that was being described in the problem using our fingers in order to determine the type of problem. In future weeks, I am excited to start work with counting on and looking at the strategy from a new perspective based on the readings I have done.
That’s all for now though!
This week was the first time we had a chance to work with both classrooms in what has seemed like a long time due to snow days and being on spring break. On top of that the students at Longfellow were getting excited for their spring break starting at the end of the week. Knowing that it would be a few weeks before we saw the students again I didn’t want to try and push new concepts, but rather we reviewed the concepts that we had been working on the past term. One of the major concepts that my group has been working on is matching a numeral to a quantity. This has been a major focus for this group due to the necessary skills it requires that are needed for addition. The activities that we did this week were all based around this idea that there is a numeral that correlates to each quantity. I had made some different 3 wheels from poster board that either had 0-5, 1-10, or 11-20 dots. The students needed to correctly count the dots and find the clothespin that had that number and pin it onto that section of the wheel. Out of all the students only two needed help to complete the 0-5 wheel. I was surprised when some students wanted to take the challenge to complete the 11-20 wheel, and some where able to complete it successfully! The majority of the students are ready to work more with the teen numbers and to start being challenged with more complex concepts. One thing that i found surprising in a good way was one student was able to demonstrate counting on to me while working with the ‘Line em’ Up’ app. He needed to find where the 8 went and instead of starting to count from 1 he started at the last placed number in the order (6) and counted until he found where the 8 needed to be placed! I am excited to start working more with the students and my research topic of ‘what is the best way to assess kindergartners and their math skills’ after their spring break and I hope for more pleasant surprises:)
This past week I worked with both classes on addition concepts using the add sub application on my iPad. When working with the students, it is clear that some of them are beginning to grasp the concept of addition. For example, after a couple addition problems I asked a group of students if any of them knew what we were doing. One student was able to tell me that we were adding. To follow up I asked the student if he could tell me what adding was. His response was, “adding is when you put two things together to make them bigger.” The students understanding of addition was also represented when they were using the features of the app. Next to each addend there is a corresponding number of squares. In order to figure the addition sentence out, students can count all of the squares to find the sum. I didn’t explain this to the students, yet all of them knew that in order to find the answer they had to count all of the squares.
This week we continued the practice assessments with Mrs. Peterson’s class that we conducted last week in the other room. This time I pulled students out one by one to give them the practice acuity assessments that they will soon be completing on the iPads. Though watching these students complete this standard assessment, I could see that there was not a very accurate picture being protrayed of the students. There were multiple questions that caused students to struggle. For example the last question of the assessment had eight roses drawn on the paper. The question asked something along the lines of “if John planted these eight roses in his garden and planted one more, how many would he have all together?” Almost every student simply counted the flowers on the paper and said the answer was eight. Even after repeating the question for the students, they counted the roses drawn and selected the answer eight. Granted, some of my students do not understand fully the concept of addition, but many would have been able to correctly answer if a different visual was available. Another source of error was on a shape question. The question asked students to pick the answer the best described the shape of the top of the house. (triangle). The answer options were different types of shapes in written form. Not one of my students was able to correctly select the word ‘triangle’ on their own. The response i heard from students was ‘its a triangle, which one says triangle’. After talking to Mrs. Carmack about this issue, she informed us that they iPad form of the assessment did read out the options for the students, but still I felt that this was unfair to the students. For my research, I have decided to look into the best way to accurately assess kindergarteners of what they know about a given subject. From what I have read so far, the best answer that I can conclude is to have more informal assessments and ‘learning stories’ to show what and how the student understands.
Now we have a few weeks away from the students due to spring breaks, but I am excited to see what they come back understanding that they did not before break. Over Christmas there was some huge jumps! Lets hope spring brings the same!