Inside a kindergarten classroom with Augustana students

## Diving Into the Research

Our work this week has been focused on the subskills that our research linked to counting on. Jackie and I chose to take our students out together, three at a time, so that one of us could work with the students while the other videotaped and we would both get to witness what the students were doing.
The first subskill our research linked to counting on was the ability to identify the first addend does not need to be counted out because its quantity is stated in the problem. To test this, we placed a number of counters out in a line in front of the student, then placed a card above the counters telling how many were there. We then pointed at the last counter in the line and asked what count it would receive if we had counted all of the counters. All of the students who demonstrated an ability to count-on were also able to identify that the count given to the last counter was the same as the number on the card placed above them. Although students sometimes needed to be reminded that they did not need to count the counters to give the count of the last counter, all of the students we worked with were able to demonstrate this skill.

## April Showers… Bring New Understandings

The past few weeks in the kindergarten classroom have been crazy due to altered schedules for different classrooms. The past few times that I have worked with my group of students we have worked on taking questions from their standardized assessment that a majority of the students missed to see if presented in a different ‘form’ the students could be successful and demonstrate their understanding that was not shown in the results of the test. Many of the students were able to show me that they knew their shapes and the names for them verbally, but had a hard time identifying the written words. All of my students were able to draw the shapes I asked on a white board and then have a conversation with me about what makes the shapes different from each other. Another big question on the assessment that seemed to cause students problems was a question about flowers. The question showed eight flowers and said something along the lines of ‘Joe has eight flowers, how many would he have if he planted one more flower.’ The majority of the students counted the drawn flowers on the paper and said the answer was eight. The idea of having the answer not be what was shown in front of them caused confusion. While working with students individually, I tried to recreate this question is a more hands on method. I used manipulatives that looked like colorful game pieces and in the shape of a person. I would set up a given amount of the manipulatives in front of the student and then have them count the manipulatives. Then I posed the question of ‘how many students would be in my class if one student moved away?’ the students then continued to move one ‘person’ from the line and recount. Then next question that I asked was “how many students would I have in my class if two new students moved in?” The students wanted to place two more people in the line, but without having the correct number of manipulatives, they would count the given number then touch the place where the second new student should be. Some students even explained to me that they counted the number they had and just went one number higher in their head. By having students talk and explain their thinking to me, I was able to gain a better understanding of what they were doing and what the demonstrated.

## Testing for Counting-On

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.

## Interesting Findings

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.

## Assessing the Assessments

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:)

## April Showers Bring May Flowers

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.