Inside a kindergarten classroom with Augustana students

Making Strides Towards Counting On

This past week, we only had a chance to work with Mrs. Peterson’s class due to the cold weather that caused school to close on Thursday. The activity that I completed with the kids involved a worksheet that focused on comparing numbers and solving introductory addition. The students were given an addition sentence and once they read the sentence out loud then I would ask them to tell me which of the two numbers was bigger. The worksheet had hot cocoa mugs underneath each of the problems and when students determined the bigger number they were instructed to write that number in the mug and then count a corresponding number of two-colored counters to symbolize the other number in the sentence. Then as a group we would count up from the larger number that they had identified until we had as many fingers up as we had two-colored counters. I told the students that whichever numbered we stopped on would be our answer.
Something that really struck me this week was the students’ ability to compare numbers and the variety of strategies that students employed to find their answers. For some students I had to draw a number line in order for then to compare numbers, while some students were advanced enough to be able to use benchmarks and some would utilize two-colored counters to find their answer. One boy from this class was also able to use his knowledge of the number sequence to compare numbers. The addition sentence was 3+6 and when I asked him which of the numbers was larger he said six. When I asked him how he knew this he started reciting his number sequence for me starting at one. After he said the number six he said, “See six came after three.” This explanation indicates to me that this student has some sort of understanding or has knowledge of the rule that the numbers later in the sequence are larger.
Another incidence that pleasantly surprised me was how quickly students were catching on to addition facts involving adding zero or one. Several students were able to look at the problems and tell me the answer without having to use counters or the number line. When I asked a student why 2+0=2 she told me, “Miss Jackie, zero means nothing so my number isn’t going to change.” For the problem 4+1, I had a student tell me that the answer had to be five because “plus one means it’s just one more bigger.”
I’m very pleased with the progress that I have been seeing with my students and I think a lot of them, at a surface level, are really starting to understand the concept of addition!

Interesting Observations

This week was a shortened week due to the freezing winter and school being cancelled on Thursday. On Tuesday, however, we did get to go in and work with the kindergartners. This week the two objectives I wanted to work on were demonstrating addition as putting together and comparing #’s. For some of the students in my group who have had a lot of work with addition and were becoming fluent with their facts 1-5, I chose to work on story problems involving addition and subtraction with them instead of the activity that dealt with comparing numbers.
The first small group I worked with on Tuesday consisted of just two students. In order to work on addition, we used dice and the students had to roll and add. They had to figure the total, but also were asked to write the addition statement down on their whiteboards. The students in the first group had difficulty identifying which two numbers to write down as an addition statement in the beginning, but were able to identify the two quantities after a few turns. I had planned to use the roll and add activity to model counting on, but for some of the students, such as those in the first group, I decided not to introduce this next concept until they had more work with addition as putting two quantities together and were consistently able to identify the two quantities they were adding. One of the students, however, expressed timidly that her dad had told her that she didn’t have to add both numbers together and she could just count one, which I took as her having been exposed to the idea of counting on. I asked her to show me what her dad had taught her, but she was not able to show what her dad had said or she was not comfortable enough to show us. These observations support some of the research we have started reading that discuss the stages kids move through as they develop their concept of addition, especially in regards to counting on. The next activity we did was another game of bingo, further continuing to expose the students to the numbers 11-30. This time I placed two number cards in the middle of the table and the students were told to place a counter on their bingo card on the number that was either more or less than the other number.
For the group that was closer to being fluent in basic addition, counting on during the roll and add game caught on immediately. None of the students appeared to use it as a strategy for problems they did not know at first, but after modeling they all chose that strategy on their second try. During the word problem app, I observed one student using the strategy of counting back in order to solve subtraction. He would automatically go to the biggest number on the number line at the bottom of the screen and knew to count back the number of spaces he was subtracting in order to find the answer.
I was very excited to witness the different stages in understanding counting on, and hope to carefully observe how and when these students “move out” of one stage and into the next.

Back in the Swing of Things

This week was exciting because I have narrowed my research focus and so I had a chance to see what the kindergarteners knew in regards to addition and counting up. The activity that I completed with both classes this week was an introduction to addition, incorporating two colored counter manipulatives to aid in the process. To keep the students engaged, I took them in groups of two. In order to assist students that may struggle and to challenge students who have demonstrated previous knowledge of addition, I differentiated the groups so that pairs were at similar ability levels. In order to complete the activity, each student would pick a card from the deck that contained cards with a value ranging from two to ten. Following their selection of a card, the students would then count a corresponding number of two colored counters. Once both students had gotten this far, they would push all of the counters to the middle as a visual representation of combining two numbers. Finally, they would count the total numbers of pieces in the middle to find out the sum of the two numbers they had selected. Besides for addition, I also asked the students to compare numbers this week. After the students selected their cards from the deck I would ask them which number was larger and I would also ask them to explain how they knew the answer they gave me was true.
Since the kindergarteners have had limited exposure to addition, I did not anticipate that any of them would be able to demonstrate the ability to count on. During my work with Mrs. Peterson’s class I was gladly proven wrong! I was working with a pair of two girls and they were catching on very quickly to the activity that I had planned. When adding the two numbers together I noticed that one of the girls in the pair did not even have to count the total number of pieces to give me the sum. When I asked her how she was solving the addition problem she told me that she started at one of the numbers and then counted until she had the other number counted on her fingers. For example, when presented with 8+7 the student would start at 8, and when you asked her why she started at eight she said it was because it was the bigger number, then she would count up from eight until she had seven fingers up. I was completely shocked and pleased with this student’s ability to add and to count up. When I asked her how she learned to do that she told me that her older brother taught her how to do that at home. Another amazing thing that happened while I was working with that pair was their ability to compare numbers. When I asked the pair if nine or five was bigger, the same student who can count on said, “Nine is bigger because it’s closer to ten than five is.” Not only can this student count on, but she also uses benchmarks when asked to compare numbers.
Overall, I’m very pleased with the information that I was able to gather this week and I’m also very excited to find and utilize strategies that will help the other students be able to learn to add and to count on.

Back at It

This week was our first week back in the classroom after winter break. As spring break approaches, we are just starting to formulate some questions that we’re interested in researching. During my time with the kindergartners, I’ve been really interested in observing the students when they add two quantities together, and how they often have to count up both quantities to find their total, and occasionally will go back and re-count both quantities of objects if they forget their total. On the other hand, right before break I did an activity where the students were given a number on a sticky note and they had to place it on a piece of paper with a number that was two more than or two less than their sticky note number. In this situation, when the students were given a number such as 13 and asked to find the number that was two more than 13, they either went to the number line and counted up two numbers, or they simply counted up from 13 instead of starting at 1 and counting 13 and two more.
In both classrooms this week I decided to incorporate counting up into the activities we did. I also have a handful of students who still need work with numeral identification for numbers 10-30, so I wanted to find a way to incorporate that into their activities as well. One of the objectives on the students’ report cards is “decomposes numbers less than or equal to 10,” so the first activity we did was play the 10 Frame Fill iPad app. Although my main objective with playing this game was for the students to work on decomposing numbers, I also wanted to start introducing the strategy of counting on. In this app, a number of blue counters appears in a 10-frame and the students then have to identify how many more they need to make 10. Before the students went to identify how many more counters were needed, I had them verbally state how many blue counters were in the 10-frame. Before we had started the game, we had talked as a group about how many spaces were in the top row of the 10-frame. We discussed the fact that if our whole top row was filled with counters, we would automatically know that there were 5 blue counters there. At first, most of the students had to count each blue counter one-by-one if there were more than 5 counters in the frame. After they had finished counting on their own, I asked if they would like to see a quicker way to count the blue counters. I then pointed to the first row, and asked how many counters we had decided were in this row. When they said five, I then showed them how I could start by saying 5 and point to the first row, and then count up from 5 one-by-one for the counters in the bottom row. During this activity, there were a few students who could automatically identify the number of blue counters right off the bat before discussing counting on with me, and one student, “L,” stated that she knew how many blue counters there were because there were 5 in the top row and 3 in the bottom. Most of the other students, however, continued to count by ones unless prompted to do differently.
For my last activity, we played bingo to work on both counting on and numeral recognition from 10-30. For a small group of students we simply played bingo without focusing on counting on because they needed the most work just in identifying numbers. For the rest of the students, however, we played addition bingo. First, we all counted together as I placed 10 counters in a plastic bag. I chose to use the anchor number 10 so that the students could subconsciously start thinking about teen numbers as 10 and some ones. I then placed the plastic bag in the middle of the table and placed a certain number of counters next to the bag. I would then say that we needed to figure out “10+x” and mark that space on our bingo boards. The first time, I modeled the way I would count up from 10 to solve the addition problem. There were 4 students out of both classes that were doing the “10+x” addition problems on their own without having to count, but for the other students I saw them using the strategy of counting on from 10. A few students needed additional prompting after we did the first problem together, but many automatically counted on from 10 without any additional prompting. In one case, after 15 had been the total to one problem, I placed two more counters out on the table and had them add 10+7, and one student, “A,” said that she knew the answer was 17 because “15, 16, 17.” I hope to work more with counting on in future weeks. I would like to put the students in different situations to see if they continue to use the strategy of counting on and if they know which number they should count on from. For example, this week the fact that 10 counters were in a bag prevented them from counting out those 10. Next week, I hope to do an activity where students could count out the entire quantity if they wanted so that I can see if they still choose to count on. This week, the students were also told to count on from 10, but I plan to work more with them so that they can identify on which number they should count on from in different addition problems involving a variety of numbers.
But, for now, that is all!

New Year, New Adventures, and New Understandings

This was our first week back with the kindergarteners since winter break, and as usual there were some unexpected occurrences. This week my focus was to see which students are able to correctly identify numerals one through ten. To gain this information I used flash cards with the written numeral on one side and that same quantity of dots on the other. Out of the fourteen students that I worked with there were four students who were able to identify all, and seven students who made three or less mistakes! This is exciting for this group of students who at the start of Number Sense were not this far in their number identification and were in the ‘need/significant need’ group. Before break there were a few students who were able to write numbers but not identify numbers that they had written. This was very interesting to me and was going to be the focus of my research. Well, I was proven wrong…in a good way! :) All of the students who demonstrated this thinking when asked this week were able to identify all of the numbers they had written. Santa must have brought some number sense to these students along with all the goodies under the tree. One of my students was able to identify and write numbers from 1-19! at the start of the year when I worked with her through math methods she was struggling to know the numbers 1-10. There are still a few students who are struggling to learn and understand which numbers are which. Jackie, Jessica, and myself have decided to make number flash cards to send home in hopes of giving students that extra time to work on their number skills. I am excited to see if the students who do not know their numbers will come back after working at home with a new understanding. Only time will tell!

It’s Beginning to Look a Lot Like Christmas…and Hanukah!

Longfellow students are buzzing with excitement as the Holiday season rapidly approaches. The school has been decorated and as the winter program nears, everyone is beginning to feel antsy still being in school, especially the kindergarteners. This past week we had little to do in preparation for the time that we were going to spend with the kindergarteners. In honor of Hanukah Mrs. Peterson had us review the dreidel game with her students and instead of using gold coins we used skittles. In order to incorporate math we often stopped the game and had the students count how many skittle they had. Another concept that we discussed with the students is half. One of the symbols on the dreidel instructs the students to take half of the pot, and instead of splitting the skittles in the pot for them, we tried to explain to them that in order to find half you have to make two equal groups with the skittle that you have. With some guided instruction, most of the students were able to split small groups of skittles in half. The students seemed to have a lot of fun with this game; at least until their math teachers told them they couldn’t eat the skittles!

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New Experiences And Holiday Cheer

This week was filled with excitement and new experiences. Both of the classroom teachers had something in mind for us to complete. On Tuesday we were asked to play dreidel with the students. This was a new experience for both myself and some of the students. We used skittles for the students to manipulate with each spin of the dreidel. Some of the students caught on quickly and were able to tell other students what they were supposed to do based on what they had spun. One thing that was a common struggle for students was having to decide what have of the group of skittle was. Myself and the other teacher candidates assisted the students by having the students create equal groups then taking one of the groups. After a few rounds with different groups of students, I personally took a low student from each of the classrooms to work with them individually. These two students are further behind then the rest of the students in the low ability group. After discussion with the classroom teachers we thought it would be worth a shot to see if the more individualized attention would help them move closer to the other students. With these two students I worked on basic number identification of number 1-10 with large flash cards. Then we practiced the numbers 1-5 on sheets that contained a ten frame, traceable number, visual representations, and quantities of each number. Both of these students struggled with this activity but made progress by the end. I think from this first individualized encounter that this is something that we will continue, and see what progress can be made. I am excited to see how these two student progress throughout the next semester!

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In the Air There’s a Feeling of Christmas

This weeks report will be short and sweet! As the students get antsy with the upcoming winter break and holiday season on their minds, the teachers are also getting final assessments done in order to fill out report cards. Both of the kindergarten teachers had tasks in mind for us when we came in for Number Sense this week. In Mrs. Peterson’s room this week we played dreidel with the students. We took students out in small groups and each student in the group was given two skittles to use as coins. Each person then spun the dreidel and we played the game accordingly. We tried to incorporate some math into the game by having students count skittles and determine half of the skittles when called for. I had never really thought about how difficult the concept of “half” was until we tried to explain it to the students.

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Getting the Ball Rolling

This past week was our first chance to work with both of our kindergarten classes on activities that were specific for their ability levels. At the start of the term myself and fellow teacher candidates decided to place students in groups where they personally fit best to be challenged just enough and be individually successful. For this week, I have been working with the students of the lower ability group. I have previously worked with some of these students through the number sense portion of Dr. Egan’s class, Education 364 math methods. The majority of these students are just starting to grasp some of the basic concepts of numbers.
During this past week I worked with the students from both classes to help identify a quantity up to ten and write the corresponding numbers. This activity allowed me to see that within the lower level group of students that I am currently working with there is a wide range of ability and understanding. There were a few students who flew through the activity and then would assist other struggling students complete their sheet. The next activity took their understanding of relating a number to a quantity to the next level. Students were given and wheel divided into sections containing different quantities of stickers, and ask to attach the clothespin that had the numeral of that quantity on the wheel. Both of these activities reinforced the varying abilities that are in these groups for both classes. Within these activities I was able to see that this group of students need to have something physical to count. Many students were double counting in both activities due to the lack of mobility in the manipulatives.
From the past few weeks, I have noticed that there are a few students, one from each class, that may benefit from getting more one-on-one attention that is specific to their needs and abilities. I am excited to see what these students are able to accomplish between now and the end of the year:)

Start of Something New

This week was our first chance to work with both of the kindergarten classes doing activities that we had designed in order to develop their number sense. We were all very excited to begin and the students were equally as excited to see their math teachers return once again. It’s hard not to smile when you’re working with the kids because their excitement and eagerness to learn is contagious. During the first week of the term, we spent a lot of time assessing the students to find out what they already know, and also deciding how we would like to structure each of the classes. Ultimately we decided that we would split the students into groups based on abilities and that we would each work with a group for a couple weeks and then switch, so that all of the students each got a chance to work with all of their “math teachers” and so that we could each experience the children who are progressing at varying levels. We also decided that we should work with the same ability group in both classes so that we could use similar activities and so that we could notice things about students during that stage of development. Something I’m most looking forward to is to see how the students will progress with more individualized attention as well as the strategies and activities that will work best when teaching the students.

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