Inside a kindergarten classroom with Augustana students

Let’s Talk About Counting-On…

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.

Spring is Upon Us

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!

Its starting to click!

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:)

Spring Break Fever

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.

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Assessments, Assessments, Assessments.

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!

Acuity Test Prep

This week was a little crazy and as a result we only got to work with Mrs. Peterson’s class. In preparation for their upcoming acuity tests, we decided to work with her students on a practice acuity test. The test has fifteen questions and covered topics such as comparing numbers, the number sequence, shape identification, and counting objects. For the most part, the children did well on the assessments and were able to answer the questions correctly. The problems that I saw had a lot to do with how the questions were worded and the vocabulary that they used. For example, on the questions that asked the students to compare numbers, the test creators used the words less and greater when the students have grown accustomed to the words bigger and smaller. In future instruction I will be sure to use the words lesser and greater so they begin to learn the academic language that they will encounter on tests and in future classrooms. Another aspect of the test that they struggled with was the shape identification question. The question had a picture of the house and asked the students to identify what the shape of the top of the house was. Several of the students could tell me that the shape was a triangle, but they were unable to read and find the word triangle in the answer bank. It was frustrating to see students getting the question wrong, just because they didn’t know how to identify the word triangle. The final problem that I encountered was the last question on the test. The problem said that David had seven roses in his garden and then planted one more. The students were asked to indicate how many roses David has in all. Along with the word problem, the question had a picture of seven roses. A lot of the students got this problem wrong because they were used to being asked questions that ask them to count the objects, so instead of listening to the problem, they were simply counting the roses and stating the answer was seven. If I covered the picture of the roses I found that the students were able to get the correct answer. The visual did not in any way aid the students in answering the problem correctly.
With finals and spring break approaching, it will be a few weeks until we meet with the students again. We are all hoping that they will use the flashcards that we have provided them to continue practicing their numbers.

Assessing Assessments

This week proved to be an unexpected one which came equipped with picture day and substitutes, so we only had the chance to work on math with Mrs. Peterson’s class on Tuesday. During the previous Thursday with Mrs. Carmack’s students, however, we had worked with the students to practice their math assessments they would be taking for the end of the kindergarten trimester. We hadn’t ended up video-taping any of the students while they took the assessment, but after having gone through it with numerous kids we realized that we had a few questions and concerns regarding the assessment itself. After our weekly meeting, we decided to go in to Mrs. Peterson’s class on Tuesday and work with her students on the same practice assessment, this time getting some good video footage.

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100′s Day Joy and Assessment Frustration

This week in Mrs. Peterson’s class we celebrated 100′s day with the students. For the number sense time we worked with the students on making their 100′s day fruit loop necklaces. Each student was asked to put on ten sets of ten fruit loops of alternating colors. It was interesting to see how different students addressed this task. Some students needed/wanted to count each individual fruit loop. While others wanted the process to move along quicker and wanted to go by twos or count out ten fruit loops and try to place them all on at once. There was a wide range of student ability in this one simple task. Some students did not understand the concept of groups of ten and how to count by tens, while others grasped the idea quickly. I can say that i do not want to see any fruit loops for a while:)
On Thursday we helped Mrs. Carmack give her students a practice assessment. This was a standardized test that offered little room for assistance without telling the students the answer. There were some errors by students due to the fact that they could not read the written answers. There were also some visuals that added to the confusion and resulted in errors. After assessing the students we talked with Mrs. Carmack and she agreed that some of the questions were not at the correct level for the students and would possibly give a distorted view of the student’s ability. After seeing this behavior I have seen how my research topic of the best assessment type for kindergarteners can start to take shape in the classrooms. I am excited to see what I can find from my research. As well as what I can learn from the rest of this experience.

And the cold presses on..

This week was yet another shortened one due to the cold weather. It actually ended up balancing things out, though, because this week the snow day fell on Tuesday so we got to work with the students in Mrs. Carmack’s room this week. Since this group of students has all demonstrated an understanding of addition as putting two quantities together in previous lessons, and have all been able to identify which two numbers they are to add when given an addition statement, I chose to work on addition with missing addends this week. I had different missing addend problems for numbers 1-5 written on popsicle sticks for the students to draw from a pile and solve. I chose numbers 1-5 since fluently adding within 5 is one of the objectives on the kindergarten report card. The majority of the students were able to solve for the missing addend, occasionally with the help of two color counters but some students also automatically answered a few of the problems. One student in particular had just moved up from the middle group during the last lesson, and he was the only student of the one’s participating in the activity to correctly solve for all of the missing addends on the first try without manipulatives. One student who had demonstrated memorization of the a few basic facts, 2+2=4 being one example, struggled to understand the missing addend. We used manipulatives on each of her turns to help her visualize the problem. Her biggest issue seemed to be that her familiarity with adding two numbers together was causing her to want to add the addend with the total instead of finding the other addend that would help solve for the total. After completing the missing addend activity, however, we worked on an addition and subtraction story problem app and she was able to solve many addition problems without the use of manipulatives. Something I found very interesting while working on missing addends was the concept of zero. The majority of students seemed to struggle with this. I was impressed though that after talking through the problem 5+ ?=5, one student in particular applied what we had discovered about adding zero to her next problem, which was 3+?=3.
The second activity we did was the story problem app. Two students I had in my final group did not work on missing addends and simply focused on story problems. The app asked various basic addition and subtraction story problems, and then provided a number line, ten frames, and a spot for drawing pictures as strategies for solving the problems. Some of the students were able to immediately answer subtraction story problems when 1 was taken away, which shows that their concept of subtraction is developing or developed. The student who had answered all of his missing addend problems also immediately answered a subtraction problem where 0 was taken away, which I found particularly interesting after all the questions adding 0 had brought up during the previous activity.
That’s all for this week, though!

Cold, Cold, Go Away

Once again, Longfellow had a shortened week this past week due to the cold, so we were only able to work with Mrs. Carmack’s class. Since I didn’t have the chance to work with those students the previous week, I repeated the same counting on activity that I had completed with Mrs. Peterson’s class the week before.
The students have been working on addition during their daily math work and it was evident when everyone in my group was able to read an addition sentence. Even though everyone could tell me what the addition sentence was I don’t think they necessarily knew what they were saying meant. For example, one of the students read me the addition sentence and when I asked him what to do next he said he didn’t know. With assistance this student was able to solve the addition problem, but he needed to be guided through each step. The biggest struggle that I experienced with this group of students was getting them to realize that the addition sentence that they are reading is telling them which two numbers they are supposed to combine. When I was working with the same student that I mentioned previously, we had the problem 3+4. First I instructed him to count me three two-colored counters. After he did that, I asked him what number we had to add to the three and he said he didn’t know. With a couple of these students I need to continue to work on establishing the meaning behind the addition sentence that they are saying.
Something else I noticed this week is that some of the students were struggling to compare numbers. For example, one of the addition problems was 5+3 and when I asked the student which of the numbers was bigger she said three. When I asked her how she knew that she said, “cause it just is.” To examine her claim I had her count me a pile of three counters and then a pile of five counters. When she finished I took the pile of five and gave her the pile of three and then asked her the same question. This time, with the addition of the visual element, the student was able to identify that 5 is in fact bigger than 3. I had several similar instances with students in my group, so I will continue to focus on comparing numbers with and without the use of manipulatives.