Inside a kindergarten classroom with Augustana students

Exciting Discoveries!

This week in Number Sense we incorporated the week’s math focus into our work with the students. The week’s focus was centered on the numbers 11-20 (writing and creating ten frames). For many weeks the students have been able to count past 20. I was a little surprised to discover that while the students knew the sequence of words, writing them introduced a whole new set of struggles. Once I picked up on the fact that students were having a difficult time producing the numbers on their own I decided to use the Line Em Up app to show them what the numbers looked like. Many of my students needed a little guidance in putting the numbers in order on the app from 1-20. Once they had the line complete I asked them to look at the numbers and see if they noticed any kind of pattern. I was extremely happy to witness several students point out that the numbers “started over” but with a 1 in front of them. We took this new discovery and tried to apply it to writing the numbers on a white board. It was great to see the students apply this knowledge and use it to write the numbers out. They still struggled a little but they were able to reproduce the numbers with a little prompting. One of the questions that I asked to help prompt students was: “What number comes after 12?” and “If 12 is a 1 and a 2 what do you think 13 would look like?”
I was also able to move forward with some of my students in regards to the dice patterns. I have noticed some students were getting bored with drawing the dice patterns on white boards so I introduced them to an app called Tric Trac. I have used this app before with my first grade clinical class and I thought it may be too advanced for the kindergarteners but figured it was worth trying. To my surprise (and delight) several of my students rose to the challenge. Tric Trac involves rolling two dice. You then count the dice (for example: 6 and 3) the total number (9) is the number you then have to choose to equal your sum. At first it is pretty basic because you simply select the number of your sum. However, after a couple of turns you must select several numbers to equal your sum. This was a roundabout way for me to reintroduce the concept of “making a number” and allowing students to recognize that different numbers can be added to create the same sum.

A New Recognition Game

Since we only had Monday and Wednesday to work with the kindergartners, we really made sure we got down to business. The main focus for these days was to spend some extra time with the students that were struggling with simple number sense skills, like counting up to 20 and recognizing numbers.
First we worked with the students that had a difficult time counting in the teens. These students are able to consistently count all the way up to 10, after this, however, they start getting mixed up (and tend to only say teen when we try to count with them). We have tried a number of activities with these students to help cement and improve their counting past 10, like simply counting with the students and having them count with objects (blocks, cars, etc. to make things more concrete). We have also attempted to work with number symbol recognition from 1-9 with these students since most of them know how to count up to 10. Our hope was that students will start recognizing the numbers, which will eventually help their oral counting abilities. This, however, proved to be much too advanced for these students since they struggled with the numbers 5-9.
Needless to say, we have yet to find an activity that really aids these particular students. Ultimately, this leads me to questioning what other activities are out there that can help students that struggle with counting the teens? This is a great topic to look into since we are stumped on what activity to implement next.
For the students that could count past 20, we also worked on number symbol recognition. These are the students that tend to have issues with remembering and counting the 10s (20, 30, 40 50) in the correct order when we are counting by ones. For instance, they may say 28, 29, 40, …..38, 39, 50, etc. Other students in this group may simply have problems counting past a certain number, such as 27. There was one student that really piques my interest because of the way she continues to count. She says, “…25, 26, 27, 21” or on other days may say “…25, 26, 27, 28, 21”. I find it very interesting that she keeps on going back to 21, so I tried to show her that when looking at the numbers, this sequence did not make sense. However, when I attempted to explain to her how the number line works and that nine is bigger than 1 or 8 is bigger than 1, she was very confused by this. I realized that the student was not yet able to recognize the number symbols. I think the best way to get past this mistake of saying 21 instead of 28 or 29 is for the student to first learn the number symbols so she can draw from the order of the numbers 1-9 and apply the orders to numbers 21-29 (showing that the second number follows the same pattern that 1-9 does).
Trying to strengthen and improve her number symbol recognition, I had the student using the “Count Sort” app and playing the “Counting” game. This game gives the student a certain number of chips, which she has to count and then choose the correct answer from one of the two numbers given. I found, however, that this game confused the student even more because she was still not able to tell the difference between the two numbers or what amount they stood for. In need of something more concrete, I came up with a different game for the student to try. I took a scratch piece of paper and wrote down the number line from 1-9 at the top of the paper. Then, I took those numbers (1-9) and placed them around the page. The student’s job was to point to one of the numbers scattered around the page and orally identify what number it was. When she said the right answer, she was able to circle the number. If she did not know what the number was and started guessing, I would have her go up to the number line and count each of the numbers out loud starting from 1 (and going towards 9). When she was hit the number she was stumped on, she would realize that it was the number she just said out loud. She was then able to go back down to the randomized numbers, identify the number she was just stumped on, and circle it with confidence.
I then decided to make a variation of this game, which allowed the student to choose, write down, and randomize the numbers themselves. At first I had the student writing down the numbers without the presence of the number line, until I realized that the student was only using the numbers she was most familiar with (1-5). To make sure the student was including numbers beyond 5, I added the number line once again at the top of the page. In response to my addition of the number line, the student added the numbers that were greater than 5, although I think it is important to note that 1-5 were still more prevalent. It was then my turn to do the identifying and circling of the numbers. Before I started, I warned the student that I would be trying to trick her at some points and that she would have to correct my mistakes.
We then flip-flopped one more time to play the game where I was randomizing the numbers and she was identifying the number symbols orally and circling them. During this time, my student was able to recognize 9, which she was not able to do previously! I was so excited I nearly jumped out of my seat! As a follow up question, I asked the student why she knew that this number was the number 9. She responded that she knew that it was the number 9 because she had written it the game before (where she was the one randomizing the game and I was the circle-er).
Because this game was such a hit with this student, I am looking forward to trying it with the students that struggle with both counting past 10 and number recognition. Hopefully this will help them also move forward in counting orally and in other number sense skills as well!

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How does word choice affect students answers in math?

This week in Number Sense Morgan and I started investigating what students can do and what the students still need to work on. We investigated this idea further, by wondering how students are looking at numbers, patterns, greater or less, etc.

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More/Less vs. How many more

This week one of the math skills our cooperating teachers was having the students work on is the concept of one more and one less. Almost all of our students are able to answer quickly and correctly when asked questions such as, “What is one more than 5?” or “What is two less than 8?” Since this concept was proving to be simple for the majority of our group of students, we decided to make the more or less questions a bit harder. However, what we thought was a little harder was actually very difficult for the students to comprehend. Using marbles as manipulatives, we asked the students, “How many more marbles do you have than me?” I had set two piles, one for the student and one for myself on the table. The student would look at the piles, count each and then state the amount of marbles that were in the largest pile. The students had troubles grasping the concept of “How many more”.

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Week 7 Experience

This week we spent a lot of time working with our students who are still struggling with our initial number sense concepts. We have a couple of students who are still only able to count to 10. When it comes to 11-20, they get confused and will mix the numbers up or skip them all together. We counted with them several times a day to help get the idea in their head. We tried having them play Line ‘Em Up on the iPads. We noticed that at hey were not able to complete the task unless they were guessing which numbers went where. When we asked them what number they were placing, they only knew the correct number if it was less than 7. When it came to the higher numbers, they didn’t recognize the number. Several of the students were not able to start the game unless 1 was placed for them already. They would also have to recount the entire sequence before they knew what number was supposed to come next. We have started using a tracing app with them to help them learn to recognize the numbers as well as how to write them.

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Small Victories!

This week, I had a very successful couple of days with a student who I have been struggling to connect with. This student has been struggling with several aspects of number sense. I have realized in past weeks of working with her that she functions best in a game-like setting. My goal this week was to present the skills we were working on like a game. First, we started with identifying and drawing shapes. In the past we were not able to move on from square, circle, and triangle. This week, however, instead of drawing the shape and asking the student to identify it I gave both myself and the student a whiteboard and decided to see if the student could “stump” me. I would ask the student to think of a shape and say the name and we would both then draw it. If the student named and drew the correct shape then they got a point but if they drew the wrong shape I would get a point. This student became excited at the concept of competing with me and really engaged! We were able to correctly identify circle, square, triangle, cube, rectangle, cone, and diamond! I then decided to see assess the student’s understanding of shapes a little more and I drew out all of the shapes they have discussed in class and asked the student to identify each. The student correctly identified every shape except for sphere and trapezoid!
I also worked on different addition number sentences with some of the students who need extra enrichment. One of the students I work with has been developing her understanding of x+y=? for the past few weeks. This week I decided to begin introducing x+?=y to her. At first she did not understand what they word problems were asking her and required some modeling. However, after modeling the approach to these addition equations she began to understand. The most exciting part of our time together was after a few problems she stopped using manipulatives. When I asked her how she was answering these questions correctly she said: “Oh it’s easy, you just count up from the first number until you get the second number.
It has been really exciting for me to see the student’s progress as the year continues. It especially insightful to hear their own rationale behind why they do things; it definitely allows me to open my mind up and see things in a different way!

Ch-Ch-Ch-Changes

After our nice, long, relaxing break it was great to be reunited with Mrs. Peterson’s kindergartners; I was almost excited to see them as they were to see me! :) Our overall focus for this week was to do more with Randy’s different apps by incorporating them into our lessons. The 11 apps were split between Markay and I (6) and Courtney and Morgan (5). We decided to work on “Line ‘Em Up”, “Count Sort”, “Pattern Sets”, “What’s Hiding”, “Add Sub 5-1”, and “Number Line Math”.
While working with the students this week we have realized that some changes could be made to improve the apps. For instance, Markaye and I chose to work with the more advanced group by using the “Line ‘Em Up” app so that we could further test the number sequence even when the numbers did not start from a certain spot. (The settings on the app allow for variation in number of tiles and range of letters). I found that most of the students I worked with hardly made any mistakes on the number sequence even when it did not start from one. Knowing that we tested our more advanced group on counting by 10s and 5s, I think it would be beneficial to have this option on the app. This way the students would be challenged when they have excelled at putting the numbers in order. I think this change could also be beneficial to our students that have trouble mixing up which “10” goes before the other. More than one student of mine have issues on this topic. For example, many of my students want to mix 40 and 50 up even though they can count the rest of the numbers perfectly. To expand from this idea, I think it would positively influence the student’s learning if there was a speaker option that would read the number for the students before they put the number in the correct place. This would help the student make a greater association between its name, what it looks like, and where it should be place in the number sequence.

Week 6 of Number Sense

Christmas break was wonderful. I got to spend time with my family and then I went to Jamaica and taught at the Alpha Boys School.Unfortunately, Christmas break is over and it is time to get back to work. My students were all really excited to see me and I was really excited to see them. On Friday my partner and I pulled out each of the students individually and had them count as high as they could so we could update their sticker chart. 2 of the students did really well and counted all the way to 100 without making any mistakes which they could not do previously. The next step for them will be to count to 100 by 10s. 5s. and 2s.  The other students, however, were a little out of practice. One of the girls who has counted to 79 before could not get passed 30. That was a common trend for the kindergartners we worked with not being able to count past 29. My partner and I asked Mrs. C. about it and she said that she wondered about that because the district said that they only need to have their number lines in their classrooms go up to 30, but then the students are supposed to be able to count up to 100 by the end of the year. I guess we will just have to work harder to get the students back up to speed. Really this is something that I will just have to get used to because when I become a teacher I will get students who have gone a whole summer without picking up a book.

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Recognizing the Number Amount in a Pattern

It was the first week back from Christmas break and I was so excited to see the students and begin working with all of them in math again. On Tuesday Morgan and I asked Mrs. Peterson if she had any specific goals in mind that we can work towards achieving when working with the students. She said that with the new quarter beginning, one of the new assessments has to do with incorporating dominos. Morgan and I decided to use the dominos on Tuesday as way of helping the students practice number recognition in a pattern. There are still a number of students who are not able to identify how many dots are being represented in the pattern unless they count the dots. We decided to work one on one with the students who were still struggling to look at a pattern and recognize the number. The activity I decided to do included the dominos. First the student and I would like at every pattern on the dominos (1-6) and see if they could first recognize how many dots are on the domino. The majority of the students that I worked with could recognize patterns with dots 1, 2, and 3, but any pattern after 3 dots students would count the dots on the dominos. This helped me see that the students still were unsure of number recognition when looking at patterns. After going through the patterns on the dominos. The student and I would line up the dominos with the ones that matched. Since there were two patterns on the dominos, students would match the first half of the pattern with a matching pattern and continue the process until all the dominos were in one straight line. The students and I said that they could only connect if the patterns matched. Every time the students would connect the dominos they had to say the number on the dots. During this process I asked the student, “why did you connect those two dominos?” The students would respond, “…because they have the same amount of dots and are matches.” Not all students used the dominos, because some students in the class are able to look at the pattern and recognize the numbers higher than 6 dots. For those students I used the IPad app, pattern sets. The students really liked this app and I am able to adjust the settings so that if students need more time to look at the pattern they are able to do so. The goal is for all students to be able to look at a pattern and be able to say how many dots are in the pattern without having to count the dots every single time. What I am currently seeing with the students is that they are scared of being wrong and second guess the answers and count the dots anyway. There are also times when students will count the dots on a pattern and when they get that same pattern again (two or three patterns latter) they do not recognize the pattern they just counted and recount the dots again. This happened multiple times with the students I was working with and I am wondering how can I get the students to recognize not only the pattern and amount of dots in the pattern, but also recognize the patterns they just worked with? I wonder, how do the students see the dot arrangement? For instance, when working with the pattern of 2 dots the students would not have to count the dots; they could easily recognize 2 as the amount being shown on the domino. However, when working with 4 dot patterns students would have to count the dots. They could not recognize the 2 dots on the left and the 2 dots on the right for a total of four. The students would always have to count the pattern when more than 3 dots were being shown. This brought me to the question how do students view the pattern and how can I continue working with the students, so that they are making progress at recognizing the amount of dots in the pattern. This will be something that I work towards with group of students who still need more guidance in pattern recognition.

After the Holiday Break

When I returned from the holiday break, I was curious to see whether the students I had been working with the past 5 weeks would retain the information. After working with the kindergarten students this past week, I discovered that the students not only remembered the content and skills previously taught, but also developed further levels of comprehension associated with number sense skills. This development can be seen in several students who I have worked with. One student had a difficult time including the number 13 during rote counting exercises. Before break, we worked together and discussed where the number 13 lies in the number line, what the number 13 means, and how to represent the number 13. The first day back from break, this student was able to count higher than before and included the number 13 as well. A few students who had difficulty recognizing shapes and defining shapes with the correct terminology were able to do so. Skills in rote counting and shape recognition have progressed since the holiday break. One skill that needed to be addressed this week was counting by tens. Many of the students I work with cannot count by tens and therefore cannot count very high during rote counting exercises. This week, I tried a different approach to counting by tens. Instead of iPad applications, I explained how to count by tens with a dry erase board. I told the students that if they can count to ten, they can count to anything because the pattern simply repeats. I wrote the numbers 1-10 on the dry erase board and then had the students count as high as they could for me by tens. For each “ten” said, I added a 0 to the corresponding first digit. Once a student was stuck, I explained the pattern of counting by tens through the process of adding a zero to the end of the first digit. The students caught on quickly and were able to count by tens after the end of this math session. The following session, we addressed rote counting development. I approached this skill the same way I approached counting by tens. Many students are stuck on numbers such as 29 and 39. I then reviewed that the pattern repeats. We reviewed what “ten” came next and then discussed that we simply repeat the pattern by counting how we count by ones (30, 31, 32, etc.). The students caught on quickly and were able to count to 100 with some assistance. I am hoping that these fundamental skills stuck with the students over the weekend and they will hopefully be able to count to 100 (or close to it) on their own. I am so proud of the progress the students are making after 5 short weeks and I cannot wait to see how they further develop the remaining of the school year! Hope everyone had a wonderful holiday :)