This week we focused on number recognition with our students. We knew that four of our students had no problems recognizing the numbers 1-10, and were successful at much larger numbers as well. We also knew that these students were capable of writing the numbers 0-10 on their own with very little difficulty, and could successfully write the numbers 11-20 with only a few reversals. So, we decided to see what the rest of our students knew with regards to number recognition.
After two weeks of research, Courtney and I have continued to stick with our question about students’ knowledge about “more, less, and the same.” I continued with the activity I did before where I had the flash card sets for the students to make pairs of the number symbol and the equivalent amount of dots. However, when prompting the students this time, I asked the question “Do these mean more, less, or the same?” This is different because before I only prompted “More or less?” When giving the students the option to pick “the same” as an answer, the same students that chose the number symbol as more before, said they mean the same. Therefore this proves that children so understand the concept of equality in terms of number symbol and the dots. From here, I know that it is still an interesting concept that the students could not say that the two quantities mean “the same” unless they were given the option that they could say the same as an answer. This is something I want to keep exploring in different contexts.
Tuesday during number sense Morgan and I worked one on one with students improving their skills in number sense. We wanted the students to improve on number recognition and putting numbers in order without having to count 1, 2, 3, 4, 5… every time to find what the next is in the sequence. I used the app, Line ‘Em Up, and changed the setting so that rather than one tile showing up after the numbers were given a bunch of tiles were given at the bottom of the screen. Students had to decide which number would be next in the sequence and identify that number amongst other numbers.
When I was working with a student I started the number line at a number they were familiar with and use only ten tiles at first. After we did the number line once I challenged the students with larger number and increased the number line from 10 tiles to 15 tiles. Two of the students I worked with are still working on recognizing numbers 1-20. One of these students was able to put the numbers 1-10 in line (he did mix up the 6 and 9) but when I changed the number line 11-20 he did not recognize any of the numbers. I asked the student, “What number comes after 11?” I knew that this student was able to count to 16 so I expected him to know the answer. The student began counting from 1 until he could say …10, 11, 12; the answer is 12. The student did the same thing when we got to other numbers in the number line. This shows that the student still needs to work on counting on. This is a trend that I see in a lot of students. They will start counting at 1 if they do not know what comes next. The students will do the same thing when working with the domino patterns. If they know the pattern with 4 dots and then I show them a pattern with 5 dots the students do not count 4 dots, 5. They count 1, 2, 3, 4, 5 to get the answer needed.
Another thing that came up on Tuesday was the concept, “what number comes before and what number comes after?” At one time a student was given the number 8 with 7 and 9 missing (he needed to fill these numbers in). I asked the student, “what number comes before 8?” The student responded, “9”. I asked the student what number comes after 9 and they said 10. This was interesting to me, because they did not understand the distinction between before and after, but always knew the answer for after. I continued asking the same question to the rest of the students I worked with that day. All the students responded with the number that came after and never correctly told me the number that came before. I worked with each student to explain the concept of before and after then introduced the concept of a middle number. I would like to incorporate a number activity or begin using the app this coming week to review the before, after, middle concept to see if students can identify what numbers come before a specific number and what numbers come after.
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.
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!
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.
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”.
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.
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!
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.