This week, the students made substantial progress. All of the students I work with can count to 100 by tens! Many of them can count to 100 with limited assistance, if any. It’s amazing to see the growth in such a short time period. This week, we worked on similiar skills seen in the sessions last week. The students worked on identifying shapes by drawing and defining the proper name of various solid and two-dimensional shapes. We also worked on solving subtraction problems. The students love the application entitled “Math Puppy”. They love solving the problems correctly to get a puppy on the board! We also worked on ten frames. Most of the students I work with can recognize that a full ten frame represents ten objects. However, some still need to count to be reassured. I’m hoping after a few more lessons with the ten frames, the remainder of the students can recognize that a full ten frame represents ten objects. We also worked on my research question. My partner and I are interested to see how kindergarten students view numbers. The students roll two dice and either draw the number of circles or select the appropriate number of colored tiles that matches the number on the dice. The students then inform me of how they see the number. One student today included subtraction within his ways of seeing a given number! The students also really enjoy this activity. I am interested to see if students who are struggling with seeing various ways a number can be created also struggle recognizing patterns. I have not collected enough data with this category yet to have a conclusive answer. We will just have to wait and see what next week has in store!
Because of the success we had with the Randomize-er game last week with one of our students, Markaye and I decided that we would use this method to assess all of our students on their number recognition. Working with each child on a one-to-one basis, we had the children counting orally as high as they could. We have developed a pattern with the children that every time we work with them we will start off by counting as high as they can from rote memorization. This helps to reinforce their counting and reminds them that this is a consistent activity, which means that they will have to either practice at home or continue practicing with us in order to move past their trouble spots. After this, we implemented the Randomize-er Game with the students.
Through using the randomize-er game (the same game I used and explained last week), we discovered that a handful of our students could easily recognize their numbers and by taking it a step further, they were also able to write most of the numbers (1-20) out. We also realized that a majority of the children we work with have grasped the concept of number recognition with the exception of only 3 students.
These particular students struggle with recognizing numbers 1-10 and consistently confuse 6, 8, and 9. What was interesting about this discovery was realizing that these three students were also the students that have a difficult time counting very high based on rote memorization. Number recognition and rote memorization (counting orally) seem like they have a link in the way the students perform based on their particular skill set.
Once the game was implemented, these three students showed significant progress! Despite our efforts to work through these difficulties previously through counting objects, using the Count Sort App on Counting, using the Okta’s Rescue App, and repetition through counting orally, we were never able to make such a significant breakthrough with these students until now!
One student was able to count up to 30, even though she had had problems with 27,28, and 29 by reverting back to 21 instead. Another student has begun to recognize the difference between 6, 8, and 9. Finally, our third student in the bunch was able to work on 1-5, which he was able to do nearly all five on his own with reservations on recognizing 4.
The randomize-er game has proved to be a very useful tool when helping students to grasp and recognize their number symbols. I am currently talking to Randy in hopes to make this game into an App game that students will be able to use and practice on their own. Hopefully other students will be able to benefit from the Randomize-er Game too, just like our kids have!
This week, the students have made such improvements! One of my students who had difficulties counting above thirty was able to count to sixty-four! I also had one student able to count by tens! I have been working on rote counting and counting by tens every week, so it is exciting to see some students who were really struggling with these number sense skills make improvements! This week, we worked on subtraction where the difference is unknown. I used an application entitled “Math Puppy” for this skill. The students really enjoyed it because when they answered a question correctly, a puppy appeared on the screen. Various problems appeared on the screen and the students were instructed to choose the correct answer from an arrangement of numbers on a board. The goal is for the students to make a bingo with the correct solutions. In order to solve the subtraction problems, I worked with the white boards. The students drew circles to represent the minuend. After this, the students matched the number of circles that represent the subtrahead to the minuend. The number of circles that did not have a match provided the students with the answer to the subtraction problem. By Thursday, the students had gotten much quicker and accurate. We also worked with teen numbers this week. We worked on writing and recognizing the numerals eleven through twenty as well as recognizing the numbers in a ten frame. By Thursday, two of my students could write the numerals on their own! With the knowledge from last week associated with the ten frame, the students were able to solve many of the teen numbers without counting the circles within the ten frames. A few students are still struggling with recognizing one ten as a single unit, but we will keep practicing!
I apologize for my entry from last week. I thought my entry submitted, but I see it has not! I will complete two separate entries tonight. Last week, I worked with the students on the concept of “one more than” and “one less than”. I discovered that many of the students I was working with were able to add one more to a given number without the use of visual aids or manipulatives. When it come to “one less than”, many students had a difficult time comprehending what “one less than” actually meant without the use of manipulatives. The improved progress with the skill “one less than” can be seen within the two day span. All of the students I worked with were able to recognize what “one less than” was without an explanation. Some still needed a visual to guide their individual thought processes, but were able to complete the task. The students also worked on ten frames. I recognized that many students needed to count the number of circles within a ten frame, even if it was full. I began asking the students how many circles are in a full ten frame as well as one row of a ten frame. All of the students were able to answer this question. Simply verbally addressing a major component of the ten frame allowed the students to solve the problems much faster. I even have two students who have moved on to working with ten frames within the twenties! The progress associated with number sense development is clearly visible!
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.