Our first group of students continued to work on skills such as number recognition and number sequencing. On Tuesday of this week, we provided the students with a set of flashcards. The flashcards, containing numbers 11-20, were spread out in front of the students. They were then asked to locate a specific number that we stated. Once they were able to identify the symbolic number that was said, the students were then asked to sequence the number in a number line. Our focus student in this group had a difficult time recognizing many of the teen numbers (13, 15, 18, 19). This student had demonstrated that he has not yet grasped the concept for many of the numbers. For example, he picked up the number “13” and read it as “twenty-three”. As noted in prior observations, this student still continues to struggle with orally counting as well. When asked to count, this student consistently skips over the number 15. I asked this student to read the numbers on the card as I pointed to them in order, but he again skipped over the number 15 when counting; this student said 16 even when pointing to the flashcard containing the symbolic number 15. On Thursday, we had the students explore and practice number recognition and number sequencing through the Number ID app. The students showed similar struggles when using this app. Though the app did not ask students to sequence the numbers in order, many of the students still had a difficult time identifying the numbers. Julie and I encouraged students to utilize the number line at the top of the screen to assist them in identifying numbers. Our focus student, however, was unable to utilize this tool because he could not correctly count to twenty. Therefore, this student in particular showed signs of frustration and began randomly guessing numbers when using the app.

Our “second level” of students continues to work on skills such as representing numbers. We attempted to use a manipulative that we had not used yet with the students – base ten blocks. Julie and I have recently come to realize through our research paper and experience in the Number Sense Program that students need an adequate amount of time to explore a manipulative or iPad App before being expected to accurately utilize the tool to demonstrate their understanding. Therefore, we allowed used the base ten blocks with this group of students on both Tuesday and Thursday of this week. During both days of this lesson, I worked with a student who we have been working with regularly and also a new student who we are currently trying to place in a group based on his current skills and abilities. These two students demonstrated an extremely different understanding for base ten blocks. To begin, we drew a number on the white board and ask the students to represent the number using the base ten blocks. (I began with an easy number such as 5, so the students simply had to drag 5 units out). I then wrote the number ten and asked both students to represent this number with the blocks. Both students dragged out ten of the small unit blocks. I then asked the students to place their ten cubes in a line and set a long next to the set of the ten blocks. I showed students how when using base ten blocks, we can use the longs to represent a group of ten. The new student grasped the concept right away for how to represent numbers in the teens, and even beyond. At first, this student wasn’t sure of how to make numbers beyond twenty. However, I prompted him to think about how he could use both units and longs to represent these numbers; soon enough this student grasped the concept and was able to represent numbers all the way up to 100! The other student in the group, however, struggled with base ten blocks on both Tuesday and Thursday. She struggled to grasp the concept that one long is equivalent to ten units. This student consistently dragged out single units, rather than using one long to represent numbers that was greater than ten. This student struggled to recognize many of the numbers being written on the whiteboard. Thus, this student may have had a difficult time grasping the concept for how to represent a number if she is still having difficulties recognizing what the number looks like. Next week, Julie and I plan to allow the students to explore the same concept. This time, however, the students will be using base ten blocks on an iPad App. I am interested to see if there will be any changes or similarities in the students’ ability to represent numbers using base ten next week when the students are asked to use technology.

The students in our “level three” group continued to work on problem solving skills, specifically addition. On Tuesday, the students were presented with an addition equation using their flashcards and a pile of connecting cubes. The students were asked to use the cubes to assist them in solving the addition equation. Though the cubes were slightly distracting for the students at first as they wanted to play, both of the students were successful in solving the equations presented to them. On Thursday, the students were asked to complete a similar task. This time, however, the students were asked to use the Add Sub app on the ipad. The students were again presented with an addition problem and asked to utilize the color changing chips on the screen to help them solve the problems. Again, both students were able to successfully solve all problems presented to them. I did notice an interesting difference in problem solving strategies between the two students I was working with, however. Our focus student of the group demonstrated that he has not yet developed the ability to subtilize a group of objects, as he counted each chip in both addends of the problem. The other student I was working with, however, demonstrated his ability to subtilize by counting on from the first addend, rather than counting the first “x” number of chips. For example, if the problem was “6+4” the first student would solve the problem by counting “1 2 3 4 5 6 7 8 9 10,” where as the second student would solve the problem by saying “6, 7, 8, 9, 10”. Regardless of the problem solving strategy the students used, however, Julie and I both feel that these students are ready to move onto more advanced concepts and skills, such as subtraction.

As Julie and I continue to collect evidence of our focus students’ understanding and growth, we are excited to finish the last portion of our research paper. We have re-administered the ESGI Assessment to our focus students and now have three sets of data – a set of data from the fall, one from the middle of the year, and a set of data from the end of the year. Julie and I are both excited to analyze and compare the data and determine exactly how much our students have grown over the year!

]]>

This week our “level one” students continued to work on recognizing and ordering numbers. On Tuesday the students used their flashcards to practice recognizing and sequencing numbers 11-20. The numbers were presented in a random order and together we worded to put them in numerical order. I noticed an obvious struggle for the students during this lesson. Two of the students are still unable to recognize number such as 15,18,19, 20. We continued to see similar trends in their behavior such as identifying 15 as 55, confusing 18 for 19 and vice versa, and naming 20 “twenty-zero.” The other student in this group could successful recognize these numbers; however, she was unable to sequence them. I modified the lesson and had her compare two numbers, rather than fill in missing spaces and she was still unsuccessful. I gave her the numbers 12 and 18 and she told me that 12 was more. On Thursday the students explored this concept through the use of the app *Number ID*. The students were again asked to identify a number 11-20. Because this app does not ask students to sequence we asked them questions such as, “is this number bigger or smaller than 15.” Students struggled to recognize the same numbers as they had in the previous lesson. To help students identify numbers they did not know, I encouraged them to use the app’s number line. I told them to count up starting at eleven and count until they got to the number they were working to identify. This strategy was not useful for either student because they were unable to accurately count to twenty. Every time the students counted they skipped 15 in their oral sequence. Thus, the students were always one number off. After reflecting on this lesson, Lisa and I feel we need to spend more time recognizing, comparing, and counting numbers beyond 10 with this group.

Our “level two” focus group experimented with base ten blocks this week. Lisa and I usually set up our lessons in a way that would allow the students to explore a concept or skill through the use of manipulatives in one lesson and the use of ipad apps in the second. Through writing our research paper, however, we have come to understand that students need multiple exposures to the same teaching tools before they are expected to demonstrate an understanding with them. I worked one-on-one with our focus student in both lessons. Because the students have already explored base ten blocks in their classrooms, he was able to confidently tell me that one unit equaled one and that one long equaled ten. I asked him to use the base ten blocks to represent the numbers I wrote on the white board. He could easily represent numbers 1-19 without much thought or hesitation at all. However, he grew very confused when I asked him to represent numbers greater than 19. When asked to show the number 24, for example, he would first grab two longs, pause, and then grab four more longs. He did not understand that he needed to use the units to represent the ones place as he had done with the teen numbers. On Thursday we continued practicing representing numbers 20-29 with base ten blocks. He developed a greater understanding and was successful early in the lesson. When I challenged him to represent numbers in the thirties, however, he again became very confused. Thus, I do not believe he has developed an adequate understanding for base ten at this point. Lisa and I are interested to see how this student will respond next week when he is again asked to explore base ten, but through the use of the ipad app *Math Tools*.

This week our “level three” students continued to work on addition strategies. On Tuesday they were given addition equations and connecting cubes. They were asked to first represent the two qualities and then count the total number of cubes to solve. On Thursday the students did a similar activity using the ipad app Add Sub. The students were again given an addition equation and squares, which were counted to solve. The students I worked with were very successful during both lesson. They used the cubes/squares for each problem, rather than their fingers when the sum was less than ten like they had done in previous lessons. They all said this activity was “easy peasy” so I challenged them with greater sums. The students were able to some these problems just as easily. Thus Lisa and I feel confident we can begin moving on to additional concepts, such as subtraction.

After working with our focus students Lisa and I met with all students we see every other week. We used this time to catch them up in the Daily Word Problem workbooks. Lisa and I both worked with students one-on-one until all missed problems were solved. This week Lisa and I also plan on finishing the last portion of our research paper. Much of this portion has to do with our focus students and the growth they have made throughout the Number Sense program. Lisa and I are very excited to analyze their scores and development over the course of the year.

]]>

This week our “level one” group continued to focus on number recognition and counting. On Tuesday, students were given a worksheet with a number followed by blank boxes. Students were asked to identify the number in the box and count forward as they filled the boxes in with its corresponding symbolic numbers. On Thursday, students were given a similar worksheet and were again asked to identify the starting number and fill in the remaining empty boxes. In this lesson, however, students were asked to count backward, rather than forward. We found that the students were able to easily count forward orally, but struggled to write the symbolic number in the boxes. They were unsure of how they were to be written and often asked us before first attempting on their own. I also noticed that several of the students would orally stated the number “6” for example, and instead of proceeding “6,7,8,9,10,11” the students would start from one and whisper to him or herself “1,2,3,4,5,6!” (speaking louder) “7,8,9,10,11.” Thursday proved to be a bit more difficult for the students. Though they were able to successfully recognize almost all of numbers presented they struggled to state even the one number that comes before it. Even when we counted along as we point to the hundreds chart, the students did not seem to understand they were counting backwards. One student in particular was able to complete the worksheet on her own after she was given many examples. However, I noticed that this student was counting forward from one each time to figure out the number that came before the number she identified last. For example when given the number 8 the student counted to 7 starting from one, then counting to 6, again starting from one and so on. Though this student developed this strategy on her own and developed somewhat of an understanding, we hope to challenge her in future lessons to count backwards without first counting forward. We plan on continuing to focus on both number recognition and counting in the following lessons.

“Level two” continued to work on representing numbers in multiple ways. On Tuesday, students explored a new app called “Make Another B.” This is actually an app Lisa and I help Randy and Mike created based off an idea we developed after an assessment we administered to our students. Students were told to represent a number using both sets of colors. For example, when students were given the number “6” students dragged 3 green shapes and 3 pink shapes and stated “3 green and 3 pink is 6”. They were then asked to represent the same number in a different way. (e.g. 4 green and 2 pink) The biggest struggle some of the students faced was coming up with a new way to represent the same number. Many students would show 6 as 4 green and 2 pink, but when asked to show another way to represent the number many created a chain of 4 pink and 2 green. Students were reversing the colors, rather than using new numbers. Though, they were also reminded not to make a pattern, many students resorted to this strategy as well. I also noticed that a few of the students struggled with this activity because they struggled with one to one counting. They could not accurately represent the number called with the movable pieces on the app because they kept miscounting them. With much guidance, students were able to eventually come up with two ways to represent the same number. On Thursday, students were involved in a similar activity but used connecting cubes to represent the numbers. They had already explored this teaching tool before, thus Lisa and I felt comfortable explaining how they were to be used and the purpose of the lesson before they began constructing their own understanding. During this lesson, none of the students attempted to represent the numbers by creating a pattern, instead they applied what they had learned from the lesson prior. Students were able to represent numbers in multiple ways more independently then they had on Tuesday. Though we did see similar trends on Thursday (the reversal of colors and miscounting) we do feel they demonstrated a greater understanding for the content.

This week “level three” continued to work on solving problem strategies. For the past several weeks these students have been solving equations using a variety of tools. They have used dominos, the *Domino Add* app, a home made Rekenrek, *Ten Bead Math* app, and several others. This week, however, we challenged these students to solve equations using a number line. On Tuesday, students explored the *Number Line Math* app. The students were presented with an equation and drew “humps” on the screen to solve. They students did great with this activity and demonstrated an adequate understanding for the content. I knew they had developed an understanding because they were able to solve these problems independently. On Thursday, the students again solved equations on a number line, however, in this lesson students were provided with a laminated number line and were asked to draw in the “humps” to show what they were adding and how they got their answer. The students turned to the number line for assistance in solving the problems. There was one student in particular who used his fingers to add, rather than the tools we had provided him with. This student had done this is previous lessons, however, this time something different happened. When the sum was greater than ten and the student had run out of figures to count he would usually tap them on his chin trying to keep track of them or ask to use our fingers; however, in this lesson rather than asking for help he picked up his marker and used the his number line to solve! I was very impressed that this student knew what to do when his personal strategy for solving was not the best. The students responded well to both teaching tools, however, Lisa and I are interested to see how students would responded if given these tools a second time.

Overall I thought this week was a great success. I was happy to again work with the students and see such growth in them over the past few weeks. Lisa and I really do feel we are helping these students develop a greater understanding and are excited to see where the remaining weeks will take us!

]]>

“Level one” or our first group continues to work on number recognition. However, Julie and I have decided that instead of doing repetitive number recognition activities such as flash cards, we want to challenge these students more and more each week. Through moving onto other concepts and skills, our hope is that they will continue practicing number recognition while still developing higher level thinking skills. Thus, on Tuesday, we provided each student in this group with a worksheet that would help them practice their counting on skills. The worksheet presented the students with a number and asked them to write in the remaining numerals in the number sequence. For example, if the students were presented with the symbolic number 5, the students would have to write in 6, 7, 8, 9, 10, etc. until all the boxes in the row were filled. The particular student that I worked with during this activity demonstrated excellent counting on abilities. When reflecting on activities done previously in the year, I can remember students having to begin counting at number one in order to “count on”. During this activity, however, the student was able to identify what number comes after (and even before!) the presented number immediately. On Thursday, we had the students complete a similar activity. This time, however, the students were asked to “count down” or “count backwards” from a given number. We provided the example of counting down like “3, 2, 1, 0, blast off!” Once the students had grasped the concept of how to count down, they did surprisingly well! I worked with our focus student in this group, and he was able to do the first few problems independently. Once presented with numbers in the teens, however, this student became very frustrated and confused. His frustration appeared to stem from the fact that he was unable to recognize the number “15” which he was asked to count down from. One “fault” of this activity, however, was that students had to write all the numerals. To save instructional time and minimize student frustration, I began having the students count as I recorded their answers in the boxes for them.

The students in our second group continue to work on representing numbers and number value. On Tuesday of this week, we had the students explore the “Make Another B” iPad App (Julie and I actually helped Randy and Mike develop this app in previous weeks by suggesting the content and layout of the app!) This app focuses on representing numbers in different ways. The students were given a number and asked to represent the number in two ways using colored chips. For example, if given the number “6”, students could represent it as “3+3”, “4+2”, “5+1” or even “6+0”. This is a concept that our students had demonstrated no understanding for when previously tested, hence our idea for the app! While many of the students tended to represent the number by creating two patterns (for example four orange and two green and then four green and two orange), I felt that this app decreased their tendency to do so. Because the area for them to drag the chips was an open space, rather than a formatted space, the chips were not necessarily placed in a row. This app seemed to greatly benefit the students understanding and I think it will prove to again be useful in upcoming lessons that focus on the same skill. On Thursday of this week, we again had the students represent a number in two ways. This time, however, we had the students complete the activity using connecting cubes. I immediately noticed the difference in time between using the app and using the connecting cubes; it took students a significant longer time to connect the cubes than drag the chips. Because the students took longer to handle and connect the blocks than it did to drag chips on the screen, it greatly limited the number of problems the students were able to do in the given time when using the manipulatives. Other than that, however, I did not observe any differences in student understanding or performance when they used the iPad App versus when they used the manipulatives.

The students in the third group continued to work on and develop their problem solving skills and abilities. On Tuesday, the students practiced their addition skills with the use of “Number Line Math” iPad app. The students were given an “x+y=?” addition problem and asked to solve the equation using the number line by first locating “x” and then making “y” humps on the line. On Thursday, the students practiced the same skill through the same activity. This time, however, the students were given a laminated number line and a dry erase marker. The students were asked to again solve “x+y=?” addition problems using the tangible materials. In both lessons, a handful of students demonstrated some confusion about how to use the number line to solve an equation. Because the students only had limited time to explore using both the app and the manipulative, I felt that the students were not adequately exposed to these materials. Though the students have seen number lines previously, they needed assistance and guidance in understanding how to utilize these materials to solve an addition problem. Up until this point, we have focused on solving addition problems through the use of manipulatives such as counting chips, or the shapes on the screen while using an app. When presented with a different problem solving strategy, however, the students appeared confused. I am interested to see if the students would react differently, or appear to be more comfortable or confident, if we again utilized the number line to solve addition problems at later time.

Julie and I have seen tremendous growth in all of our students over the past term and a half. We too, have made tremendous strides as teachers. We are excited and eager to see where the remaining weeks take our students and us as we conclude our research and work with our Kindergarten students in the Number Sense Program.

]]>

This week we continued to focus on number recognition, one-to-one counting, and oral counting with our first group. On Tuesday, the students in this group used counting chips and flashcards to demonstrate their current understanding of number sense. The students were given a pile of chips and asked to count them. The students were then presented with three flashcards, and asked to select the flashcard that showed the corresponding number. While working with these students, it became clear that they continued to struggle with identifying numbers such as 6, 9, 11, 12, and 13. Both of the students did, however, continue to demonstrate a basic understanding of the teen patterns, as they have in previous lessons. We noticed that during this lesson a student consistently counted “13, 14, 16, 17”, forgetting 15 each time he orally counted. To try and help this student recognize that he was forgetting 15, I pointed to a number on the 100’s chart on the wall and had him orally state the number. However, when I pointed to the number 15, he again went from 14 to 16. Julie and I have made note of his struggle to remember the 15 when counting, and it is something we plan to pay attention to in future lessons. On Thursday, the students practiced the same skill in a similar manner, but this time the students used the Count Sort App with the counting setting. The students were shown multiple dots on the screen and asked to count how many in all were on the screen. The students then were asked to select the corresponding number as listed on the screen. Again in this lesson, the students demonstrated similar struggles in identifying numbers 6, 9, 11, 12, and 13, as well as higher teen numbers. Thus, we did not notice a significant difference in the students’ performance when using the manipulative versus using the iPad Apps.

The next group of students we worked with focused on place value, specifically activities dealing with ten-frames. On Tuesday, the students completed a Ten Frame Booklet – an activity that we had done previously in the year with a group who has now moved onto higher-level skills. The students were given a book of ten frames, each page containing blank ten frames and a number in the teens. After identifying the number, the students were asked to make marks/dots in the ten frame boxes to represent the number shown on the page. Some of the students struggled to independently complete this activity, while others were able to correctly complete the booklet with little to no guidance. Some of the students who struggled were unable to identify the number, and others were unable to make the correct number of marks in the ten frames that corresponded with the symbolic number on that page. One student demonstrated a particular example of misunderstanding of place value. The sentence on the pages read “16 is ten ones and ___ more”. The students were to identify 16, make 16 marks, and write 6 in the blank. When asked “how many more”, however, this student responded with 4, meaning that four more boxes needed to be filled in on the second frame. On Thursday, the students practiced the same skill again by using the iPad App Count Sort with the ten-frame setting. The students were shown ten-frames that were partially filled in. The students were asked to determine how many dots were in the ten-frames and select the corresponding number on the sides. I felt that this App proved to be easier for some students to use; the students seemed to have an easier time in “reading” the ten-frame, rather than constructing the ten-frame on their own. Furthermore, by providing the students with the pre-filled ten-frame, it allowed them to work through more problems. However, many of the options listed for numbers beyond ten were number reversals. This proved to be very easy for the students, as they were able to easily distinguish between 51 and 15 before even counting the dots. Julie and I learned shortly after, however, that there is the option to present the students with more than two number choices, which would eliminate the reversal concern. Thus, in the future, Julie and I will be sure to explore all settings and options before using the iPad Apps with the students.

The final group that we worked with this week focused on addition skills. On Tuesday, the students worked with the Ten Bead Math iPad App. The students used this app as an aide to solve the given addition problems. On the screen, the students were shown a “row” containing five white beads and five red beads. The students could drag white beads to the center to represent one of the addends, and the red beads could represent the other. On Thursday, the students were again given a sheet of addition problems. This time, however, the students were given beads on a pipe cleaner to use as an aide. On both Tuesday and Thursday, the students did not seem to enjoy using the beads to help with the addition problems. Rather, many of the students preferred to use their fingers to do simple addition problems. Furthermore, many of the students had difficulties moving the beads both on the iPad screen and on the pipe cleaner, and thus became very frustrated. Overall, we did not note a big difference in the students’ abilities to solve the addition problems when using the pipe cleaners versus using the iPad apps. Rather, the students preferred to use a familiar method of counting, such as using their fingers.

Julie and I are extremely grateful for the experience of working with the Kindergarten students so far! We have seen tremendous progress in our students thus far, and we are excited to see how much more they will grow over these next ten weeks! We plan to continue doing research over our spring break, and brainstorm useful and creative lessons that we will be able to use when we return!

]]>

Our students at level 1 continued working on number recognition and oral counting. On Tuesday students were given a set of chips and were asked to count them. They were then shown three flashcards and asked to pick the card that represented the number of chips they had just counted. This activity allowed the students to practice both number recognition and one-to-one counting with hands-on materials. On Thursday the students work on the same skills by doing relatively the same activity. Using the ipad app, Count Sort (counting), students again counted the number of dots shown on the screen and chose the number they had just counted out. We did not find that one lesson was more successful than the other and do not believe the students prefer one tool to the other. After reflecting on both lessons we have found that the students can successful recognize most numbers 1-20, however there is till an obvious struggle to recognize numbers such as 9, 11, 12, and 13. Both students have picked up on the patterns of the teen numbers 15-19. One student in particular, went from saying a 1 and a 5, to five teen, and finally fifteen. Lisa and I understand that there is much more we need to do with the students at this level, but we are proud of their progress thus far. We also noticed that the students could only count accurately when they had separated the chips they had counted from the chips they had not. When students simply pointed at chips, some were forgotten or counted multiple times. Lastly, another observation we made was in their abilities to orally count. We have one student who can count pretty consistently, however the other has forgotten 15 every time he was asked to count past 14—even when the student was prompted or reminded it was forgotten.

This week the students at level 2 focused on ten frames. On Tuesday students completed the Ten Frame Booklet. They were given a teen number and were asked to represent that number using the ten frames. For example, students were given the number 16 and were asked to make 16 dots (one in each box of the ten frame). Most students understood that when the first ten frame was completely filled in that it meant 10. However when asked how many were left over most students said the teen number (in this case 16.) After many examples and much guidance majority of the students were able to complete the remainder of the booklet on their own. On Thursday students focused on this skill again by using the ipad app Count Sort (ten frame.) When using the ipad I found students were more prone to counting all the dots in the ten frames. Almost all the students I worked with could recognize numbers 1-7 using the ten frames. However, for numbers 8-20 they counted each dot one by one. I asked each student what the first ten frame represented and all students knew it was ten. I prompted them to count up from ten, rather than counting each individual dot but they were unable to pick up this concept unless asked. I personally did not find the Count Sort ten-frame app particularly useful for this lesson. I did not like that the options for numbers beyond ten were mostly reversals. For example, when 17 when shown in the ten-frame the students only options were 17 and 71. Many students knew to choose 17 without really even looking at the ten frames. I also did not like that many of the opinions were obvious. For example, 1 was shown in the ten frame and their options were 1 and 10. Thus, I do not think the app was appropriate to use for all of our students.

Lastly, the students in level 3 focused this week on addition. On Tuesday students were asked to solve addition problems using the Ten Bead Math App. I found that many students did not work well with this app. Many struggled moving the individual beads and grew uninterested quickly. We noticed similar behaviors on Thursday. Lisa and I gave each student a pipe cleaner with 20 beads on it, 10 white and 10 red. (just as they had used on the app) I noticed that the students did not use the stringed beads when the sum could be made using their fingers. Problems such as 3 +2 were all solved using their fingers or in their head. However, when students were given problems such as 9+4 they turned to their stringed beads for support, but they did not seem comfortable using them without our assistance.

Overall we thought this was a successful week, however we do not feel confident enough to move on to new skills. Thus, Lisa and I will continue to plan lessons based on these concepts and skills when we return. We plan to research more later this week and also over our Spring break. We hope to come back with new ideas and ready to make more progress towards our research paper.

]]>

This week, the group with our first focus student continued to work on number recognition, one-to-one counting, counting on and oral counting. On Tuesday, we had the students practice these skills using the Line Em Up iPad App. Our specific focus student, however, was unfortunately absent this day so we were unable to observe how the student performed when using technology to enhance these skills. The other student who was in class showed significant signs of struggle in recognizing numbers beyond 5, especially when the number line at the top was removed, as she used this as a support to count up to the number to help in identifying what number was being shown. On Thursday, we took a slightly different approach, and decided to introduce an activity that focused heavily on oral counting, while also enforcing number recognition. After reflecting on this activity, Julie and I noted something quite interesting. One student, who struggles immensely with number recognition, proved to have a better understanding of oral counting. Where as the other student in this group (our focus student) has proven to have a better understanding of number recognition, but struggles immensely with oral counting.

For the next four groups of students, we created a “How Many More?” worksheet where the students were asked to “match up” the cubes in two adjacent towers, and determine which tower has more cubes. The students then had to fill in a sentence that stated: “There are ___ more purple than green”. Most students in this group proved to do excellent on this worksheet, as many of them were able to correctly complete the worksheet with minimal to no assistance. The biggest struggle that I noted during this activity was the confusion over which way to place the “greater than” or “less than” sign when asked to compare two numbers; this is something that Julie and I have been continuously working on with the students. On Thursday, we also practiced this skill, this time using interlocking cubes. The students were given a worksheet with problems labeled ___ (CIRCLE) ___. With guidance, the students were asked to create two cube towers, and record how many cubes were in each tower on the blank lines. The students were then to determine which tower had more cubes, and place the corresponding “greater than” or “less than” sign in the circle. Again, every student I worked with demonstrated an excellent understanding of comparing numbers. Additionally, I was extremely impressed by some of the students’ and the understanding they demonstrated when I gave them more challenging problems. For example, I set a problem up where I created two equal sets of towers – some of the students were able to identify that the towers were the same and even know to put an equals sign between the two numbers!! Other students demonstrated an understanding of how to balance two of the towers, which is a skill that Julie and I hope to help the students master over the next weeks.

Our last group worked on addition using dominos this week. On Tuesday, we had the students use the “Domino Add” iPad app. All of the students in this group that I worked with demonstrated an excellent understanding of addition. When shown a domino on the screen, the students knew where to put the addends, and also that when combining the total of the two addends, it produced the sum of the equation. The students then did the same activity on Thursday, however this time using actual dominos. Again on Thursday, the students seemed to grasp the concept and were able to complete the activity on their own. Therefore, we did not see any drastic difference between using technology or manipulatives for this week’s lesson.

This week allowed for Julie and I to document a lot of interesting data and observations, which we feel will prove to be useful in our final research project. We plan to continue creating lessons that correlate with what Mrs. Carmack and Mrs. Arnold’s students are currently doing in the classroom.

]]>

This week our first group focused on both number recognition and oral counting. We choose to not focus on the same skill both days this week because we felt our students needed a break from number recognition. We also knew the oral counting sheet would allow us to still collect evidence of their number recognition skills. On Tuesday this group used the Line It Up! App. Only one member of this group was present but we noticed similar trends compared to her performance weeks prior. We noticed this students was still confusing numbers 7,8,9,10, 11. However, for the first time she began to demonstrate an understanding for the teen numbers! We noticed she used the one hundred chart (hung on the wall) to help identify and order numbers. We we believe this helped her catch on to the pattern of the teens. On Thursday we shifted our focus to oral counting. Each student was given the What Comes Next worksheet. First students needed to state the given number and then orally state the three numbers that followed. We hoped we would gain an understanding of their oral counting or counting on abilities. We continued to see these students struggle to recognize the same numbers in past lessons. However, we soon come to realize oral counting is a skill that needs attention as well. One particular student could not count past ten. When shown 11 he stated that 12, 18, 14, 16 followed. Thus, Lisa and I agreed this student must continue to work on this skill.

Four of our groups, or the student at our second level, worked on comparing numbers. Lisa and I created our own worksheet, How Many More?. The worksheet showed two towers of blocks. The students were asked to count the blocks in each stack and tell us which stack was greater. We also challenged them to write this out using the greater than, less than, and equal to sign. The students were also asked to write how many more were in one pile compared to the other. We found that the students could complete this worksheet easily with little to no help from us. One common mistake I came across, however, was that students were counting the amount that was the same in both stacks, rather than what was left over. Students with a stack of 5 and a stack of 3 would state that there were three more in five, instead of two. We soon realized the students were counting their “matches.” On Thursday we continued to focus on comparing and balancing. The students were asked to do the same thing they had done on Tuesday; however, they were not given a worksheet with drawn stacks of blocks. Instead students made their own stacks (their own problems) and solved the same way. The students performed just as well as they had on Tuesday. The students showed a greater interest and were glad to “play” with the blocks.

Our students who are performing in our level three range worked on problem solving skills. Next week the students will begin to work on their addition skills using dominos in their classrooms. On Tuesday students used the Domino Add App, while on Thursday they did the same activity but with actual dominos. Students were first asked to count the number of dots on one side and write it and then do the same for the other. Before students counted or added all the dots together they were asked to write out the equation. All of the students were able to do both activities easily and on their own. We saw no obvious difference between how they worked with the ipad vs. how they worked with the dominos.

Lastly, on Thursday we worked with half of the students who see us once every other week. These students worked on comparing and balancing numbers with the Math Balance Beam. I felt these students were extremely excited to use this tool and even more excited when they had made the scale balance. This activity was defiantly more successful with this group than the groups of students who had done it weeks prior. These students understood how the scale worked as well as what it represented. They were also able to balance the scale and come up with different fact families on their own.

Overall, I thought this was a successful week that provided Lisa and I with a lot of great evidence of learning. We will be continuing our research for the remainder of the week and are excited to see where things take us.

]]>

For our first group we continued working on number recognition. We still feel strongly that these students have not yet developed an understanding for numbers beyond ten. Because these students are so far behind when compared to their peers Lisa and I talked to Randy, Mike, and Ms. Carmack about altering the schedule. After we explained our reasoning and provided evidence everyone was on board and more time was allotted for these particular students as well as several other struggling groups. On Tuesday Lisa and I created “goo-bags,” which allowed the students to trace and recognize numbers in a fun and engaging way. The student I worked with seemed really into the lesson. She worked really hard and remained focus. On Thursday these students again focused on number recognition through the ipad app “Number Id.” After reflecting on both lessons we believe the students were more focused and demonstrated a greater understanding while working with the “goo-bags.” Though both of these students have demonstrated signs of improvement, we are not convinced they have mastered number recognition. One student still confuses 6,7,8,9 while the other is struggling with 11, 12, 13, 15. Thus, we will be continuing our efforts towards mastering number recognition next week.

We also continued to implement technology and hands-on learning into our lesson plans with our others groups as well. This week students who had moved beyond number recognition and comparing numbers were challenged to not only compare numbers using the greater than, less than, and equal signs but to balance them as well. On Tuesday these students used the app “Balance Math.” At the end of the day Lisa and I admitted this was not our best day. The students were unfocused, confused, and not interested in the app. Lisa and I grew even more frustrated as the students were simply guessing random weights or choosing colors that matched. We told the students to add numbers and also helped them by using our fingers and the counting chips, but no improvements were made. On Thursday these students worked on the same skill but instead used the Math Balance Beam. Walking into this lesson Lisa and I felt confident that this lesson had to run more smoothly than the last. However, this lesson seemed to cause just as many difficulties. The students had associated one 10g weight with one object. They were unable to understand that when one weight was placed on the number three it meant three or that when two weights were placed on the two it meant four and not one. We again used chips, separated them in piles and counted them, but the students still did not seem to understand the concept of balancing. After reflecting on our lesson and our observations we believe the problem was in our planning. We challenged the students to focus on multiple new concepts and skills at once, instead of introducing them one at a time. We ran into similar problems with our final groups. Our final groups completed a worksheet that focused on addition, comparison, as well as balancing numbers. The students were very confused with our directions and became bored quickly. Overall, Lisa and I agreed that this week’s lessons provided us evidence of understanding. It also served as a lesson to us, which will enhance our future planning. We now know we need to focus on one new skill at a time. We also must consider how complex our lessons and activities are as well as determine if they may be too advanced or complex for our students.

]]>

This week, Julie and I continued to implement both technology and hands-on leaning into our lesson plans, as this will serve as the basis for our research question. On Tuesday, we had the four groups – who have recently demonstrated mastery of number recognition and ordering – practice comparing and balancing numbers using the “Balance Math” App on the iPad. Many of the students had difficulties in figuring out how to use the app. Furthermore, it became slightly frustrating when many of the students were simply guessing how to balance the two sides of the scale based on the color of the weights, rather than applying what they know about addition and number comparison. Although this activity provided us with insight as to where our students are in terms of their number sense, we felt that the App did not provide much of a benefit for our students. One group that did show ample improvement, however, is the group of two students – E and J – that Julie and I have been continuously working with to master number recognition. On Tuesday we created “goo-bags” which allowed the students to trace numbers in the bags and identify them. While both of these students have shown that they still mix up numbers such as 6, 7, 8 and 9, it is clear the progress they have made and will continue to make over the next days.

On Thursday, we essentially worked on the same skills with the students, but we reversed the type of learning they were doing. So, the students who used the “goo-bags” to work on number recognition used the “Number ID” App. While neither of the students in this group have yet to demonstrate mastery of number recognition, it is a continual progression, and we are confident that our students will get there with additional practice. The students who used the Balance Math app on Tuesday, used the Math Balance Beam to work on comparing and balancing numbers. The skills tested in using this hands-on manipulative proved to be too advanced and complex for our students’ current level of understanding. When placing a 10g weight on a number on one side, say on a 4, the students were unable to grasp the concept that one weight dangling represented a 4, rather than 1 object as they observed. Even when using chips to help split the representation of 4 into two piles, the students were still left confused and frustrated.

Thus, for next week we have decided to take a step back. After discussing a plan of action, Julie and I decided that we do not want to challenge our students with an activity that requires multiple skills they have not yet mastered. Therefore, next week we plan to work on simply comparing numbers rather than comparing and balancing numbers at the same time. Especially as we have began to narrow down our research topic and observe progress and learning in our students, Julie and I are excited for what is to come over these next weeks.

]]>