On Thursday students did the opposite activity as they had done the week prior. (The students who worked with ipad apps worked with the flash cards and the addition tube model and vise versa.) Last week, I worked with students from two particular groups that both used the ipad app Line It Up. They still confused numbers such as 8 and 9 and struggled to recognize teen numbers. Thursday, however, things began to click! I am not sure how or why it happened now, but it was remarkable to see. I had these students first state the number shown on the flashcard. I would then compare the number to another one on the table. Students would tell me if the new flashcard was bigger or smaller then the card pointed to on the table and then place it in line with the other flashcards. Together we made a “train” for numbers 1-10. Then I had students recognize the teen numbers and place them in a train below the first one they had created. After several were placed on the second train I asked the students if they noticed anything. I helped them see that fourteen for example was under the four. I would cover the one in fourteen and say “four and four they are the same.” I would uncover the one and say, “this number has a one in front so it cant be a four anymore.” Soon the students realized that the second row or train was much like the first row they had created but that they were teen numbers. Students were then able to place sixteen, eighteen, and other teen numbers under their corresponding single digit number and recognize it correctly. I think making these trains this way allowed them to visually see the relationship between the numbers.

After meeting with these two groups, I was confident that it was the hands on activity and materials that helped the students pick up this pattern and recognize all numbers one through twenty. I felt that maybe the flashcards and other manipulatives really did help students learn better than the ipad apps. But then I met with my next group. These students have already developed a slightly better understanding than the groups prior, but still confuse many teen numbers and have not yet picked up on the patterns for numbers nineteen and beyond. This week these students used the ipad app to recognize, compare, and order the numbers. I first warmed them up to the activity and got them familiar with the app by starting with numbers 1-10. This was clearly too easy for them. We then moved on to the teen numbers. Though they struggled at first, it was not long before they were recognizing and ordering numbers on their own. I wanted to be sure they understood all the teen numbers before moving on so I had them order the numbers several times. By their third time, they told me “this is so easy Miss. D!” So I challenged them with larger numbers. By the end of their session they were successfully recognizing and ordering numbers 20-35. I was amazed at their level of growth, but also their level of focus and motivation. These students are usually distracted during lessons and have trouble staying on task. However, on Thursday they were cooperative and engaged throughout the entire lesson.

We have one middle group that is beyond number recognition but is not quite ready for activities that are at the difficulty level of the students who meet with us once a week. Though they work on the same skill, they do so in a slightly modified way. On Thursday we continued working on comparing two numbers. However, this time we did not use a worksheet for this group, but rather an ipad app called Balance Math. I worked with one student who had used this app for the first time. After a few examples he was able to use the app on his own. He understood that he had to make the two sides equal in order for the scale to be balanced. At first I think he was randomly guessing different combinations until it was balanced. But as I questioned his moves he began understanding how and why he was balancing the scale correctly. Eventually he even said “this is easy peezy!” He enjoyed using the ipad and the opportunity to experiment and explore on his own.

Our final two groups, that meet with once a week, completed the same comparison worksheet that the other two groups had done in the week prior. Last week the students were asked to color in the circle that had the larger number. However, after administering the acuity assessment we discovered that these students should have learned or will learn this year the greater than, less than, and equal to sign. Thus, these students were first asked to color in the circle and then add in the appropriate sign. We explained two strategies to help the students, the alligator and dot method, (two dots are placed next to the larger number, while one is placed by the smaller number, the dots are then connected to make the sign.) There were also pictures of the signs placed on the bulletin board to help them. All students were able to make the correct sign, despite the little instruction they had been given!

This week Lisa and I also began researching for our project. We are excited for the lessons that are to come as we begin to dig deeper into our topic.

]]>

On Tuesday, we decided to change things up a bit. This was the first day that which we would be placing the students in the newly arranged groups (before break we re-arranged the groups based on their ESGI Assessments). Some students were simply moved around within the groups, while some students were placed into a group that we would be seeing both days a week, rather than only one, as we felt some students were not receiving the adequate amount of attention we deemed necessary. Tuesday served as somewhat of a trial run for both us and the students, as we made quite a few observations that will be beneficial for future lessons and research.

Julie and I organized Tuesday’s lesson in a way that would help us explore both the advantages and disadvantages of teaching Mathematics using technology versus hands-on manipulatives. When teaching the lesson, we alternated every other group, switching off between using an app on the iPad and printed flashcards. So, with the first group, we had the students identify the numbers on their flashcards (which were used previously before break) and then furthermore arrange them in a number “train”. The use of the flashcards allowed us to work on number recognition with those students who were still working to identify lower numbers, as well as number ordering. For the next group, we had them do essentially the same task, but rather by using the “Line It Up” iPad app. We then had the students who have already demonstrated mastery of number recognition (the remaining groups) work on comparing numbers. We gave the groups a worksheet where they were asked to circle the larger or bigger number. Additionally, they were given a sheet with ten-frames and counting chips in case they needed to use manipulatives to help with physically seeing the difference between two numbers.

This week, we also continued with our daily word problem booklets. Julie and I constructed an “Adding Tube” that would allow students to do a join-result unknown addition problem in a hands-on and interactive way. The students were asked to drop a designated number of marbles, based on the first addend, through one tube. Through the other tube, the students were asked to drop the next set of marbles, based on the second addend. The students then counted the total number of marbles that were dropped through the separate tubes. Half of the groups did an addition problem in this manner, while the other half of the groups used the Word Problem iPad app to compete an x+y=? word problem. We hope that each week we can use solving these word problems with both manipulatives and technology as a way to observe how our students’ are developing in terms of their number sense.

Julie and I are both excited and eager to focus our research in even more over the next few weeks. We’re hoping to integrate both technology and hands-on learning into the remainder of our upcoming lessons. On Thursday of this week, and again on Tuesday, we will be administering the McGraw Acuity test to each of our students. However, after we analyze those results, we hope to finalize our groups (we also have two new students!) and then continue on with our research.

]]>

This week was the first week we began working with our newly formed groups. There are four groups we meet with once a week and six groups we meet with twice a week. Of these six groups we feel there are three levels of understanding—two groups of students who hold a solid understanding for numbers 1-5, three groups that demonstrate an understanding for numbers 1-10, and one group of students who are understand but confuse numbers 1-20. Because of the large range of understanding Lisa and I have been differentiating our lessons for each group. However, this week we approached our lesson planning and delivery a bit differently with a new idea in mind. We have decided we will be planning two versions of the same lesson each week. For example, this week the six groups that meet with us two times a week practiced recognizing, comparing, and ordering numbers. Because our first two groups can only confidently recognize numbers 1-5 our focus was to help them expand their understanding for numbers 1-10. One group used flash cards while the other used Randy’s Line It Up ipad app. Both groups worked on developing the same skills just in slightly different ways. (The other three groups worked with either the flash cards or ipads as well, however their focus was on all numbers 1-20.) Next week the students will do the opposite of what they did on Tuesday. (If they used flash cards, next week they will use the Line It Up app) By planning our lessons this way students will get the opportunity to work with different materials. We also hope to compare how students worked with the different materials and use this information in answering questions for our research project.

One of the groups we see twice a week (the group that demonstrates the greatest understanding for numbers 1-20) was challenged to do the same activity as the students that meet with us once a week. All groups worked on comparing numbers, however our first group (the group we see two times a week) received a slightly less difficult worksheet. Students were given a worksheet with sets of two numbers ranging from 1-30 and were asked to color in the greater number. Almost all of the students completed this task quickly with little to no guidance, thus we feel we can introduce a new concept or skill next week.

All students, both in the groups we see once a week and the groups we see twice a week solved a word problem in their Daily Word Problem book. Half of the groups solved a problem using Randy’s app, Word Problems, while the other half used a contraption that Lisa and I created. (Students solved by dropping marbles down two different shoots and then adding the total number of marbles left in the container) Next week the students will do the opposite of what they did this week. (For the remainder of the year students will alternate using ipads and manipulatives to solve daily work problems) Again we hope we can collect data and record observations that may help us in answering our research question.

On Thursday we administered the Mathematics portion of the Acuity test for Mrs. Arnold’s class. (Tuesday will be spent testing Mrs. Carmack’s class) This test was slightly different from the ESGI assessment we had administered before break. This assessment had several questions that focused on addition and fact families. Many of the questions were difficult for our students, especially the ones we see two times a week. Though they struggled through the test, Lisa and I were able to collect more data about their existing knowledge, which will be helpful in future planning.

I am looking forward to meeting with the students next week and seeing if and how they react differently than they did to the materials they used on Tuesday!

]]>

Lisa and I discussed we would use this assessment and our own observations to regroup students based on their existing levels of understanding and ability. We have not yet covered everything that is included in the ESGI assessment- for example shapes, one to one counting, or comparing two numbers. Thus, I had to take this into consideration when I was grouping the students. Though, we had a good idea of how the students would be arranged I wanted to be sure I had enough evidence to support my claims. I reviewed all lessons and compared each student’s performance to their test scores, to ensure no student was placed in a group they should not be just because they had an exceptionally good or bad day when tested. After this analysis a few of my initial placements did change. Lisa will too analyze the results sometime before next week and make her own groups. We will then collaborate and compare groupings to arrange our new groups. Majority of the groups I made have four students, which would allow Lisa to work with two students while I work with the other two. However, I did assemble two groups with only two students. These students have not yet demonstrated an adequate level of understanding and abilities compared to that of their peers. Thus, by arranging these groups this way Lisa and I will be able to work with these students one on one, which would ensure they are getting the assistance and attention they need.

In the lessons thus far we have been working with students in their groups. Though I have arranged the students in groups with a similar intention in mind, we came up with a new idea based on their individual ESGI assessment results. I discussed with Lisa and we both feel the students would benefit most if these groups fluctuated based on the concept being introduced. For example, students who consistently recognize only numbers 1-10 correctly were grouped together. However, I found that some of these students demonstrate understanding for a concept, for example recognizing shapes, which others do not. Thus, we will group students differently based on their existing understanding and the concept or skill being covered. We believe this will help us differentiate our lessons more effectively and accommodate to our students’ needs.

In our meeting this week Lisa and I shared an idea we had for our final research project. At the end of each week we discuss different ideas we may consider the focus of our research project. However, we both seem to be coming back to the same idea. We hope to analyze and compare student learning when they use manipulatives vs using ipad apps. We plan to first introduce a lesson with materials and then use the apps to reinforce it and then do the opposite (introduce a concept with apps and then transition in more hands on materials) We may also approach this idea in other ways as well, for example some students always use materials while others always use apps. This is a topic we have become very interested in and are excited to see where our findings may take us down the road if we choose to pursue it.

]]>

The current groups were created before the school year started; Dr. Egan administered the ESGI Assessment to each student and created the groups based on their scores. Due to the change in skill sets, as well as the unpredictability of our Kindergarteners, Julie and I feel that we need to do some re-grouping of our students. We plan to analyze the latest results of the ESGI Assessment, as well as the notes from our own observations, to determine the most effective way to re-group our students. Additionally, after we create these new groups, we plan on meeting with the Kindergarten teachers to ask for their input.

For every session thus far, we have consistently kept students in the same groups, regardless of the skill being practiced. However, after administering the ESGI Assessment, we realized that many of our students have strengths in one area, yet still need additional practice in another area. For example, one student may be struggling to recognize numbers, but excel in recognizing shapes. Where as another student may be struggling to recognize shapes, but excel in recognizing numbers. Thus, Julie and I stumbled across the idea of changing the groups daily, depending on the activity we have planned.

Through administering the ESGI Assessment, Julie and I were able to practice administering assessments, and also learn a lot about our students’ current sets of skills. We are eager to change things up, and re-group our students in hopes of providing them with the most beneficial learning experience. We have even started brainstorming ideas about a potential research topic for the remainder of the year. Wish us luck that these new groups work out, and stayed tuned to hear how it goes!

]]>

Throughout this flashcard activity, Julie and I observed a few concerning problems with the current grouping of students. Some students within the same group struggled to recognize numbers one through five; whereas other students in the same group clearly demonstrated their ability to recognize numbers one through twenty. Many of these same students also demonstrated their knowledge of the patterns for numbers in the twenties.

Our concerns were further solidified on Thursday, where we did a shaving cream number recognition activity with the same students. We carefully spread shaving cream on the table and asked the students to write numbers in the shaving cream using their hands. While this activity challenged the students to write the numerical symbol for numbers one through twenty, it allowed Julie and I to observe what the students individually know about number sense. Again, we noticed that some students within a group struggled with recognize lower numbers under ten, while other students clearly demonstrated their ability to recognize numbers one through twenty. Many students even went above and beyond our expectations, identifying numbers in the twenties, thirties, and even up in the hundreds!

Julie and I both felt that the shaving cream activity was an excellent learning experience for both the students and us. We both agreed that this hands-on activity allowed for a more meaningful learning experience for the students, as many students showed significant gains by the end of the activity. Furthermore, working with the students one-on-one allowed for us to closely observe what the students know about number sense at this time, and what they still need additional practice with. Next week, Mrs. Arnold and Mrs. Carmack have asked us to administer the ESGI Assessment to all of the Kindergarten students. We’re hoping that through this assessment, we will gain an even better sense of how to re-arrange the students into groups that will be most beneficial for their learning.

]]>

Prior to Tuesday’s lesson Lisa and I created a set of flash cards for each student. We felt by giving them something they could call their own they would have more interest in the activity. We also discussed the possibility of sending flash cards home with students to practice on their own later down the road. Lisa and I split up the groups and each worked with two-three students at a time. We separated numbers they had recognized from ones they had not. After showing all cards, Lisa and I showed the numbers they had missed a second and third time. Though we worked with different students, we noted similar observations. It was clear that some students could confidently recognize all numbers 1-20 with little hesitation, while others could only successfully recognize numbers 1-5 consistently. Working with flash cards and repeatedly practicing number recognition helped a lot of students begin to identify the pattern of the teens numbers. Their responses changed from “a three and a one” to “a one and a three, three teen, wait no thirteen!” It was great to see such excitement and joy as students began finding more success.

Lisa and I acknowledged that our students’ understanding for number sense and ability to recognize numbers has grown. However, we did not feel comfortable enough to move on to a new concept or skill. On Thursday instead of asking students to recognize numbers that were presented to them, they were challenged to write the numbers on their own. Each student sat at a table with a mound of shaving cream in front of him or her. Lisa and I feared the shaving cream would cause distractions and the students would become more interested in playing than doing the work. However, the students did what they were asked and the lesson ran smoothly. The students were each orally stated a different number and were asked to write the number in their shaving cream pile. They then smeared that number and wrote the next. We thought this would be a fun way to engage the students in the lesson. The students seemed to really enjoy the activity and began noticing patterns and expanding the understanding they had demonstrated during Tuesday’s lessons.

Students that meet with us once a week have already demonstrated that they can successfully recognize numbers 1-20, thus we instead challenged them to identify the missing number in a sequence of numbers. Each student was given a worksheet with gingerbread men and sequences of numbers. They were asked to fill in the number missing on the unlabeled gingerbread man. Majority of the students completed this task easily on their own. There were a few students, however, that needed a little guidance. Though we talked these students through it, they were able to correct their mistakes on their own. We feel this task might have been almost too easy and now know we can push these students further.

Our observations from this week highlighted the fact that many students are placed in groups that they should no longer be in. We have several groups where one student can recognize all numbers, while another student in that same group can only successfully recognize numbers 1-5. Next week we will be helping Ms. Arnold and Ms. Carmack assess their students using the ESGI assessment. We will use this data and our own observation to more accurately group students based on their current level of understanding. This regrouping will allow Lisa and I to plan lessons based on students’ current levels of understanding and their individual needs.

]]>

Julie and I began this activity by tracing each student’s hands on a piece of paper and cutting them out. While the students were waiting for their own hands to be cut, we allowed them to color their traced hands to minimize distractions. Once we assisted the students with tracing, cutting, coloring, and gluing their hands onto a larger piece of paper, we then began practicing mathematical skills with our students.

Mrs. Arnold and Mrs. Carmack had asked us to first begin the activity by asking the students to count all the fingers on their turkey hands. All the students were successful in doing so; some students were even able to tell us that they had ten fingers without counting each finger! After the students completed this task, we were to ask each student to individually create an addition and subtraction problem. The first students that we pulled into the hallway significantly struggled with this task. Some of the students were able to utilize the fingers on the turkey to determine the answer to a problem that we provided them with, but few students were able to actually create their own problem. Some students did, however, begin to show improvements with their addition and subtraction skills after practicing multiple equations, especially when using the fingers to assist them in adding or subtracting.

The students who, at this point, had demonstrated a better understanding of addition and subtraction, excelled at this activity. Many of the students did not even need to use the fingers to assist them in solving the addition and subtraction problems. However, some of the students found it to be more useful and accurate when doing so. I noticed that two students in the last group, “M” and “J”, really shined when creating addition and subtraction problems. These two students not only were able to create addition and subtraction problems within the ten fingers provided, but they used extremely high numbers to orally tell me problems. For example, one of the students shouted “200 plus 200 equals 400” and “400 plus 400 equals 800”! This goes to show that these particular students have a much deeper understanding of addition and subtraction compared to the rest of their peers.

Even though we were only able to work with the students for one day this week, Julie and I both thoroughly enjoyed this activity. Because of the time reduction, we had to work with larger groups of students than we were used to. While it was difficult at times to manage such large groups of students, we feel that it was a great learning experience for both us and the students. The students were able to practice their counting, addition, and subtraction skills in a fun and exciting way that incorporated the festive holiday theme.

]]>

To begin the activity Lisa and I first traced our students’ hands on half sheets of paper. As students decorated their traced hands to look like turkeys, we helped others cut them out. The hands were then glued near the top of another piece of construction paper just high enough for the fingers to extend past the page. This placement would allow the student to use the fingers on their cutout hands to count and solve addition and subtraction problems.

Each student was first asked to count the total number of fingers. We observed some students demonstrate one to one counting skills by folding each finger over after he or she had orally assigned it a number. We also noticed some students respond “ten” without having to count up the fingers. Though they took somewhat different approaches, each student was able to count to ten easily. Some students continued to count beyond ten, which indicated they have mastered an oral sequence for a larger range of numbers. Next they were asked to make an addition sentence. Students that have showed signs of struggle in the past were able to answer our questions, for example 2+3=? “5” However, they were unable to create an addition sentence or equation on their own. Some of these students were then challenged to solve or create a subtraction problem, but they were also unsuccessfully.

Towards the end of the lesson we met with all of the students we usually see once a week. They too created the same craft and were asked the same questions. However, Lisa and I saw something different. These students were easily able to make their own addition sentences or equations. They did not need an example from us and many did not need to use the turkey craft or the fingers as a tool for assistance. As soon as one student said one equation, another would excitedly blurt out another. It was amazing to see how much these groups already knew and how excited they were to show off for Lisa and I. We did, however, see some students struggle with creating subtraction problems. Many were able to solve equations given from Lisa or myself, but they were unable to make their own. At this time we also noticed more students using their turkeys for assistance. Some of the students also seemed to be confused when we said the word “minus,” instead they preferred to use the words “take away”- as in “5 take a away 2 is 3.”

Overall, I thought this was a great learning experience for our students. They were activity engaged in their learning process, enjoyed creating the project and talking all about what they were doing and eating for Thanksgiving. This was also a good learning experience for Lisa and I. We learned to better manage our time as well as a larger group of students.

]]>

Because we had only met with four students prior to our teaching, we wanted to get a better idea of the students’ existing level of understanding. Based on our teaching and observations made during our experiences with our students (a group of students that will be seen two times a week) in EDUC 360, we knew we would need to continue focusing on number recognition. These four students struggled recognizing numbers beyond ten. Thus, we thought number recognition for all numbers 1-20 would be an appropriate skill to assess for all students. We decided to play a Bingo game that would provide evidence of which numbers 1-20 students were able to recognize. We found the students who have in the past showed greater signs of struggle with number recognition were unable to successfully recognize numbers beyond ten. On the other hand, students that performed better on the ESGI assessment had no problem recognize all numbers. Thus, we found that this activity or game was too easy for these students.

After our first lesson we knew most of our students had not yet mastered number recognition for numbers 10-20. Thus, we knew this would be a skill we would need to focus on again in our following lesson. Students each took turns rolling two large die. Each face of the die was labeled with a number 10-20. Students were asked to orally state the number they had rolled. They were then asked to find the symbolic number on their worksheet. (each symbolic number was written inside of a falling snowflake) Once students had again identified the number they had rolled they were asked to color the snowflake in. After reviewing our notes and observation collected throughout the lesson, Lisa and I recognized common trends of misconception. Some students, who have a partial understanding, demonstrated a misunderstanding for the tens place value. For example, these students would state the number 13 as 23 or 15 as 25. We also noticed some students beginning to pickup on the pattern of the teens numbers. It was easier for them to recognize sixteen for example because they recognized the six and knew they just needed to say six and add the word teen. However, when they came across numbers such as twelve or thirteen, they orally stated these numbers were two teen and three teen. Other students, however, demonstrated no understanding for these numbers and simply guessed until they had said the correct number. Thus, it is clear we must continue focusing on number recognition for numbers 10-20.

Based on our observations from our previous lesson, Lisa and I knew we needed to plan a more challenging activity for the students we only met with once a week. We took a worksheet out of the activity packet that was given to us by Ms. Carmack and Ms. Arnold during our first meeting. Together Lisa and I created a mini booklet that focused on creating ten frames. The students were first to identify the number on the page. For example, they would orally state 15 when asked. Students would then put a dot in fifteen individual boxes. Lastly, students were asked to fill in the missing part of a sentence. The sentence stated: 15 is one group of ten and ____ ones left over. In this case the students would write the number five on the line. In the beginning of the activity we noticed the students were counting the dots. Once the students had counted to ten they would count the remaining dots starting at one. However, after the first few pages students began to recognize patterns in the ten frames and no longer had to count the dots. After reviewing our observations and reflection on our lesson, we feel these students have a adequate understanding of ten frames and are comfortable moving forward with this group.

Though we have found that we will mostly likely need to continue creating different activities and two lessons based on the needs and existing skills of our students, we felt it was important for them to have similar experiences each time they met with us. In our initial meeting Ms. Arnold and Ms. Carmack requested that Lisa and I help the students solve a word problem using specific problem solving strategies each time we meet with them. We found this to be a great opportunity to establish a level of continuity. Each student will solve his or her daily word problem on a half sheet of paper. These half sheets will then be assembled into a book. Students will use extra time to decorate their book and make it their own. We felt creating individual books would excite the students and give them something to recognize their immense progress and keep at the end of the year. Because the students were creating the same booklet with the same word problems, Lisa and I knew we would need to differential our instruction. We decided students we meet with on a weekly basis will be asked to solve their problem first on their own. After an appropriate amount of time, we would then assist them in reaching the correct answer. Allowing them to solve the problem on their own will provide us with evidence of their understanding as well as allow us to better understand their train of thought or way of thinking through the problem. We are excited to give our students their books next week and explain how it will continue to get bigger as the year progresses. Lisa and I are also looking forward to evaluating students’ individual work in solving these word problems as we feel this may potentially be something we further explore and research later in the year.

]]>