Blog Post 2

After a week filled with illnesses, snow days, and half days, I have very little to report in the area of mathematics this week. The students did an activity through their literacy centers that required the use of dice to complete. The students had to roll a die and then the number they roled determined the sight word they wrote. By completing this task, the students showed they they were able to recognize the numbers 1-6 in defferent representations. Because of our lack of math this week, I also asked two children an extra question from the CGI textbook (in addition to the required interviews). The question was "10 Children were playing soccer. 6 were boys and the rest were girls. How many girls were there?" I was curious if the students would be able to attempt a math problem posed in this way. I was not allowed to take pictures of the students, only their work. Student A counted out 10 ten manipulatives and asked me to repeat the question. I did, and she said there were 6 girls too. This student's work shows me that she has the beginnings of the concept of subtraction--she knew to have 10 manipulatives (a whole to subtract a number from) but she wasn't sure of the procedure from there. The second student I asked, Student B, counted to ten on his fingers (silently--he put a new finger up each time, and mouthed the number the corresponded to each finger, but did not actually speak aloud). He then counted again (he nodded his head which showed he was counting, but he didn't move his fingers or speak out loud, so I'm not sure exactly what/how he was counting) and told me there was 2 girls on the team. This student showed me that understood some of the concept of subtraction--starting with a whole, taking some away--but needed practice/exposure to the concept of subtraction, the procedure, as well as more exposure to word problems.

Blog 2

I just got back from an all-day field trip with my students. Unfortunately, after a snow-day and then a full day of romping in the woods, there is little to report mathematically. Fortunately, I did have a conversation with one student last week that I will reflect on. I will make an effort to snap two photos for next week's blog!

One student is a fifth grader who hangs out with sixth graders. These three girls are all very motivated and excel at their school work. This fifth grader, whom I will call Darcy, is very timid and often follows the other girls example. When these girls get done with all their work, which always happens days before its due, they are encouraged to go online and seek out a new learning experience of their choosing. They usually choose art or language related subjects. So you can imagine my surprise when Darcy brought me a worksheet of algebra problems and asked me "to explain it real quick."

I did not know her background with algebra, but the problems were of the 2x-4=10  variety. When we began to go over it, I realized that she did not know a lot, but was very intrinsically motivated to begin. I wound up drafting problems that first dealt with subtracting from the right and left, and then made the reverse side a "challenge" side with problems that division and multiplication was necessary. Making up a worksheet gave me a lot of insight into how careful you have to be when sequencing math problems. After I showed her how to do some, I left her with it for the night. The next day, she came back with the entire sheet completed and begged for more. We did this for a few days, and I did not realize why she was so anxious until I saw her teaching her two friends how to do algebra!

She was incredibly proud of her newfound skill, and her intense dedication to learning how to do things  made me remember how proud I used to get when I knew things before my peers. It filled me with a sense of intelligence, capability, and leadership because I knew I could help my classmates. When students are able to learn things so well that they can turn around and teach others, it can result in a powerful ownership and pride of knowledge as well as an awesome network of highly specialized students.

This Montessori model of rewarding kids doing their work with freedom to choose more work seems like it would not be much of a motivation to learn, but many children have found interests and niches that they had never had before.

Math Buckets KW

Today my class worked with math buckets. My teacher explained to me that she had been trying to set these up all of last semester and finally was able to. She created a chart where the students are listed high, medium, and low in their math skills. The chart has pictures which represent the labeled drawer for the students math buckets. 

The students knew which bucket when she went through and pointed to the picture corresponding with their bucket. She changes the difficulty of the bucket to go with the students working with it, but the bucket content is similar each time, just different difficulty levels. That way each student works their different math skills each time they do math buckets.  I worked with one of the low skilled groups today. Their bucket was Darth Vader which consisted of the apple bingo activity.

 
I held the apple bag and both the boys would grab one apple at a time. They would have to tell me the number and then when they did correctly they were allowed to color in the apple with the same number. One boy ran into difficulty with the teens. When he would get a number like 14, he would respond with 24. I tried to explain to him that if there is the number 1 in-front, it is not going to be in the twenties, but in the teens. After a little bit of practice, he was able to catch on and tell me the correct teen numbers. With doing this activity a couple more times, I would confidently say that both these boys would be able to identify all their numbers up to twenty. 

Student Blog 2- Casey Droste

Today my students had a sub so we worked on a math worksheet that had to do with fractions.  The students went through and did the worksheet on their own and then we went over the answers.  The work is done individually but the students are allowed to ask for help.  I used the work of a students prior to their corrections and it was a student who did no ask for any help on the assignment.  There was no lesson taught before the worksheet it is all from prior knowledge of fractions.

The front side which was labeled Max and Min to me seemed the least effective.  The students Sarah seemed to go through the exercise with easy but looking at it now, after I have seen the answers, I know it was not that easy.  Problem 1. asks the students to tell whether the shaded part of the shape is ½ of it and then explain why.  The second drawing, b), looks to almost everyone to represent ½ of the square but according to the answer key there is a missing part of the shaded top right square that makes it unshaded and therefore not entirely half.  This question was a trick question, no student in the class realized this and neither did myself or the substitute teacher.  The last drawing which was f), most students and myself saw as not ½, the parts do not look equal in anyway but the answer key said that they are technically half.  I think that this question on the worksheet was horribly designed and should not be used.  Sarah and many of her classmates understand the representation of ½ but now have to deal with these tricks of poor picture representation and feel tricked afterward. 

The other side of the worksheet did a much better job of portraying portions of a shape.

Besides the horrible design Sarah did a great job, one of the problems I would like to point out are on the first side question 5. For question 5 Sarah was asked how many kittens were left after Jonathan sold 7, we learned in the previous problem that Jonathan sold 1/5 of his kittens and that 4/5 of the kittens were left.  Sarah saw that 1/5 of the kittens was equal to 7 and that the total number of kittens was 5/5; 7 X 5 = 35.  Sarah ended up writing that answer as 35 but the question did not ask for the total of kittens, it asked how many were left, 35 - 7 = 28.  I think a way to help Sarah with this problem is first asking her to tell you what she did wrong, most of the time these students realize very quickly and can tell you they just forgot to subtract.  I am thinking it could be possible that Sarah just assumed because she had to do the multiplication of 7 X 5 that she was all done and that she did not even think to look back at the question.  If this is the case I think giving Sarah more problems like this one, story problems that have more than just one operation/step to them will help her to get more familiar with them and remind her to check what the question is actually answering.  Knowing Sarah I predict she will see what she did wrong and when pointed out will remember to look back on questions, at least for a little while.  I believe it would be best to help her through this stage, that I feel a lot of students go through, and getting her to check for the real question, look more into the question for what they are answering will get across on a deeper level if we give her more practice with the help of someone.  Eventually she will catch onto this idea and it will stick with her forever.

Student Work #2

Above is a photo of my mentor teacher writing a word problem on the white board, it reads:

"Yesterday I made 10 cookies. Mr. Wilson ate 3 cookies. How many cookies left?"

After calling on students, Mrs. Wilson walked the students through writing this problem in 'short form' as she called it, or "10-3+__"

Following, Mrs. Wilson called on students to make-up story problems that they could work through as a class. The photo below is an example of a student's work/made-up story problem. The goal of this was to ensure students knew the difference between addition (or put-together problems) and subtraction (or take-away problems).

 

One student said, "Outside I saw 3 birds and 1 nest. How many things did I see?", so Mrs. Wilson wrote this story problem on the white board (shown above). The student was then asked if they created an addition or subtraction problem, and then was asked to explain how they knew (or what the 'hints' were) to determining the type of problem they created.

 

Having students create these problems was great, because they were engaged and felt involved. When solving the these problems, the students would come up to the white board and move the yellow and red round magnets to represent the problem.  This is great for visual learners that cannot do the addition in their head yet.  Others that do not need the visuals could write the problem as "3+1=4". Both of these demonstrations are great represntations of the story problem written.

 

I anticipate that students could count on their fingers or use counter items, such as the yellow and red magnets on the white board. Student may also draw pictures.

 

The student created this problem, then stepped back and thought about exactly what they said.  She first noted that the first number was '3', so she told Mrs. Wilson to write the number 3 on the board.  Then the student noticed that the next number was 1, and asked Mrs. Wilson to write that number next. The student did not determine that the story was an addition problem until they re-read the last sentence of the problem, which asked for the total amount of items seen outside. After determining this, she told Mrs. Wilson to write a plus sign between the two numbers.

 

The student indeed realizes how to create addition problems, but I am unsure if she knows how to create subtraction problems. I would like to see what sort of problem she could create if asked to write a subtraction problem.  I also can determine that she clearly knows that addition includes putting two groups of things together, seeing that birds and nests are different items.

 

To advance her knowledge, I would ask the student to create another problem, write the numbers herself and draw/use counters without assistance.  In addition, I might ask her to create a subtraction problem since she only created an addition problem.

 

 

Student Work- Katie Hall

This week, the students in my second grade classroom were working on 2-digit addition. This is the worksheet that they were focusing on specifically. 19 out of the 24 students finished this worksheet without issues, but there were five students who I worked with individually. This particular photo was not a student I worked with, however.

While working with one student, I had him finish the worksheet alone, and then I would work with him afterwards to help with what he could not understand. He had to use the cubes to finish this addition. He had such a difficult time, and became extremely frustrated when he would get an answer wrong. THe problem was that he was working way too fast. When I had him slow it down, he was able to use the cubes and get the correct answer. He even was able to stray away from relying on the cubes towards the end of the worksheet.

Stephanie Wilson - Student Work #2

At the beginning of this lesson, my MT asked the students a poll question: Do you like warm weather or cold weather? The students wrote their names on the white board under whichever one they chose. Afterwards, they were given this worksheet to fill out as a class following along with the teacher, who was working on the overhead. Students were asked to color in the suns for the number of students who chose warm weather, and color in the snowflakes for the number of students who chose cold weather. Then they were told to tally the amount in each category.

The big idea of this assignment was to demonstrate multiple ways of representing a number or group of people: the students each wrote their names under which category they chose, they filled in the suns/snowflakes, and they tallied the numbers up. The purpose of this assignment was to get students to think about different ways that they are able to count things. The tallying portion was the most important part of this assignment in my opinion because the students work on tallying every morning during calendar time (as a way of counting the days of the school year), and this was a way to determine if the students were understanding the process of this. Most of the students seemed to have a fairly good grasp of the concept of tallying, although some of them struggled a little with the crossing tally to make a set of 5 and then counting by these tallies.

This particular student was brand new to the classroom starting today, and it was extremely obvious that he was above-average compared to the rest of the class. He was easily able to do this assignment, although you can see that he was not up-to-par with tallying as the rest of the class was. His work is in blue, and I showed him the correct way to tally this number in the orange. The cause of this was probably that his old school did not spend time on tallying that my class does. So he will need to work on this task more, but I think he will be able to pick it up very quickly.

Since my classroom as a whole is at a low level academically, my teacher had to physically do the work with the students and have them copy exactly what she was doing. This in itself is an extremely low-level practice, because the students are not asked to apply themselves in any way other than simply copying the answer. I think in order to make this task more cognitively demanding, the obvious solution would be to make the students complete this task on their own. But another way to do this would be to have students come up with more ways to represent this poll. For example, they could make a circle graph, bar graph, etc.

Gingerbread Man Counting- Jamie Blankenship

            My kindergarten class has been working on counting from 1 to 10.  This week, my teacher wanted to test each student's ability to accomplish that task individually. The students were separated and had to cut out the gingerbread men that had the numbers 1 through 10 beneath them.  By themselves, the students had to paste the pictures in order.
             Although many of the students were able to accomplish this task, there were several of the students that really struggled with this. Some students somewhat knew how to numerically order the pictures and only mixed up a few.  Other students seemed to be very lost and pasted the numbers in what seemed to be no particular order.  This can be seen in the picture above.  This particular student started off with correctly ordering number one and number two.  He then got confused and followed that number with a 5 and then a three.  I have noticed on other occasions, during math time, this student often says the numbers out of order and struggles with counting.  He does do better at counting a number of objects or naming the numbers.  I think this student needs a lot more one-on-one practice so that he can become more capable and confident when counting.

Student Work #2

Every day that I am in my placement during math time, the students complete the task called "BIG 4." The students divide their paper into 4 sections and have to complete questions that cover different topics they are learning about from their math textbook. The teacher displays a version with all the questions but without the answers. After enough time, the students are called up by their popsicle stick to come up and answer any question and explain how they got their answer. 

The purpose of this  math task is to continue practicing various topics and problems the students have already learned or are learning currently. The four areas the students are covering today are the following:

1. division with remainder 

2. addition and subtraction with 4 digit numbers

3. rounding to the nearest hundred including numbers in 1,000s and 10,000s

4. word problems including time 

The students have to complete all of the problems individually and come together and go over answers as students come up to the teacher's copy and answer and explain each problem. Every time they do this task, the problems are different and change as the topics and concepts change when learning them in class. 

A effective approach to this task is to make sure the student writes down the instructions for each square so when they look back on their notes they know exactly what the teacher was expecting of them. For example, in the bottom right square, *Erica* did not write down the word problem question but instead just the numbers needed to answer the question the fastest. Another way that the teacher approaches this task is very helpful. Like I said, she calls on students randomly and allows the students to pick what question he/she wants to answer. This allows the students to become comfortable in front of their peers and increases confidence to answer math problems in class. I also like how when the student gets the question wrong, the teacher has the student stay up in front of the class and talks through how they completed the problem and how they can correct it. A approach a student can take is the one that Erica took which is to not completely fill out the four squares with all the information like I said earlier. Even though she got all the answers correctly it could lead to silly mistakes. Another approach this student took in this task is to not show any of her work on how she got her answer. She got all the answers correct but did not show how she got to that answer. I am not sure if the teacher wants the students to work up to only showing their answer or if it is okay to show work. Erica demonstrates that she is at that stage where she can do all her work in her head and only has to write the answer neatly without work. 

Erica demonstrates that she is able to answer all her math problems correctly and a stage, like I stated before, without showing any work. The correct division problems shows that these problems are becoming memorized facts in her head and she is able to compute these by memory and doesn't have to count on her fingers. As well, the word problem asking how long a time period was between 3:45PM-5:10PM, was answered correctly and demonstrated Erica can add time in her head. she demonstrated she can add the minutes of time correctly and also the hours correctly. A student could have added the hours together to get 7:55 but Erica shows that she understands that an hour represents one thing and the minute represents another. Erica and other students that are demonstrating higher knowledge than others should have a more advanced "BIG 4" worksheet to complete so they do not get bored. Erica finishes early and allows for other students to ask her for her answers and how to do problems instead of doing them individually. 

Student Work Post 2

This is a paper that my mentor teacher had me grade while she was out at recess with the students last week. It is a simple division practice worksheet that has 100 division problems the students have been working on for a couple of weeks now. My mentor teacher used it as a review before moving on to teach the students about long division and division with remainders. In order to remember the division, I expected the students to recall the multiplication facts that they had memorized before learning the division facts, or attempt to use math families. I also thought that the students probably used their fingers to keep track of how many groups of the second number in the problem could be made. Finally, as we learned last week, the students may even think to double in order to get to the multiplication fact they don't know and solve the division problem. I expected the students to use their memorized multiplication facts to solve the problems. I just assumed that my mentor teacher had taught them how to think of the problem in terms of multiplication the way my fourth grade teacher was, which makes division very simple, given that you have your multiplication facts memorized up to 12.

However, while I was grading the papers, I came across this particular student's paper and I thought it was interesting the way that she used paper and pencil to solve the problems involving the division of 11 and 12 that she apparently did not remember. This student wrote out the number 11 or 12 as many times as she thought was the answer, then added them up to make sure that she was right. I find it particularly interesting that she did not use any form of doubling during this process. She simply counted by twos to add up the ones column and then counted the ones in the tens column to get the answer she was looking for. To me, this reveals that even though she has gotten past the more tangible items for counting such as counters or fingers, she has not quite reached the more abstract method of finding the fact family by either doubling or simply doing the two-digit multiplication. This also may have been done before the students learned how to do multiplication with one two-digit number (they just learned it recently), so I think this method would be developed for her if she were to do the worksheet again knowing how to do multiplication that way.

If I didn't already know that they have now learned it, I would suggest that the next steps for advancing her learning would be both multiplication with larger numbers and long division with remainders. However, the students have not learned long division with two-digit answers yet, and I think that will be an important step in advancing her abstract knowledge of division. I also think it might be helpful and a big time-saver for this student to scaffold for her how to do long addition problems through doubling. Maybe show her that it is an option when trying to find out an answer like that, then see if she does it on her own later.

Student Work 2

The first image I posted was the story problems that go along with the work shown in the other pictures. This sample is from their math book. The first problem the teacher worked on together with the students. She showed them different examples of how to solve these problems. She went through each example with the same numbers and had the class copy down what she was writing. She asked them questions along the way to see if they understood how to fill out the chart. I have not seen the students work on story problems in the classroom before so I was unsure of how well they would understand the problems. 

The second story problem asked the students to solve for a word problem in two steps. As long as the students showed their work in the space below, they were able to solve the problem however they knew how. The teacher went through the first half of the second word problem with the class and had them pick out what they felt the best way possible. She had the students raise their hands to share with the class how they solved the first part of the problem. The choices they were given to solve the problems are doing a Change problem where you have a starting number and an ending number and you have to find the change (positive or negative). The second way they could solve the problem was Parts and Total. The larger space is for the total and then there are two smaller squares left for them to fill out the parts of the total. The third way to solve the problem is Comparison. It gives them a larger quantity box and a smaller quantity box and the students have to solve for the difference. Depending on what numbers the word problem gave the students they all seemed to choose different ways to solve the problem. 

The students work shown in the second picture shows the student solving the first part of the problem using comparison and getting an answer of 42 by showing their addition at the bottom. The next part of the problem they choose to solve it using change. They plugged the numbers into the spaces provided and wrote at the bottom that they counted back in order to get their answer. This work shows that the student understands how to use different methods for problem solving. The understand that just because you are given certain numbers it doesn't necessarily mean that they can all be plugged into the same equation. They show an understanding of where the numbers need to be placed in order to solve the problem. 

 I think it is important that teachers provide their students with these different strategies in case they struggle with one or the other. I think it is especially important for story problems since they can be very difficult for some students to pick out the important parts of the problem. Sometimes story problems give you more number than you actually need but for the second graders they are given only the information they need in order to have an easier time solving the problem. 

Liz Slusher- Student Work #2

During one of the math centers the kindergarten students were exploring the concepts of “lighter” and “heavier” by using a balance scale and various objects. Below is the transcription of a conversation between two children who were trying to find out “Which is lighter, 1 domino or 3 pencil-top erasers?”

Child A: “It’s my turn to put things in the scale!”

Child B: “I know. Three erasers are heavier because 3 is way more than 1.”

Child A: “Yeah but dominoes are really hard so they’re probly real heavy too.”

Child B: “It doesn’t matter about hardness, how many only matters.”

Child A put the 3 erasers in one side, and the domino into the other side of the balance scale.

Child A: “Yeah! The hard domino went down so erasers really are harder!”

Child B: “Yeah erasers are lighter because they’re higher in the air even though there’s three. Weird!”

Both of the children understand that when using a balance scale, the lighter objects with rise, and the heavier objects will lower. However, both of the children also have some misconceptions on what makes objects heavier or lighter. Child A was convinced that they “hardness” of an object always affect its weight. Setting up an experience where this child could explore weighing a softer object such as play dough and a harder object such as a pen, the child would be able to explore and understand that how hard or soft an object is, may not always determine how heavy it is. Child B has the misconception that more of an object will always make it heavier than a lower quantity of another object. Allowing this child to weigh 5 feathers and 1 quarter would show him that the 5 feathers are lighter than the single coin. Setting up exploratory experiences like these, along with discussions as the children explore, would create meaningful experiences to help them further develop concepts of weight, while decreasing their misconceptions and current misunderstandings.

Blog 2--Taylor Cummings

I haven't seen student work this past week, due to half days and the students not having school.  This is a picture of the next lesson the students are going to be learning about, measuring with cubes. The students have been working with cubes for the past month and learning how to create patterns with the different colors.  For my student interview, I am going to ask a few students,"How can we use cubes to measure a pencil?" It is going to be interesting to see if they can figure out how to use the cubes in order to measure the pencil I give them.  I am going to use a student with a low math ability, a student with a medium math ability, and a student with a high math ability.  I want to make sure that I have a broad range of responses, so I will be able to see what I need to focus on when teaching this lesson to the whole class.

Learning how to measure is a key component in mathematics and will be a very important concept for the students to understand.  Using the cubes as a starting point is a great idea because the students are already familiar with the cubes and how to use them.  I think the hardest concepts that these students will have is understanding what measuring something means and understanding that items have a length.  Students will need to understand that there are many different forms of measurement, not just using cubes. It will be a good idea to incorporate using string or rulers to measure something when it is evident that students understand how to measure using cubes.

I am excited to see how the students will do with this new concept :)

Work Blog 2

Every morning during calendar time, my MT has the students count how many days they have been in school. She does this by using straws and once the students get to ten in the ones place, they take a rubber band. bundle it up and put in into the tens place. But first she has them guess how what the next number would be for the day. On this day for example, she said yesterday they had eight bundles of ten and four ones how many bundles of ten and ones will we have today?

One of the students raised their hand and said 85 which is correct. The teacher repeats the students answer and says yes if we have 8 bundles of ten and 4 ones and we had one more to the ones pocket we get the number 85 which means we have been in school for 85 days.

However, after she reviewed this, she asked the students how they come up with the number 85 and their responses were really interesting to me and solidified what we have been learning in class that students figure things out different ways. One student said she took 4 ones and added one more and knew that was five. Another student said the same thing but then added on that the tens pocket didn't change because we need ten ones to add another to the tens pocket. Another student raised her hand and she said well I know that 4 is 1 away from 5 so if you add one day it would be 85. These answers prove that students used both addition and subtraction just to figure out this simple math problem in their head.

While this is just a simple math task that the students take part in everyday, it really opened my eyes to the fact that as a teacher I have to make sure that I explain math in many different ways. Students will understand things differently than others. These students are kindergarteners and their already finding their own way to work out a problem. I look forward to the future and finding out different ways the students do math!

Ashleigh Bunten Student Work # 2

In my Kindergarten classroom, they are currently learning how to write number sentences. My teacher has given them counting books where they will practice solving word problems. By drawing the pictures, like the four cars above, they are able to use visual cues to help them solve the problem until they can do the math in their heads. This specific problem was copied from the smart board to help the students get practice solving these problems. The purpose of this project is to show a way how students can solve word problems they cannot complete in their head. By drawing the cars, the students are performing a type of direct modeling because they can count the number of cars to get the final answer. The task is also designed to help students get practice in writing number sentences because they get more complicated as they get older. By having the teacher model the task on the board, all students received the same type of instruction and had the same understanding.

            My mentor teacher did not give the students other strategies to complete this task. She just had them copy this example from the board and put it into their counting books. This causes the students to not think about how this relates to math; and just copies from the board to finish the assignment. To make this assignment more effective for the students, the teacher should have explained that this is not the only way to solve a word problem. Students at this age should be told that everyone thinks of math in different ways, and that is a good thing. Also the assignment could have included using counters to help solve the problem and the student could draw how many counters they needed.

            The type of anticipated response that the teacher could expect is if the student copied the teacher’s example from the board. The problem of this is that it does not show if the student knows how to solve the problem. The example does not give the student an opportunity to think about math and learn more. The other type of response is that a student forgot to draw all of the cars or did not write the number sentence correctly. The negative aspect of these responses is that they do not show the teacher that the students know how to solve number problems.

            The student is supposed to listen to the word problem, and then draw pictures to model how many items are needed to solve the problem. The drawing should help students to visually represent the problem and not solve it in their heads. This math task does not show the student’s math knowledge, because they were not solving the problem on their own. This page in their counting book only shows the teacher that the student can follow directions and nothing else. I believe that the students should be able to solve the problems the way they feel most comfortable and put that in the book. Students could use counters and then draw circles showing how many they needed to solve the problem. Or the students could use the same strategy the teacher taught them, but the page is not on the board for students to copy. I think this is great practice for the students, but their math knowledge needs to tested, and not their ability to follow directions. 

Goerke_Student Work #2

This is a picture of something that the children work on each day in the morning with my mentor teacher. The children are working on counting up the days of school; their goal is the 100^th day of school. They are all very excited about achieving this goal. Every morning the task is to see how many days they are at school and then make sure this number is on the correct day. So if it were the 85^th day of school they would need to make sure that there are 8 bundles of 10 in the tens column and then 5 popsicle sticks in the ones column. They all count this out together by saying, “one, two, three….” for the tens and then “one, two, three…” for the ones column. The learning goal is to pay attention to the tens and ones places and how many sticks go in each. If it were the 90^th day of school, the teacher would scaffold the rebundling by showing or asking a student how to make it so that 90 is represented with the popsicle sticks in the correct places. (9 bundles of 10 and 0 sticks in the ones place). This task does not really show individual students’ elicit thinking unless the teacher was to specifically ask an individual student how to rebundle the sticks. The teacher usually asks the class as a whole.

            The specific strategy that the teacher uses to successfully approach this task is by having the students all count the sticks as a whole. Another strategy is for if the day turned to the 90^th day, the teacher would call on a student to help figure out the rebundling of the tens so that there are 9 tens and 0 ones.

            A student might solve this by counting out the sticks in the tens and making sure it matches the correct number in the tens column of the number of the day of school. So if they know that it is the 87^th day of school, then they would count the ones to make sure there are 7 ones and then they would count the tens to make sure there are 8 bundles of tens. A possible error could be on the 90^th day, for example, where the student may not rebundle and then they may get confused with the different place values.

            This task shows that the students are currently counting the days until the 100^th day of school. This task gives them an exciting way to learn place value and the order of numbers, such as 60 then 70 then 80, etc. This shows me that because the students have learned these high of numbers, then they may be capable of counting this high.

            Lastly, two different ways to advance my students’ mathematical thinking for this task would be when they reach the 100^th or even extending it to 101 or extending it further to 120^th day. These extensions all add a different dynamic to the place value system. Another way to extent it could be to create an addition problem out of it. The teacher could ask if I was on the 85^th day yesterday and now were are on the 87^th day today, how many days have gone by? Then the students would have to add 2 to 85. My placement is kindergarten, so I am not too sure if that would be way too advanced. I’d have to try it! 

Student Work #2 - Anna Kue

Every Friday the 4th graders in my classroom are given a piece of homework to bring home to be completed and brought back to school on Monday. The homework usually consists of a math worksheet like the one shown here. Recently the homework sheets have just been multiplication worksheets cut in half so the students only have 21 questions to do over the weekend rather than 42. This particular worksheet is "2 digit x 1 digit" problems.

This particular student answered all of the questions but 2, and the answers to the 19 other questions are correct. The two unanswered questions aren't any harder than the rest, so I'm a little confused as to why she skipped those especially because they are in the middle of the worksheet. This student is an ELL student but is one of the most talkative in class. She is always quick to raise her hand and offer an answer even if she can't put into words exactly what she means, she has the knowledge. I don't think that the students know that the teacher doesn't grade their homework so I still am not sure why she didn't answer those two questions.This however does not matter in the end because my mentor teacher simply gives the students credit for returning their homework and does not check the math problems to see if they are correct. Therefore even though she skipped a couple problems, she still receives full credit for returning her homework.

The big idea of the homework is to give students the opportunity to practice their multiplication at home, but I feel that it would be benefit the students more if it was graded or if the math worksheets were more interesting than the repetitive worksheets. 

This student definitely knows how to do multiplication and I think that it would benefit her to know that she is doing great on these larger problems. It is clear that she solved these problems on her own without the use of a calculator because you can see her thought process on the paper as she borrows and carries the numbers.

Student Work #2

This week I did not see any math in my placement. They usually do a math worksheet in the morning for their class warm up, but this week they changed things up. This was a word search which included some of their spelling words. This was the warm up the students had on their half day, and I think this was just a time filler so that my MT could take attendance and gather things to complete report cards that were do the next day. This was a task that was used to wake the students up and give my MT some extra prep time, and it served its purpose. However, this does not elicit a great amount of student thinking.

The students really do not even know how to spell the words in order to complete the task. I watched this students look at the word bank, and at each letter in the word, and then go search for a word that looks identical to it. This task was something that all of the students could complete, regardless if they could read or speak English. Most of the students found all of the words, and then turned it in to get credit.

It is hard for me to fully analyze this piece of work, because it is not a math problem, or a task of great difficulty. The students that I observed went about it in the same way as I described  above. I am unable to guess or suggest how to advance the students knowledge with this piece of work. However, I can make suggestions to help the worksheet demand a little more thinking among the students. If the worksheet did not have a word bank, then the students would be forced to find words in the puzzle that they know are words, and therefore know (or have an idea) of how to spell. This will give the teacher some insight on where the students are at with their understanding of the spelling words and other vocabulary words. Another idea is to have the students create cross word puzzle with their spelling words. They would then have to create clues for each of the word and be forced to be creative and thoughtful in the construction of their work. The two ideas I just presented, I feel, would be more useful and helpful to the students and the teacher.

Week 3-Chelsee

This student was able to answer all of the problems correctly. The big idea to this problem is to see if students know how addition works. I do not feel that this worksheet is the best test to see if students understand the big idea. This assignment does not allow me to see if the students actually understand how addition works. All of the worksheets that we have been presenting to students has been set up in this format. This can cause students to understand addition as a pattern and not actually understanding how addition works. This worksheet is an example of join result unknown. To further students thinking I would present these problems in a sentence and have the students set up the math problem (78+46=__). To further this students thinking I would create 5 to 10 word problems involving 2 digit numbers when added together need regrouping. This would help to create a high level task and allow students to choose their method when solving the problem.

This assignment does allow me to see that my student is able to carry(regroup) into the tens and hundreds place. This tool is something that my MT and I have been working on for awhile now.  The students are very precise when placing the regroupment above the value spot. In past weeks the students were very unorganized and would forget to add in the regrouped number.  We corrected this problem by having the do their math problems on graph paper for a few days.  Although this worksheet does not show the students have a good understanding of the big idea, it does show that they are able to regroup.