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Signature Assignment

EDUC 603 Child Development & Education

Signature Assignment Worksheet

Subtraction In The First-Grade Level

Erika N. Nelson

December 16, 2013

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Section I: Concept Analysis & Interviewee Profile

Identify the concept

I will be focusing on concept of subtraction, specifically at the first grade level.

Subtraction is the most basic math concept next to addition. Subtracting one number from

another means you are taking away a certain amount from another and can tell you how

many are left. The symbol for subtraction is the minus sign (-). In a subtraction equation,

there are names for the numbers. Minuend is the number that is to be subtracted from.

The subtrahend is the number that is to be subtracted. And the difference is the result of

subtracting one. For example: 9 – 4 = 5. Nine is the minuend, four is the subtrahend, and

five is the difference. When subtracting, the highest number always goes on the top, or is

written first.

The identity, or zero, property states that any number minus zeros always equals

that number, such as 3 – 0 = 3. Also, when any number is subtracted from itself, the

answer is always zero, such as in the problem 6 – 6 = 0.

Subtraction is anticommutative, meaning that changing the order of the number

changes the sign of the answer, such as in the problems 9 – 3 = 6 but when you switch the

minuend and the subtrahend. 3 – 9, then your difference is now a negative number, -6.

When working with larger numbers, such as double or even triple digits, you need to use

the property of borrowing. Sometimes, when subtracting large numbers, the top digit in a

column is smaller than the bottom digit in that column. In that case, you need to borrow

from the next column on the left.

Other rules of subtraction include negative and positive integers. A negative

minus a positive equals a negative integer, i.e. -5 – 3 = -8. A positive minus a negative,

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equals a positive integer, i.e. 5 – (-3) = 8. Negative minus negative equals a negative, i.e.

(-5) – (-3) = -2. And lastly, a positive minus a positive equals a positive integer, 5 – 3 = 2.

To put it simply, two like signs become a positive sign, such a problem is 6 – (-3) = 6 + 3

= 9. They are “like signs” when they are the same as each other. It can also be said that

two unlike signs become a negative sign, such a problem is 6 – (+3) = 6 – 3 = 3.

An example of a first-grade subtraction word problem would be: Carter and his

mom go to the super market to get a pumpkin for Halloween. There are 10 pumpkins on

the shelf. If Carter takes away 2 pumpkins from the shelf, how many are left? The answer

is 8, because 10 – 2 = 8. Here is a type of visual a first grader might use:

Subtraction is also related to the operation of addition because it is an inverse of

that concept (“Inverse relationship between,” 1999). For example, subtracting 10 from 6

to get 4 is the opposite of 4 plus 6, giving you 10. This is why the two concepts are taught

together and are closely related to each other.

Interviewee profile:

Grade Level: The two interviewees are first grade students at Punahou School. I have

chosen these students because I work closely with them every day in the After School

Care program.

Age: Between the 5-6 years old.

Language status: English.

Gender: Male. There is no reason why I chose a certain gender; these students were

simply willing to volunteer for my project.

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Unique information relevant to your learner & concept: When I was looking for students

to volunteer to be a part of my project, I first went to the two students that were the most

social towards me. It was interesting to find out that one of the boys loves math and the

other one doesn’t care too much about it. So it will be very interesting to say the least to

see how my interview will go with the one student who loves the subject and the other

who doesn’t care so much about it.

Section II: Learning/interview Task

Describe the task:

Supplies needed:

Pencil and eraser

Several sheets of blank paper

Counting cubess (manipulatives)

To begin, the interviewer and the child will sit at a table with the supplies. The

interviewer will begin the interview by telling the child that they will be read a word

problem and that they may use the materials provided for them to solve the problem.

Instructions to the student:

You will be read a word problem. You may take notes on your paper while I read.

After I have read it you may ask to have the word problem repeated in case you are

confused or need clarification. Please use words, pictures, and numbers to explain how

you got your answer and how come you think your answer makes sense and is correct.

Jimmy has a bag that contains 9 animal crackers. He gives some to his sister and now has 3 animal crackers left. How many animal crackers did Jimmy give to his sister? Use pictures, words, and numbers to show how you solved the problem.”

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Describe your reasoning

This problem-solving task addresses the concept of the student’s current

understanding of first grade subtraction because it deals with animal crackers being given

to another person therefore the amount of animal crackers are being reduced.

The task is engaging because it centers on something that is relevant to the child,

eating animal crackers. I will try to use all of the five productive “talk moves” for

supporting classroom discussions (Van de Walle, J.M., Karp, K.S., & Bay-Williams,

J.M., 2013). In using these “talk moves” it will help me to get the student to talk about

the mathematics they are using.

Then while the student is in the process of actively working on solving the

problem, I can provide appropriate support if needed. If a strategy is not working for the

student, then I should introduce a strategy to them, being careful to introduce it as

“another” way, not the only or best way to solve the problem. This is called introducing

an alternative method (Van de Walle, J.M., Karp, K.S., & Bay-Williams, J.M., 2013). If

the student is stuck, I can ask questions such as, “Did you try to make a picture?” or

“What is it about this problem that is difficult?”

This phase is also an excellent opportunity for me to find out what my student

knows, how they think, and how they are approaching the task at hand. If the student is

looking to me for approval of their results or ideas, I will try to shy away from being the

source of telling them if they are right or wrong. Instead, I will respond by saying “Can

you check that somehow?” “How can you decide if it is right or not?” “How can we tell if

that makes sense?” By asking these type of questions I am reminding the student that the

correctness of the answer doesn’t lie in the answer key, but in the justification of the

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answer.

The task can be solved in a variety of ways. The child can use their fingers to

count, they can also use the paper to draw it out, or they can even use the manipulatives

(counting blocks). If they solved the problem by drawing a picture, then I will ask them

to write it out with words and numbers. If they solved to problem by using numbers, then

I will ask them to draw a picture and write it out with words, and vice versa. Just so I

know that the student is well rounded in the different ways to solve a word problem.

How is this task planning to encourage..?

1. Active processing

The child will be presented with the word problem. There will be no input from

the interviewer as to how to solve the problem. Because of this the child might feel a bit

overwhelmed as he or she try to figure out how to go about solving the problem. The

child will need to think of the different ways they can do so, i.e. pencil and paper, the

manipulatives.

2. Minimizing cognitive load

The interviewer will read the problem to the child and will encourage them to

write down notes on the paper provided in order to help them keep track of important

details. The child is allowed to ask the interviewer to read the question again in case they

did not fully grasp it the first time it was read. The task has a time limit of twenty minutes

in order to limit any frustration or lack of focus.

3. Direct Modeling

The visual or model the interviewee uses may convey more than what they can

communicate. They can either use a pencil and paper to show their work or they can use

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the manipulatives that are provided for them. The child will be asked to both explain and

illustrate their solution in order for the interviewer to effectively assess whether the

student learned what the interviewer was conveying.

Focusing on the learner

This task is related to the learner’s interest because it involves food that they are

used to eating, animal crackers.

Physical development

The child will need to be able to use their hands to use the manipulative provided

for them and to be able to write notes and answers.

Section III Assessment Plan

Brief Task Description:

The interviewee will be read a word problem. The interviewee needs to think and

use the materials to help them solve it. The interviewee must use words, pictures, and

numbers to explain their answer and must give an explanation for why their answer

makes sense and is correct.

The Word Problem:

Jimmy has a bag that contains 9 animal crackers. He gives some to his sister and

now has 3 animal crackers left. How many animal crackers did Jimmy give to his

sister? Use pictures, words, and numbers to show how you solved the problem.”

Low Understanding:

The interviewee would demonstrate low understanding when they show little to

no understanding of the problem. For example, the interviewee will not understand that

the concept of the problem is to use subtraction. The interviewee used no strategy for

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solving the problem; an example of this would be the interviewee simply guessing the

answer. The interviewee would have significant errors or omissions in their work. The

interviewee has an answer that does not make any sense. The interviewee provides an

explanation that is very hazy and/or shows confusion or cannot be clarified. The

interviewee does not meet the requirements of using words, pictures, and numbers to

explain their answer. Such an example is the interview is unable to draw a picture, write

the answer in words and numbers to explain their answer.

Medium Understanding:

The interviewee would demonstrate medium understanding when they show good

understanding of the problem. For example, the interviewee will understand the concept

of the problem is to use subtraction. The interviewee used a strategy for solving the

problem; an example would be counting with their fingers, using the manipulatives, or

drawing a picture. The interviewee would have work that is mostly correct, errors, if any,

are minor. An example of this would be, the interviewee has drawn out a picture correctly

but might have miscounted how many animal crackers are left. The interviewee has an

answer that may not fully make sense or solve the problem. The interviewee provides an

explanation that is pretty clear. Some details may be missed or some help may need to be

provided to give a full explanation. For example, the interviewee cannot fully convey

what their picture depicts so the interviewer must use scaffolding questions to help the

interviewee explain their explanation of the answer. The interviewee mostly meets the

requirements of using words, pictures, and numbers to explain their answer. Such an

example is the interviewee is able to show the interviewer two out of three requirements.

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High Understanding:

The interviewee would demonstrate high understanding when they show thorough

understanding of the problem. For example, will thoroughly understand the concept of

subtraction to solve the problem. The interviewee used a strategy that best fit the

problem. The interviewee would have work that is correct. The interviewee has an

answer that makes sense and clearly solves the problem. The interviewee provides an

explanation that lays out the solution to the problem clearly and complete. A possible

explanation the interviewee might give is, “the answer is six because I crossed out each

animal cracker until there are three left.” There is a deep understanding of the solution

and/or there is more than one solution indicated/explained. The interviewee meets the

requirements of the problem using words, pictures, and numbers to explain their answer.

An example is the interview was able to use all three requirements to solve and show

their explanation.

Phase IV Field Testing

Field Testing Experience

Student C was the first of the two interviewees. At first he told me he was nervous

to do the interview because he was scared it was going to be too difficult. But I reassured

him that if it was really too hard for him I would try to help him the best that I could.

When we finally sat down for the interview, student C seemed very eager to start and it

was a comfortable environment for the both of us. It was comfortable because student C

and I know each other through working with each other every day in his After School

Care program. Student C had a lot of difficulty trying to solve the problem but he didn’t

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let it damper his mood, he continued to have a smile on his face. At the end of the

interview, he wanted some more word problems because he was having that much fun.

Personally, as I sat down to begin my interview with student C, I felt especially

nervous. I had never been on this end of the interview spectrum, the interviewer. I was

scared I would forget the instructions, scaffolding questions, or that student C would have

a question or problem that I would be unable to answer. However, I felt comforted in

having my notes near me and with the fact that if student C did have a problem and I

could not answer it, we would just have to work together and come up with a solution.

Student N was interviewed the next day from student C. Student N, I was by one

of his teachers, was the student that liked math the most so I figured he would be the

most excited to have the interview with me. However, I found out that he treated it as a

little more of a hassle and wanted to get it done as soon as possible. This confused me

because why would this student want to get through with it in a hurry when supposedly

this is his favorite subject? But, once I started reading the word problem and he started to

think about how to solve it, I could see a slight twinkle in his eyes. The love for math

finally came out and he was able to complete the word problem with very little problem.

Personally, as I interviewed student N, I felt more confident in conducting the

interview since I had prior experience with student C the day before. However, I still felt

slightly nervous as I began the interview and while student N was working on solving the

problem because I was scared that student N would find the new problem effortless and

finish rapidly. But, my emotions calmed as student N continued to work in a steady

fashion and hit a minor bump in his work. I know I should not be wishing my interviewee

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to have difficulty, but at the same time I did not want the interview to seem

uncomplicated and undemanding.

Successful Scaffolding

I had some scaffolding questions that I used on both students. The first general

scaffolding question I used on both interviewees was, “How about trying to take notes as

I read the problem again?” I needed to ask this because both interviewees were either

asking me to keep repeating the word problem or were stuck and could not remember the

problem. When I asked both interviewees about taking notes as I read them the problem,

they felt a little more at ease. I think both interviewees thought the problem was going to

be simpler so they did not initially take notes. However, after I made that suggestion, the

interviewees were still a little stumped as to write down as notes, so I guided with another

scaffolding question, “Should you try writing the numbers from the problem down?”

Writing the numbers down seemed to help them visualize the problem better and both

interviewees were able to continue working on the problem without asking me to repeat

the question.

When the interviewees would give me an answer they came up with, I would

scaffold using, “How can we tell if the makes sense?” Both interviewees would begin to

explain their thought process of how they came up with that answer and would catch

where they went wrong or where their answer did not make sense and would tell me,

“wait, that’s wrong” And would try fixing it or would try a different method.

When they told me their final answer, I would ask, “What makes you think that is

correct?” Because I asked this question instead of just telling the interviewees if they

were right or wrong, I was able to get their thought process of how they got the answer as

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well as their explanation of why they believed it to be correct. For student C he replied

with, “I have nine fingers up and I grouped three and counted how many were not

grouped.” Student N replied with, “I crossed out the nine animal crackers until there were

only three left and then I counted how many I crossed out, it’s six.”

I also used different scaffolding questions for each student because I had to base

my questioning off of their progress and difficulty they were having. For student C, the

scaffolding questions I used specifically for him was: “Did you try drawing a picture?”

“What should you draw first?” I led student C with these questions because initially his

answers he was giving me were just guesses, there was no true math method being used.

Therefore, once I introduced him with an alternative method of drawing a picture, it

opened his mind more and he began solving the problem better. I also used the question,

“What does it mean by ‘giving’ something away?” Student C was having slight difficulty

comprehending the wording of the problem, more specifically “Jimmy gives away

cookies.” Therefore, when I asked student C what he thought “giving away” meant he

replied “you have less of what you have” I think having him say that out loud made him

realize that it was a subtraction problem.

I used different scaffolding questions for student N. After student N had his notes

taken from the word problem, he sat for a moment in silence staring at the numbers until

he asked me “I don’t know where to go from here.” I then asked him to “think of

subtraction, how would you use subtraction to solve this problem?” Once I said that, he

started replying with “Nine minus…” and then took off on figuring the rest on his own.

When student N would give me his answers I would ask him “how did you come up with

seven?” or “how did you come up with six?” He would be forced to think about the work

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and method he used, his first answer of seven was wrong and he found his mistake, he

miscounted. When he answered again with six and I asked how he came up with that, his

explanation made better sense and he was even able to explain to me why his initial

answer of seven was wrong.

Unsuccessful Scaffolding

The only unsuccessful scaffolding question I had was, “Why don’t you try an

alternative method and try writing it as an equation?” This scaffold question did not work

because the response from both students was that they did not know how to write

equations. They told me that normally their teacher gives them the equation and then they

solve it, they were not used to being given a word problem and then thinking of how to

write the equation down. Therefore, I told them to skip that part and we would do it

together at the end after they figured out the answer.

Developmental Assessment

For student C, whether I presented him with my original question or with the new

question, the first strategy he used was guessing the answer. According to my rubric, I

would not count that as a strategy because the student is not making an attempt to solve

the problem properly. He then tried counting with his hands, but this word problem was

too difficult to do a simple count with hands, so that ended up not working for him. When

I told him to try using an alternative like drawing a picture, a new strategy emerged. I

asked student C, “What should you draw first?” His response was the number of students

and then the number of animal crackers. For the drawing his strategy included grouping

the animal crackers by three until he had a total of six groups then he counted how many

animal crackers were left, two. Finally, student C had successfully solved the problem by

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using the strategy of drawing a picture and I could award him with a high understanding

of communication/explanation.

When I presented student C with the new/easier word problem, surprisingly he

knew exactly what strategy he wanted to use, counting with his hand. He ended up

holding up nine fingers, grouped together three of them and then counted how many were

left over, six. Therefore, his strategy and reasoning was successful, he was able to explain

in words and pictures after that but he was unsuccessful in explaining it in numbers/an

equation i.e. 9 – 6 = 3

For student N was on the right track with solving the problem. When I told him to

try to think of how would you use subtraction to solve the problem he started with “Nine

minus…” Then he blurted out seven and asked me if I could tell him if it’s correct or not.

He then asked if he could draw a picture. He started drawing nine animal crackers and

then started crossing them out until he was left with three and then counted how many he

crossed off. Therefore, based on my rubric he had a high understanding of strategies and

reasoning as well as a high understanding of communication/explanation.

Normative Development

I am basing both interviewees level of understanding with the 2010 Hawaii first-

grade Math Common Core Standards. The standards include having a solid foundation in

whole numbers and subtraction. They are able to solve word problems that call for

subtraction of within twenty, by using objects, pictures, and a written and verbal

explanation to represent the problem. They also understand subtraction as an unknown-

addend problem, example 9 - ? = 3, which is what the word problem consisted them of

having to figure out. Based on the interviewees being able to meet the Hawaii first-grade

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standards, both student C and N have a level of understanding that is consistent with

normative development.

Jean Piaget’s cognitive development theory that children think in qualitatively

different ways at different age levels supports what my first-grade interviewees know and

should know (McDevitt & Ormrod, 2010). At this age level, the interviewee’s are not

able to think in advanced mathematical ways; therefore counting with their fingers or

drawing pictures to solve a math problem is normal. Led Vygotsky’s cognitive

development theory mentions that children have an actual developmental level in which

they are able to perform only a limited amount of tasks without the help from an adult. A

child’s level of potential development is the child’s ability to complete task at a more

challenging level with the assistance of adults. Therefore, children are able to complete

more challenging tasks/math problems with the assistance of adults (McDevitt &

Ormrod, 2010). This supports that although my original word problem was hard for

student C, with some assistance/scaffolding provided by the interviewer, he was able to

complete the challenging word problem.

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References

Common core standards. (n.d.). Retrieved from

http://www.hawaiipublicschools.org/TeachingAndLearning/StudentLearning/

CommonCoreStateStandards/Pages/home.aspx

Inverse relationship between addition and subtraction. (1999). Retrieved from

http://www.eduplace.com/math/mathsteps/1/b/

Ixl learning. (2010). Retrieved from http://www.ixl.com/standards/hawaii/math/grade-1

McDevitt, T. M., & Ormrod, J. E. (2010). Child development and education. (4th ed.).

Upper Saddle River, New Jersey: Merrill.

Van de Walle, J.M., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle

school mathematics: Teaching Developmentally 8th edition. Upper Saddle River,

NJ: Pearson.

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erikanelsoneportfolio.weebly.com€¦ · Web viewYou will be read a word problem. You may take notes on your paper while I read. After I have read it you may ask to have the word