**Fowler Portfolio EMAT 3400**

By:Amanda Allred

By:Amanda Allred

**Introducing Dulce!**

**I had the privilege of meeting with a fourth grade student named Dulce each week for our Fowler study. Dulce is a fourth grader who loves her family and making bracelets. She also enjoys the color pink and wearing hair bows in her hair. Dulce is a very artistic girl who loves to draw and paint.**

Goals

While working with my Fowler friend there were a few goals I tried to work on with her including trying to get her away from using algorithms(MCC3.OA.7), understanding the decomposition of numbers in base-ten(MCC2.NBT.1), and solving multi-step word problems with remainders (MCC4.0A.3)(MCC3.OA.8). I really wanted Dulce to focus on procedural fluency in several different ways instead of only relying on the classroom algorithms she learned in class. With Base-ten numbers I wanted Dulce to master the conceptual understanding with decomposing hundreds and telling me how many tens were in them. In addition to these goals Dulce and I worked on multi-step problems and breaking the problems apart into manageable pieces and applying the right procedures to each part of the problem.

Understanding negative numbers, fractions and multiplication

**Mathematical Content Covered Week #2-7**

Week#

2- We worked on multiplication and division;

3- We worked on Base ten; decomposition, multiplication, and division using the crates of candies pictures

4- We worked on problems related to the book we read that I made up- Base-ten and two step multiplication and division problems.

5- we worked on multi-digit problems using multiplication and division.

6- we worked on negative numbers and played the number line game

7- we worked on equivalent fractions.

Negative Numbers

My Fowler friend knew that there were numbers that existed to the left of zero on the number line and correctly identified them by name; negative one, negative two etc. She did well with adding negative numbers to positive numbers and to other negative numbers. She ignored the negative signs when she was posed with problems asking her to subtract two negative numbers. This tells me that she does not fully understand the concept of taking away negative numbers from a negative number.

Fractions

My Fowler friend was able to connect fractions with drawings and she understood that fractions consisted of equal parts. She was able to add and subtract fractions to come up with the correct solution. She did not fully grasp equivalent fractions. When asked if 1/3 and 4/12 were the same she said no. This interview told me that my friend understood what fractions were and what they looked like, but did not fully understand the concept behind equivalent fractions.

Multiplication

My Fowler friend can multiply some single digit numbers by recalled facts. She sometimes struggled with some multiplication facts and leaned on derived facts to get the answer. For example. 3x4, she would use 3x2 twice to come up with the answer. but later on in the interview to come up with 3 x8 she would use 3x4 twice. She saw the reversibility in multiplication problems like 7x2 is the same as 2x7. She did really well with multiples of 10, but struggled with other lower two digit numbers, often referring back to derived facts.

Learning

Over the seven weeks I was with my Fowler friend I focused on figuring out how my student solved problems. I used the phrase, "I see just how you got that" if she was completely wrong on a problem. I did not, until the fraction interview, realize that I could nudge her along to come up with a different solution by talking about the problem specifically. Each week that she would get a problem or two wrong, we would just keep going instead of trying to figure out the right answer. She could explain to me how she got it and on those problems I could clearly see her mistakes but she did not. I realize now that I could have talked about them with her and possibly pointed out the particular mistakes and she would have solved them correctly. So, because I did not continue on with my questions on each problem, her learning in our interview was not very clear to me.

As a side note I do think she learned that numbers can be decomposed more than just by ones, tens and hundreds place. With my question I posed from the literature week I was able to get her to decompose problems in different way and she succeeded. In the week before that she told me there was only one way to decompose a number. For example 342- has 3 hundreds, 4 tens and 2 ones.

Follow up Problem Set:

Fractions

My Fowler friend is having a hard time with equivalent fractions, so I would like to work with her on that.

I think her conceptual understanding of equivalent fractions needs to develop. While working with my Fowler friend on the fraction interview, she was unable to make the connection that 1/3rd and 4/12 was the same amount.

Equivalent Fraction Problem Set

I would begin my activity with the hexagon blocks we used in class. I would have my Fowler friend show me multiple was to make one whole using different color/sized shapes. I would have my friend show me how many smaller pieces can go into 1, 1/2, 3/4 etc. after completing this activity, I would then pose a few equivalent fraction problems.

If Jane ate 1/3 of the cookie cake and 2/3 of the cookie were cut into 4 equally size pieces and Roberta ate 2 of them, Did Roberta eat more, less or the same amount of cookie cake as Jane?

( I would have her use the blocks to figure this out)

Equivalent Fraction Problem Set

There are two equally sized pizzas, one with 12 equally sized pieces and one with 2 equally sized pieces. If Austin eats 6 of the 12 piece pizza and Jimmy eats one of the two piece pizza, Did Austin eat more than Jimmy, less than Jimmy or the same?

Explaining the Equivalent Fraction Problem set

The problem set I created would show my Fowler friend that there are multiple ways to represent the same fraction. She would then realize that equivalent fractions are possible when given the same sized whole.

i think my activity would show her there a multiple ways to make the same fraction and my problems posed would drive that concept home for her.

CCGPS Standard

MCC4.NF.2

Compare two fractions with different numerators and

different denominators, e.g., by creating common

denominators or numerators, or by comparing to a

benchmark fraction such as 1/2.

Recognize that comparisons are valid only when the two fractions refer to the same whole.

Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

This semester has been a learning experience for me. I learned that as a teacher, teaching isn't about giving the answers to problems, but more about asking the right questions so that our students can figure it out on their own. I learned through my own experiences in this class that I will remember and soak in so much more if I can figure out how something is done versus just being told. This changed my original thoughts about teaching because when the semester started, I thought just having the right answer given to me was the most efficient learning method.

Working with my Fowler friend was definitely teaching once I realized I could say more than, " I see just how you did that". Once I realized that we could ask more questions in different ways, I think that is when it really became teaching for me. It wasn't about just letting her get the right or wrong answer, it became a journey to figure out the right answer together.

Once I implemented the talk moves, like did you figure that out or the repeat and echo strategies, it made my Fowler friend either think harder about her answer or double check her work. When she did this, more often than not, she was able to see her mistakes and correct them. I did not really focus on diving into the problems when she continually got them wrong, though. I think if I would have posed new problems on my own when she got something wrong that would have helped in the teaching process. As mentioned previously, I did not realize I could do this until our very last interview on fractions.

Personal Reflection

My Talk Move Card

Classroom Algorithm

Lattice

Base-ten Decomposition

Classroom Algorithm

Big 7

The End

Thanks for a great semester! I am amazed at how much I have learned in four short months.