EDMA 608 – Kate Mullin – Case Study

Victim Subject: Clare Mullin, Age 9, Grade 3

Problem 1: WORM JOURNEY (page 21)

A worm is at the bottom of a 12-foot wall. Every day the worm crawls up 3 feet, but at night it slips down 2 feet. How many days does it take the worm to get to the top of the wall?

Clare’s Protocol

Clare: Read the problem. Used a methodical subtraction-addition process to solve.

Kate: “Okay, so can you tell me the strategy you used for solving your problem?”

Clare: “So, it said he went up three so I started with three and said that was Day 1. Then he slid down two. Then I added that answer plus three and I would come up with Day 2. And then I did it until I came up to 12.”

Kate: “And can you tell me about that little number you’ve put over here?”

Clare: “That means for each day.”

Kate: “That’s the day their on?”

Clare: “Yeah.”

Kate: “How come you didn’t put it here by the twos?”

Clare: “Because, um, that’s when they slid down.”

Kate: “And, so, you got to 12 and that was at what day?”

Clare: “Day 10.”

Kate: “Okay, and you wrote that over there.”

Problem 2: BASEBALL SEATING (pg 284)

A family of five, consisting of Mom, Dad, and three kids (Alyse, Jeremy, and Kevin), went to a baseball game. They had a little trouble deciding who was to sit where. Alyse would not sit next to either of her brothers. Kevin had to sit next to Dad. Mom wanted to sit on the aisle but not next to any of the children, although she could sit next to her daughter as needed. How was the seating arranged?

Clare’s Protocol

Clare: Read the problem. Drew five lines on the paper. Wrote in seating from aisle to center.

Kate: “Okay, can you tell me how you figured it out?”

Clare: “I knew that Jeremy could sit anywhere.”

Kate: “So, did you start with him? Did you just put him anywhere?”

Clare: “I figured out that he could just go in the empty space that didn’t have anyone. And I knew that Mom wanted to be on an aisle. And she said that she could be by Alyse, so I put Alyse there (indicating seat next to Mom) and I knew she couldn’t be next to any of her brothers so I put Dad next to Alyse. And then I put Kevin next to Dad because he wanted to sit next to him and then I put Jeremy on the end because that was the only open space left.”

Kate: “Was there anything confusing about this problem for you?”

Clare: “No.”

Analysis:

Both of these problems seemed to be at an appropriate skill level for Clare. I must admit, I was a little disappointed, as I wanted to see her struggle on at least one of them so I could have some common errors to analyze. Boy that sounds terrible coming from the mouth of her mother.

Instead of struggling, Clare approached both problems in the same fashion. She read the problem aloud for both of us, then spent a minute or so thinking about it before beginning her calculations. She was deliberate in finding each of her solutions. There was no extraneous diagramming or rearranging of data. While I would have loved to have seen this on her paper, I could see the wheels turning in her head. She didn’t ask me any questions about techniques or for any clarification on the problems.

For the worm journey problem, you can see that Clare methodically works through the calculations. After she had added a couple threes and subtracted a couple twos, she went back and started writing the days the worm had journeyed next to each of her calculations. I was wondering how she would keep track of this, but her system was flawless. When she ran out of space on her paper, I found it interesting how she just continued her calculations in the next column over without moving her “working number” to the top. As an educator, it is my preference to see students move the number at the bottom of the page to the top of the next column when they run out of room, as I feel it helps reduce mistakes, but Clare just looked from the bottom number to the operation she planned to perform and did her calculation. I managed to not comment. Then, without a hint of uncertainty, Clare completed the calculation that indicated she had climbed to the top of the wall (12 ft), marked that it was the 10 th day, and wrote “10 days” to the right of her work.

For the baseball seating problem, Clare read the problem, processed the information mentally, thought about her strategy, and then got to work. She wrote out each of the family members in order, from the aisle to the inside seat without hesitation. After she completed the problem, I asked her about her strategy. Her response was essentially that she took the information and used it to fill in the appropriate boxes.

Knowing Clare’s abilities, not only in math but also in reading, allow me to analyze her problem solving a bit more. She has always been a strong math student. She grasps concepts easily and forms mental pictures of what she is learning. In addition, she is a strong reader, particularly when it comes to comprehension. Because she has the ability to easily read a problem and make a picture of it in her head at the same time, Clare finds problem solving to be fun and challenging, but not scary. When I commented to her that she had solved her problems too easily and not given me much to work on, she eagerly offered to try some more problems until we found one that worked better.

What I am seeing is a problem with my problem selection. I underestimated the ability of my own child.

While my selection of problems for Clare might not have been the best for this assignment, what I have seen in my years of experience in varied classrooms across the state has helped mold me as a teacher. Regardless of the population I am working with, I know that I can teach my students and they can learn. I find it imperative to determine individual skill levels and then push each of my students as hard as I can at their particular academic level. Students will experience the most success in the classroom when the curriculum is presented to them at a level that is appropriate to their learning level. If I have students who struggle with reading comprehension, they will struggle with word problems. Regardless of their

math ability, I cannot expect them to figure out the solution to a problem when they don’t understand the words in the problem. To work around this, I can read the problems to them and work on helping them decipher the problem. Or I can prerecord the problems to have available to the students so they may listen to them as many times as necessary. Depending on the day and the classroom, I might do either of these. I believe there is a solution for most problems that are encountered in the classroom. I don’t, however, think that many of these solutions are quick and easy. If I am expecting my students to work hard every day, they should expect the same from me.

Jumps off of soapbox.