ED 608
Case Study Follow-up
Chris Stegall
Preliminary: I chose 4 students with varying degrees of math and reading ability to solve problems using the Make a List strategy . The first problem was a straight math problem using analog clocks. The second problem was a story problem that embedded the problem solution in the text.
Jasmine has excellent reading skills but her math skills and confidence are low.
Sierra has excellent reading and math skills
Austin has low reading skills but his math skills and problem solving abilities are very high.
Brian has high abilities in both reading and math but his attention span and his performance in both
areas is very low.
Outcome: Sierra, Brian and Austin were successful solving the clock problem. All three visualized the clock and came to a conclusion. Sierra made a drawing but came quickly to a solution. Jasmine could only reach the solution for the clock problem by looking at another sheet and then figuring it out.
The second problem was a text based problem involving matching students, trees and snacks. Jasmine,
Austen, and Sierra were all successful solving the problem independently. Brian ultimately refused to participate saying it was too hard. Sierra used a tree diagram to help her solve the problem. Austen solved the problem mentally without drawing anything. Jasmine matched the elements of the story to the characters. When asked how she solved the problem she said, “It’s all there in the story, Mrs.
Stegall. This wasn’t math, this was reading.”
Instruction: Rather than instruct these four separately and assess them I chose to instruct the whole class since this is an important strategy that is only cursorily covered in our math program. They received instruction along with everyone else.
In the intervening weeks, twice a week for 15 minutes, I gave the class a list problem from the
Mindware book Grid Perplexors level A to the entire class. In the first two weeks, I gave the class 5 minutes to attempt a solution independently and then we worked through the problem together until we arrived at a solution. As time went on I spent less time modeling how to create the list and gradually giving the class more independence to solve the problem on their own. We would reconvene and share our answers and strategies.
Assessment: On Friday, December 9, I gave the whole class the following two problems from the 2001-
2002 Dec/Jan. third grade issue of Teacher’s Helper along with scrap paper to assess how well each student used different strategies, especially making a list to solve the problem.
Problem 1
Football
Annie
X
Malorie x
Reid o
Connor
X
Jake x

Board game x/
Book o
Puzzle
Yo-yo x x o x x x x x x x
X
X
O
X
Clues:




x x x o
Annie gets the book because she likes to read. None of the boys wants a board game and Annie has the book so Malorie gets the board game. Connor likes to be challenged so he gets the puzzle. Reid must get the football since Jake doesn’t like football and Connor has the puzzle. Jake is left with the yo-yo.
Problem 2
Arranging Reindeer
Santa is having some of his reindeer over for a dinner party. Read the clues below to determine the seating arrangement at the table.

Dasher wants to sit next to Santa

Rudolph wants to sit at the end of the table near the salt and pepper shakers

Cupid doesn’t want to be next to Prancer or Rudolph.

Dancer doesn’t want to sit next to Prancer because he sat with him at lunch.

Blitzen doesn’t care where he sits

Prancer wants to sit directly across from Rudolph.

Comet wants Rudolph and Santa to sit beside him.

__________Prancer______________
Turkey
Blitzen
Cupid
Dasher
Santa
Dancer
Salt Pepper
Rudolph
Comet

Outcome:
I gave students 10 minutes to solve both problems. The original blackline for this activity is far more engaging but I couldn’t get the original Teacher’s Helper to attach to my document. So I created the key for them both here. Here are the results of all of the original students who took the pretest, their commentary, written-if any- strategies and how they performed on the final assessment. Overall, the class took longer than the time I had set aside for this but for the most part was able to try both with few errors.
Sierra- Sierra wrote on her Santa Seating which order she used her clues to determine the seating arrangement as well as crossing them off. She did make mistake where Prancer, Dancer and Cupid. She did the first Gift Exchange problem with no scrap paper and no errors.
Austen - Austen finished both problems in 7 minutes with no use of scrap paper or explanation beyond
“That was easy! “
Jasmine- Successfully completed the Gift Exchange problem without error or scrap paper but she did circle each clue and then circle the name on the grid to match clues to problems. She also got 100% on the Santa Seating problem. When I asked her about her work, her response was, “I’m starting to get this Mrs. Stegall! This wasn’t hard like the others were.”
Brian - Brian made no errors on the gift exchange but made two errors on the Santa Seating. He completed both in the allotted time which was a dramatic improvement over refusing the second one.
His comment when asked about his strategies he said, “These are easy, Mrs. Stegall!”
These weren’t exactly dramatic improvements but just the overall attitude toward trying these problems and the improvement in success after relatively few lessons in learning these strategies was very encouraging. The most dramatic improvements of the four of them was Brian followed closely by
Jasmine. Jasmine’s confidence in her own abilities as a math student were what was important to me. I wish I had had the nerve to try this case study using the Working Backward method just to have a sense of my own improvement.