A CONTINUING INVESTIGATION INTO THE
USE OF CASE STUDIES IN THE TRAINING
OF IN-SERVICE AND PRE-SERVICE MIDDLE
SCHOOL MATHS TEACHERS.
GARY HARRIS, JULI D'ANN RATHEAL
SOUTHERN RIGHT DELTA
(ΣΡΔ'09)
Gordons Bay, South Africa, December 3, 2009
Acknowledgements
A project of the West Texas Middle School Math Partnership
Funded by the National Science Foundation
MSP grant # 0831420
Any opinions, conclusions, or recommendations expressed here are those of WTMSMP personnel and
do not necessarily reflect the views of NSF.
Case Study Background



A small school in a rural community. The school has
a history of being underperforming the state
English tests and marginal on the mathematics tests.
The student body is 75% Hispanic, 5% African
American, and 20% Caucasian.
Ninety percent of the students qualify for the free,
or reduced, lunch program.
Case Study Scenario
At the beginning of her third period class Ms. Hammel
tells the class how pleased she is that the class did
so well on their last unit test.
She also tells them that she looks forward to them
doing even better on next Friday’s unit test over
fractions.
Scenario Cont’d
She then pairs the students up, trying to make each
pair have one student she thinks should be able to
do things pretty well and the other being a student
that might need some help.
She then hands out a set of problems for the pairs to
work on, and encourages them to make sure that
they both understand each problem before moving
on to the next one.
Scenario Cont’d
As the students work on the problems Ms. Hammel
walks around the class, looking over the students’
shoulders to see how they are doing, and to offer
help and answer questions.
She purposely stops by Johnny and Jose’s table to
provide encouragement as both of them typically
struggle with new content and Jose had not done
well on the previous unit test.
Ms. Hammel notices that they have completed the first
problem correctly and praises them by saying “I like
the work you two have done. Great work!”
Scenario Cont’d
After a few minutes, she observes that the majority of
the class has successfully completed the first
problem and comments to the class, “It looks like
everyone is working hard on these problems.”
Problem
In problem 3 the students have to compute
1 2
 . Ms. Hammel notices that Miguel and Susie
2 3
3
have gotten the answer 5 . She asks them how they
got their answer. Miguel immediately responds that
he added the two top numbers and the two bottom
numbers. Of course, Ms. Hammel knew this is what
had been done. #1. What should she do next?
Problem Cont’d
Ms. Hammel asks Susie what she thinks of that answer.
Susie responds that she first thought it was supposed
to be done differently but Miguel had convinced
her that this was the right answer.
So Ms. Hammel asks Miguel to explain how he arrived
at his answer.
Explanation
Miguel tells her that he is a big basketball fan. This came
as no surprise since Miquel is a starting guard on the
school’s basketball team, and even as a sixth grader
has gotten the attention of several area high school
coaches. Miguel reckoned that if he hit 1 out of 2
three point shot attempts in the first half and 2 out of 3
in the second half, then he would be 3 out of 5 for the
game, which is 60% for the game and that is a good
percentage.

#2. How should Ms. Hammel react to this explanation?
Reaction
Ms. Hammel paused for a second and then replied “Yes I see,
you are absolutely correct if you are computing your 3-point
shooting percentage for the whole game.”

How can she convince Miguel and Susie that 3 is
5

not correct and that the correct answer is 7 ?
6
Return
Video
Self-Efficacy Analysis: opportunities
missed, opportunities grasped
At the beginning of her third period class
Ms. Hammel tells the class how pleased
she is that the class did so well on their
last unit test.
She also tells them that she looks forward
to them doing even better on next
Friday’s unit test over fractions.
Analysis Continued
She then pairs the students up, trying to make
each pair have one student she thinks should
be able to do things pretty well and the
other being a student that might need some
help.
She then hands out a set of problems for the
pairs to work on, and encourages them to
make sure that they both understand each
problem before moving on to the next one.
Analysis Continued
As the students work on the problems Ms. Hammel
walks around the class, looking over the students’
shoulders to see how they are doing, and to offer
help and answer questions.
She purposely stops by Johnny and Jose’s table to
provide encouragement as both of them typically
struggle with new content and Jose had not done
well on the previous unit test.
Ms. Hammel notices that they have completed the first
problem correctly and praises them by saying “I like
the work you two have done. Great work!”
Analysis Continued
After a few minutes, she observes that the
majority of the class has successfully
completed the first problem and
comments to the class, “It looks like
everyone is working hard on these
problems.”
Analysis Continued
In problem 3 the students have to compute
. Ms. Hammel notices that Miguel
and Susie have gotten the answer . She
asks them how they got their answer.
Miguel immediately responds that he
added the two top numbers and the two
bottom numbers. Of course, Ms. Hammel
knew this is what had been done.
1 2

2 3
3
5
Analysis Continued
Ms. Hammel asks Susie what she thinks of
that answer. Susie responds that she first
thought it was supposed to be done
differently but Miguel had convinced her
that this was the right answer.
So Ms. Hammel asks Miguel to explain
how he arrived at his answer.
Analysis Continued
Miguel tells her that he is a big basketball fan. This came as
no surprise since Miquel is a starting guard on the school’s
basketball team, and even as a sixth grader has gotten
the attention of several area high school coaches. Miguel
reckoned that if he hit 1 out of 2 three point shot attempts
in the first half and 2 out of 3 in the second half, then he
would be 3 out of 5 for the game, which is 60% for the
game and that is a good percentage.
Ms. Hammel paused for a second and then replied “Yes I
see, you are absolutely correct if you are computing your
3-point shooting percentage for the whole game.”
What actions might she take here?