| Introduction | Implementation | Assessment | First Time | Observing Students | Presentations | Debriefing |
What are Case Studies for Kids?
Case Studies for Kids are problem activities explicitly designed to help middle school students develop conceptual foundations for deeper and higher order ideas in mathematics as well as other disciplines. Each task asks students to mathematically interpret a complex real-world situation and requires the formation of a mathematical description, procedure, or method for the purpose of making a decision for a realistic client. Because groups of students are producing a description, procedure, or method (instead of a one-word or one-number answer), students’ solutions to the task reveal explicitly how they are thinking about the given situation.
Each case study consists of four components:
1) Newspaper article: Students read the newspaper article to become familiar
with the context of the problem.
2) Readiness questions: Students answer these reading comprehension questions
about the newspaper article to become even more familiar with the context.
3) Problem statement: In groups of three, students work on the problem statement
for 60 – 90 minutes.
4) Process of sharing solutions: Each group writes their solution in a letter
to the client. Then, each group presents their solution to the class. Whole
class discussion is intermingled with these presentations to discuss the different
solutions, the mathematics involved, and the effectiveness of the different
solutions in meeting the needs of the client.
In totality, each case study takes approximately 3-5 class periods to implement.
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CLASSROOM IMPLEMENTATION
SUGGESTIONS FOR “CASE STUDIES FOR KIDS”
RECOMMENDED SUPPLIES
(depending on the actual activity implemented):
· Overhead transparencies and transparency markers/pens
· Calculators
· Rulers, scissors, tape
· Markers, colored pencils, pencils
· Construction paper, graph paper, lined paper
· Paper towels or kleenex (for cleaning transparencies)
· Manila folders or paper clips for collecting the students’
work
· Optional: Computers with programs such as Microsoft Word and Excel
RECOMMENDED PROGRESSION
OF THE ACTIVITY:
Newspaper Article and Readiness Questions:
The purpose of the newspaper article and the readiness questions is to introduce
the students to the context of the problem. Depending on the grade level and/or
your instructional purposes, you may want to use a more teacher-directed format
or a more student-directed format for going through the article and the questions.
Some possibilities include:
a. More teacher-directed (½ hour): Read the article to the students
and give them class time to complete the readiness questions individually.
Then, discuss as a class the answers to the readiness questions before beginning
work on the problem statement. This approach also works well when you can
team with a language arts teacher, and they can go through the article in
their class.
b. More student-directed (10-15 minutes): Give the article and the questions
to the students the day before for homework. If you wish, you may provide
some class time for the students to complete the article and questions. Then,
on the day of the case study, discuss as a class the answers to the readiness
questions before beginning work on the problem statement.
c. More student-directed (10-15 minutes): Give the article and the questions
to the students in their groups right before the students begin working on
the problem statement. The students answer the questions as a group and then
proceed to work on the problem statement.
Working on the Problem Statement (45-75 minutes):
Place the students in groups of three. If classroom management is an issue,
the teacher may form the groups. If classroom management is not an issue,
the students may form their own groups. Encourage (but don’t require
or assign) the students to select roles such as timer, collector of supplies,
writer of letter, etc. Remind the students that they should share the work
of solving the problem.
Present the students with the problem statement. Depending on the students’
grade level and previous experience with case studies, you may want to read
the problem statement to the students and then identify as a class: a) the
client that the students are working for and b) the product that the students
are being asked to produce.
Allow the students to work on the problem statement. As they work, your role
should be one of a facilitator and observer. Avoid questions or comments that
steer the students toward a particular solution. Also during this time, try
to get a sense of how the students are solving the problem so that you can
ask them questions about their solutions during their presentations.
Presentations of Solutions (30-45 minutes):
The groups present their solutions to the class. Each presentation typically
takes 3 – 5 minutes. You may want to limit the number of presentations
to five or six or limit the number of presentations to the number of original
solutions to the case study.
Before beginning the presentations, encourage the other students to not only
listen to the other groups’ presentations but to also a) try to understand
the other groups’ solutions and b) consider how well these other solutions
meet the needs of the client. You may want to offer points to students that
ask ‘good’ questions of the other groups, or you may want students
to complete a debriefing page in which they explain how they would revise
their solution after hearing about the other solutions.
As students offer their presentations and ask questions, whole class discussions
should be intermixed with the presentations in order to address conflicts
or differences in solutions. When the presentations are over, collect the
students’ work.
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Assessment of Students Work:
You can decide if you wish to evaluate the students’ work. If you decide
to do so, you may find the following Assessment Guide helpful:
Performance Level Effectiveness: Does the solution meet the client’s
needs?
Requires redirection The product is on the wrong track. Working longer or
harder with this approach will not work. The students may need additional
feedback from the teacher.
Requires major extensions or refinements The product is a good start toward
meeting the client’s needs, but a lot more work is needed to respond
to all of the issues.
Requires only minor editing The product is nearly ready for the client to
use. It still needs a few small modifications, additions, or refinements.
Useful for this specific situation No changes are necessary to meet the client’s
immediate needs.
Share-able or re-usable The tool not only works for the immediate solution,
but it would be easy for others to modify and use in similar situations.ORThe
solution goes above and beyond meeting the immediate needs of the client.
Note: If you use this Assessment
Guide for grading purposes, please keep in mind that a performance level of
“requires only minor editing” or higher indicates a satisfactory
solution. For example, you may want to assign a grade of B for “requires
only minor editing”, while assigning an A for the next two higher levels.
If you give a written score or letter grade after assessing the students’
work, we encourage you to provide the students with an explanation (i.e. written
comments) as to why they received that score and/or how their solution could
be improved. In particular, we found it helpful to phrase the feedback as
if it was coming from the client of the problem. So for example, in the volleyball
problem, the client is a team of program directors that is trying to devise
a system for creating fair and equal volleyball teams, and feedback to the
students could include statements such as the following:
"We understand how you formed your three teams of six members each from the eighteen members, but we need more information from you about how we are going to apply your procedure when we have over 200 campers."
IMPLEMENTING
A CASE STUDY WITH STUDENTS FOR THE FIRST TIME:
You may want to let students know the following about case studies:
· Case studies are longer problems; there are no immediate answers.
Instead, students should expect to work on the case study and gradually revise
their solution over a period of 45 minutes to an hour.
· Case studies often have more than one solution or one way of thinking about the problem.
· Let the students know ahead of time that they will be presenting their solutions to the class. Tell them to prepare for a 3-5 minute presentation, and that they may use overhead transparencies or other visuals during their presentation.
· Let the students know that you won’t be answering questions such as “Is this the right way to do it?” or “Are we done yet?”. You can tell them that you will answer clarification questions, but that you will not guide them through the case study.
· Remind students to make sure that they have returned to the problem statement to verify that they have fully answered the question.
· If students struggle with writing the letter, encourage them to read the letter out loud to each other. This usually helps them identify omissions and errors.
OBSERVING
STUDENTS AS THEY WORK ON A CASE STUDY
You may find the Observation Form on the following page useful for making
notes about one or more of your groups of students as they work on a case
study. We found that the form could be filled out during “real-time”
as you observe the students working or sometime shortly after you observe
the students. The form can be used to record observations about what mathematical
concepts the students are using, how they are interacting as a group, how
they are organizing the data, what tools they use, what revisions to their
solutions they may make, and any other miscellaneous comments.
OBSERVATION FORM
Observer: _____________________________________ Date: ________________________
Group: _______________________________________ Activity: ______________________
Math Concepts Used: What mathematical
concepts and skills did the students use to solve the problem? Group Interactions:
How did the students interact within their group or share insights with each
other?
Data Organization & Problem Perspective: How did the students organize
the problem data? How did the students interpret the task? What perspective
did they take? Tools: What tools did the students use? How did they use these
tools?
Miscellaneous Comments: About the group functionality or the problem. Cycles
of Assessment & Justification: How did the students question their problem-solving
processes and their results? How did they justify their assumptions and results?
What cycles did they go through?
PRESENTATION FORM
As the groups of students present their solutions to the class, you may find
it helpful to have students complete the following presentation form. This
form asks students to evaluate and provide feedback about the solutions of
at least two groups. It also asks students to consider how they would revise
their own solution to the case study after hearing of the other groups’
solutions.
PRESENTATION FORM
Name_____________
· While the presentations
are happening, choose TWO groups to evaluate. Look for things that you like
about their solution and/or things that you would change in their solution.
· You are not evaluating their style of presenting. For example, don’t
write “They should have organized their presentation better.”
Group ________________ & ____________________
What I liked about their solution:
What I didn’t like about their solution:
Group ________________ & ____________________
What I liked about their solution:
What I didn’t like about their solution:
· After seeing the other
presentations, how would you change your solution?
· If you would not change your solution, give reasons why your solution
doesn’t need changes.
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STUDENTS’ DEBRIEFING
FORM
You may find the following form useful for concluding the case study with
the students. The form is a debriefing tool, and it asks students to consider
the mathematics that they used in solving the case study and to consider how
they would revise their previous solution after hearing of all the different
solutions presented by the various groups. Students typically fill out this
form after the group presentations. Sometimes students find question #2 confusing,
so using this question is optional.
STUDENTS’ DEBRIEFING FORM:
Name _________________________________
Date__________________________________
1. Please mention the mathematical “big ideas” and skills (e.g. ratios, proportions, etc.) you used in solving this activity.
2. Imagine circling each of your big ideas and skills in #1. Think about how
related these big ideas and skills are in your solution. In the box below,
redraw your circles with the big ideas and skills inside them, but arrange
your circles so that those ideas and skills that seem similar are close to
each other and those that don’t seem related are far apart.
3. After solving this activity, circle the score that best describes how well
you understand the mathematical ideas you used.
Not at all A little bit Some Most of it All of it
4. How difficult do you think this activity was?
Easy Little challenging Somewhat challenging Challenging Very Difficult
AFTER SEEING ALL OF YOUR CLASSMATES’ PRESENTATIONS, WHAT DO YOU THINK
WOULD BE THE BEST WAY FOR THE CLIENT TO SOLVE HIS/HER PROBLEM
| Introduction | Implementation | Assessment | First Time | Observing Students | Presentations | Debriefing |
Case Studies for Kids! |
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