Math Buddies
A problem solving partnership between
elementary school students and future teachers
Matt Ciancetta, Laurie Burton & Cheryl Beaver, Western Oregon University
“Teachers” and “Students”
During this session we will refer to…
 the pre-service teachers who are enrolled in
Math 396 as “PSTs”
 the 4th and 5th grade students as “students”
 the teachers of the 4th and 5th grade students as
“partner teachers”
 the course instructors as “instructors”
Math Buddies Pen Pals: A component of
Math 396 (Elementary Problem Solving)
Goals for the Math 396 course are:
 to help PSTs become better mathematical problem solvers
 to introduce techniques and materials helpful in improving
student problem solving abilities
 Mentor elementary and middle school students in problem
solving processes
To meet these goals the PSTs engage in solving and analyzing
challenging problems and participate in the Math Buddies
experience.
Planning and launching the problem
solving partnership
 Getting buy-in from the partner teachers is of major
importance!
 We had several meetings prior to the start of the term.
 We solicited as many suggestions and ideas as possible from our
partner teachers and offered suggestion of our own.
 What will benefit the partner teachers without making extra
work for them?
 Physical make up of the journals
 Types of problems
 Feedback and scoring
 Timelines for student work and teacher work and logistics of
transporting the journals
Examples of Journals
 Individual Journal
 Each PST was assigned 2 students (a few had 3 students).
 Each student worked on the problems and sent his or her own
write up for their Math Buddy (PST) to examine, score and
respond to.
 Group Journal
 Each PST was assigned 2 or 3 groups of students (3 - 4 students
per group).
 Each group worked on the problems and sent their write up for
their Math Buddy (PST) to examine, score and respond to.
Implementation (for a 10-week term)
1. Send introduction problem to the students before the
college term begins.
2. PSTs solve introduction problem; Math Buddies are
assigned; Receive and analyze introduction problem
solutions from students; Write rough draft of
introduction letter.
3. How to write for 4th & 5th graders (training by Writing
Center)
4. Send the 1st problem and an introduction letter with
comments on introduction problem (but no scores)
Implementation (for a 10-week term)
5. Training on use of State Rubric
 (Oregon Council of Teachers of Mathematics & Oregon
Department of Education. Winnie Miller [email protected],
Jill Sumerlin [email protected])
6. Writing Cycle for 1st problem
 Solve the problem
 Receive journal (with student solution)
 Score & write response
 Send journal (with scores and response)
 Receive journal (with solution revision*) *not always revised
 Score & write response
Implementation (for a 10-week term)
7. Send 2nd problem
8. Writing Cycle for 2nd problem
9. Send 3rd problem
10. Writing Cycle for 3rd problem
11. Culminating activity
 Pi Day Fun Fair (Winter term)
 Campus Tour (Spring term)
Problem Selection
 2 or 3 variations on the same problem, with increasing
complexity
 Example: Cows, Ducks & Unicorns (Winter 2012)
 2 or 3 problems with increasing complexity
(related math topic but unrelated context)
 Example: Problem Set 1: Counting (Spring 2012)
Writing Cycle Example
 Recall that our Writing cycle is
 Solve the problem
 Receive journal (with student solution)
 Score (iterative process with instructor feedback)
 Write response (iterative process with instructor
feedback)
 Send journal (with scores and response)
 Receive journal (with solution revision*) *not always
revised
 Score
 Write response
Writing Cycle
Solve the Problem
Cows, Ducks and Unicorns
Solve the problem
Briefly share solutions at table groups
Writing Cycle
Receive Journal & Score
Oregon Scoring Guide math rubric
 Mathematics Problem Solving Official Scoring Guide
 Mathematics Problem Solving Scoring Guide: Plain
Language Version
 1 hr 45 min (and HW) was enough to get our PSTs started on
using the scoring guide.
 Oregon Council of Teachers of Mathematics & Oregon
Department of Education.
Winnie Miller [email protected],
Jill Sumerlin [email protected]
Writing Cycle
Receive Journal & Score
Examine student work (if needed, use the “translation”)
 Teacher’s scores
 Discussion
Writing Cycle: Write a response
 Response Process
 Friendly Start; Praise; Suggestions; Closing; Signature
 How to write for 4th & 5th graders (training by Writing
Center)
Friendly Start
Start notes to your Math Buddy with a greeting; use
their name and a friendly opening sentence. If they
sent you a note and asked questions, feel free to
respond to them.
Writing Cycle: Write a response
 Response Process
 Friendly Start; Praise; Suggestions; Closing; Signature
Praise
Write two sentences, if you can, specifically praising what
your Math Buddy did correctly. For example: "I looked at
your ducks, cows and unicorn problem and I like how
you .... “ Avoid phrases like "great job" unless they did all
three levels so perfectly they can't possibly be improved.
Try to address their mathematics here, not just their
handwriting or picture drawing.
Writing Cycle: Write a response
 Response Process
 Friendly Start; Praise; Suggestions; Closing; Signature
Suggestions
Write two sentences specifically prompting your Math
Buddy to move forward, give simple examples if you can
(but don't give away any answers). For example: "Will you
help me understand how you _______ by showing how
you _______."
Writing Cycle: Write a response
 Response Process
 Friendly Start; Praise; Suggestions; Closing; Signature
Closing
Close with an encouraging phrase. For example: "I am
excited to read your continued work on the ducks, cows
and unicorns problem”.
Signature
Sign your name
Writing Cycle: Write a response
Focus on “Praise” and “Suggestions”
Write a few sentences of “praise” and a few sentences of
“suggestions” for the student (original, translation).
Share with your table group
Examine PSTs response
Suggestions for the PST and discussion
Writing Cycle
 Send journal (with scores and response)
 Receive journal with solution revision* (translation)
*not always revised
 Score & Write response
Discussion on student’s revisions:
 improvement in scores?
 Improvement in writing?
Challenges in group solution write-ups
 Students do enjoy some aspects of group work (check
out the group names!)
 Often not one cohesive answer from the 'group’
 It seemed like all of the students would work on the
question and then decide which solution to submit as
the team solution
 Sometimes different team members would even work
on different questions
Culminating activity
Pi Day Fun Fair (Winter term)
Students visit campus for about 1hr 45min of activities
 Co-designed by PSTs and instructors
 Implemented by PSTs
 Opening activity (measuring Pi)
 Fun Fair (4 stations – money, crossing the river w/ducks,
card games, math motion)
 Pi Chain activity (digits of Pi)
 The PSTs and partner teachers gave a lot of positive
feedback
 The students gave a lot of positive feedback
Culminating activity
Campus Tour (Spring Term)
Campus tour (PSTs showed students the campus)
Estimation activity (students estimated length, area, and
volume around campus)
 They did not get measuring tools.
 The groups that had the closest estimate for each won a prize.
 The PSTs gave a lot of positive feedback, and Cheryl seemed to
get a sense that it went well.
 The PSTs did have some trouble with behavior management
while walking around the campus.
 The ratio was one teacher to twelve elementary
students. Each group had a chaperone, but they were often
parents that did not do any behavior management.
A Warm Fuzzy Thought
(from a partner teacher)
I received an email today from a former student. She is currently
studying at OSU to become an elementary ed teacher. In part she
wrote:
I'm really curious about whether we focused on problem solving so
much when I was in 4th and 5th grade because it was a state
requirement or did you choose to. I'm taking a course on math for
elementary teachers and we're focusing a lot on problem solving
techniques. It comes really easily for me because we focused on it
so much in your class but most of my classmates are really
struggling. Did they not have to learn them? Either way I'm really
glad we focused on it so much in your class. It really helps!
A Warm Fuzzy Thought
(from a partner teacher)
(Response) Yeah, it was a state requirement then, the Crisis Topic du
Jour. Since then, we’ve chased reading scores, writing scores, math
scores, and even some science scores. The cycle goes on.
Anyway, I got to thinkin’ that if she remembers it from two of my
first years teaching (2000-2002), these kids this year are going to
remember much more because the product they are getting is SO
much better than what I was teaching back then! There is no
doubt in my mind that the greatest improvement this year will
have come from the Math Buddy partnership and the
cooperation among everyone concerned. You’re all great folks to
work with!
THANK YOU
Any questions?
Matt Ciancetta ([email protected])
Laurie Burton ([email protected])
Cheryl Beaver ([email protected])