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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 Gui
de Mathematics Problem Solving Scoring Guide: Plai
n 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 StartStart 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
PraiseWrite 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
SuggestionsWrite 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
ClosingClose with an encouraging phrase. For example:
"I am excited to read your continued work on the ducks, cows and unicorns problem”.
SignatureSign 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])
