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 4 th and 5 th grade students as “students”  the teachers of the 4 th and 5 th 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 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 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 4 th & 5 th graders (training by Writing Center) 4. Send the 1 st 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 Jill Sumerlin 6. Writing Cycle for 1 st 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 2 nd problem 8. Writing Cycle for 2 nd problem 9. Send 3 rd problem 10. Writing Cycle for 3 rd 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) 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) 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 Official Scoring Guide  Mathematics Problem Solving Scoring Guide: Plain Language Version 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 Jill Sumerlin

Writing Cycle Receive Journal & Score  Examine student work (if needed, use the “translation”)student work translation  Teacher’s scores Teacher’s scores  Discussion

Writing Cycle: Write a response  Response Process  Friendly Start; Praise; Suggestions; Closing; Signature  How to write for 4 th & 5 th graders (training by Writing Center) How to write for 4 th & 5 th 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).originaltranslation  Share with your table group  Examine PSTs responsePSTs response  Suggestions for the PST and discussion

Writing Cycle  Send journal (with scores and response)  Receive journal with solution revision* (translation) *not always revisedsolution revisiontranslation  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!)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 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 ( ), 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 Laurie Burton Cheryl Beaver