What I wish I knew two years ago: practical tips for the beginning Moore Method practitioner practical tips for the beginning Moore Method practitioner Patrick X. Rault SUNY College at Geneseo Legacy of R. L. Moore 2011 Conference

My experience Teaching & Learning : PROMYS math camp : Emerging Scholars 2008 Fall: Proofs (lecture) ‘09 Spring: Number Theory (PROMYS) 2009 Fall–’10 Fall: Proofs - Ed Burger’s book (IBL) - Ron Taylor’s JIBLM script (MM) - Low evaluations, increasing. ‘11 Spring: Number Theory (MM) - John Boller’s U Chicago script. - High evaluations! Support 2010 Spring: $1000 AIBL mentor - “Find your own voice as a teacher” (White) 2010 Summer: MAA Prep & Legacy 2010 Fall: Visit Berry & Augusta 2010-’11: T. Mahavier mentor 2011: AIBL “course release” -Split class into 2 small sections Book: The Moore Method: A pathway to learner-centered instruction Advice: Start small and take change carefully & slowly 2Rault - SUNY Geneseo

Book & script selection Theme (not just “proofs”) Contact the author: axioms vs. assumptions Modify – Stepping stones: “Too easy” vs. “too hard” – Addendums – JIBLM: Rault < Boller, Taylor Content: lecture to fill syllabus requirements 3Rault - SUNY Geneseo

First class: Slowly shift expectations Lecture Students at board Class discussion English and innate love of puzzles “… n is even. By definition of even there exists an integer such that n is twice this integer. Call this integer k”. Mysteries vs. axioms 4Rault - SUNY Geneseo

Selling Relentless 5 minute speeches – “Hard for me because…” but “good for you because…” – FAQ: answers YOU believe in Wording: – “We have difficulty learning how to use quantifiers” Positive environment – Comfortable being critiqued (collaboration?): food & ice-breaking? – Participation (quality, not quantity): “Free” 50%, flexibly decreased for excessive absences/lateness, cell phones, facebook – Address issues early (e.g. “Its hard to catch up in math, please come to my O.H. tomorrow” ) – Track daily involvement Previous students: sequences, visits from former studs 5Rault - SUNY Geneseo

Motivation & independence “5 minutes per day can solve these problems – start today” – Hallways: “Did you get B7?“ – “I learned that daydreaming about propositions actually leads to useful insight. When I have no insight into a proposition I use concrete examples to help myself understand what is going on.” (Student) Availability – Plethora of office hours, 5 minutes per student, ONE AT A TIME – Help wanted: “What have you tried?” – Complete proof: “What are you worried about” – Significant help: similar (unscripted) problem Expert students ahead of the game: office hour presentations Presentation & critiquing skills: NOT discovery based 6Rault - SUNY Geneseo

Day-to-day Prepare lectures & worksheets: – “A lot of exams this week?” Critiquing vs. leading questions: – “Why is line 5 true?” vs. “Don’t you mean ____.” Significant changes on the board – Lemmas and delayed resolution give slow students a chance – “The format of the class gave you the time to ask questions and get a firmer grasp … time to explore and self-discover” (student) Solidarity of fairness – Near solution: “Does he/she almost have it? Should we let him/her come back at the start of class next time?” Visit others’ classes 7Rault - SUNY Geneseo

Evaluations Faculty: weeklong observation, with discussion Students: – The instructor’s teaching style stimulates active learning and interest in the subject matter. Strongly Disagree. – Please comment on the instructor’s teaching style and interest in the subject matter. “He doesn’t teach because this is part of an ‘active learning’ experiment. Although we are learning, … we would love to just be TAUGHT something…” – SALG-M instrument Summaries – Essay: “Tell me about something you learned this semester that you feel is important beyond just this class.” – Journal: Top 5 accomplishments & 5 learning experiences 8Rault - SUNY Geneseo

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Why do we work so hard? (Students) “I accomplished things in this class that I never thought I was capable of…” “I have always been very uneasy about proofs. I often got frustrated and gave up. This teaching/learning style helped to motivate and empower me. I accomplished things in this class that I never thought I was capable of.” “I would suggest making this a required course for math education majors … I have never learned more in any math class I have taken.” “I gained…confidence…when I ‘discovered’… the rule for n- boards…That was really cool. If…I was solely a math major, I would be much more interested in mathematics research.” 10Rault - SUNY Geneseo