Hear from two experienced math educators who are using new techniques to foster rich discussions and conceptual learning in math. Learn about free online resources to apply these techniques to your school.
Would introduce the idea that there are many opportunities to have deep discussions throughout the lesson sequence, however the openers and closers provide assistance for teachers and integrate the 5 talk moves. Etc..
Fostering Rich Discussions in Math
Rich ClassroomDiscussions in Math4:00 pm eastern timeMay 16, 2013Hosted by
Hosted bywww.conceptuamath.comThe PresentersMary ElizabethMendenhall• ProfessionalDevelopment andProject Leader in Math• Griffin RESA, RegionalEducational ServiceAgency near Atlanta• Metro-South GLRS,Georgia LearningResource Service,special education• Leading large CommonCore math project• Eightcounties• Low tomixedsocioConnie Laughlin• ProfessionalDevelopment Specialist• Author, Math Coach• Retired Middle SchoolMath Specialist• Her project• Mequon-ThiensvilleSchool District,Wisconsin• Common Core focus• High achieving, high-socioeconomicgroupingArjan Khalsa - moderator• CEO, Conceptua Math• Taught grades K-6 from1976 - 1983• University instructor• UC Berkeley• San Francisco StateUniv.• FOSS author (scienceprogram)• CEO, IntelliTools(assistive technology forgrades pre k – 8)
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Hosted bywww.conceptuamath.comMath Discussions: Important and DifficultEmphasized:NCTM Focal PointsLeading ResearchersCommon Core StandardsCommon Core Standards for Mathematical Practice1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.
Hosted bywww.conceptuamath.comProductive TalkProductive talk is classroom talk by students andteachers that supports the development ofstudents’ reasoning and their abilities to expresstheir thoughts clearly.Stein and Smith. 5 Practices forOrchestrating Productive MathematicsDiscussions. 2011Chapin, O’Connor, and Anderson.Classroom Discussions: Using Math Talk toHelp Students Learn. 2009
Hosted bywww.conceptuamath.comChapin, O’Connor, Anderson. Classroom Discussions: Using Math Talk to Help Students Learn. 2009Productive Talk Moves1. Revoicing: Teacher repeats some or all of what thestudent has said. Students verify.2. Repeating: Asking students to restate someoneelse’s reasoning.3. Reasoning: Asking students to apply their ownreasoning to someone else’s reasoning.4. Adding on: Prompting students for furtherparticipation.5. Waiting: Using wait time.
Hosted bywww.conceptuamath.comOpeners and Closers: Daily Math DiscussionsThe Lesson Sequence Employed in theGriffin RESA ProjectOpener:• 10 – 15 minutes of discussion• Teacher facilitated• Activate prior knowledge• Introduce visual models• Introduce mathematical conceptsGuided Lesson:• 10 – 20 minutes of student work• Independent with teacher supportCloser:• 5 minutes of discussion• Teacher facilitated• Summarize• Check for understanding• Link lessons to big ideas and key concepts
Hosted bywww.conceptuamath.comVideo of an OpenerLook for these talk moves:• Wait Time• Reasoning through Think, Pair, Share• Adding On
Hosted bywww.conceptuamath.comThe Opener ContinuesSome qualities of good classroom dialogue:• Independent student thinking• Sharing with other students• Connecting ideasNote the classroom culture.
Hosted bywww.conceptuamath.comVideo of a CloserLook for these talk moves:• Wait Time• Repeating• Reasoning through Think, Pair, Share• Adding OnNotice how comfortable the students are intalking with one another.
Hosted bywww.conceptuamath.comOutcomes Data: Fractions with Like Numerators24%52%26%30%12% 4%69%82%72%82%75%87%0%20%40%60%80%100%Cowan Rd ES Crescent ES Austin Rd ES Pike ES Upson Lee N ES Daughtry ESComparing Fractions - Gen Ed(Common Numerators)Gr 3-5 Griffin RESAPre (Sept 2012) Post (Apr 2013)14% 6% 0% 13% 0%50% 55%75%44%21%0%20%40%60%80%100%Cowan Rd ES Crescent ES Austin Rd ES Pike ES Upson Lee N ESComparing Fractions - SWD(Common Numerators)Gr 3-5 Griffin RESAPre (Sept 2012) Post (Apr 2013)
Hosted bywww.conceptuamath.com76%24%Always/ UsuallySometimes/ RarelyTeacher Self-Assessments76%24%Always/ UsuallySometimes/ RarelyTeachers areComfortable TeachingFractionsTeachers are Utilizingthe 5 Talk MovesResults of the Pilot
Hosted bywww.conceptuamath.comGaining Deep Mathematical Knowledge• Concerned about deep knowledge– Students can be strong procedurally. . .– . . . but lack deeper understanding.• Attending to precise language– Studying math progressions inCommon Core Standards– Adding more discourse into thecurriculum– Daily Openers and ClosersPetit. Focus on Fractions: Bringing Research into The Classroom. 2010
Hosted bywww.conceptuamath.comAnalyzing an OpenerTeacher behaviors:• Knowledge of the language in the CommonCore• Employing talk movesStudent behaviors:• Using preciselanguage• Explaining theirreasoning
Hosted bywww.conceptuamath.comStudents use Precise Language
Hosted bywww.conceptuamath.comMultiplication of Fractions – FosteringUnderstanding• Students have procedural knowledge.– 3/4 x 2/3 = 6/12– They could multiply across without understandingthe meaning.• Deep understanding was needed.Real Life Situation Analyzing the ProblemSarah wrote 3 1/2 pages in an hour andshe spent 1 3/4 hours writing her report.How many pages long was her report?“groups of”1 ¾ groups of 3 ½ pagesJeremiah mowed his lawn. The lawn was3/5 of an acre, and he mowed 3/4 of thelawn. How many acres did he mow?“parts of”3/4 part of 3/5’s of an acre
Hosted bywww.conceptuamath.comMultiplication of Fractions – Deep LearningRich DiscussionPointsThe story problemand paraphraseModelsEquation
Hosted bywww.conceptuamath.comMultiplication of Fractions – Results
Hosted bywww.conceptuamath.comReflecting on Lessons Learned Today• Rich classroom discussions• Students:– Thoughtful– Speaking freely– Expressing different viewpoints– Using precise language• Teachers:– Using wait time– Revoicing– Repeating– Adding on
Hosted bywww.conceptuamath.comStrategies for FosteringRich Discussions• Make sure your lesson plans incorporate richclassroom discussion.– Time is allocated– A culture is created• Teach content that is engaging.– Visual– Conceptual– Real life• Use productive talk moves.• Study and employ the Common Core Standardsfor Mathematical Practice.
Hosted bywww.conceptuamath.comwww.conceptuamath.comEasy Access to Rich Classroom DiscussionsStart a Classroom PilotWe are repeating this webinar next Wednesday at 5:00 pm eastern.https://www.conceptuamath.com/app/pilot
Hosted bywww.conceptuamath.comContact InformationMary Elizabeth Mendenhallmaryelizabeth@bellsouth.netConnie Laughlinlaughlinconniem@gmail.comConceptua Mathwww.email@example.com
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