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MathBase* Discover the wonders of mathematics through sequenced problem solving.

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Why MathBase? Current mathematics curricula: –Emphasize procedures and skills –Focus on manipulating symbols –Lack context, meaning, discovery –Problems are seen as an end in themselves –Topics are presented as distinct ideas

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The MathBase vision Support and provide curricula that: –Develop conceptual understanding underlying procedures and skills –Integrate reading problems, translate to symbols, perform appropriate manipulations, interpret results –Use problems as windows into general ideas. –Discover connections between ideas and topics

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Foundations Concepts and approach designed and used at Phillips Exeter Academy Instruction is student centered “Harkness Table” discussion model Application to more average students in larger classrooms requires a creative adaptation – MathBase!

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Traditional Approach Text presents information concisely Technical language impedes comprehension Summary is good for reference, not for understanding

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Traditional Approach Examples show mechanics clearly Focus on a specific skill No context Students mimic procedures

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Traditional Approach Exercises are grouped to focus on a specific skill Lots of symbolic repetition Required procedure is generally known in advance “Problem solving” tacked on at the end Disjointed problems Information given to align with selected procedures.

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Traditional Approach Result: Many students –Try to memorize facts and formulas and execute procedures in rote ways –Have difficulty with open ended problems –Can’t apply concepts to new situations –Feel incapable of grasping math –Don’t see math as useful or important –Give up

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MathBase Approach A resource that provides an imaginative sequence of problems that –Lead students through ideas –Have multiple possible answers and approaches –Encourage students to ask and know why something works the way it does –Spirals through different ideas that eventually connect.

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MathBase Approach Initial problems are open ended Reading is integral Technical terms are introduced after the concept has been developed Connections between problems are emphasized Symbolic and verbal practice more balanced Pace and amount of symbolic practice can be customized

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MathBase Implementation: Web based database –Openly available –Collaborative Wiki type structure with moderated problem submissions Customizable extractions –Extract as Word, PDF or HTML –Extractions include links to other resources Online textbooks Kahn Academy, Wolfram Math, etc. Animations

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Using MathBase Users can extract problems to address a wide range of content and process options –Full curriculum –Specific standards (Core, AP, IB, state, etc.) –Supplemental or extension problems –Topical units –Spiral units with multiple related topics –Topic or exam review

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MathBase pedagogy Students do 6-10 problems per night (50 min classes) –Develops rhythm, confidence, reading Students present problems to peers –Develops verbal skills, written communication, spontaneous thinking –Develops listening skills, critical thinking –Supports multiple approaches Instructor models questioning –Other approaches? –What if …? –Have you seen this before…? –How is this related to …? –Ensures appropriate connections and understanding

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Teacher Support: Content includes –Problem sets –Answers –Commentary describing context and connections –Pacing guides –Predefined extractions for common needs

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Implementation Challenges Class size constraints on discussion model Appropriate pace and level (conceptual and reading comprehension) of problems –Can be addressed over time by adding more problems

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Next Steps Identify Collaborators –Content providers Include copyright permissions from PEA, IB, etc. –Content reviewers –Technical (database) design & template Develop alpha and beta user base –Private & public schools & districts –Specific teachers Develop business model & funding –Business/project plan –Private, public, corporate partnership

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Contact Bob Alei –(505) –www.aleimath.blogspot.com/2012/01/mathbase.htmlwww.aleimath.blogspot.com/2012/01/mathbase.html

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