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Math 277: Geometry for Elementary Teachers. Prepared for: NSF Site Visit June 8, 2005. Design Team Members. Prof. Ric Ancel Mathematical Sciences Dr. Hank Kepner Curriculum & Instruction Melissa Hedges Teacher-in-Residence. Review of Standards. National Standards (PSSM) - PowerPoint PPT Presentation

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Math 277: Geometry for Elementary TeachersPrepared for:NSF Site Visit June 8, 2005

Design Team MembersProf. Ric Ancel Mathematical Sciences

Dr. Hank Kepner Curriculum & Instruction

Melissa Hedges Teacher-in-Residence

Review of StandardsNational Standards (PSSM)Wisconsin Model Academic Standards for 4th and 8th gradeMilwaukee Public Schools Learning TargetsMET Report

End result: Compilation of a comprehensive list of Geometry topics

Course Goalsand Anticipated OutcomesDevelop students:ability to visualize problemsfamiliarity and facility with a wide range of geometry facts and problem solving techniquesunderstanding of logical structure of geometry axioms, conjectures, theorems and counterexamples

Course OverviewGeometry as a measuring toolGeometry of the EarthGeometry as a logical systemRigid motions and symmetry

Topic 1: Geometry as a Measuring ToolPythagorean theoremSimilar trianglesMeasurement of large scale distances and heightsUnits and accuracy issues

Topic 2: Geometry of the Earth Spheres, planes, lines, great circles, axes and antipodes Latitude and longitude coordinates Rotation of Earth and seasons Eratosthenes and class measurements of the Earths circumference

Topic 3: Geometry as a logical systemThe axiomatic method Axioms for geometry Theorems and proofs Incomplete proofs of basic geometry theorems Incomplete proofs of properties of quadrilaterals and their diagonals

Topic 4: Rigid Motions and SymmetryPatty paper constructionsTranslations, rotations, reflections and glide reflections: definition, construction and identificationGroup concepts for rigid motions: identity, composition and inverse

A typical day in classIntroduction to the subject by the teacherSmall group exploration of subjectReport by groups to whole class and class-wide discussionConnect to sample activities from K-8 curriculumDiscuss and assign homework

Sample Problem 1Which of the following types of sets can occur as the intersection of a sphere of radius r and a plane in 3-dimensional space?a) The empty set b) One point Two points A circle of radius r A circle of radius < r A circle of radius > r A non-circular ellipseTest your answers by slicing an orange.

Sample Problem 2Rank the distances between the following five pairs of points on the globe from smallest to largest.a) 62S, 85E and 62S, 110Eb) 70S, 140W and 80S, 40Ec) 62N, 170E and 62N, 170Wd) 12N, 115W and 37N, 115We) 17S, 10E and 17S, 15Wc < a < e < d < b

Classroom approach to a problemStudents discuss problem in small groups with occasional coaching from teachers.Representatives of groups present their solutions to class.Class discourse on student solutions facilitated by teachers

Accomplishments and ChallengesAccomplishmentsDesign team collaborationClass format encourages student engagement and enthusiasm.Daily lesson plans

ChallengesRefine activities, add topicsThought provoking written homeworkTension between concepts needed to learn geometry vs. the large number of topics taught in school

Topics to be shoehorned into courseTrigonometry?Creation of proofs in incidence geometryVolume and surface area of cylinders, cones and spheresUse of dynamic geometrySymmetry of plane patterns: cyclic, dihedral, frieze and wallpaper groupsTesselations of the plane