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Crowley, demonstrates that the NCTM now recognizes that there are two basic questions concerning geometry education: How is geometry best taught? How does a student learn geometry? ZAZZ;+Q$A  GThe van Hiele Model is based on four levels of geometric understanding:2H$$4$Level 0: Visualization  students are aware of space, but only as something that exists around them. Level 1: Analysis  through observation and experimentation students begin to discern the characteristics of figures. Level 2: Informal Deduction  students can establish the interrelationships of properties both within figures and among figures. Level 3: Deduction  the significance of deduction as a way of establishing geometric theory with an axiomatic system is understood. Level 4: Rigor  non-Euclidean geometries can be studied and different systems can be compared. xB\ m x |Y Part Two: A View of Problem Solving and Applications contains four articles. The focus of this section is to create real-world problems, which require the use of geometric concepts in order to be solved. Part Three: Activities in Focus contains five articles. The new  hands-on approach to geometry teaching can easily be understood through articles such as Visualizing Three Dimensions by Constructing Polyhedral and Conic Section: An Exciting Enrichment Topic. dZ4}7+ Part Four: A Look at Geometry and Other Mathematics continues to stress the need for geometry to be part of the whole of mathematics. Included are four articles: Probability in High School Geometry Mathematical Applications of Geometry Geometry for Calculus Readiness Geometric Counting Problems Part Five: Preparing Teachers again advocates the need for complete teacher training. It contains two articles: Activities with Teachers Based on Cognitive Researcher and Geometry for Secondary School Teachers. ZZZZ3pNCTM Standards 1989$lThese three NCTM Yearbooks demonstrate growing changes in the pedagogical philosophy of teaching geometry. This evolutionary process resulted in the driving force of geometry methodology in today s classrooms: Curriculum and Evaluation Standards for School Mathematics, NCTM 1989 (known as the 1989 Standards). Followed by the Professional Standards for Teaching Mathematics (1991), and Assessment Standards for School Mathematics (1995)8 F / +Reason for standards:(NCTM states,  These standards are one facet of the mathematics education community s response to the call for reform in the teaching and leaning of mathematics. They reflect, and are an extension of, the community's responses to those demands for change. The NCTM Standards is an attempt to improve all of mathematics education with the inclusion of all students. The specific standards relating to geometry education for grades nine through twelve are as follows: VZM f 5GRADES 9-12 Increase Attention Decrease AttentionL6    @Integration across topics at all grade levels Coordinate and transformation approaches The development of short sequences of theorems Deductive arguments expressed orally and in sentence or paragraph form Computer-based explorations of 2-D and 3-D figures Three-dimensional geometry Real-world application and modeling AA Euclidean geometry as a complete axiomatic system Proofs of incidence and betweenness theorems Geometry from a synthetic viewpoint Two-column proofs Inscribed and circumscribed polygons Theorems for circles involving segment ratios Analytic geometry as a separate courseZCall for new and improved standards: Principles and Standards for School Mathematics 20008[$5$Principles and Standards for School Mathematics is intended to be a resource and guide for all who make decisions that affect the mathematics education of students in prekindergarten through grade 12. The recommendations in it are grounded in the belief that all students should learn important mathematical concepts and processes with understanding. There are three components of the 2000 Standards: Principles of School Mathematics Content Skills of School Mathematics Process Skills of School Mathematics |ZkZZ/ sk!Principles for School Mathematics"!(The Equity Principle The Curriculum Principle The Teaching Principle The Learning Principle The Assessment Principle The Technology PrinciplezNPrinciples and Standards for School Mathematics Content Skills Process Skills4O/PNumber and Operations Algebra Geometry Measurement Data Analysis and Probability LProblem Solving Reasoning and Proof Communication Connections RepresentationXPrinciples and Standards for School Mathematics- regarding Geometry ALL STUDENTS should-~Y0$Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Specify locations and describe spatial relationships using coordinate geometry and other representational systems Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning and geometric modeling to solve problemsZTechnology in GeometryyAssessing Justification and Proof in Geometry Classes Taught Using Dynamic Software, by Enrique Galindo (Mathematics Teacher 98 January: 76-82). Implications of Using Dynamic Geometry Technology for Teaching and Learning, by John Olive (Paper for Conference on Teaching and Learning Problems in Geometry 00 May, can be located at http://jwilson.coe.uga.edu/EMT899/Olive.doc hzZSLo+,Galindo s suggestions:(Use a build-up strategy--pencil and paper, moving toward manipulatives such as Geo boards; concluding with the dynamic software. Progression of the students should move from the general to the specific, concluding with the student testing their conjectures using the geometry software. Testing their own personal conjectures should lead the student to desire to prove their conjectures.RZ`Statement from Dr. Olive: At the secondary level dynamic geometry environments can (and should) completely transform the teaching and learning of mathematics. Dynamic geometry turns mathematics into a laboratory science rather than the game of mental gymnastic, dominated by computation and symbolic manipulation, that it has become in many of our secondary school. As a laboratory science, mathematics becomes an investigation of interesting phenomena, and the role of the mathematics student becomes that of the scientist: observing , recording, manipulating, predicting, conjecturing and testing, and developing theory as explanations for the phenomena. |Z| >Concerns of the future of geometry teaching (class discussion)?>$OTechnology Curriculum Assessment Motivation Training Administration Colleagues !-Reflection and Conclusion (class discussion).-$What are the objectives of learning and teaching geometry? What are my own experiences of learning and teaching geometry? 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WilsonGEMAT.G4.9:Microsoft Office 98:Templates:Presentation Designs:Dad's TietJames W. 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Crowley, demonstrates that the NCTM now recognizes that there are two basic questions concerning geometry education: How is geometry best taught? How does a student learn geometry? ZAZZ;+Q$A  GThe van Hiele Model is based on four levels of geometric understanding:2H$$4$Level 0: Visualization  students are aware of space, but only as something that exists around them. Level 1: Analysis  through observation and experimentation students begin to discern the characteristics of figures. Level 2: Informal Deduction  students can establish the interrelationships of properties both within figures and among figures. Level 3: Deduction  the significance of deduction as a way of establishing geometric theory with an axiomatic system is understood. Level 4: Rigor  non-Euclidean geometries can be studied and different systems can be compared. xB\ m x |Y Part Two: A View of Problem Solving and Applications contains four articles. The focus of this section is to create real-world problems, which require the use of geometric concepts in order to be solved. Part Three: Activities in Focus contains five articles. The new  hands-on approach to geometry teaching can easily be understood through articles such as Visualizing Three Dimensions by Constructing Polyhedral and Conic Section: An Exciting Enrichment Topic. dZ4}7+ Part Four: A Look at Geometry and Other Mathematics continues to stress the need for geometry to be part of the whole of mathematics. Included are four articles: Probability in High School Geometry Mathematical Applications of Geometry Geometry for Calculus Readiness Geometric Counting Problems Part Five: Preparing Teachers again advocates the need for complete teacher training. It contains two articles: Activities with Teachers Based on Cognitive Researcher and Geometry for Secondary School Teachers. ZZZZ3pNCTM Standards 1989$lThese three NCTM Yearbooks demonstrate growing changes in the pedagogical philosophy of teaching geometry. This evolutionary process resulted in the driving force of geometry methodology in today s classrooms: Curriculum and Evaluation Standards for School Mathematics, NCTM 1989 (known as the 1989 Standards). Followed by the Professional Standards for Teaching Mathematics (1991), and Assessment Standards for School Mathematics (1995)8 F / +Reason for standards:(NCTM states,  These standards are one facet of the mathematics education community s response to the call for reform in the teaching and leaning of mathematics. They reflect, and are an extension of, the community's responses to those demands for change. The NCTM Standards is an attempt to improve all of mathematics education with the inclusion of all students. The specific standards relating to geometry education for grades nine through twelve are as follows: VZM f 5GRADES 9-12 Increase Attention Decrease AttentionL6    @Integration across topics at all grade levels Coordinate and transformation approaches The development of short sequences of theorems Deductive arguments expressed orally and in sentence or paragraph form Computer-based explorations of 2-D and 3-D figures Three-dimensional geometry Real-world application and modeling AA Euclidean geometry as a complete axiomatic system Proofs of incidence and betweenness theorems Geometry from a synthetic viewpoint Two-column proofs Inscribed and circumscribed polygons Theorems for circles involving segment ratios Analytic geometry as a separate courseZCall for new and improved standards: Principles and Standards for School Mathematics 20008[$5$Principles and Standards for School Mathematics is intended to be a resource and guide for all who make decisions that affect the mathematics education of students in prekindergarten through grade 12. The recommendations in it are grounded in the belief that all students should learn important mathematical concepts and processes with understanding. There are three components of the 2000 Standards: Principles of School Mathematics Content Skills of School Mathematics Process Skills of School Mathematics |ZkZZ/ sk!Principles for School Mathematics"!(The Equity Principle The Curriculum Principle The Teaching Principle The Learning Principle The Assessment Principle The Technology PrinciplezNPrinciples and Standards for School Mathematics Content Skills Process Skills4O/PNumber and Operations Algebra Geometry Measurement Data Analysis and Probability LProblem Solving Reasoning and Proof Communication Connections RepresentationXPrinciples and Standards for School Mathematics- regarding Geometry ALL STUDENTS should-~Y0$Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Specify locations and describe spatial relationships using coordinate geometry and other representational systems Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning and geometric modeling to solve problemsZTechnology in GeometryyAssessing Justification and Proof in Geometry Classes Taught Using Dynamic Software, by Enrique Galindo (Mathematics Teacher 98 January: 76-82). Implications of Using Dynamic Geometry Technology for Teaching and Learning, by John Olive (Paper for Conference on Teaching and Learning Problems in Geometry 00 May, can be located at http://jwilson.coe.uga.edu/EMT899/Olive.doc hzZSLo+,Galindo s suggestions:(Use a build-up strategy--pencil and paper, moving toward manipulatives such as Geo boards; concluding with the dynamic software. Progression of the students should move from the general to the specific, concluding with the student testing their conjectures using the geometry software. Testing their own personal conjectures should lead the student to desire to prove their conjectures.RZ`Statement from Dr. Olive: At the secondary level dynamic geometry environments can (and should) completely transform the teaching and learning of mathematics. Dynamic geometry turns mathematics into a laboratory science rather than the game of mental gymnastic, dominated by computation and symbolic manipulation, that it has become in many of our secondary school. As a laboratory science, mathematics becomes an investigation of interesting phenomena, and the role of the mathematics student becomes that of the scientist: observing , recording, manipulating, predicting, conjecturing and testing, and developing theory as explanations for the phenomena. |Z| >Concerns of the future of geometry teaching (class discussion)?>$OTechnology Curriculum Assessment Motivation Training Administration Colleagues !-Reflection and Conclusion (class discussion).-$What are the objectives of learning and teaching geometry? What are my own experiences of learning and teaching geometry? What does the research reveal about learning and teaching geometry?A THE END<$HAVE A SAFE AND HAPPY HOLIDAY SEASON%%,/H#$%&'()*+, - . / 0 123456789:;<=>?@P# @( =;p; l  C < M  l  C <    H  0޽h ? T3f3fr$J2 $BA