Using Dynamic Geometry Software to Create Mathematical Proofs使用动态几何软件创建的数学证明.ppt

GeoGebra – The Mathematician’s Tool Mark Dawes md437@cam.ac.uk [University of Cambridge, UK] What do I do ? I teach the new mathematics teachers at Cambridge University I work with teachers in the East of England to help them improve their teaching I teach mathematics in a high school in Cambridge This talk How GeoGebra is used in school How GeoGebra could be used in school I will use my experience of schools in England. There will be lots of examples! Teachers learning to use GeoGebra The first file they make … “How can I use GeoGebra?” This is the question teachers ask me In reality this is three questions “How can I use GeoGebra?” Q1] “How does GeoGebra work?” For example: How to draw a circle How to create a Pythagorean diagram How to label an angle How to draw the graph of a function “How can I use GeoGebra?” Q2] “How can I use GeoGebra in the curriculum?” For example: Which topics can I use it in? Which ages of students? “How can I use GeoGebra?” Q3] “What is the pedagogical rationale behind using GeoGebra?” Seymour Papert – creator of “Logo” “In my vision, the child programs the computer.” (Papert, 1980) In English schools: Three modes of using GeoGebra Three modes of using GeoGebra Three modes of using GeoGebra Three modes of using GeoGebra Question: “Make a conjecture about the triangle in a semi-circle. Prove it.” John’s Conjecture Maddie’s Diagram Different ideas Homework “Draw any quadrilateral. Join the midpoints of the sides in order to make a new quadrilateral. What can you tell me about the new quadrilateral?” Homework “Draw any quadrilateral. Join the midpoints of the sides in order to make a new quadrilateral. What can you tell me about the new quadrilateral?” Homework “Draw any quadrilateral. Join the midpoints of the sides in order to make a new quadrilateral. What can you tell me about the new quadrilateral?” How these students used GeoGebra To visualise To make a conjecture To convince To help provide the eleme