COURSE AIMS AND OBJECTIVES: The goal of the course is to educate students / future teachers how to apply Information and communication technologies (ICT) in preparing and delivering their forthcoming lectures, as well as in their own growth and research.
COURSE DESCRIPTION AND SYLLABUS:
I Concepts of ICT applications in mathematics education
1. Introduction. Standards of modern mathematics education. Organization of teaching mathematics with regard to available equipment (classrooms equipped with calculators, LCD projectors, one or more computers ... ).
2. Principles, planning and presentation of lectures. Choosing topics and problems in mathematics, convenient to be explored and presented using ICT.
3. Software tools. Types of tools that can be used in teaching and their features: general tools (spreadsheets, presentation software), specialized tools (graphical calculators, dynamic geometry programmes, professional mathematical programme systems). Multimedia. Advanced ICT applications (digital tutorials, distance education).
II Mathematical topics presented using ICT
1. Elementary functions. Analysis of graphs. Visualizing solutions of equations and inequations.
2. Differential and integral calculus. Giving motivation and illustration of basic concepts in differential and integral calculus.
3. Visualization of proofs in geometry. Performing proofs (Pythagora's theorem, Euler's line, Nine-point circle, etc.) using animations.
4. Geometry constructions. Euclidean constructions. Dependence on given elements. Animation of constructions. Geometric place. Second order curves. Solving challenging problems using computers.
5. Vector. Vector definition and vectors operations using computers.
6. Plane transformations. Isometries (rotation, translation, reflection), homothety, similarity.
7. Stereometry. Intersections of solids (polyhedra, oval solids) with lines, planes and other solids. Conic curves as intersections of cones with planes.
8. Analytical geometry in plane and space. Drawing curves and surfaces.
9. Polar coordinates. Drawing curves and surfaces in polar coordinate system.
10. Data analysis. Drawing data in a suitable way. Elements of probability and statistics.
11. Research and experimenting using computers. Solving various problems in mathematics using ICT.
- A. J. Oldknow, R. Taylor: Teaching Mathematics with ICT
- M. Serra: Discovering Geometry: An Inductive Approach, Quizzes, Tests and Exams
- M. Serra: Discovering Geometry: An Inductive Approach, Teacher's Resource Book
- J. Murdock, E. Kamischke, E. Kamischke: Discovering Algebra: An Investigative Approach, Teaching and Worksheet Masters
- J. Murdock, E. Kamischke, E. Kamischke: Advanced Algebra Through Data Exploration, Constructive Assessment in Maths: Practical Steps for Classroom Teachers
- T. D. Gray, J. Glynn: Exploring Mathematics with Mathematica
- E. Don: Schaum's Outline of Theory and Problems of Mathematica