Methodology of teaching sciences with computational perspective

Introduction

• About iCSE4school project
• School in digital era

Science Education with SageMath

• xWhy SageMath?
• SageMath in nutshell

Teaching materials: Mathematics

• Limit and continuity of a function at a point
• From point to point
• Amazing approximation
• RSA asymmetric cipher.
• Polynomial approximation
• First order differential equations

Teaching materials: Physics

• Examining string vibrations
• Sound Waves
• Acoustic Effects
• Accelerated motion
• Collisions

Bavarian final secondary-school examinations in mathematics

In this chapter we present numerous examples how SageMath computer algebra system can be usefull in problem solving. We have choosen matriculation exams with mathematics which have been conducted in years 2013-2016 in Bavaria (Germany). Many tasks one can solve just by typing solve (..) which demonstrates usability of the software, but is the same timenot very educational. Therefore in some problem the simulation and visualization are used as addtional tools helping in understanding the underlying theory. As a result, the following materials may serve as practical “cookbook” on SageMath.

Analysis

• Maximal domain and tangent of the square root function
• Function and its codomain
• Nonlinear equation
• Function and its aniderivative
• Properties of the graph of the function
  • Part 1
  • Part 2
  • Part 3
• Properties of the logarithm
• Properties of the x sin(x) function
• Intersection point
• Integrals of semicircle
• Asymptotes
  • Problem 1
  • Problem 2
  • Problem 3
• Extremum of the function
• Zeros and antiderivative
• Properties of sin(ax) +c
• The construction of periodic functions
• Graphing the antiderivative
• Inflection points
• Optimisation problem in analytical geometry
• Properties of the square root function
• Rational function
  • Problem 1
  • Problem 2
• Nonlinear equation
• Properties of graphs of functions
• Properties of sin(2x)
• Construction of the function given its properties
• Determine parameter when the derivative vanishes
• Domain and values of the lograrithm
• Intergral of a symmetric function
• Qubic function
• Properties of the function
• The construction of functions given set of properties
• Graphical integration

Stochastics

• Blood types statistics
• Statistics of a medical test
• Random Game
• Survey
• Null hypothesis
• Expected value of election process
• Two red and three white balls...
• Bernoulli process
• Random variable and expected value
• Tree diagram
• JIM - survey data analysis
• Scrapbook
• The wheel of fortune
• Biathlon
• Talkshow
• Tree diagrams
• Tossing a coin
• Seminar problem

Geometry

• The pyramid
• Straight lines in 3d
• The prism
• The plane
• The cuboid
• The sphere
• The triangle
• A house
• The parallelogram
• The pyramid and vectors
• The cube
• Lines and points in 3d
• Planes and vectors

Conclusion and outlook

• How to successfully implement the methodology