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The reform Of mathematics 2010-20…

The reform Of mathematics 2010-20…. The reform Of mathematics in 2010. THE MANDATE OF THE WORKING PARTY. To adapt the European syllabuses to the changes in the national syllabuses over the last 20 years. To consider the enlargement of the EU from 10 to 27 member countries.

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The reform Of mathematics 2010-20…

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  1. The reform Of mathematics 2010-20…

  2. The reform Of mathematicsin 2010

  3. THE MANDATE OF THE WORKING PARTY • To adapt the European syllabuses to the changes in the national syllabuses over the last 20 years. • To consider the enlargement of the EU from 10 to 27 member countries. • To integrate the changes induced in the teaching of mathematics by the development of technology. • To reconsider the syllabuses and the Baccalaureate with regard to the changes implemented at the universities in member states of the EU. • To find a compromise between the different teaching cultures and assessment methods of teachers coming from all the member states. • To create an in-service training structure for the teachersto guarantee a high level of teaching and to insure common standards for examinations.

  4. THE PHILOSOPHY OF THE REFORM • The teaching of mathematics cannot be replaced by the simple use of technology. Technology is a tool and not the content of the syllabus. • The teaching of mathematics must be opened to more exploration, problem solving, reasoning and reflection. • The basic concepts and skills in mathematics must be well understood before using technology. • The classrooms have to be transformed into laboratoriesof mathematics in order to change the teaching methods,to encourage exploration and discussion. • Teaching of mathematics needs a larger differentiation between strong and weak pupils, a higher motivation of the pupils and a larger interdisciplinary approach. • The use of the technical support must be the same for all pupils, at all the levels and guarantee equal conditions at examinations.

  5. THE BASIC DECISIONS OF THE WORKING PARTY • The syllabuses define the competences, the knowledge and the skills the student must be able to handle. • All syllabuses are presented in 3 columns. the skills in using the tool to deepen notions, to explore problems and/or to search for solutions the knowledge and the skills the student must be able to handle without any technological tool

  6. THE BASIC DECISIONS OF THE WORKING PARTY • Evaluations are always based partly on examinations without any support of a technical tool and partly on examinations with this tool. • All students in all European schools use exactly the same technical tool in class, at home and during all their examinations.

  7. THE FORM OF THE SYLLABUSAN EXAMPLE FROM THE S4 SYLLABUS Pupils must be able to / understand: • recognise that one value depends on another value and define a function accordingly • know and recognise a linear function y = mx + p • transform an equation ax+by=c in the form y=mx+p and the converse • recognise that the graphical representation of ax+by=c ( inclu-ding when b=0 or a=0 ) is a straight line and the converse (with and without a calculator) • understand the meaning of m and p • define geometrically m and p • Pupils must be able to /understand: • use of the Graph option (variation of m and p) • use of the Window (grab and move) • use of Intersection and Slope • draw the graph of a linear function • use cursors to vary m and p • use Function table to plot a set of (x, y) values and the graph of a linear function Linear dependency and proportionality - 1st degree functions and equations

  8. BASIC EXERCICE VERSUS PROBLEM SOLVINGAN EXAMPLE OF A CLASSICAL EXERCISE • Consider the family of functions fdefinedby: withreal and strictlypositive and notingthat C is the curve representingfin the orthonormalplane. • Determine the realvalue of sothat the curve passes through the origin. • Show that all the curves C have a minimum and express thecoordinates of this minimum as a function of . • Determine the equation of the curve uponwhich these minimumsliewhen the range of  is real and strictlypositive. • In the remainder of thisquestiontake=2 notingforsimplicity f2=f and C2=C. • Determineforthisvalue of : The zeros of the function f; The asymptotes of • the curve C; The regions of x forwhich f increases and forwhichit • decreases, and anyextrema of f; The point of inflexion of C; The equation of • the tangent to C at the point of inflexion. • 5. Sketch the curve C and the tangent at the point of inflexion in the • same diagram. • Let A(t) be the areadefinedby C, the horizontal asymptote and the linewithequation y = t where t is real and strictlynegative. Calculate A(t). • 7. Calculate: lim A(t) when t -∞

  9. BASIC EXERCISES – REAL PROBLEMS

  10. BASIC EXERCISE VERSUS PROBLEM SOLVINGAN EXAMPLE OF AN REAL PROBLEM Proof, that if you put the five points on the right inside the triangle, at least 2 of them are not separated by more then 1 cm. Here the proof And now the 5th point? 2 cm 2 cm 1 cm <1cm 1 cm 1 cm 2 cm 1 cm 1 cm Paloma or Dirichlet principle

  11. TEACHING MATHEMATICSWITH THE SUPPORT OF TECHNOLOGY Mathematics will always need knowledge, skills and techniques on the one hand, reflection, strategies and proofs on the other. The new syllabuses aim to strengthen these two foundations of mathematical thinking by introducing a new balance in the way these two basic aspects of mathematics are taught in the European schools.

  12. TEACHING MATHEMATICSWITH THE SUPPORT OF TECHNOLOGY The aims of the syllabuses will be reached by:

  13. TEACHING MATHEMATICSWITH THE SUPPORT OF TECHNOLOGY • The use of the technology will begin in the 4th and 6th year of the secondary cycle and grow steadily up to the baccalaureate. • The syllabuses and the assessments take into account the age of the students and the level they have chosen to study mathematics.

  14. THE USE OF TECHNOLOGYDURING THE ASSESSMENT • All examinations evaluate the students on • their basic knowledge and skills without the use of technology, and • on their competences in real problem solving with a technological tool available if required. The assessment of the students in these 2 fundamental aspects in the teaching of mathematics is done according to the following scheme:

  15. THE USE OF TECHNOLOGYDURING THE ASSESSMENT

  16. THE USE OF TECHNOLOGYDURING THE ASSESSMENT

  17. CHARACTERISTICS OF THE TECHNOLOGYPART I

  18. CHARACTERISTICS OF THE TECHNOLOGYPART II

  19. CHARACTERISTICS OF THE TECHNOLOGYPART III

  20. CHARACTERISTICS OF THE TECHNOLOGYPART IV

  21. Ti-nspiretechnology HANDHELD & COMPUTER SOFTWARE Dynamic linked multi representations Unique Mathematical Spreadsheet All In One = One Interface (PC & HH) Investigations Document based  Saving of Calculations Reasoning

  22. Multiple Representations of Concepts

  23. Multiple Representations of Concepts

  24. Graphs & Geometry: Geometry - Objects • Point • Line • Segment • Circle Arc • Ray • Tangent • Vector • Circle • Triangle • Rectangle • Polygon • Regular Polygon

  25. Graphs & Geometry: Geometry - Tools • Measurement Tools • Length • Area • Slope • Angle • Text • Coordinates & Equations • Calculate • Scale

  26. Geometry – Constructions • Perpendicular • Parallel • Perpendicular Bisector • Angle Bisector • Midpoint • Locus • Compass • Measurement Transfer

  27. Geometry – Transformations • Symmetry • Reflection • Translaton • Rotation • Dilatation

  28. Graphs & Geometry Views PlaneGeometry View Graphing View PlaneGeometry View WithAnalyticWindow

  29. Parametric Function Polar Scatter Plot Four Types of Graphs

  30. Polar Roses • to see an example of the interactivity • Click the graph

  31. Representation of Families of Graphs

  32. Grab, Move and Graph Quadratic functions Observe the role of the parameters a, b and c. • to see the example • Click the graph

  33. Calculator Calculus Algebra Statistics Matrices Complex Numbers

  34. Calculator Polynomial Tools • Remainder of Polynomial • Quotient of Polynomial • Greatest Common Divisor • Coefficients of Polynomial • Degree of Polynomial

  35. Calculator Series • Enhanced Summation & Taylor Approximation • Dominant Term of Series • Asymptotic Series

  36. Two Other Important Characteristics of the Tool The potential use in other subjects Some connectivity features

  37. Data Collection Sensor Data Logging Easy Link CBR 2

  38. Data Collection

  39. Compatible Sensors

  40. Connectivity Handheld to Handheld • Document Transfer • Operating System ( OS software ) Transfer

  41. Connectivity Computer to Handheld • Document Transfer • File Browser • Backup/Restore • Operating System OS Installation • Screen Capture

  42. Connectivity Computer to Classroom • Document Transfer • Send & Collect • Redistribute • Delete • Operating System OS Installation

  43. CONTACT DETAILS Mr. Wolfgang Fruhauf Secretary European school of Alicante Wolfgang.fruhauf@escuelaeuropea.org Mr. Pierre BrzakalaSecondary inspector, responsible for mathematics, physics and ICT Mr. Luc Blomme ICT coordinator European school of Brussels III Luc.Blomme@eursc.org Members of the working party in the European Schools

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