/ European Schools
Office of the Secretary-General
General Secretariat

Ref.: 2010-D-242-en-2

Orig.: FR

Arrangements for acquisition of the ‘calculator’ foreseen by the new mathematics syllabuses

BOARD OF GOVERNORS OF THE EUROPEAN SCHOOLS

Meeting on 14, 15 and 16 April 2010 – Brussels

2010-D-242-en-21/1

Decision of the Joint Teaching Committee

At its meeting of 4 and 5 February 2010, the Joint Teaching Committee approved the entry into force of the new mathematics syllabuses for secondary years 4 and 6 and, hence, their new philosophy, subject to a legal opinion concerning the arrangements for acquisition of the ‘calculator’ implicitly foreseen by these new syllabuses (handheld mobile unit).

The reason is that in future, the mathematics syllabuses for years 4-7 will be supported by a technological tool, which will have to be used by both pupils during their schooling and teachers for teaching. This tool may also be used for science subjects and economics.

This technological tool consists of software, the characteristics of which can be found in Annex 1 (ref.: 2010-D-571-en-2), as approved by the Joint Teaching Committee. The tool selected by the working group and its group of experts isTI-Nspire CAS. This software can be used at present on computers (Mac or Windows operating environment) and on thehandheld mobile units marketed by TEXAS INSTRUMENTS.

Questions raised by the Joint Teaching Committee

A number of the questions asked at the meeting of the Joint Teaching Committee necessitated a more detailed examination of the legal feasibility of imposing on parents the purchase of these handheld mobile units, of a specific brand and model. The brand’s competitors might see in it a misuse of powers – designed to get round the procurement system – and bending of the rules of free competition, which the procurement system is also intended to safeguard.

Outline reply

The questions asked need to be analysed from two angles. The first is the possibility for the Schools of imposing on parents the obligation to purchasematerials and equipment for use at school; the second is the relations which may be established between the European Schools and suppliers of materials and equipment.

According to the legal opinion given, the schools can require pupils to have the materials and equipment necessary for delivery of the curriculum.

Thus, provided that due reasons – either in relation to the syllabus of the course, or in relation to the examination requirements, or in relation to the equality of pupils – are given for each technical specification, no complaints can be made about schools’ imposing the purchase of a calculator meeting those specifications.

This therefore justifies not using a procurement procedure.

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Further to this opinion, the Mathematics Working Group was requested to provide a thorough and detailed analysis justifying each of these specifications in relation to the aforementioned criteria. The report on this analysis appears in ANNEXES 2 and 3 to this document.

Parents should be provided with a list of the possible calculators; if the list comprises a single model, it will be imperative to mention that “in the current state of the market, it seems that this is the only calculator which has the characteristics required by the syllabuses.”

Should it be the case that in the future a competitor offers a product with the required characteristics, parents should be left free to choose the type of handheld mobile unit.

The same line of argument is applicable to the software selected.

It is for this reason that ANNEX 4 stipulates that a group of experts must be formed, whose mandate is to regularly reconsider the choice of technological tool made, in the light of future technological developments and of developments in what is available commercially on the market.

Independently of this document, you will find in Annex 4 the composition of the group of experts as decided by the Mathematics Working Group.

Financial implications

The cost of the mobile unit is approximately €150. Taking account of the number of pupils in the secondary at the beginning of the 2009-2010 school year, that would represent, over a period of four years, for a total of 6 groups of pupils (years 4 and 6 in 2010 and 2011, year 4 in 2012 and 2013), a market of around9,960 mobile units, i.e. an approximate cost of€1.5 million.

As it is up to the parents to buy this mobile unit, the European Schools will not, therefore, be involved in any procedure associated with these purchases.

Consequently, purchase of this mobile unit will have no impact on the budget of the European Schools.

Proposals of the Joint Teaching Committee

In view of the above, it is proposed firstly, that the Budgetary Committee should express a favourable opinion on the conclusions of the Mathematics Working Group (in Annexes 2, 3 and 4)and on the choice of technological tool made by its group of experts and secondly, that it should recommend that the Board of Governors approve the addition of such a mobile unit to the list of materials and equipment for use at school required for the curricula, which is given to parents by the schools at the beginning of the school year, including the aforementioned reservations about the type of mobile unit imposed.

Opinion of the Budgetary Committee and follow-up

At its meeting of 14 to 16 March 2010, the Budgetary Committee expressed a favourable opinion on the proposals of the Joint Teaching Committee requesting it firstly, to express a favourable opinion on the conclusions of the Mathematics Working Group (in Annexes 2, 3 and 4) and on the choice of technological tool made by its group of experts and secondly, to recommend that the Board of Governors should approve the addition of such a mobile unit to the list of materials and equipment for use at school required for the curricula, which is given to parents by the schools at the beginning of the school year, including the aforementioned reservations about the type of mobile unit imposed.

However, the Budgetary Committee recommended that the document be supplemented for the Board of Governors, seeking further information on the following points:

-a) request for clarifications regarding the procedure for purchase of the hardware;

-b) possible financial implications of acquisition of the hardware for teachers;

-c) cost of the software accompanying the mobile unit;

-d) translations of the syllabuses;

-e) in-service training for teachers;

-f) implications of the absence of a Greek version of the software.

Responses to the requests for further information made by the Budgetary Committee

a)Clarifications regarding the procedure for purchase of the hardware

The legal opinion given by the General Secretariat’s legal advisers is that the schools may require pupils to have the materials and equipment necessary for the curriculum to be taught.

Consequently, the schools must not be involved in any way in the purchase procedure or in the actual purchase of this hardware.

In addition to what has already been said above about the question, the following purchase procedure alone must be followed:

1/ The schools will indicate to parents the type of hardware to be purchased, although it is imperative for it to be stated that “in the current state of the market, it seems that this is the only calculator which has the characteristics required by the syllabuses.”

Should it be the case that in the future a competitor offers a product with the required characteristics, parents should be left free to choose the type of mobile unit.

2/ The schools may not tell parents which suppliers they should approach to purchase the mobile unit or even give them a list of possible suppliers.

3/ The group of experts, whose composition will be as described in Annex 4 to this document, will regularly reconsider the choice of technological tool made, in the light of future technological developments and of developments in what is available commercially on the market.

b)Possible financial implications of acquisition of the hardware for teachers

There will be no financial involvement of the schools in acquisition of the hardware for teachers, who will be expected to purchase the hardware in question out of their own pockets.

At present and until 31 October 2010 (see ANNEX 6), there is a special offer allowing teachers to purchase the mobile unit in question and the software at the promotional price of €60. Teachers can also purchase the software separately for €25.

In conclusion to points a) and b), as the schools’budget does not come into play in purchase of the mobile unit for either pupils or teachers, no procurement procedure needs to be envisaged.

c)Cost of the software accompanying the mobile unit

As the mobile unit for pupils comes with the software required as part of a package, there is no extra cost to be factored in.

The software for teachers is currently available at the promotional price of €25.

d)Translations of the syllabuses

The years 4 and 6 syllabuses which enter into force in September 2010 will be translated, in accordance with the decision on the subject taken by the Board of Governors and with the procedures in force, which stipulate notably that“syllabuses must be translated in the Schools by teachers of the subjects concerned, as the General Secretariat’s translators do not have the subject knowledge and skills required to translate properly documents of an exclusively pedagogical nature.”

The translations will therefore be produced with the assistance of teachers and will need to be finalised for the beginning of the 2010-2011 school year. The working group and the Office will make every possible effort to ensure that they are available by the deadline set.

e)In-service training for teachers

Since the 2007-2008 school year, almost a hundred teachers have received training in use of the mobile unit chosen by the group of experts, on the one hand, and in the new mathematics syllabuses, to equip them to teach them, on the other.

As regards the 2009-2010 school year, for budgetary and practical reasons, the ‘Mathematics’ Working Group envisaged organising decentralised in-service training courses. Some of them have already taken place or are planned up to July 2010. A document concerning these training courses will be approved by the Joint Teaching Committee by means of the written procedure.

Details and clarifications concerning these training courses appear in ANNEX 5 to this document, with particular reference to in-service training prior to the entry into force of the new syllabuses and to the structure of ongoing in-service training provision after their introduction.

f)Implications of the absence of a Greek version of the software

There is no commercially available Greek language calculator. As mathematical language is universal, the mathematical part of the tool will not pose any problem for Greek pupils. However, for the text editor part, whose use is not specially required by the syllabus, an update of this part of the software should allow texts also to be written using the Greek alphabet in the future. A specific request regarding the possibility of producing an interface in Greek will be submitted to the manufacturer in due course.

Proposals

In view of the above considerations, it is proposed that the Board of Governors should express a favourable opinion firstly:

-on the conclusions of the Mathematics Working Group (in Annexes 2, 3 and 4);

-on the choice of technological tool made by its group of experts.

Secondly, further to the opinion expressed by the Budgetary Committee and, taking account of the further details added to this document at the Budgetary Committee’s request, it is proposed that the Board of Governors should approve:

-the arrangements for acquisition of the ‘calculator’ foreseen by the new mathematics syllabuses as described in this document

-the addition of such a mobile unit to the list of materials and equipment for use at school required for the curricula, which is given to parents by the schools at the beginning of the school year, including the aforementioned reservations about the type of mobile unit imposed.

The adoption, with entry into force in September 2010, of the years 4 and 6 mathematics syllabuses by the Joint Teaching Committee and the Budgetary Committee will thus be confirmed.

ANNEX 1

/ European Schools
Office of the Secretary-General

Ref.:2010-D-571-en-2

Orig.: FR

/ MATHEMATICS SYLLABUS YEAR 4 to YEAR 7
Characteristics of the technological tool to be implemented

APPROVED BY THE JOINT TEACHING COMMITTEE AT ITS MEETING OF 4 AND 5 FEBRUARY 2010

Entry into force in September 2010

General Overview

This document is intended to describe the characteristics of the technological tool to be implemented in the context of the mathematics syllabus of the secondary classes 4 to 7 of the European Schools. The teacher will use this technology in the classroom and the students will use it at home or during the lessons, tests, exams and the baccalaureate.

Other scientific disciplines must also profit from the use of this technology.

To be selected for use in the European Schools, the technological tool must meet all the characteristics listed in this document.

1. Multi-platform Use

The technology must be available in two different versions:

1.1 As a software on a computer,

to be used by

  • the teacher in a classroom equipped with a computer connected to a projector
  • the pupils in an ICT room or at home

1.2 As a mobile unit (handheld)

to be used

  • by the teacher in a standard classroom
  • by the pupils during the lessons, the tests, the exams and the baccalaureate
  • at home by the pupils who don’t have access to a computer
  • by the pupils in the study hall, in a science lab, in an economics class, etc.

The two modes of use should offer the same features and use identical commands with the same syntax.

2. Use, Storage and Exchange of Documents

The technology should be document-based supporting all different modules. The documents should be saved as regular files and be transferable between computers and mobile units as well.

Files must be compatible: the fact that a document was originally created on a computer or a mobile unit should be immaterial to its future use: it must be possible to continue to use it on any of these two platforms.

3. Modular design of the technological tool

The technology must support the interactive use of the following modules:

3.1 The Dynamic Geometry Module

It must at least allow:

  • the construction of standard geometrical objects
  • the modification of these objects
  • the interactive manipulation of the objects
  • the measuring of lengths, areas, angles, slope of a line, etc.
  • the creation of animations of geometric shapes and the search for loci

3.2 The Interactive Graphics Module

This module should allow the study of functions and families of functions with one or more parameters, and also highlight their properties.

The technology should at least have the following tools:

  • Automated and manual framing
  • Search for critical points
  • Simultaneous display of multiple graphs
  • Use of one or more sliders to represent "parameters"
  • Handling graphs interactively

3.3 Cohabitation of different types of geometric and graphics objects

It is necessary:

  • to have an easy interaction between the two types of objects (geometric and / or graphics)
  • to be able to represent different types of objects simultaneously in a single module

3.4 The Computer Algebra Module

This module must allow the user:

  • to carry out all calculations described in the algebra and analysis syllabus: arithmetic, rational fractions, factorisation or development of factoring expressions, solving equations, calculation of derivatives, primitives, scalar product, vector product,determinants etc.
  • to conduct counts (number of combinations, permutations,) as well as to use the laws of probability and the associated cumulative distributions (binomial, normal distribution, etc.)
  • to solve a problem step by step, to allow students to focus on the learning of the algorithm for solving the problem, while eliminating the risk of calculation errors.

3.5 Interaction between the calculation module and the module of dynamic geometry

It must be possible to:

  • define a geometric object using the values of variables defined in the calculation module
  • conversely, to retrieve in the calculation module the values of some geometrical variables.

3.6 The Spreadsheet Module

Using a spreadsheet is very useful in several areas of mathematics, especially for the study of sequences and statistics.

The technological tool must have a spreadsheet module allowing:

  • all conventional treatment, relative or absolute cell references, quick copying of a formula, conventional representations (bar graphs, histograms, pie charts circular), statistical calculations;
  • Dynamic interaction with other modules;
  • The making of formal calculations directly in the spreadsheet;
  • compatibility to copy-paste data from another source

In addition to the spreadsheet, the technological support must have a specific educational tool allowing the user to:

  • create and adjust a scatter plot by placing a movable line that can freely be moved
  • directly obtain a linear regression
  • work from data contained in the spreadsheet
  • use all types of graphs

3.7 Text Editor Module

The technological tool must include a text editor module to:

  • enter text including mathematical expressions and formulae, notations on the geometry and to assess the value without needing to open the calculation module
  • create documents intended for assessing students' knowledge, to give instructions to students, etc

4. Special conditions concerning the use of technology during an exam/baccalaureate

To avoid fraud, the technological support must have a special "exam" mode in which only the resources of the standard calculator and specific documents for this examination will be available during the duration of thetest.

This special mode does not require the removal (and therefore the potential loss) of data stored in the mobile unit before the examination starts.It is enough to deny access on a temporary basis and must be easy to implement.

5. Special conditions for use in science

5.1 Units and Constants

To better meet the needs of science teaching, the technological tool must allow direct use of physical constants and work on numbers with units.

5.2 Sensors

The mobile unit must have a port for connecting various sensors to store data from experiments directly into a spreadsheet; to analyze the data collected interactively using the different modules available.This use must be possible outside a science lab, in a standard classroom or during field trips.

6. Physical characteristics of the mobile unit

  • It must be possible to update the software of the mobile to avoid the regular change of the mobile unit itself.
  • When working on the mobile unit, the screen size should be sufficient to allow the manipulation of geometric objects, the study of graphs, displaying formulas.
  • The mobile unit must have a colour display with a graphics resolution of 480 * 640 pixels or alternatively, a graphic resolution of at least 240 * 320 pixels with 16 grey levels.
  • The mobile unit must have an alphabetical keyboard, a scientific keypad, a mouse port or another pointing device to replace the use of a mouse.

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