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MathsNet's Policy Statement

In August 2001, The Royal Society published its report "Teaching and Learning geometry 11-19". A copy is available on the Royal Society website.
MathsNet is fully supportive of this document, and would tentatively suggest that its Interactive Geometry resources do promote the principles and recommendations of the report.

The report suggested these Key principles:
  • Key Principle 1: Geometry should form a significant component of the mathematics curriculum for all students from 11 to 19.
  • Key Principle 2: Any choice of curriculum should be underpinned by a rationale.
  • Key Principle 3: The geometry curriculum should maintain breadth, depth and balance, and be consistent with Key Principle 2 and the objectives in Recommendation 3.
  • Key Principle 4: Geometry should be given a higher status, together with a fair share of the teaching time available for mathematics.
  • Key Principle 5: Students in 16-19 education should have the opportunity to continue further their studies in geometry.
  • Key Principle 6: The assessment framework for the curriculum should be designed to ensure that the full range of students’ geometrical knowledge, skills and understanding are given credit.
  • Key Principle 7: The most significant contribution to improvements in geometry teaching will be made by the development of good models of pedagogy, supported by carefully designed activities and resources, which are disseminated effectively and coherently to and by teachers.
  • Key Principle 8: It is a matter of national importance that as many of our students as possible fully develop their mathematical potential. Geometry, with its distinctive appeal, should make mathematics attractive to a wider range of students.
The report makes 16 recommendations:
  • Recommendation 1: We recommend that curriculum and assessment specifications be reviewed to ensure that geometry forms a significant component of the mathematics curriculum for all students from 11 to 19.
  • Recommendation 2: We recommend that the title of the attainment target Ma3 of the National Curriculum be changed from ‘Shape, space and measures’ to ‘Geometry’.
  • Recommendation 3: We recommend that the geometry curriculum be chosen and taught in such a way as to achieve the following objectives:
    a) to develop spatial awareness, geometrical intuition and the ability to visualise;
    b) to provide a breadth of geometrical experiences in 2- and 3-dimensions;
    c) to develop knowledge and understanding of and the ability to use geometrical properties and theorems;
    d) to encourage the development and use of conjecture, deductive reasoning and proof;
    e) to develop skills of applying geometry through problem solving and modelling in real world contexts;
    f) to develop useful Information & Communication Technology (ICT) skills in specifically geometrical contexts;
    g) to engender a positive attitude to mathematics; and
    h) to develop an awareness of the historical and cultural heritage of geometry in society, and of the contemporary applications of geometry.
  • Recommendation 4: We recommend that the current geometrical content of the English secondary school mathematics National Curriculum be regarded as a reasonable basis for an appropriate and rewarding geometry education for all pupils.
  • Recommendation 5: We recommend that the mathematics curriculum be developed to encourage students to work investigatively, demonstrate creativity and make discoveries in geometrical contexts so that students develop their powers of spatial thinking, visualisation and geometrical reasoning.
  • Recommendation 6: We recommend that the mathematics curriculum be developed in ways which recognise the important position of theorems and proofs within mathematics and use the study of geometry to encourage the development of logical argument appropriate to the age and attainment of the student.
  • Recommendation 7: We recommend that the mathematics curriculum be developed to provide ample opportunities for students to use geometry for practical problem solving through mathematical modelling in both 2- and 3-dimensions.
  • Recommendation 8: We recommend that the geometry curriculum be developed to give greater emphasis to work in 3-dimensions and to make better use of Information and Communication Technology (ICT).
  • Recommendation 9: We recommend that the use of the word ‘numeracy’ in government publications and announcements be replaced by ‘mathematics’ to ensure that geometry is accorded its rightful position.
  • Recommendation 10: We recommend that geometry should occupy 25% - 30% of the teaching time, and hence a similar proportion of the assessment weighting, in the 11-16 mathematics National Curriculum.
  • Recommendation 11: We recommend that the total time allocated to mathematics 11-16 be monitored to ensure students spend at least 3 hours a week on mathematics, so that sufficient time is given to the teaching of geometry, and to other aspects of mathematics.
  • Recommendation 12: We recommend that a fundamental review be made of all 16-19 mathematics provision. This should include considering how: a) the structure and content of the current AS/A-level Mathematics and Further Mathematics specifications can better meet the needs of students and include a greater emphasis on geometry; and b) other post-16 mathematics qualifications, such as Free Standing Mathematics Units (FSMUs) and AS-level Use of Mathematics, can enable students to have the opportunity to continue their study of geometry.
  • Recommendation 13: We recommend that in the 16-19 curriculum the key skill, ‘Application of Number’, be re-titled ‘Application of Mathematics’ and that the range of qualifying mathematical studies be broadened so that students continue their study of geometry.
  • Recommendation 14: We recommend that a review be made of the methods of assessment and examination used in mathematics at Key Stage 3, at GCSE and in post-16 qualifications to ensure that appropriate credit is given for the attainment of specific geometrical objectives.
  • Recommendation 15: We recommend that the relevant government agencies work together, with bodies such as the mathematics professional associations represented on JMC, to provide a coherent framework for supporting the development of teaching and learning in geometry. This will involve:
    a) the recognition and development of good practice in geometry teaching through pilot studies and research;
    b) the design of programmes of continuing professional development and initial teacher education;
    c) the production of supporting materials; and
    d) the establishment of mechanisms to provide supporting resources, including ICT.
  • Recommendation 16: We recommend, in terms of mathematics in general, that: a) better publicity and information be provided to schools, students and parents about the career opportunities afforded by studying mathematics; and b) ways be sought to encourage schools and colleges to attract more students to study mathematics post-16, particularly at A-level.
Page 10 of the report:
The revision of the National Curriculum by QCA in 1999 gave the opportunity for greater exemplification of the ways in which Information and Communication Technology impacts on many subjects and their teaching. Yet there is very little specific reference to the use of ICT in the mathematics National Curriculum in general, and in geometry in particular. Geometrical software is now widely used in, for example, engineering and design. Through government and commercial initiatives many secondary schools and colleges have acquired powerful Computer Aided Design and Computer Aided Manufacture (CADCAM) packages for use in teaching Design and Technology. By contrast relatively few schools have access to software for teaching geometry in mathematics. Yet by using such software in appropriate ways, pupils can apply their ICT skills to increase their knowledge and understanding of geometry. The software also provides them with the opportunity to acquire and practise geometrical skills. Opportunities occur when pupils create, analyse and interpret dynamic spatial images; make and test conjectures about geometrical relationships that they can manipulate; and record and present the results of their investigations.

As with any approach to teaching, the educational use of ICT needs to be well thought through and carefully planned. The TTA has produced documentation to accompany the current programme of lottery funded ICT training for all teachers in which it emphasises the importance of a critical approach to the use of ICT. This expects teachers to know where, when and how to apply ICT to enhance the teaching and learning of their subjects. This advice is particularly important in geometry where a variety of approaches is needed including mental, practical, and ICT enhanced work. Increasingly powerful software is becoming available in education, such as that designed for simulations in science and geography, much of which relies on sophisticated mathematical algorithms. Pupils and teachers in all subjects need to be cautious about accepting computer produced results without question, and mathematics is probably the subject best placed in the curriculum in which to engender a critical approach. In teaching geometry, caution is particularly needed to avoid making assertions based solely on computational illustrations.

Page 28:
“The current school curriculum, particularly up to GCSE but also even at A-level, fails to give pupils much idea of the nature of mathematics as an intellectual subject. ... Euclidean geometry is an ideal topic in this context, since it can be handled at school level and give some idea of the intellectual nature of mathematics.” Chair of Mathematical Physics Group of Institute of Physics, and ex-school teacher

“I do not think that there is any point in trying to learn geometry as a spectator, by which I mean being shown pretty pictures, being told certain geometrical facts, but largely avoiding getting to grips with proofs, reasoning, and problem-solving. ... (Dynamic geometry packages) are useful tools for the geometer, ... [but] I do not think that playing around with these packages is any substitute for learning how to construct and write out an argument.” University lecturer in mathematics
© MathsNet 2001