MATHEMATICS

The Mathematics course at LSS in Years 7 – 11 aims to fit the needs of the top ability range of Students for which a grammar school traditionally caters as well as fulfilling the requirements of the National Curriculum and GCSE.

All pupils follow a course eventually leading to Higher Level G.C.S.E by the completion of Y11. In their first year in the school the boys are taught Mathematics as a form subject but subsequently are placed in sets according to ability. Out of a thirty period week each boy will be allocated four periods of Mathematics per week.

In Year 8 three differentiated sets follow topics in parallel but set 1 works to a greater depth. From Year 9 the pupils are placed in one of four differentiated sets. Set 1 works at a faster pace aiming for level 8 at KS3 and eventually the A* grade at G.C.S.E. At the end of Year 11 as well as sitting GCSE Mathematics these pupils are entered for a Free Standing Mathematics Qualification (FSMQ) in “Additional Mathematics”. Pupils in set 2 are aiming to achieve a minimum of a high level 7 at KS3 and a minimum target grade of A at GCSE. Corresponding minimum targets for the remaining pupils are respectively level 7 and grade B. All Y11 students are also entered for a GCSE qualification in Statistics.

At AS and A2 Level students follow a Mathematics course consisting of modules in Pure Mathematics (C1, C2, C4 and C3), Mechanics (M1) and Statistics (S1). A group in each of Years 12 and 13 are also concurrently studying for an A’Level in Further Mathematics which requires the study of a further six modules (FP1, FP2, FP3, S2, M2 AND M3). Students are allocated 6 periods per week whilst Further Mathematics students receive a total of 8 periods per week.

ENTRY REQUIREMENTS FOR MATHEMATICS AT A’ LEVEL:

Mathematics:

Students are required to have achieved at least a grade B in GCSE Mathematics as well as having a sound understanding of the content and concepts from the Higher Tier GCSE. However, this in itself is not sufficient to guarantee success at A’ level. Students are expected to work hard throughout the course as well as maintaining a high level of motivation and interest.

Further Mathematics:

Students are required to be able to demonstrate real talent and enthusiasm for the subject and to have achieved at least a grade A in GCSE Mathematics as well as being prepared to work with commitment throughout the course. This course is particularly recommended to those students who require mathematics for their Higher Education; particularly in Mathematics, Engineering and Science courses as well as those students who have ability in Mathematics and enjoy it for its own sake.

External Examinations

G.C.S.E:

1387 MATHEMATICS - EDEXCEL
1389 STATISTICS – EDEXCEL

FSMQ:

6993 FSMQ (Additional Mathematics) - OCR

AS:

8371 MATHEMATICS (C1, C2, & S1) - EDEXCEL
8372 FURTHER MATHEMATICS (+ FP1, M2 & S2) - EDEXCEL

A2 Level

9371 MATHEMATICS (+ C3, C4 & M1) - EDEXCEL
9372 FURTHER MATHEMATICS (FP1, FP2, FP3, M2, M3 & S2) - EDEXCEL

AIMS

Aims are essentially declarations of intent that give direction and shape to the scheme of work or teaching programme. Although they lack detail that the course’s learning objectives have, they should remain in the forefront of the teachers' mind at all times when he or she is considering the provision of experiences, which lead to the mathematical development of the student.

The general aims are to develop:

1. a mathematics course fitting the top ability range of pupils and students.

2. a positive attitude to mathematics as an interesting and attractive subject.

3. an appreciation of the creative aspects of the subject and an awareness of its aesthetic appeal.

4. an ability to think clearly and logically in mathematics with confidence and flexibility of mind.

5. an understanding of mathematics through a process of enquiry and experiment.

6. an appreciation of the nature of numbers and of space, leading to awareness of the basic structure of mathematics.

7. an appreciation of mathematical pattern and the ability to identify relationships.

8. mathematical skills and knowledge accompanied by the quick recall of basic facts.

9. an awareness of the uses of mathematics in the world beyond the classroom. Students should learn that mathematics will frequently help them to solve problems they meet in every day life or understand better many of the things they see, and provide opportunities for them to satisfy their curiosity and to use their creative abilities.

10. persistence through sustained work in mathematics which requires some perseverance over a period of time.

11. confidence in mathematics, shown by the ability to express ideas fluently, to talk about the subject with assurance and to use the language of mathematics.

12. the ability to work in a systematic way. (This does not only mean that attention is given to careful and accurate execution of routine tasks. It also involves appraisal and review as the execution of the task proceeds. Also it means choosing particular strategies which may be a set routine or an exploration).

13. imagination and initiative;

14. a willingness and ability to work both independently and co-operatively.

THE PLACE OF MATHEMATICS

(The nature of mathematics and why we teach it)

Mathematics, at least in the form of arithmetic, has had an important place in the education of children for a very long time. The obvious reason for this is that numbers are part of everyday life and adults find it useful to calculate at work, while shopping and when engaged in sports and pastimes.

For many years, speed and accuracy in working out sums on paper was important whereas today, with a widespread use of electronic aids, such skills are less vital. However, it is still important to know whether the answer arrived at is reasonable, and consequently there remains the need for the understanding of the processes used, and the ability to estimate what might reasonably be expected as an answer. Facility with mental arithmetic is as important as ever. Mathematics is useful - at one extreme each person needs to know enough arithmetic to make simple purchases, count change, check wages and understand a popular newspaper. In the broader sense mathematics is of fundamental importance for the understanding of the physical sciences and technology as well as being the key to many other areas of knowledge.

In recent years it has become more important to understand the various ways in which mathematical information is presented. Graphs of various kinds and statistical tables are commonplace in the newspapers and on television. Students can get both pleasure and insight if the work is suitable and its implications are sufficiently probed by the teachers.

There is a great deal that mathematics can do for our students. Clearly, it is not essential that every man in the street should know that the ratio between the circumference and diameter of a circle is about three and one-seventh and is represented by the Greek letter ?. Most people get through life reasonably well without realising the shell of a nautilus, the florets in the head of a daisy and a spider's web are all arranged, nearly enough, in the form of equiangular spirals etc. However, many people who have been made aware of these curious but orderly aspects of nature may gain more pleasure in life as a result. There is a whole range of relationships and patterns of a mathematical kind that catch student's imagination and, though they are not essential, it is a pity if some of them are not included.
Mathematics is part of our culture - not only do we teach mathematics to understand the creative achievements of the human mind and the behaviour of the natural world but also to demonstrate the power and enjoyment of doing mathematics for its own sake.

In the course of learning mathematics students have to learn a good many other things. For example, they have to learn to be neat and tidy; for muddled working may produce a wrong answer. They should learn to be careful and they ought to learn to be discriminating. They should learn to check what they have done: they should learn that understanding and knowing how to do something is as important as getting the right answer.

I.C.T. and the Mathematics Curriculum

Subject specific and generic software is used to support and enhance the teaching and learning of mathematics. I.C.T. is used by teachers to enhance their teaching through the use of their wirelessly connected tablet PC’s in conjunction with ceiling mounted data projectors. Using suitable software teachers are able to introduce new ideas and concepts either to enhance conventional approaches or get across new work that would be more difficult to convey by traditional means.

The Mathematics curriculum makes use of spreadsheets for modelling but in addition to the EXCEL spreadsheet other mathematical packages are available: Logo, Autograph and Omnigraph are available on the school’s curriculum computer network for such activities as graphical work and geometrical transformations.

The Mathematics department has a class set of laptop computers which can be issued so that students can work on projects that require using software on the school network or download data from the network. For example, Year 11 students have been able to gain access to real data which they have been able to analyse using statistical techniques and then write up the coursework required for their GCSE coursework in Mathematics and Statistics.

Mathematics Across the Curriculum

The department contributes to Numeracy across the Curriculum in line with the whole school policy. Not only does the department contribute directly in the form of content taught but also helps to set the agenda for defining the focus for a particular year.

The following are some considerations which are taken into account when formulating a policy on mathematics across the curriculum:

• Mathematics is often considered a service subject for other curriculum areas, but given the emphasis on using and applying mathematics in realistic contexts, we should perhaps also consider other subjects as serving the mathematics curriculum. Although, as a mathematics department, we should clearly take a lead in mathematics use across the curriculum, responsibility for delivery should be shared with host subjects.

• From time to time an audit of what mathematics is used, and when, in other areas for each year group may prove useful. This may lead to the rescheduling of topics either within the mathematics scheme of work, or that of the host subject.

• Other subject areas clearly do make use of mathematics. If the approach taught in mathematics and that used in host subjects are not complementary, confusion rather than reinforcement of concepts can result for pupils. It should be our responsibility, as a mathematics department, to indicate the preferred approach to topics. It should be the responsibility of other subject areas to take account of the methodology in planning their own work.

• Consistency across the school need not be limited to methodology. Host subjects could be encouraged to be using the correct mathematical terminology (e.g. histogram vs. bar chart). A vocabulary list similar to that produced in preparation for KS3 SATs in mathematics is a useful starting point.

• Given the familiarity of pupils with ICT, particularly Excel, they are skilled in producing graphs from data. The use of appropriate graphs given the data and its context should be reinforced.

• Appropriate and efficient use of calculators should be made in other subject areas.