4.2 PLANNING AND ORGANISATION
The way in which a school organises itself for teaching and learning depends on the vision of education encapsulated, for example, in the school's mission statement, on the collective gifts of the staff, and on the perceived needs of the students. Issues such as time allocated to different subjects and grouping of students within subject areas are addressed against the background of such views. These Guidelines cannot presume to dictate, or to offer detailed suggestions; rather, they can pose some key questions that may inform school planning.
TIMING
One of the eight areas of experience which constitute the curriculum at junior cycle level is "mathematical studies and applications". The current NCCA recommendation is that this area should be allocated at least ten per cent of curriculum time. As pointed out in Section 1.2, the length of the former Higher level syllabus, in particular, was one of the problems to be addressed by the revision. In fact both the Higher and the Ordinary level syllabuses have been shortened, and this should facilitate appropriate learning in the time available. Given the concern about recent poor performance in the Junior Certificate examinations, it is important that sufficient time is allocated for students to develop the required concepts and practise the associated skills.
Once time allocations are made, teachers are faced with the problem of pacing their teaching suitably. Decisions are a matter for the team of teachers of mathematics in the school (as part of school planning) and for the individual teacher. While no prescriptions can be made in this area, two recommendations might be taken into account.
- A slow start, in which an effort is made to establish concepts as well as to develop skills, can provide a firmer basis for later work, and time "lost" at that stage can be regained subsequently.
- The course committee specifically recommends that some work in synthetic geometry is undertaken in each of the three years of the course. However, this does not mean that the formal aspects should be addressed in First Year, when "hands-on" practical and discoveryoriented approaches may be more appropriate (see Section 4.3 below).
To facilitate planning and record-keeping, spreadsheets listing the topics on the syllabus for each level are provided in Appendix 4.
GROUPING
With three distinct syllabuses being provided for Junior Certificate mathematics, decisions have to be made at some stage as to the level at which students should work. Depending on school policy with regard to ability grouping, formal differentiation if it occurs at all may take place as early as the beginning of First Year or as late as shortly before the examinations. The choice of an appropriate time is difficult. On the one hand, premature differentiation may close off avenues of progression at senior cycle level (and hence beyond) for some students; on the other, the three syllabuses are geared to different types of learning, and delayed differentiation may mean that students are faced with material or teaching approaches not suited to their current needs.
Again, prescriptions cannot be made. However, in addition to the issues already raised, the following specific points should perhaps be taken into account.
- Very late differentiation may allow inadequate time for the students to "fine-tune" their approaches to the relevant examination (a source of difficulty suggested in the Chief Examiners' Reports). This applies a fortiori, obviously, when a student takes papers at a level for which s/he has not been prepared.
- When the Foundation level syllabus was first introduced (as Syllabus C for the Intermediate Certificate), it was envisaged that it might be taught by methods more familiar at primary than at second level: that is, in ways suitable for the concrete operational level at which students would still be working. If students remain in Ordinary level classes until they are thoroughly confused, and until they are convinced both that mathematics does not make sense and that they will never be able to do it, they may obtain only limited benefits from eventual transfer to Foundation level.
- However, particular problems are raised by early selection for the Foundation level with respect to progression to the senior cycle and to eligibility for various careers as a result.
Certain teaching approaches may help in allowing students to be kept together, and may give them every opportunity of developing their mathematical abilities before decisions have finally to be made. The approaches include those described in Section 4.3.