Memorandum submitted by S Forrest, Teacher of Mathematics in a comprehensive school (11-18) in the Wokingham Authority (Berks)


National Key Stage Tests


The current KS3 tests include many good questions but the overall KS3 assessment system generally does not help the teaching and learning of Mathematics and in many ways actually hinders those things.


Past KS3 papers are often used in classrooms not for the mathematical value of exploring/discussing particular topics/questions but instead merely to practise exam technique in the hope of boosting attainment. This can "switch off" students from maths, with its repetitive nature and its implied emphasis on results for the school rather than improved understanding for the individual.


Last year my Headteacher asked me for my reaction to the KS3 Maths results so I started talking about the progress of individual students and how pleased I was for them. He brushed these comments aside, merely wanting to talk about percentages at each level and comparisons with other year groups/other schools.


The grade boundaries for the KS3 papers also concern me, e.g. on a level 5-7 paper, to award a level 7 for any mark of 87 or more out of 150 is very unhelpful. This does not differentiate between very different levels of attainment. Also, if one third of the questions are targeted at each of the levels 5,6 and 7 then a student who answers all the level 5, most of the level 6 and none of the level 7 questions correctly is being awarded level 7, which seems ridiculous! This system is misleading to students, parents, senior leaders, ... (and gives rise to difficulties over value-added scores, setting arrangements, ...).


The KS3 tests, rather than reflecting levels of mathematical understanding, often indicate more about 'teaching to the test'/exam coaching.


The KS3 tests could provide 'assessment for learning' opportunities if teachers were to use individual questions in lessons for teaching purposes, as some (few?) teachers do. However the KS3 tests currently give rise to a far greater focus on summative assessment rather than formative assessment.


Testing can help to improve levels of attainment e.g. by motivating a student to work hard and to revise or by the follow-up of misconceptions after a test. However currently the actual effects of the KS3 tests seem more often to be stressed teachers/students/parents and pressure from senior leaders on staff to deliver results.


Schools do feel very much accountable for KS3 performance but this, in my school, has unfortunate side-effects e.g. (1) undue focus on league tables and a search by senior leaders for different ways of analysing results to allow a favourable comparison with other schools. (2) attempts to 'assist' measures like free school meals numbers to go into the PANDA (now Raise online?) (ie seeking out more children to apply for free school meals, not for the well-being of the child, but to help with the way in which the school will be categorised!) (3) Pressure from senior leaders to enter students at the next KS3 level upwards e.g. if teaching level 6 and 7 material in the main, enter students of the 6-8 paper to give school results a boost, even though the resulting level 8s will be virtually meaningless.


I believe that there is widespread 'teaching to the test' (and beyond that, 'teaching to the textbook'). 'Hot-housing' at KS2 to boost level 3s to 4s and likewise 4s to 5s certainly occurs and impacts on year 7 teaching, where we need seemingly to 'back-track' and consolidate understanding of material which would supposedly have been covered. This can lead to controversies with senior managers and with parents who are unhappy that we are studying level 5 work (and assessing students as level 5) even a year after the nominal achievement of L5. Thus the narrow focus of teaching, when test results are given too much importance, provides a poor basis on which to build future understanding.


If the personalisation of assessment leads to tests being taken (and retaken) at times to suit individual students, this could well worsen the current situation. Testing would be happening even more often, presumably interrupting lessons. If testing punctuates a student's schooling, rather than being a permanent fixture, there is more chance of real education/learning taking place (provided that assessment is not all 'high-stakes'). Personalised assessment might well also cause significant administrative problems. Furthermore large banks of questions would presumably be needed to produce many different versions of tests, and a reliance on ICT would be highly problematic as a trail version of Key Stage 3 ICT tests in my school has just demonstrated (with frequent technical issues).


Any pressure on schools to push pupils to take tests earlier would be undesirable. The emphasis needs to be on learning, with regular formative assessment ('assessment for learning') but only occasional summative assessment ('assessment of learning'). There is already pressure in my school to accelerate students (e.g. early entry GCSE during KS3, early entry AS level during Key Stage 4). The effects seem mainly to be pressurising students unduly, cutting corners with learning and sometimes taking students out of other lessons to boost performance in the acceleration subject(s)! I am not aware yet of any examples where acceleration has really been enjoyable or inspiring for the students concerned.


Testing and assessment at 16 and after


The questions set in GCSE papers are generally reasonable (although many teachers prefer the style of the KS3 tests). The issue again is the high stakes accorded to GCSE, especially to grade C. There is massive pressure in my school to 'boost' students to grade C, virtually by any means, especially in Mathematics and English because of the new measure for schools of the percentage of the cohort achieving 5 or more grades A*-C including Maths and English. C/D borderline students are constantly mentioned in staff briefings. They are assigned mentors, and extra after school classes are provided for them (at the expense of students above or below them on the ability range). There have been instances of highly motivated, more able students asking to go to certain revision classes after school, and being told that the classes will not be relevant for them as the focus will be exclusively on 'turning Ds into Cs'. No alternative provision has then been made for students in that subject. Furthermore the value which society/universities/F.E. colleges/employers should accord to grade Cs attained in this way is doubtful.


Regarding changes to GCSE assessment, there seem currently to be many unknowns, for instance regarding links between Functional Maths and GCSE, and also the new second GCSE in Maths.


The removal of GCSE Maths coursework is certainly a positive measure. In reality the coursework was an artificial exercise. It did not enhance the learning of Maths. It tended to assess an ability to 'jump through hoops' (ie coursework criteria) rather than genuine creativity and reasoning skills. There was widespread abuse of the system, with teachers disclosing too much to students (e.g. about what to include), with teachers leading their classes through the tasks and with teachers marking and correcting draft versions of coursework and returning the work to students for improvement (which was against the rules). Many students nationally were submitting work which was actually attributable more to their teachers and/or parents and/or school friends and/or private tutors and/or internet websites than to themselves!


Uncertainties about the new 14-19 diplomas give cause for concern. Functional Maths will be a part of them and it should be taught by Maths specialists but how this will be managed on the ground is unclear (as students from each school will presumably go to different venues depending on which diploma they are doing but also come back to 'base' for some teaching). There are concerns that Mathematics will be assessed differently within each diploma, with questions not set centrally but instead by a whole host of awarding bodies in the various vocational/commercial sectors.


Modular assessment does alter the scope and style of teaching (and the approach of students). It certainly boosts exam results both at GCSE and at AS/A2 level (which was perhaps a reason for its introduction by commercially-driven examining bodies competing for business?) At each assessment students are only tested on part of their course, so teaching may well have been very sharply focused on the criteria for that module (at the expense of deeper understanding and of making links between concepts in different modules). The fact that students can resit modules can also be harmful, with some students not taking the first sitting seriously and ending up with large amounts of modules to sit in the January/June of the A2 year from each of their subjects. Testing, rather than learning, becomes dominant again.


University entrance decisions will now be made based on actual module marks as the grades were not found to be sufficiently informative. Likewise the setting of entrance tests by individual universities suggests a dissatisfaction with the data provided by Key Stage 4/5 (GCSE, AS, A2) tests.



Coursework is still an option in some AS/A2 Maths modules but my school does not choose to do it. This is because it did not enhance students' understanding of the subject (but instead tested how well they could adhere to published marking criteria) and because the external assessment of the coursework varied greatly in standard from session to session.


May 2007