Tag Archives: Exam management

2022 GCSE exam content changes : from the modest to the severe


As anticipated the exam Boards such as Edexcel and AQA have published their “advance information” changes to assessment content for the 2022 exams including GCSE. If you recall, the purpose is to offset the difficulties pupils have endured due to the Covid disruptions. The indication is this is just for 2022.

I myself would have kept the content pretty much the same but made the questions easier by making them more on-syllabus, and less obtuse and wordy; but anyway we now have the Boards’ pretty specific topic list of what will or won’t be assessed, and I have taken a quick look at my specialities for Edexcel Maths and AQA Triple and Combined Science (see also web links at the end of the article which cover all subjects). I am sure teachers will be explaining these to pupils and parents alike, but here is my immediate take, initially on Higher.

Towards the end of this document, I also include a little on grade boundaries, formulae sheets and Mock exams and finish with some overall conclusions and take-aways. Also I have included an update on topic-targeted mocks I’ve created.

But let’s start with what is in (the “main focus areas”) and what is out.

Maths Edexcel

For Higher Pearson Edexcel Maths, the amount of content reduction is very low, so most topics are still in there – about 90 topics are listed as “main focus areas” i.e. are “in”. It looks like a few difficult ones like Quadratic Sequence, Completing the Square, Congruence, Volume of cone and sphere, Proofs, and Iteration are excluded from assessment now.

Sometimes there is some ambiguity: compound interest is mentioned in the formula sheet but not in the list of included assessed topics so perhaps will be needed for growth, decay, depreciation; while for Angles the easier parallel line topic seems excluded while the more difficult polygon and circle theorem topics are included.  

Mostly the topic list is precise enough to revise from but not so specific so as to tell you the question – this is as it should be.  But sometimes the description is so specific that you can almost anticipate the question – such as capture recapture, and equation of a tangent to a circle.  

Overall the Maths changes are fair. About 90% of topics remain included. Any exclusions are spread fairly evenly across the main headings of Algebra, Geometry etc.

Ideally (like science below) a list of exclusions (as well as inclusions) would have been stated by Pearson, but hopefully my pointers above will help and no doubt teachers will firm up on these in due course. The implied exclusions will reduce revision time slightly, but note the preamble does ask teachers to teach the full content anyway.  

Science AQA

For AQA science the picture is different from Edexcel Maths; from modest exclusions for Chemistry to almost the opposite for Biology i.e. very few Biology inclusions (Bizarre, I know!). Let me explain.

First Triple. For Chemistry the content at first sight seems to remain largely untouched. There are only two minor “not to be assessed” exclusions listed – nanoparticles and (strangely considering their importance) greenhouse gases.

There are a large number of topic headings listed as “main focus areas of assessment” such as Periodic Table (section 4.1.2). So far so good.

But then you think, what about 4.1.1?   This is the all-important atomic and electronic structure section – which helps you understand 4.1.2 Periodic table – yet is not listed in the inclusions. Similarly, section 4.8 is not mentioned at all – Chemical analyses such as Chromatography and Flame tests – and yet the core Practical involving Flame tests IS included.

(And although I have not looked at Foundation in detail, strangely there are MORE listed topics in Foundation than Higher; so while atomic structure is not listed in Higher, it is included in Foundation. My take on that is this: in Higher there won’t be a specific question on, for example, atomic structure; but pupils would be advised to learn it anyway because it informs so many other parts of the syllabus from Periodic table onwards. I wonder if the Examiners have thought the communication of this through! I think maybe teachers will agree with me and err on the side of caution and continue to teach fundamental topics like this anyway)

I think there is some clarification needed on what needs to be revised. In the preamble to the lists (for all Sciences) the Board indicates that topics not specifically listed as “in assessment” may still be included in “low tariff or linked questions” which confirms my view that pupils should still revise most of the syllabus to be on the safe side.  

On balance I think the list of Chemistry “in topics” does indeed help and is sometimes very specific , like section 4.10.4 (Haber process/NPK fertilisers – so there’s almost certainly a question on this- and it links to another inclusion on Reversible reactions) ; although sometimes less specific (like 4.4.3 Electrolysis). I think they are trying to pinpoint the particular questions likely to be asked.  For all the sciences the devil may be in the detail: the specific numbered subsections may sometimes give the game away.  Myself and teachers will no doubt be trying to second guess these questions!

Note that for Chemistry and all Sciences the Board emphasise that the type of question will not change and the general scientific methods including maths skills and practical experiment interpretation are still needed. The specific core practical list (a bit reduced ) is well pinpointed and I strongly recommend pupils revise the short videos available on these; high chance of specific questions on these practicals.

 For Physics the list of inclusions is narrowed down considerably to essentially Particle Model, Energy, Forces, Momentum, Pressure, Waves and Space.

And unlike Chemistry above, the list of “exclusions from assessment”  is very long and specific. So out go most of Electricity, most or all of Radioactivity and Atomic Structure, and Magnetism altogether. And yet there is some ambiguity to resolve. Section 4.2.4 energy transfer is included and this includes Power, Current and Voltage i.e. electrics; and yet the basics of that, namely amps, potential and circuits from 4.2.1 to 4.2.3 are specifically excluded.

Some of these exclusions are topics which have been a staple for pupils at school since Year 7 and before and it seems actually unfair on pupils to exclude the basics of electricity and magnetism which for some would have been easier than let’s say Space. I suppose you can’t have it both ways: since broad education is meant to be more important per se than the exams themselves, in a sense it does not matter if they are examined on a topic. On the other hand, to “waste” five years work with just a few month’s notice may annoy many pupils, who having already finished the topic by now and would be quite happy to be examined upon them.  

For Biology triple, like Physics there are considerable reductions; the inclusions are narrowed down to Cell Structure, tissues, organ systems, diseases, antibodies, nervous systems, hormones, reproduction, parts of ecosystem.

There are a long list of exclusions, for instance the whole of staples like Evolution won’t be assessed. And again there are ambiguities: nothing from the large section on Section 4 Bioenergetics is included; and yet only a small part ( Taking Exercise) is specifically excluded. Bioenergetics describes the core biology fundamentals of Photosynthesis and Respiration and pupils have learned these no doubt from year 7 and they have featured in almost every past paper. To not test pupils on this seems perverse.  But since very little has been specifically excluded from section 4, should pupils after all revise it anyway? My take is that there won’t be a specific question on section 4 Bioenergetics, but it would be prudent to still revise as it infuses the remainder of the syllabus and there may be a “linked” or low tariff” question on this core topic.

Similarly, 4.5.2 Nervous System is a main focus area, but from it 4.5.1 (structure function), 4.5.2 (brain) and 4.5.3 (eye) are excluded. This is useful as it leaves only 4.5.4 (temperature), implying a specific question. But it would be unwise to ignore the introductory 4.5.1 as it informs 4.5.4.

The list of required Biology practicals, as for other sciences, is reduced but still very specific. So the staple Quadrat and Mass of Potato chips practicals are included as ever and the fact they have survived points very clearly to a question this year (as almost every year) and their video should be watched, understood and learned.

In Combined Science (Higher) the picture is similar as for Triple;

Combined Chemistry lists several very specific inclusions, similar Included content to Triple Chemistry,  and almost zero exclusions mentioned.  

For Combined Physics a focus on Energy and particles as with Triple, but this time including Radiation and Motor Effect and EM Waves (so Combined has more extensive content than Triple!) And again ambiguity: series and parallel circuits are excluded as an assessment topic, yet the required practical on these is Included. Similarly 6.7.2 the Motor Effect – which has its roots in magnetic fields –   is included, yet 6.7.1 the basics of magnetism is excluded.

For Combined Biology, a very short specific list of inclusions and very long list of exclusions. The list of inclusions is slightly different to Triple, for instance Photosynthesis is included.

Discussion on science lists.

There is some ambiguity to be resolved, by the AQA Board or perhaps by teachers. If something is neither included in assessment, nor specifically excluded from assessment, should it still be revised, to be safe, in case “linked or low tariff” questions arise? I think in some cases a topic can be eliminated altogether, but in others it would pay to revise just in case; so some detailed analysis will be required to make that call. If the Exam Boards’ “exclusion lists” are taken too literally, some precious revision may be missed which in fact may contribute to “linked” questions.

For English, if a set book is excluded that presumably can safely be put aside. But for chemistry, if “atomic structure” is not to be assessed, then it would be a mistake to simply not revise it, because it informs so much of the surviving other topics.  

Grade Boundaries
The Boards have indicated that boundaries will be set somewhere between normal, and the last two years.

Mock exams
Many schools have already penciled in exams for after half term in late February 2022. The dilemma for teachers is, shall we complete the syllabus testing as normal to encourage a full learning experience; or shall we adjust them to exclude the “not being assessed” topics, in order to avoid wasted revision time? No doubt teachers will be crawling through the fine detail of today’s lists, just like I have done above!

Formula sheets
For Physics, as before the formulae are extensive. For Maths, intriguingly, some of the few formulae which were given last time are not this time (for spheres and cones) confirming their probable absence from assessment. While formulae like quadratic formulae and sin and cosine rule are included now, indicating their probable inclusion in assessment.

In conclusion

The Boards have rightly kept their promise to publish by February 7th

The timing of the announcement seems about right; earlier, and some topics would not have been taught at all; later and some revision time would have been wasted.

The Exam Boards in their announcements and preambles have stressed they still want as much of the content to be taught and revised as possible. But with their list of exclusions, inevitably the precious, finite teaching and revision time will not be devoted to topics on the “not to be assessed”  lists.  This is useful , as long as care is taken when dropping topics.  

Maths is relatively untouched compared to the sciences and revision should still cover around 90% of topics. The basics are all still there and the exclusions are often niche standalones.  

Chemistry has very few specific exclusions, and a broad list of main inclusions, but gaps in this list indicate some additional topics will not be assessed.

Physics and Biology have long lists of exclusions and short lists of inclusions. The topics have been considerably reduced.  In my opinion reduced too much – some fundamentals have been eliminated.    

But for the Sciences the sub-section numbers listed from the specification which do survive as “included” can often give very specific pointers to the content of the question

A key phrase in the Sciences preamble is “Topics not explicitly given in any (main focus) list may (still nevertheless) appear in low tariff questions or via ‘linked’ questions, (but) topics not assessed (at all) either directly or through ‘linked’ content have been listed as “not to be assessed”.

Hence there is some ambiguity to be resolved in Science in terms of what topics to revise – there are three categories: first, about 70% are essential to revise; and then (15%) topics not listed as key focus areas, yet are fundamentals so may crop up in linked or low tariff questions, and so should probably be revised anyway; and finally (15%) those definitely excluded from assessment – only these can be truly de-prioritised.   

The type of science question is not altered i.e. could still include unusual applications, maths calculations, and practicals: the core practicals listed are very specific and may indicate precise questions – so have high revision priority.

I think the above lists will be communicated and ambiguities resolved for pupils in the coming weeks. If any parent or pupils have questions please don’t hesitate to ask your teachers, or myself as I believe I can help.  


Pearson Edexcel web link to changes in 2022 assessment

AQA web link to changes in 2022 assessment

Update March 7th 2022

I have created Mock exams featuring two or more questions on every one of the Paper 1 , 2 and 3 Higher and Foundation maths Pearson Edexcel inclusion lists. Their specific topic list for each paper is very useful, for instance: in Higher Maths the highly niche topic of Capture Recapture appears only in paper 2 and likewise Frequency Polygon only Paper 3, and a quick refresh just before those exam dates would pay dividends.

I also created topic targeted Mocks for AQA Triple and, separately Combined science, and together with Maths these proved very useful to pupils in their actual Mocks especially as I added my own explanatory notes over and above the sometimes rather bare official mark schemes. I also managed to get some of the very latest exam Board questions in too.

I have also begun to research the 2022 topic lists for the specialist qualifications like Further Maths, iGCSE, and OCR FSMQ and also the Edexcel Sciences.

Playing the examiner’s game

This morning on Radio 4 I heard the story of author Ian McEwan helping his son to write an English essay on one of his own books, only for a low grade to be awarded. The reason – the essay did not answer the question in the way the examiners wanted. As exam season approaches this a crucial topic – I firmly believe that knowing how to interpret questions and structure answers can add many percentage points to a score. Here are some things to look out for:

Command words. Especially on longer mark questions, certain words or phrases in the question require certain responses. For example, in Business Studies and many Humanities subjects the words “evaluate” or “assess” trigger the need to present balanced arguments with evidence and coherent analysis, followed by a conclusion with a definitive yes/no answer with justification.  So, if “evaluate Brexit” (perish the thought!) came up, you would need two Leave points, two Remain points followed by your own preference with the most important point, and reason why, for instance, the economy was more important that immigration control (or vice versa).  Some students miss out the conclusion, and miss almost half the available marks.

In Science, command words include “design”, or “describe an experiment”. Normally this involves a practical experiment, perhaps a core practical, and students should describe not just apparatus and substances, but also the control variables (what you keep the same), the independent variable (what you deliberately change) and dependent variable (what you measure); safety precautions; how you would present results; and how you would ensure reliability, precision and accuracy. A glossary of terms makes dull reading but is vital to understand. Practical write-ups in exercise books are well worth revisiting.

In Maths, the phrase “show that” may involve a proof or rearranging a formula to make it “look like” the required expression, while “must show your working” or “give reasons” means just that – for instance in a geometry question, you could get the right numerical answer but omit English reasons like “alternate angles rule” and fail to get full marks.

Attitude: it is tempting to answer the question you want to answer, rather than the one you have really been asked. So pupils must read questions very carefully, and as well as Command phrases pick up key words and clues in the stem of the question like “more than” or “only” or “double” – examiners have included them for a reason, not for show.

Examiners do now have the annoying habit of asking “real world” wordy questions rather than simple numerical ones. They assume pupils would prefer to answer a question like “Johnny runs part of the London marathon at 5 miles per hour, setting off from Westminster with both hands on Big Ben vertical, and traveling for 15 miles. At what time does he arrive”. Rather than simply “Speed = 5 mph. Distance = 15 miles. Set-off = 12 o’clock. When does he arrive?”  Well, I know which option real-world pupils would prefer, but we just have to get used to the fact that Maths questions are increasingly “applied” rather than “pure”, obtuse not transparent, and so practice makes perfect when it comes to approaching long winded questions.

In general, the examiners and their questions are the only ones you have got, so you simply must play their game and recognise what they are after. If they insist on asking Biology questions about drunken rats (they did!) you should just go with the flow and not flounce out. What is more useful, taking to Twitter afterwards and complaining about a stupid question, or showing resilience and attempting a tough problem?

Assessment Objectives. The curious underworld (which for a time I inhabited) of examiners and their mark schemes is dominated by these “assessment objectives”. So, in Business Studies you gain marks for knowledge, analysis, application and evaluation. In Biology you can accrue marks as you mention one by one in the long questions the relevant systems and organs, processes, and substances and compounds. In Maths “method marks” may be awarded, but only under quite strict guidelines, for instance if you have correctly written a defined key step in your working.   One way to find out about these is to read the publicly available mark schemes and examiners comments on the past paper web sites. In Maths, for instance reviews published by exam boards include lots of pearls of wisdom and often start with, “many pupils were let down by inability to perform basic maths” (In non-jargon, they couldn’t add up).

Examiners have hundreds of papers to mark in a short space of time, so the key is to make it easy for them to award good marks – by mentioning key words or phrases or numbers in the answer which matches their mark scheme, and by displaying well-ordered neat working. A relatively short sharp answer can out-mark a much longer one if you hit the examiners trigger points.

Know the specification. These have got more complicated, partly because of changes like “9-1”. So, for Science GCSE, there is Higher and Foundation in each of Double and Triple. It sounds obvious but revise what you have to revise, and especially if you are going to drop a topic, ignore what’s not required.

Second guessing the content.   It’s a mug’s game to spend time predicting the questions, but a sure-fire topic in all three Sciences is environment and associated climate change, global warming and renewable energy. Also, after let’s say two of three Maths exams, if you have had a Box Plot and Cumulative Frequency but no Histogram, well you can guess what’s coming next. Mr Barton’s Maths website issues an annual prediction, as does Tutor2U for Business.

Structure as well as knowledge. In summary, of course revision of pure facts is important, but it only gets you so far; practicing real questions and comparing your answers to examiner’s mark schemes can get you much further. If you can’t beat examiners, then join them, play their game and give them the answers in the form they require.

Footnote: an old school-friend who read this article reminded me that our Geology teacher Dusty Rhodes (so named because he threw the blackboard duster at us for minor indiscretions – times change!) used to write “ATQ” all over our scripts before awarding marks of zero or 1/4. ATQ of course means “answer the question” – so some things don’t change. For a pupil who has revised well, not ATQ is one of the biggest remaining risks.

What to expect in the 11-plus

What to expect in 11 plus entry exams

I have just completed some Maths tutoring for two excellent students hoping to join a grammar or independent school in South West London.  Their approach was exemplary, their Maths was already well in advance of Year 6, and they wanted to get even better, being prepared to work very hard in lessons and at home. One full practice paper was not enough for homework, they coped with two a week.  Their parents hoped for a free or reduced fees place, but if not I have no doubt they would try to find a way to sacrifice to pay fees.

With the recent news about possible expansion of grammar schools, it made me think about what would happen if my two students did, or didn’t, make the grammar schools, and also how the various entry exams compared to each other, and to traditional year 6 SATs standards.  In other words, what should pupils expect in their exam?  Let’s start with this.

The entrance exam

My focus was upon my local South West London schools, 10 fee paying private independent schools and 8 free, state, selective grammar schools.  I drew broad conclusions about the latest exam processes, likely to be reasonably applicable outside London too. The first thing to say is that in these 18 Schools, it is very difficult to find free sample papers or even sample questions on their websites.  This is to avoid advantaged children “buying” their entrance through expensive “teaching to the test” tuition.  However, for some of the Surrey schools typical common entrance papers can be purchased, some schools just outside this area do publish sample papers, and of course national publishers like CGP and Bond make practice papers available.

So you can piece together what the typical test will look like.  Maths rather than English is my speciality so here are some of features of the typical Maths entrance paper.

The number of questions will be between 25 and 50, students have 45 minutes to 75 minutes to complete, so at 1.5 to 2 minutes each these are short sharp questions.  But the complexity varies significantly from beginning to end, so you should expect to spend 30 seconds on the easy ones and perhaps 3 minutes on the difficult ones. The ability to work fast is almost as important as the ability to answer the question.  The paper typically divides, in order of questions, into what I’ll call the four quartiles of difficulty.   Remember that the higher the reputation of the school, the higher the demand for places, the higher proportion of questions in quartiles 3 and 4, as follows:

1st quartile  – simple KS2 topics
Number : Addition, subtraction, multiplication, division (always without calculator)
Fractions, percent and decimals, number lines
2nd quartile – tricky KS2 topics
Number and measurement: clock times, square and prime numbers, ratios, units of measure
Algebra: graph coordinates, sequences, simple algebra expressions,
Geometry:, Angles along straight lines, at a point and in triangles, areas and perimeters of regular shapes, recognise 2D and 3D shapes, simple translation and reflections.
Data : Mean (average),Tables, Pictograms, Bar Charts, Pie Charts, Line graphs
Problems: Inverse Logic problems such as “what number did I start with”
3rd quartile – still KS2 but highly developed problems
 Factor pairs, place list of fractions and decimals in ascending order
Algebra: Solving linear equations, Create equations from areas and perimeters, including odd shapes;  substitution of numbers in equations
Geometry: Combination of angles rules in one problem, Nets, angles round a clock-face circle Rotations, Symmetry, Mirror (e.g. what would “WINTER SALE” be on a window’s other side
Problems: Speed x times = distance problems, Number reasoning, Railway timetables, Time-zones

4th quartile – Beyond KS2 to KS3 and KS4 GCSE, and Puzzles
: Exchange rate conversions, Fibonacci sequence, Prime factor trees, Ratio problems such as cake recipe; HCF and LCM; powers.
Algebra: simultaneous equations created from e.g. prices of burgers and soft drinks, Multiply double brackets using grid or FOIL
Geometry Parallel line angles, enlargements and scale factors, 3-D cuboids
Data: Venn diagrams, Probability, Mode, Range and Median
Problems: Sudoku-like magic number puzzles, Shapes representing operations, number machines Shortest route problems such as through the streets of New York; full page multi-paragraph problems featuring combination of numeric and verbal reason logic culminating in for example, which of five children got a present, which of five animal lives on which island?
This last, 4th quartile frequently goes well beyond KS2 in two respects. Firstly, what I’ll call “puzzles” – which ironically will never resurface in secondary exams. Secondly, school syllabus content stretching well into KS3 Year 8 and 9 even in rare cases up to KS4 GCSE level (yes!). This last quartile contains the differentiator questions, the ones you have to be able to do to be really confident of gaining entry. When tutoring an 11 plus pupil followed by a GCSE pupil I sometimes find myself using the same sample questions.

Most of the school websites say, to be politically correct, that the questions should be suitable for any KS2 student (only one admitted that some questions may stretch to KS3). Parents should not be fooled. With demand outstripping supply by 4 or more to 1, the higher reputation schools do throw in the puzzles and year 7-11 level questions to identify the brightest pupils.


How many exams?

The table below shows, for the 8 grammar schools sampled in SW London, most have 2 stages, although the Sutton set start with the common SET test. The 10 independents all have just one stage except St Pauls, which starts with the common ISBE test, and most have an interview to confirm selection. Most schools feature Maths, English and either a separate verbal reasoning test or similar questions within English. What is noticeable is that Non Verbal Reasoning is becoming quite rare now (thank goodness – awfully difficult to teach!)


Maths English Non Verbal
Comments Sample Maths available
Tiffin Boys  Y Y  N 2 stages,  and stage 1 counts 10% each Maths and English, Stage 2 counts 40% each Maths and English  for entry. No
Tiffin Girls  Y Y N 2 stages, and stage 1 is Maths and English OMR multi choice, passing gets you to Stage 2 Maths and English which alone determines entry No
Below are the Sutton Grammars taking  common SET
Nonsuch High for
 Y Y N 2 stage, 1st  English and Maths common SET multi choice, then joint second stage Maths and English with Wallington High School for Girls No but SET samples can be ordered
High for Girls
 Y Y  N 2 stage, 1st English and Maths common SET multi  choice then joint second stage Maths and English with NonSuch High School for Girls As above
Greenshaw High  Y Y  N 1 stage only Maths and English common SET multi choice. Pass for eligibility for  60 places. As above
Sutton Boys  Y Y  N 2 stages, first is common SET English and Maths multi choice , to get you to second stage Sutton specific English and Maths. 1st and 2nd stage tests all affect final entry, ratio is 2:2:3:3 As above
Wallington County  Y Y N 1 stage only, Maths and English common SET, pass to be eligible for  place As above
Wilson’s Sutton  Y Y N 2 Stage , first is common SET Maths and English, second Maths and English. Count in ratio 2:4:4. As above
Maths English Non Verbal
Comments Sample Maths available
Hampton  Y  Y  N 1 stage, 3 exams : English, Words and Reasoning, Maths and an interview A few questions
Halliford Y Y Y 1 stage Maths, English, Verbal and Non Verbal reasoning No
Lady Eleanor Holllis Y Y Y 1 stage tests in Maths, English, VR, Non VR followed by Interview No
St Catherine’s Y Y N 1 Stage tests in Maths and English then interview No
Y Y N 1 Stage tests in Maths and English then interview. Note : it confirms some KS3 material will be tested. Yes full paper
Y Y N 1 stage tests in Maths and English Plus write a personal statement No
Kingston Grammar Y Y N 1 stage English Maths and verbal  reasoning followed by an interview Yes most of a sample paper
Reeds Y Y N 1 stage tests Maths English and Verbal Reasoning No
Y Y N 1 stage test Maths English and Verbal Reasoning Yes a full paper
St Pauls Y Y Y 1st stage ISBE / GL Multiple Choice in English, Maths, Verbal and non Verbal reasoning. 2nd stage is English and Maths and interview No but ISBE sample papers can be ordered

Grammars – the pros and cons.

Through the lens of my two students, if they started Year 7 even in the best of the local state schools, they would be so far ahead that they would, to be honest, be bored and held back. Like many bright children they need the challenge. The supply of free grammar schools is limited. At many of our local grammars the ratio of applicants to places is 4 to 1 and at some even higher, where queues around the block form at the start of exam day. (Some now phase exams through the day to avoid this).  In business, if supply is limited and demand is high, you increase prices or create more capacity – in this case by creating more grammar schools, because prices are fixed at zero.

However the downside is of course that if the brightest pupils are creamed off from state schools, the overall standard must surely fall. This is detrimental to the remaining pupils, who lose the chance to learn from the approach and abilities of high achieving pupils, and dispiriting for teachers who enjoy challenging them and getting a positive can-do response. Some teachers would surely jump ship. Some Headteachers have said this would recreate “secondary moderns”.

One compromise – which one of our local state schools already employs – is to offer a limited number of exam-selective places, while mainly offering free places for local pupils.  The question then is, do you sprinkle the selected pupils among the classes, or “set” from the start.  The problem with the first approach is that schools are constrained by the national curriculum which prescribes certain content for certain years, so the brighter pupils would be constrained by the pace of the slowest.  The alternative is to “Set” from year 7 and effectively teach the top set Year 8 or 9 level content from age 11, and take all GCSE’s  (not just Maths) a year early.  This “grammar stream” approach is advocated by former UCAS Chief Executive Mary Curnock Cook Or go further (as my old school used to do) and identify the brightest year 7 pupils and to remove them at year end from Year 8 and place them straight into Year 9 (we were called “removes”).

Is tutoring needed?
As noted above, the questions definitely stretch beyond standard KS2 (whatever schools say). The question is, how do you get access to, and practice these.  In theory, purchase of Bond or CGP practice books can do the trick, but the risk is that the pupil will miss the personal explanation and without homework being set, may not practice enough, and even these excellent publications don’t include the outrageously tricky questions which do crop up.  Note also that while common entrance papers like SET the Selective Eligibility Test can be purchased, frequently these are only for Stage 1 permission to sit the really challenging Stage 2 papers which are not formally available. So structured learning, and exam tips are needed over and above school provision. Parents might provide this but many would struggle with the vital end of paper questions. Extra tutoring is your insurance policy (but not a guarantee) and this can come in several forms, including private one to one,  or exam centre cramming.     

What is tutoring providing?

What you are trying to do is this: First make sure the basics of KS2 are in place. Second, introduce the pupil to a selection of KS3 topics which may crop up. Third, help the pupil work at speed. Fourth, teach exam techniques. Finally set a sufficient quantity and quality of challenging tasks from which gradual improvement instils confidence – the “more I practice the luckier I get”.  What is difficult to teach is the natural mathematical abilities such as puzzle solving and spatial awareness, and my guess is that is why such puzzles are included – there may be disadvantaged pupils who cannot afford tutoring yet have that innate mathematical ability which money can’t buy.

In conclusion

The 11 plus is highly challenging. A good KS2 performance – an 11 plus “pass” – will probably not be enough to get through. There are many pupils and parents willing to take up that challenge, to achieve that extra level of excellence. Schools, the State and Tutors all have a part to play in meeting that demand.

Chinese Maths in English schools

News that Chinease Maths techniques are to be introduced to English schools needs some explanation and examination.


Initially to be piloted in around half of our primary schools, the technique involves learning techniques more by rote,  asking one child to answer a question, then asking the remainder of children to repeat the answer. The class does not move on until all the class has “got it”. The brighter children avoid being held back because they have a role in leading the other children with the first answer.   There are some similarities with Kumon, namely keep practising by repetition until “mastery” of a topic is achieved to an advanced level, but differences too: Chinese Maths emphasises the role of the respected teacher at the front of class, Kumon relies more on self learning through worksheets.

Chinsese children themselves are believed to be 2-3 years ahead by the time they move to Year 11; so 16 year olds in China are already at the same level of maths as an 18 year old A level student in the UK.

There is a view that culturally some British pupils are not ready for this and our cultural diversity and child centred participation doesn’t sit easily with chanting and learning by rote which is common and part of the educational ethos in China. The benefits are not at all questioned.

Chinese Maths versus English real world approach

More important I believe is this. The direction in Maths and Science in England is to introduce more “real world” relevance to exam questions, not just at GCSE KS4 but also at earlier KS3 and KS2 as well.

So while introducing a “back to basics” learning approach in Maths is very good, not least because we are slipping down the international educational league tables, I wonder if joined up thinking is taking place in Government in terms of the following two factors:

If teaching methods move in the direction of focusing upon  purely numerical excellence, and yet examiners insist on setting real world applied questions where the maths technique is merely a small means to an end, do we risk the recent Biology GCSE “drunken rat” exam problem ? By this I mean that the children aim to learn the syllabus and technical methods to the best of their ability, and they put a lot of effort into mastering the knowledge and technique required in the syllabus, but meanwhile the examiners smother the questions in “real-world” unfathomable words and situations.  So the child learns the techniques but can’t do the exam questions because they haven’t been schooled in the methods of deciphering them, or applying the technical knwledge they have acquired.

An example in Maths itself is the 2015 GCSE question that went viral. The question involved two techniques rarely seen together: algebra, and probability. One can imagine pupils achieving high levels in these two topics individually using Chinese techniques of practising lots of examples, but being unbable to piece together the required jigsaw which requires a different sort of skill altogether.

Mile long and centimeter deep

One other phrase associated with Chinese Maths is interesting: their criticism of the British Maths syallabus is that it is a “mile long but a centimetre deep”.   There is something in this.  For GCSE Maths there are five basic topics such as Number and Algebra but within those there are many sub-topics making around 80 in all. One wonders if all of these are necessary, for instance frequency density histograms are beloved by specification setters but in practice are never used by businesses. Could some topics be left out allowing time for in-depth understanding of the core?

But we are where we are: my philosophy as a tutor is to “teach to the test”, whether GCSE exams or earlier end-term tests. Because that’s what parents want. And the last thing a child wants is to open an exam paper and find there are topics they don’t even recognise. So you have to teach the whole syallabus, not just the mathematic principles but the ability to understand and answer increasingly inscrutable questions.

Measuring success

In summary there will almost certainly be benefits and we need somehow to catch up on global competitors. An intangible benefit may be a cultural change, to make Maths excellence expected rather than optional. But ultimately, the acid test is this: will the programme lead to better GCSE results, either higher marks, or the same marks at a younger age? This may depend on whether the new techniques are compatible with the direction of Maths exam question designers. Sound learning of fundamentals is essential and surely must be improved – so we have to start somewhere; but it may be only the first base-camp stage in achieving the summit of maths mastery. We may not be able to judge success for half a decade.

Brexit through lens of A Level Business Studies

The AQA Business Studies  A level Buss 4  exam is coming up, and Section B (a 50 minutes essay) is rumoured to perhaps contain a Brexit question.   Jim Riley, former businessman and consultant turned on line business academic, runs the excellent Tutor2U website with his twin brother. It covers business and humanities subjects and as well as briliantly assembling a knowledge bank offers sound advice on structuring exam question responses. He lists the various subjects covered already in the Section B past papers – margers, integration, planning, innovation etc. – and points out that European business is one of the few subjects not covered yet. It’s time may have come.

With that in mind I constructed – and answered myself – a possible Brexit question using Jim’s recommended layout of intro – 3 points (2 for 1 against) – conclusion. Here it is:

“In the event of a vote to leave the EU, would the risks of economic shock for the U.K. outweigh the benefits of controlling our borders to reduce immigration?”

In the upcoming Referendum the people of the U.K. will vote on whether to remain in, or leave, the European Union. The E.U. is a collection of 27 independent countries with a population of 500 million. Trade within the EU is governed by the Single Market, in which there are very few trade barriers or tariffs between members, and where trade agreements are negotiated on-bloc to the rest of the world.  Any reduction in Single Market access is likely to affect trade and cause uncertainty in financial markets, which may in turn diminish public finances.  In the EU there is free movement of goods and services, and also people for employment. This means that a dis-benefit of membership is reduced control over who settles in Britain, leading to an increase in net migration in recent years, which both changes the nature of the U.K. and itself puts pressure on public services.  In this essay we will examine some of the possible economic shocks of Brexit, and balance that against benefits of getting back control of our borders.

First let us examine trade barriers associated with Brexit and their effect on individual companies. The medium term economic risk of leaving the EU will be to reduce U.K. firms’ access to the Single Market. The impact will be to inhibit trade and increase trade barriers, in three respects. First financial tariffs, which U.K. firms may have to pay to export to EU countries; second the complexity and uncertainty of doing business with Europe would increase; and third inability for a prolonged period to strike new trade deals to replace EU deals as they unwound. If we examine Porter’s 5 competitive forces, new entrants to markets find it difficult to compete against existing companies if high barriers to entry exist. Brexit would create these barriers. This would reduce the ability of U.K. firms to compete against for instance German and French rivals, specifically new growth business would be difficult to secure, and existing business exports lost. Decisions on investment size and location would be at risk.

What evidence have we that trade might be more difficult? At a high level, the German finance minister has confirmed that Britain would be excluded from the Single Market, while President     Obama of the U.S.A. has said that Britain would be at the “back of the queue” in developing a U.K. independent agreement with the U.S.A. At a very local level, the former leader of the Republic of Ireland has said it is likely that trade tariffs would have to be introduced for products coming across the Northern Irish (UK) border into Eire. Tariffs vary – for instance 32% on wine, 4% on gas, and around 10% on cars and wheat, but typically they might average around 5% which would make UK products 5% more expensive when selling into Europe. Companies would either increase their prices accordingly to maintain profit margins – but this would risk losing sales volumes – or cut costs by 5%; for instance their labour costs.   An example of the increased complexity of doing business post Brexit is the risk to the “financial passport” which the UK financial services sector has by being in the EU.  This would put at risk the attractiveness of London as a financial centre for banks, insurances and currency trading.

So in summary the threat to individual companies of Brexit would come through trade barriers, tariffs and market access which would make individual UK firms un-competitive. Collectively, this would produce an economic shock to the UK.

If the economic case against Brexit is compelling, why as we approach Referendum Day is the Leave campaign pulling ahead in the polls? The answer lies in one word – “immigration” – and one phrase “get back control of our borders”.  Net immigration is running at about 300,000 each year. This means that the difference between gross immigration (600,000) and emigration i.e. people leaving, around 300,000, is about 300,000 net and has been increasing since the end of the 2008 recession as demand for labour has picked up. Free movement of labour is legally binding in the EU and so when David Cameron tried to win concessions from the EU before the vote, all could he achieve was a restriction on immigrants claiming benefits rather than a restriction of numbers per se. The attraction of the UK has increased to migrants as the minimum wage (the lowest wage employers must pay to employees) has risen. The rise of EU immigration has had economic, business and social effects. First, economically, more immigrants have increased pressure on social services like the NHS social housing and schools, at a time when budgets are already under pressure. Businesses need a supply of labour and are tempted to take the cheapest labour from Europe, and this in turn has a social effect. Namely communities especially on the East Coast are changing, with many different nationalities for instance Polish beginning settle and open their own supermarkets. The Leave campaign asserts that a way of addressing these issues is to “get back control of our borders” by leaving the EU, thus eliminating the requirement to accept immigrants without a proper assessment of their skills and suitability. This will be especially important as the EU expands in future, possibly taking in countries like Turkey and Albania which are nearer trouble spots in the Middle East.  This security issue makes it ever more important to control our borders.

In summary the case for controlling our borders and hence immigration rests on difficulty in providing social services, a desire to preserve the UK’s ethnic mix, and worries about the future security of the UK. The Leave Campaign argues that the only way to address these issues is to leave the E.U. This is so important that any short term economic problems, if they arise, are insignificant especially if we no longer have to pay our EU membership fee of around £350 million a week, as advertised on the Leave Battle Bus.

Now let us use this membership fee to compare against macro-economic risks and assess whether a U.K.–wide economic shock would occur.  The fee amounts to £18 billion a year. A rebate of £5 billion occurs immediately leaving a net £13 billion payment. Our public expenditure is £750 billion a year so this represents 1.7% saving. Our Gross Domestic Product (GDP, the sum of all economic activity in the U.K.) is around £2000 billion so the saving would be 0.7%. Both of these savings are significant but how certain are the savings and would they be offset by economic risks of EU withdrawal? We have argued above that individual companies would find it more difficult to trade with the EU post Brexit. This in turn would reduce sales revenues and hence profits of U.K. companies, collectively meaning less corporation tax would be paid to the Government, and that jobs would be lost and unemployment would rise. This fall in Government revenues coupled with increased demand for unemployment benefit would lead to inability to balance the UK finances, which would require public national debt to rise, unless income tax rose or services like welfare or health care were cut.  The evidence to support this is that several independent economic forecasting bodies such as the Institute of Fiscal Studies (IFS), the International Monetary Fund, the Organisation of Economic Development and the Bank of England, have been warning of the economic effect of “Brexit”. There will be a short term shock and long term permanent shrinking of the economy. For instance the IFS have estimated that the negative effect of Brexit will create a £20 billion – £40billion fall in available public finances. This more than offsets the £13 billion gain. Taking a £30 billion midpoint, the net loss would be £17 billion, or 2% of public spending and 1% of GDP – indicating a recession. The Chancellor has claimed he will need to propose a short term emergency budget to increase taxes and lower public spending in reaction to these forecasts. He also has said that long term by 2030 the economy would be 6% smaller than otherwise would be the case, meaning a £4,300 loss of GDP per person. Other evidence for a shock very close to the date of the referendum is that share prices on the FTSE 100 index and value of the pound have fallen in correlation with the polls favouring Brexit, which leads to uncertainty in the markets.   Finally it is not certain how much of, or when, we would get the $13billion back, especially if some savings were maintained to preserve trade deals.

Summarising, the collective impact of companies’ difficulty in trading post Brexit would be both a short term shock and long term drag for the UK, which would offset the benefits of regaining the membership fee.

In conclusion I believe that on balance the high risks of economic shock following Brexit outweigh the benefits of reducing immigration for the following reasons. Leaving the EU would create barriers to trade for companies from a variety of factors like tariff increase and loss of trade agreements and this would in turn diminish competitiveness and restrict investments. The collective sum of these difficulties would mean a diminishing of the total public finances which the majority of economists agree would significantly outweigh the savings of the membership fee.  Forecasts are difficult and vary but the common factor of most is the sign – “negative”. The impact will be tax rises or spending cuts or increased debt – none desirable. However, this does not mean that staying in the EU should proceed without change. If immigration continues at its current level forever then clearly the U.K. would eventually, literally run out of space, and so I recommend that if the U.K votes to stay in the EU it uses its 2017 Presidency of the EU to continue the case for reform.  The most important argument for remaining is to avoid a recession and more austerity, caused by financial uncertainty and inability of companies to trade as they did before in Europe.

Biology GCSE drunken rats question

Three of my tutorial contacts talked to me today independently about the GCSE Biology exam that is going viral. I Googled “#aqa biology” and sure enough a torrent of links and Tweets popped up.

It seems that AQA included  questions in Biology GCSE biology about drunken rats, why boys drink beer and girls drink wine, including under aged drinking references, and a Business Studies question about what is an independent company.

Almost simultaneously a number of Scottish students complained that their Maths exam did not reflect the syllabus, and crucially “a common complaint was that the exam bore little or no resemblance to past papers and exemplar papers”.

What is going on? Let’s examine the issues, which raise important questions in general about the direction of exams. AQA are a terrific exam board, but have they got this one wrong?

First, this is not the same as last year’s most-tweeted GCSE Maths problem about “sweets in a bag: show that n²-n-90=0.” .  That was difficult, but on-syllabus, albeit requiring two rarely connected parts of the syllabus, probability and algebra. Not the same either as the “Scottish crocodile” question which was valid but ambiguously worded.

This year’s problems perhaps reflect a disturbing trend among exam boards. To appear to be “relevant”, “on-message”, “out of the box”, “contextual with society”, to focus on the “ethics of science” and “how science is applied” – rather than test simple scientific fact.  Also, a surely mistaken desire to be “cool with the kids”.  There is a whiff of Millenium Dome here – let’s make science exams more interesting and the kids will abandon their computer games and flock to science!

While some of these aspirations may be desirable their inclusion in vital exams is clumsy, unannounced and too dominant.  If such questions are included, it reduces room in the Hour test for basic questions about biology fundamentals. The implication is that examiners see science more as a matter of opinion, not fact.

Examiners, perhaps inadvertenly give the impression that they do not appreciate that teachers and children work very hard to learn the syllabus, practice on past papers, and despair when they open the exam paper and see a whole series of questions bearing little overt relation to the syllabus. They take the syllabus very seriously – more so than the examiners perhaps. It is like training all year to climb Ben Nevis, you reach the top exhausted, remove a prearranged stone from a cairn to claim your reward, only to find a message saying “Ha Ha, fooled you, you’ve climbed the wrong mountain!”  A teacher estimated that “only 25% of the course content” was covered in the Biology exam.

To paraphrase Donald Rumsfeld, known unknowns we can cope with, it’s the unknown unknowns that are the problem.

The question about “what is an independent company” was no doubt aimed at the idea of fair, not biased testing, and perhaps “controlled” and “independent variables”, but surely a better question would be, “why is an independent company used”? (for drug testing)?

biology2Some challenging examination of science experimentation and data analysis is fine – I am a data scientist and welcome the inclusion of graphs to represent data, and questions about interpretation.  Healthy living and drug testing are indeed in the Unit 1 specification. But when questions are sexist, appear to condone breaking the law, or are from another subject altogether, things have gone too far surely.

How many boxes can you tick in one question? Sexism, under-age drinking, animal testing, drug-taking, newspaper accuracy! One is tempted to ask, what were the examiners on when they wrote the question?! But seriously, didn’t the management have a quick sense check, and quietly suggest, ”I think you should have another look at this one, it is inappropriate”. Important social issues, but in a Biology exam? Better on Nicky Campbell’s excellent “The Big Question” on Sunday morning TV?

This raises questions about quality control at AQA, which along with Pearson/Edexcel and OCR is truly a great and professional organisation. (An independent company in fact, non-profit making)  I had assumed the Q stood for quality (actually it is for “qualifications” and AQA should remember that’s why pupils take the exam). One hopes this is a temporary blip. Questions like these are actually reducing standards not improving them.  If the majority of syllabus topics are no longer included in the exam, what’s the incentive to learn them?

I am detecting another general trend across exams. In their desire to become more challenging (good!) examiners are including more and more words in their questions, but not following through to ensure that the English is correct and unambiguous (bad!). An experienced tutor told me recently that sometimes a pupil often “has to guess” what the examiner wants.

Another question in the Biology exam is about Malaria. OK so far, it is in the syllabus. But the question is shrouded in “extras” – for instance needing to know Maths GCSE standard form “power of 10” notation. A core of scientific experimentation is to change and test one independent variable at a time – but here the examiners themselves are simultaneously testing biology, and beyond-basic maths.

AQA have responded and are standing by their exam, saying they do not want it to be “predictable”. I have taught and trained many pupils and adults and what I have found is this: provided they are given clear instructions with no surprises they will pursue a difficult task to completion, otherwise many become confused and disheartened. The danger for AQA is that in their efforts to make science more “interesting” and “challenging” they will discourage interest, especially as these questions were in the basic science Unit 1 paper. They seem more appropriate for advanced students

The fact that AQA felt the need to explain the question on social media at all suggests it wasn’t very clear in the first place. The fact they defended it suggests we should expect more of the same, we should “expect the unexpected”.  This will mean more teaching time is dedicated to predicting and practicing for these flowery questions, and less time for the fundamentals of biology.  Examiners may be surprised, but optimising your grade really does matter.  Appliance of science is of course important, but not at the expense of simply knowing the fundamentals?

At the risk of sounding like a “grumpy old man”, and another thing: core Unit 1 science GCSE contains no questions about electrical circuits or electrical safety but generally contains questions in Biology, Chemistry and Physics about the evils of fossil fuels,  carbon dioxide and global warming. On-message indeed!

The other issue emerging is the annual use of Twitter and other social media by pupils to vent frustrations with exams. While I am not a great fan of “trial by social media” I think this method of scrutiny is here to stay and exam boards must expect more in the future.

In summary, my beef is this. Though “application of science” is directionally right, and AQA are a fine organisation, the quality control on questions needs to be stepped up.  We need less social posturing in science exams. The syllabus content may be reasonable, but the questions do not sufficiently or overtly reflect the syllabus.  And when they do, they are shrouded in unnecessary, periphery extras, obscuring the basic facts around the subject.

If an 11-year old were to learn the subjunctive

If an 11-year old were to learn the subjunctive…..then so what?  Would they say, “if only I could use the subjunctive mood in my conversation, how cool would I look!” Perhaps not!

It seems ridiculous that such young children should learn the finer points of grammar like the subjunctive, or be tested on the difference between a preposition and a subordinating conjunction (the distinction which I heard the Schools Minister Nick Gibbs get wrong live on air), or that 6 year olds should face national tests on punctuation, tenses, nouns, adverbs, statements and verbs.

On the other hand, consider this. The U.K. is falling down the international league tables in English education. Yet we invented the language. Shouldn’t we be nearer the top?  Whereas we might soon be behind the Marx Brothers’ imaginary countries like Freedonia  or Moldova (OK that turned out to be a real one).

Also I rather like the idea of 11 year olds knowing more than me about English grammar. Not difficult I admit.  I was never really taught it at school until I did Latin, taught by our wonderful North of the Border Latin master whom we nicknamed “Scotch Mist”.  “The having been marched up the hill Romans won the battle”, or “he was so stupid he was fed to the lions”.

As ever I turn to pop music. All of these songs use the subjunctive mood to a degree. “If I were a rich man” (Fiddler on the Roof).  Correct. “If I was” (Midge Ure); incorrect – should be “were”. ”If I was a boy” – Beyonce: incorrect – likewise. “If I were the only girl in the world and you were the only boy” (Dean Martin – correct), and the classic Tim Hardin/Four Tops “If I were a carpenter”; correct.

I guess that if you are going to raise standards you have got to start somewhere.  Possibly these tests are a step too far, but on balance it is better to aim too high than low, and they are a counter to the seemingly unstoppable rise of Twitter-like abbreviations.  If the building blocks of Maths like fractions are being taught at an early age, why not do the same for English?  Maybe the ability of children to pick up grammar, if taught, is greater than we think.  We shall find out in due course.

Let us not forget in this “Shakespeare year” that the Bard, or rather Macbeth, whispered one of the greatest subjunctives of all. “If it were done when ’tis done, then ’twere well
It were done quickly

So to finish here are two sample tests, first  KS2 English for 11 year olds, in which you will find the controversial “subjunctive” topic in question  41, and also for KS1 6 year olds   Can you manage them?  (I didn’t even score 100% in the KS1 grammar test! But then I am a scientist and mathematician so there is something reassuring about that!)

Big data helps Maths GCSE revision

Big data is a term used increasingly to describe the use of large amounts of data gathered electronically to determine insights otherwise lost in the detail. It is often characterised as the 3 V’s, Volume ( e.g. terrabytes); Variety (e.g. social media insights as well as surveys) and Velocity (fast data transfer and processing). A famous early example was use of location-specific Google searches on flu medicine to predict and track the spread of a flu virus through America quicker than conventional methids.

How can this principle help revision? Well, a subset of Big Data is simply “more data than usual” – big data light to coin a phrase – and I have done this with Maths past papers. Not just answers and methods are available on line for all past papers – that is well known – but also examiners’ comments are available question by question.

erInitially I have looked in detail at 4 past papers, 100 questions, and captured the comments from each, 130 in all, for which the examiners highlighted common causes of lost marks from tens of thousands of entries. Then I grouped them and tallied them GCSE style in a frequency table and chart as seen left. This sheds light on general areas for revision, with (lack of) “basic maths skills” ferquently bemoaned by examiners, as well as subtle tips such as “read the question very carefully and make sure you show working”.

Then, further I picked out twenty very specific examples of errors that seemed to occur – this time syallabus technical content rather than functional categories above – and wrote and illustrated a list of “20 things examiners do and don’t like to see”.  A typical one is shown. I recently took some examiner marking training and I can assure you this is true. If a question asks you to “express a number as a product of its prime factors”  then merely listing them, with commas, will lose you a mark, if the “times” sign is missed out. Even if the numbers are riight as above.

I have put these and other tips together into an Easter/Summer Term special lesson covering:
– reminder of key basic maths skills, especially the ones that get overlooked
– exam technique :  start, during and end of exam
– problem solving techniques for difficult, wordy, end of paper high mark questions
– active revision methods
– the twenty things examiners do and don’t want to see.

With half time biscuits covering the Jack Black “school of rock” Math video.

misAnother phrase used in the Big Data field is “wisdom of the crowds”.  This is being applied superbly by the excellent on-line Maths tutor “MrBartonMaths” (he is also a real teacher). One of the blog pages he runs is “Diagnostic Questions – Guess the Misconception” where students are invited on-line to answer a multiple choice question and give their reason (a typical weekly question is shown). Typically around a thousand students vote (hence the “crowd”) and reveal what errors are often being made (in the example A is correct of course, C was the most common error). The misconceptions are both the students’ errors, and tutors’ sometimes incorrect expectations of what errors might be most frequent.

A lot of data is available out there on-line – the key is to process and present it in the best way to understand and hence help students.


Headmaster suspended for letting pupil take exam early

A headmaster in Wolverhampton has been suspended, and then reinstated after an enquiry, for allowing a pupil to take a GCSE English exam a day early. The reason seemed a little lax, namely to allow the pupil to go on holiday with their parents.

One assumes the enquiry involved checking his phone records and those of his friends in the few hours after the exam!

It reminds me of another “exam made easier” story from June when the answer to one GCSE question was helpfully supplied in another question, in the same paper. An AQA Chemistry paper contained the following:

2a. Fill in the blank. Limestone is mostly calcium ————
5b Limestone is made mostly of calcium carbonate…

In terms of making exams easier, let’s finish on a more serious note, well slightly more serious; allowing computers in exams.

googlemathsThe head of the OCR exam board suggests that Google be allowed in exams. The responses have varied from “ridiculous” and “rubbish” to “it would test resourcefulness and initiative rather than just your memory”.

Another proponent of the use of computers in exams is Dr. Sugata Mitra who conducted the famous experiment to place a computer in a hole in the wall adjacent to an Indian slum and found 7- year old children very quickly picked up skills with no assistance. It is a topic that won’t go away. But that is for another blog!

Crocodile Maths problem goes viral

crocptintAnother maths exam problem has gone viral after the earlier “sweets in a bag” Twitter storm. This time a Scottish Highers Maths question about crocodiles and zebras (yes!) proved insurmountable. Over and above the technical solution (see below) there were a number of interesting aspects for us English in GCSE – land.

First,  the Scottish exam structure is completly different to England’s. There is no mention of GCSE or A-Level, so Higher in Scotland is roughly equivalent to A-Level in England, as it is described as a “pre-University qualification”.

Second, could such a question appear in English Maths GCSE ?  Very unikely for the reason above, and because the best solution involves calculus, which is still not in the new GCSE 9-1 syallabus. Calculus is in IGCSE, but even so the crocodile problem would swallow up time as a very tricky differentiation is involved. It is, however, still just possible that a problem like this could be in our GCSE 9-1 syallabus because an alternate solution for it is through “iteration”.  But solving it this way would surely eat up time, since perhaps 9 iterations might be needed with awkward square roots.

Third, it shows that quality control of questions is vital, especially when exam structures are changing. Ambiguity can be a killer. In this case many of the “descriptive” parts are not black and white (unlike the poor hunted zebra) .  For instance how important is the width of the river? This makes even the first two “easy” parts tricky as you spend time understanding the English meaning.  A shame – I feel the crocodile question writer (from Dundee?) crafted a potentially great question, but was let down at the end by the oversee process.

Fourth it shows there is a strong interest in Maths amongst the general public (I assume not crocodiles!) as the web post was No.1 in the charts for the BBC’s most read posts.  This is encouraging!

Finally it shows there is no place that examiners won’t go to make questions less purely numeric, and more “challenging”. Another question involved toads and frogs down a well – let’s not go there.

For the record, the techncial solution (in summary!)  is as follows – and it’s not a snappy answer!

(1) When x is 20, substituting in the equation for T gives T = 10.4 seconds
(2) When x is 0, substituting in the equation gives T =  11.0 seconds.

The minimum time T occurs when the dertivative (the differential) is equal to zero i.e. a turning point.
Differentiating the equation and solving, we find x = 8. Substituting back in the original equation, we find that when x = 8, T = 9.8 seconds.  We can prove that this turning point is a minimum by feeding in x values either side of 8 and showing that T is above 9.8 in both cases.

And that leads to the non-calculus “iteration” method, that in theory an English GCSE pupil could cope with. But you would have to start at x = 1, evaluate T, then use x = 2 and evaluate T again, and follow T down all the way down to x = 8, and find that T reduced to 9.8, Then for x = 9 find that T begins to increase again, i.e. a minimum had been reached at x = 8.

As I said, not snappy!

In conclusion, the question would not appear in GCSE south of the border due to content, and I don’t think it would make it to A-Level becasue of ambiguity – but its a salutory lesson for examiners.



England’s rugby demise – a GCSE lesson.

England’s rugby team failed the test as the Wales match approached its climax. This has lessons for how to approach exams. 

England exited the Rugby World Cup after losing to Australia, but for me the damage was done against Wales. I would argue that first loss was associated with “game management” and the parallels with “exam management” techniques are striking as we shall see.

A few weeks before the tournament, most critics would agree that the two teams were well matched. Then a few weeks before the match, Wales lost half their back line to injury, and during the match lost another half. Any small England selection errors were more than neutralised by Welsh misfortune. So duly, with 20 minutes to go, England were cruising, 10 points to the good, chances to extend.  And yet they lost. Why?

In my view, the following: some bad luck with events, but mostly game management.

Harold MacMillan, former U.K. Prime Minister, once famously answered a journalist who had asked what could blow Governments off course: “events, dear boy, events”. England could not cope with events that should have been surmountable.

When Lloyd Williams hopefully kicked cross field, the oval ball could have bounced anywhere but in fact bounced perfectly into the hands of Gareth Davies to score. Bad luck, but it is how you react to events, and England’s game fell apart from there.

Another penalty conceded – more inability to understand what the referee wanted. (Are England penalised more than others despite, or because of, complaining a lot?)  Then the fateful decision to go for the win instead of kicking for goal, not in itself illogical – the kick was missable, and risks sometimes are needed  –  but the decision to throw short at the line out, and risk being pushed into touch, was poor.  Then one final chance, possession lost.

Stuart Lancaster, England coach, is reportedly a fan of the book and philosophy “The Score Takes Care of Itself” , in which Bill Walsh describes his experience as an American NFL Coach, arguing that the preparation, the little things, make the difference in leadership.  Admirable, but no amount of preparation can overcome a coach or player’s inability to react to, or influence, events as they unfold.

Stuart is clearly a fantastic coach who oozes integrity, but before the tournament he said one thing which surprised me along the lines of, “my input to a match ceases just before it starts”. This refers of course to preparation, but did it betray an element of believing that events would follow the natural course, and so for instance substitutions would always follow at the preordained time?

You feel that New Zealand would also have taken the line out instead of the kick, but would have found a way to control it and win, borne of the confidence of winning late many times. They would have found a way to win.

The great sports people and teams keep their game management together as the pressure builds. Think, in contrast, of poor Jean van der Velde, the inexperienced French golfer who found himself only needing to avoid a triple bogey at the last to win the 1999 Open Championship at Carnoustie. In golf, we have “Course Management”, choosing the right clubs for distance, terrain, conditions. Unfortunately, Jean seemed to forget these guidelines, going via railings and rough to water. After removing socks and shoes he holed out for a 7 but lost the playoff,

England had one more chance, against Australia, but their confidence had gone. England lost the 1991 World Cup final against Australia because, by common consent, they listened to the critics and tried to play with flair instead of playing to their pack strength. Has the same thing happened recently?  England have focussed on addressing their perceived weakness – the attacking flair –  but judging by the way the Australian pack won scrum penalties, and had the edge at breakdown, it seems that England have let their forward advantage go.

And so England lost heavily to Australia. it probably would not have mattered had they beaten Wales. And that I would argue was due to Game Management.

Exam management

Think of the Maths exam as that rugby match. You are cruising through a twenty question paper, then just after half way you see a difficult question.  You get stuck, you take too long. You begin to panic, you answer a question on “direct proportion” but forget the principle of feeding back the answer to double check. It turns out to be a wrong answer.

Then you see an algebraic question which requires a quadratic equation to be solved. However much you try, you cannot get the factors. But you haven’t noticed the question says “answer to 3 decimal points” (if so you would realise there are no factors as such, you have to use the quadratic formula).

Then a question involving Pi asks you to leave the answer “exact”, but instead you insert many of its ongoing figures rather than leaving Pi itself in. More marks lost.  You fail to understand what the examiner wants, and what he will penalise you for.

You think you have an easy compound interest question. But you misread that it requires the final amount, not the interest paid. And you waste time doing the manual calculation as well, because you cannot find the “x to the n” button on the calculator.

A question on graphs  is on the next page. You think, “this used to be my strength, but now It is all about Real Life Graphs, with wordy problems about bike rides and punctures. It’s a weakness now, I will have to pass!”

The next one looks easier. But no, it’s on Transformations. I can remember Reflections, but not the one that also begins with “Tr”? It all seemed so easy on my “maths-to-go” and “maths R us” websites. For a moment you remember an old black and white video you saw, what was his name, Brain Clough? “We had a good team on paper. Unfortunately football is played on grass”. You muse that this exam is the reverse, I can do the questions on the computer, unfortunately exams are on paper”.

Then finally you come to the last question. The bell will sound in a few minutes. It looks difficult but features probability, your strength. Decision time. Should I go back and pick up some easy marks by finishing an earlier one, or go for the five marker? You go for the latter.

But what’s this, it starts with probability and bags of sweets, and ends with an algebraic proof of n² – n – 90 = 0.  “I have no clue how these things are connected! I give up”!

In conclusion

Could this happen, or is it just that nightmare where you dream you haven’t done your revision? Well consider this. It has happened and very recently. Thousands of students were approaching their Maths paper’s end – almost injury time so to speak – when they came across exactly that probability question above.  The complaints caused a Twitter storm. Read the story, it went viral,

In fact a reasonable student could have solved this, had they stayed calm at the vital moment andlinked two seperate methods.  Exam management, just like game and course management, can be the difference between achieving your goals and just missing out.  You still made you’re A* to C, but not the A*.  You have the abiility, but the sheer mechanics let you down

The week between the Australia match and the final, irrelevant match against Uruguay will be the longest week of the team’s lives. Plenty of time to reflect on what might have been, just like the Summer Holidays for a student who might think “if only…”.