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A Tale Of Two Schools (Or How OFSTED Are Still Pushing Fuzzy Maths)

December 22, 2014

You may have noticed that I haven’t been scouring OFSTED reports for terrible things for most of this this year. Partly because for some of the year I knew Robert Peal would be doing it for his Civitas Report, but also because the old problems regarding teaching style finally seemed to be sorted, and while people did draw my attention to peculiarities in reports, there was not a consistent problem other than, perhaps, a certain level of inconsistency in judgements that made inspectors very unpredictable.

However, in the last week of term I was contacted by a primary school teacher who informed me:

…in order to meet the demands of the reasoning element of the new National Curriculum, our maths teaching must be inquiry based and founded in solving problems. It is now a whole school target. Pages of correct calculations are bad and we have been told to make question two really difficult because there is no point in children practising things they would get right.

As you may be aware – I wrote about it at some length here – the big disagreement in maths teaching is about how fluency in recall of maths facts and use of standard algorithms should be balanced against fuzzy maths – attempts to develop “problem-solving” and “conceptual understanding” as generic skills rather than part of, or the result of, one’s knowledge. The pedagogical side of this is that fuzzy maths tends to be advocated by those who are less keen on direct instruction, more keen on groupwork and discovery learning, whereas the teaching of maths facts and standard algorithms is usually via direct instruction and sustained practice.

This teacher is being forced to comply with the ideology of one side, the side that is usually fashionable but has far weaker evidence for their position. This is still not uncommon in schools, even though the new curriculum now emphasises the importance of fluency. But what surprised me was that it turned out that part of the justification for this edict being inflicted comes from OFSTED’s opinions about two small Stockport primary schools which were inspected this year. One, Ladybrook Primary School, was subject to a full inspection. The other, Tithe Barn Primary School, was visited by a subject survey team from mathematics. The inspectors who inspected Ladybrook declared it to be “outstanding in all respects” and noted that “Teaching is outstanding and results in pupils making outstanding progress throughout the school”. The maths subject survey inspectors at Tithe Barn, decided that while teaching and achievement in mathematics were good, the overall effectiveness in mathematics required improvement, as did the leadership and management of mathematics and the curriculum in mathematics.

Neither of these inspections seemed to show any sign of OFSTED’s recent unwillingness to prefer one teaching method to another. The report for Ladybrook told anyone looking for indicators of what OFSTED want that part of the reason for giving a grade for outstanding behaviour and safety was because:

Pupils’ attitudes to learning are very impressive. Pupils told the inspectors how much they enjoyed their learning, describing it as ‘interesting and fun’. They explained that they had targets not only in areas such as literacy and mathematics, but also in thinking skills. When asked what thinking skills were, they explained that they were ways in which learning could be improved, such as ‘having a go’ and ‘keeping going’…

Part of the reason for saying the teaching was outstanding was:

…Basic skills of literacy, numeracy and communication are woven seamlessly into interesting topics, many of which are innovative. Pupils develop levels of skill far above those expected for their ages, such as accessing relevant information from Internet websites. Year 6 pupils were seen making exceptional progress in their learning and understanding in a lesson about Japan where they were able to summarise information succinctly from both written and verbal sources. They took turns acting as teachers to small groups of their peers, clarifying areas that some found difficult.

At the same time, as this report was implying that topic based learning (even for numeracy) and letting kids research things and teach other was part of outstanding teaching, the letting feeding back on the maths survey was saying that the problem with maths teaching at Tithe Barn was:

Attention has been given to checking consistency of teachers’ approaches to teaching methods of calculation, but pupils’ mathematical understanding, their problem solving and reasoning skills have not been monitored nor findings used to identify how teaching might be improved

…because pupils are working at above average standards, more discriminating use of the resources is required to ensure pupils are challenged appropriately and have their understanding deepened.

Pupils’ written work indicates a lack of focus on developing understanding, reasoning and problem solving, in contrast to the strong emphasis on mathematical knowledge and methods, which enables proficiency. The current practice of working through exercises in the textbook means that not all pupils get to complete the ‘think’ question at the bottom of the text book page or to explain their thinking. Likewise, the problems in the text book page are often directly linked to the methods pupils have just learnt, which provides practice, but means they do not have to think hard enough mathematically about how to solve the problem.

Few Early Years Foundation Stage activities, particularly outdoors, relate to shape, space and measures, for example, to support children’s problem solving with and understanding of patterns, shapes, capacity and mass…

…they do not move pupils on quickly enough through repetitive exercises in the new textbooks…

…Children’s knowledge of counting and number is above average by the end of Reception. Fewer children excel in their knowledge and understanding of shape, space and measures, in part because of a lack of resources and challenging activities, particularly outdoors. Your plans to refurbish and improve the outdoor space are timely

 Areas for improvement, which we discussed, include… adjusting the curriculum so that it meets the needs of all pupils and places a greater focus on developing pupils’ understanding, reasoning and ability to solve problems…. [and] making sure that children in the Early Years Foundation Stage have plenty of chances in the outdoor area to solve problems and reach high standards, particularly in shape, space and measures

I think the latter is particularly clear about the opinions and priorities of the inspectors where it comes to the relative merits of teaching numerical fluency through traditional methods and of attempting to teach understanding and problem-solving through discovery methods.

However, these are just two schools, and there is the argument that if one is performing well and the other is disappointing then there has to be some comment given on what is right or wrong with their teaching and it should be taken to reflect what was seen, not the ideology of the inspectors. If the progressive teaching approach achieved great results and the traditional maths teaching achieved poor results then that should be indicated. It’s in investigating this possibility that the bias in this case becomes clearer as the remarkable thing about the schools is how much they have in common. Both are officially outstanding. Both got 97% of students to make the expected progress in maths this year. Both had around 30 students in Year 6. The only differences that might be relevant when judging their effectiveness is that Ladybrook had far more disappointing results in previous years (which when you only have 30 students’ results to look at in a year, seems an odd thing to ignore when judging achievement) and that Tithe Barn’s last inspection (unless there’s an inspection that hasn’t been published yet) was in 2009. But they look like schools which have maths teaching at a similar level of effectiveness for year 6 in 2014.

Screenshot 2014-12-19 at 22.02.17 Screenshot 2014-12-19 at 21.55.34 Screenshot 2014-12-19 at 21.56.14

This similarity in achievement, is what makes the feedback from inspectors so curious. Now I should, obviously, be careful to say that I’m in no position to judge whether the judgements are wrong, but it’s worth asking what a headteacher of a primary school in that region would think. What would a head do if they knew that 97% making expected progress in maths in 2014 (after years of underachievement) was part of what indicated being outstanding in all respects where a school appears to be using progressive methods?  What if they knew that the same amount of progress in maths, as part of an ongoing record of strong achievement in a historically outstanding school, could still lead to your overall effectiveness in maths being labelled as requiring improvement if you are using traditional methods of maths teaching? I think that it is inevitable that they would conclude that it is still safest to assume OFSTED hasn’t changed when it comes to primary maths. There may, of course, be deeper reasons for these judgements that the data and the comments on teaching methods don’t show, but the message that OFSTED are giving in these reports is that if you want to be seen as doing outstanding maths then forget about results outside the year of the inspection, stop practising number work and switch to doing numeracy as part of projects. Possibly you might also want to consider sending your EYFS kids outside to do shape, space and measure.

One final note, the Ladybrook Primary inspection was done by a couple of additional inspectors. There are other indicators in the report that they may not have been completely on top of what OFSTED are currently saying. However, the Tithe Barn maths report was conducted by two HMI including the OFSTED lead HMI for maths, Jane Jones, who has a long history of recommending fuzzy maths approaches over traditional teaching (most famously in the Made To Measure report of a few years ago).

5 comments

  1. I too have recently been in a staff meeting led by the DH who is also the Maths leader. She also led us to the NRICH website and basically made a big deal out of ‘problem solving’ skills. The basis for this mini-CPD was the fact that we are now being encouraged to not let children exceed the ‘levels’, or that year’s learning. Basically, the interpretation is that, instead of looking to increase fluency through lots of practise and memorisation, teachers are being minded to switch to ‘higher order thinking’ and ‘problem solving’.

    I made myself loudly heard in that staff meeting: the guidelines in the new Maths curriculum are explicit. We are to, without deviation or alteration, enable fluency in number. Fluency in number can only be achieved with practise and a good foundation in the efficient methods of calculation. Fluency is demonstrated by speed of recall. I said that not even the top mathematician in my class had the fluency required of this new curriculum.

    Additionally, I mentioned that the maths planning package we use is heavily weighted to the informal methods, to the point where the script even says ‘Teachers must say that Frog (counting on) knows best when it comes to subtraction’. To be fair, the DH had listened to what I said about the guidelines for the new SATs, in that points for calculation will only be awarded for demonstration of efficient/formal methods. All teachers present were told about the fact that formal methods of calculation are not only compulsory teaching, but should be the preferred method for children’s calculation. I have a feeling that if it weren’t for this commandment in the curriculum and as part of the SATs marking policy, primary schools would still insist on prioritising outside ‘measuring’ fun across all year groups, ‘creativity’ in maths and discovery learning.

    I am very sure that the ‘Think’ question is at the bottom of our textbooks too. I know for a fact that there are no where near enough questions in those textbooks for children to do, in order to commit skills and knowledge to long term memory, or for children to become more efficient.

    In terms of EYFS, I am in the middle of analysing the EYFS framework. Have you read it OA? See how many progressive/fuzzy phrases are used! In the EYFS stage, weight/measure is given equal weighting to number. Additionally, the preferred method for learning is ‘active learning’ and ‘play based’. Have a read. Enjoy.


    • Yes EYFS is built on those ‘fuzzy’ assumptions. This is especially clear in the non statutory guidance ‘Development Matters’. At my son’s primary school the next training day will be on problem solving in maths. It is interesting that with the new curriculum to embed that has a new focus on fluency it is problem solving they think needs yet more attention.


  2. Reblogged this on The Echo Chamber.


  3. Great post. This is the constant debate in the teaching of maths: “The pedagogical side of this is that fuzzy maths tends to be advocated by those who are less keen on direct instruction, more keen on groupwork and discovery learning, whereas the teaching of maths facts and standard algorithms is usually via direct instruction and sustained practice.” Grateful I do not have to ensure OFSTED reports.


  4. I’m just a lurker here, not even a teacher, but I follow the arguments, often with interest. When I see in a title the words “Fuzzy Maths”, though, I must say I wondered why junior school children were having to grapple with the work of Lotfi Zadeh et al.



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