Thoughts on Learning Nothing

"The idea that students can be intensively, productively and successfully engaged in a task and yet learn nothing as a result seems to me to be the most profound idea in all of educational psychology."

So tweeted @dylanwiliam a number of days ago referring to mathematics classrooms. And his statement has worried me since I read it. 

Here are my thoughts. 

Of course students can be "intensively, productively and successfully engaged" within a maths lesson, but not doing any mathematics. In this category I include what I call the 'colouring'  tasks you find on many maths worksheets. Many of these do not involve the students in any mathematical thinking at all. They are not engaged in mathematics. 

Of course students might not be learning what I intended them to learn, and maybe this is what this statement means. When planning I tend to think about 'learning possibilities' rather than objectives. I have in mind possible mathematical trajectories where a task may lead. This includes the constant re-framing of the task according to what I notice going on, fed by the multitude of in-the-moment decisions I make. These rely on my experience and knowledge of both the mathematics and the learners and this changes every lesson, as the learners respond to what plays out. This is how learning is built. It certainly does not involve me concluding someone has learned "nothing". What is learning "nothing"? How would I know this? How would I recognise "learning nothing"?

Learners might be involved in something and might not appearto be 'learning'; perhaps for example when they are spending time handing manipulatives. Maybe I have been working with some Y1 children on number bonds within 10 and 20. At the end of the session perhaps they are unable to answer my question "What number pairs up with 11 to equal 20?" Does this mean they have learned "nothing" during that task? Do they understand my question? What can they tell me? If they are unable to answer me verbally, maybe they can answer whilst looking at an image? 

Perhaps the statement confuses performance with learning. Maybe (some? all?) my children are unable to perform the required objective, in this case, to name the complementary pairs of numbers that total 20. But they (some? all?) may well have learned, if I have crafted my lesson well, that there are a finite number of pairs and begin to see links to the pairs of numbers that equal 10. It is my job, each and every interaction, to find out what they havelearned and build from there. How might I craft my lesson so that they learn to think mathematically? In this example the children may have been building and discussing sticks of cubes, or Cuisenaire trains, to total 20. But in order for them to be "intensively, productively and successfully engaged" in mathematical thinking, I will ask them to:

•   find ways to check there are always 20, 

•  how they are sure they have found all the pairs,

•  organise the pairs and look for (and explain) a pattern they notice, 

•  write the horizontal number sentence to match each pair,

•  play "Which number is missing?" as they take it in turns to hide their eyes and remove one stick. We'll ask each other "And how do I know?" 

But this is a suite of lessons (or sessions). In order for them to be "intensively, productively and successfully engaged" in mathematics, the practical task is one part. And may last a while. Maybe longer than 'one lesson'. So is it correct to assume that these students were, at any point"...intensively, productively and successfully engaged in a task and yet learn(ing) nothing as a result"?If I view this as one small episode in a series of planned interactions where my students and I 'meet' the pairs of numbers that equal 20 in many different ways (coins, bead-strings, patterns...) and link this to other mathematical knowledge, we have plenty of opportunities to re-visit this to ensure they have learned this particular 'something'. Learning takes place over time, not necessarily within a lesson (to paraphrase Pete Griffin) and the drive to make sure that every student is learning something every lesson (or every interaction) might lead me to conclude that "students can be intensively, productively and successfully engaged in a task and yet learn nothing as a result." 

My conjecture, after thinking about this statement, is that it is not possible to be intensively, productively and successfully engaged in themathematicsof a task and learn "nothing". And that is my job as a teacher, to intensively, productively and successfully engage learnersin mathematics. My teacher-questions and interactions should focus the students on the mathematics; encouraging explaining, describing, reasoning, predicting and link-making. Tasks that do not include this, whether or not they are deemed to be 'discovery' or 'practical' or 'practice' or or 'direct instruction' are not mathematics tasks. Even when they take place in a maths lesson. 

I am not sure the idea that Dylan William refers to in this tweet is profound. It is either blindingly obvious or lacks nuance in considering learning. More worryingly, it might be used to denigrate ways of working in mathematics lessons that include exploration, inquiry, discussion and handling manipulatives; and that seeks to promote direct instruction by an adult as the only effective way to teach and learn mathematics. And that is what worried me.

Roller-skating or tidying? Which is mathematics to be?

Roller-skating or tidying? Which is mathematics to be?

Helen J Williams 

“Mathematics could be like roller-skating, but usually it’s like being told to stop roller-skating and come in and tidy your room.”

Richard Winter, 1992

This has long been one of my favourite quotations in relation to learning mathematics. Winter follows on by saying:

“This is not a superficial matter.”

I dug out Richard Winter’s article this week and was reminded that it has a lot to say about play, work, young children’s strengths as well as cultural domination; which he accuses mathematicians of being complacent about.

What is it about maths that makes many of us feel inadequate and quick to admit we could never “do it”?

The difficulty isn’t something within the mathematics itself, it is in how mathematics is taught, how it is perpetuated culturally as a seat of mystery, power and (yes, still) intimidation; and, critically in classrooms, how much space we provide for learners to think and make sense of what is offered. 

I know this is true. I was maths-phobic at secondary school, it took me two attempts to achieve my GCE (remember them?) and yet I have enjoyed teaching mathematics for (well) over 30 years, I have attended maths conferences for 30 years and now love the puzzles and problems that are posed. 

Winter tells of observing his daughter engaged in philosophical and metaphorical conundrums from infancy. One wonderful story is at 10.5 months where she enjoys ‘mis-taking’ a feeding bottle for a plastic cone. I have a similar experience of my 11-month-old relishing the use of a diving flipper for a “Bag! Bag!” Referring to some eleven-year-olds quoted in an APU document on mathematical development, who abandon their theories in the face of contradictory data, Winter poses the question:

“If infants can take their pleasure in such philosophical ways, one wonders indeed what can have happened to (these) eleven-year-olds.”

What changed for me mathematically was that I became interested in the sense my Reception learners were making of what I was offering them mathematically. I started asking questions “I wonder what they would do with this”, and observing more closely, sharing what I was noticing with colleagues (those who would listen!). I started to try things out that were more in-tune with them as individuals:

How many of those do you think you can hold in your hand? What about both hands? Why do you think that? How far will all those stretch, do you think? Why? What if we tried that game with a different dice? How shall we record that? What do you think?

And I tried hard to be more silent. I started to listen toas well as listening for. 

At the ATM mathematics conferences I attendedhttps://www.atm.org.uk/Association-of-Teachers-of-MathematicsI was able to choose what I took part in, to try things out in a safe and non-judgemental space, to work with others, to think alone.

Early years in particular allows the space and freedom for young children to explore theirs and others’ ideas, to predict, to reason, to explain, to wonder. But often these opportunities are missed where there is a tendency to overcorrect, to steer children closely through a series of small, pre-determined (by whom?) steps, to carefully avoid the making of mistakes, the challenging, the pure, wild enjoyment. In fact to apply what we know works in other curriculum areas to mathematics. Winter argues for a reversal of the following common teaching sequence (largely unquestioned since the Cockcroft Report of 1985): 

Teacher exposition, Discussion, Practical work, Routine practice, Problem solving, Investigation. He argues, and I would agree with him, that children arrive at school very able to apply knowledge to solve problems; in short, to do mathematics; and we often as teachers make mathematics difficult for children by over-complicating what we ask them to do, by undermining their natural perceptions (by treating their thought processes as inferior), and by whilst startingwith games and play, for example, quickly turning these experiences into those that resemble tidying your room.

My ‘to do’ list for early years mathematics begins:

·     go outdoors, to run, do big and noisy, build, climb, collect, 

·     do lots of Cuisenaire play; there really is nothing else like it for exploring relationships between numbers,

·     play with dice; many different types to invent games, 

·     provide lots of different collections, all of large amounts, of both natural and manufactured items to endlessly count, sort out, line up, use for making mini-collections, 

·     collect purses, wallets and small containers to fill, shake, empty, count in and out of, compare,

·     provide paper of all sizes and shapes, tape and scissors to cut, fold, unfold and re-shape,

·     collect large (and tiny) containers and bags to fill and lift, with sand, water, stones, beads…

·     make some balances, including huge outdoor ones,

·     find a great variety of measuring items to use, discuss and compare,

·     collect blocks, boxes and beautiful geometric shape collections to create patterns, constructions, cityscapes and enclosures,

·     put out the calculators and large sheets of paper and pens for ‘free writing and drawing’. 

Enjoyment excitement and motivation are not dirty words. 

Neither is play (“Play - where a grasp of the basic situation is the beginning ofcreative individual improvisation” Winter, 1992)

As Winter says:

“All successful education, I would argue, aspires to the conditions of play.”

References

Cockcroft W.H., (1982) Mathematics Counts: Report of the committee of inquiry into the teaching of mathematics in schools (The Cockcroft Report). London: HMSO

Winter, R., (1992) ‘ ‘Mathophobia’, Pythagoras and roller-skating’ in N. Nickson and S. Lerman (eds.) The Social Context of Mathematics Education: Theory and practice. London: Southbank Pres

No. I won't calm the hell down. Bolder Beginnings in Mathematics

Six weeks ago, Ofsted's Bold Beginnings Report into the Reception Curriculum was released: https://www.gov.uk/government/publications/reception-curriculum-in-good-and-outstanding-primary-schools-bold-beginnings
I was looking forward to what it had to say, and had met with some R practitioners earlier in the month and had discussed what they thought would be useful. Pointers and examples of what others were doing and what we all might do to support our children though the R year, and into Y1, based firmly in what we know from research.

I am still angry about the actual report. Open the report and the Executive Summary opens with: 

"A good early education is the foundation for later success. For too many children, however, their Reception Year is a missed opportunity that can leave them exposed to all the painful and unnecessary consequences of falling behind their peers."

 

Maybe they thought no-one would read it over Christmas. Or maybe they thought no-one would think this a strange way to begin a report that you would want Reception teachers to take on board and develop. Leaving aside where the evidence for this statement comes from (where?), and that every R teacher I have come into contact with consider it an integral part of their job to learn and develop their teaching (despite one I came across in 1991); and that term "falling behind" - as a 4 or 5 year old? That old deficit model rears it's head again.
I have been trying to pin down exactly what I am still angry about.

Part of this is related to how the lively debate that has ensued has been received. 'We' - ie those of us who have laid down more clearly than I am here their objections to the report - have been accused of being "over excitable", "defensive", "a backlash", "mobbing" Ofsted, "caterwauling" "misinterpreting" "railing against it" and more besides. Why so much antagonism? Would the same people - all educators themselves - be happy if I used these terms about those of them objecting to a report into A Level or GCSE maths, I wonder?
But I wouldn't. I would read the objections and try and understand the level of anger and horror (yes horror). I wouldn't dismiss them, I certainly wouldn't tweet patronising tweets with no knowledge of the background into international early years education in this case, A level and GCSE maths in the fictional case. I wouldn't agree with it all. I wouldn't be happy with some of the tension and tone. But I would attempt to understand where these come from.

Part of my continuing anger is to do with how the report is written. Colin Richards' (@colinsparkbridg) piece for Schools Week on tone is illuminating: https://schoolsweek.co.uk/bold-beginnings-how-not-to-write-an-ofsted-report/.
I too am guilty. When I was contacted on December 8th for my first reaction to the report, my first word was "bullshit":
 https://www.tes.com/news/school-news/breaking-views/my-response-ofsteds-new-report-reception-teaching-best-retire-now
Suddenly it's adversarial. But it didn't need to be Ofsted.
Over the last 6 weeks I must have come into contact directly and indirectly with over 100 Reception and Y1 teachers. Without exception they are upset by the report. Those of us working in early years are left picking up the pieces from this.

And my anger is to do with the content of the report and the fact that the recommendations (which most busy headteachers will read at least first if not only) do not lead from the findings. (Delving deeper into the findings makes me really angry. Try the technical documents and judgement record (scroll down): https://www.gov.uk/government/publications/reception-curriculum-in-good-and-outstanding-primary-schools-bold-beginnings)
The Reception curriculum cannot be usefully considered in isolation from the rest of the EYFS, neither as isolated from the Y1 and Y2 curriculum. Looking at the mathematics section, arguably, on the surface, not quite as controversial as the reading and writing sections, there is an unhelpful example of R children working with 3-digit numbers and several references to "schemes". Why? Where is the reference to the work being done to building the strong foundations our young children - who start school earlier than much of the world - and building these playfully? Instead we get:

"It was clear what children could achieve. The schools that ensured good progression frequently used practical equipment to support children’s grasp of numbers and, importantly, to develop their understanding of linking concrete experience with visual and symbolic representations. More formal, written recording was introduced, but only when understanding at each stage was secure and automatic."

and:

"Leaders who had ensured that progression in mathematical concepts from the very beginning frequently used practical equipment to support children’s learning of new concepts."  

Is this news to anyone? Frequently? What does this actually mean in practice? Formal recording only when ...etc? Has no-one read Martin Hughes (1986!)? https://www.wiley.com/en-gb/Children+and+Number:+Difficulties+in+Learning+Mathematics-p-9780631135814

Back to the practitioners I met before the report was out. We were looking forward to analysing the mathematics examples reported to see what was useful to us in relation to what else we are reading from international research about how 4&5 year olds learn mathematics. When I meet with them next we will spend some time picking up the pieces from the tone of Bold Beginnings, the feedback from the rest of their schools regarding the recommendations and the national messages being received and sent about the report. We will then spend most of the time together sharing the playful mathematical experiences we are exploring in our classrooms and analyse what these tell us about our children's learning, and then we will work together on positive images of early years 'direct maths teaching'.
Oh. We were doing all that anyway.

Bold Beginnings is not bold at all. It contributes nothing to the useful debate on early years mathematics education. I agree the profile of early mathematics needs to be raised, I have been working on it myself for some years; but Bold Beginnings is a (deliberately?) missed opportunity to recommend a full programme of CPD and engaging, practical and useful ideas based on research. Instead the writers opted for "schemes".
That's why I am angry. And I am not going to calm the hell down about it.

If you don't organise an induction, rest assured there will be one; just not the one you may want

This was said to me a while ago on a school governors' training day. The speaker was talking about including all staff in training, particularly referring to part-time staff such as lunch-time supervisors. 
The blog by @jillberry102, read it here: http://www.capita-independent.co.uk/resources/blog/are-character-and-thinking-skills-important-knowledge-and-understanding ,
on what should be the primary focus of schools made me think of this advice.
And I am not at all sure I can separate the teaching of knowledge and understanding from the wider "softer" (by which I might mean immeasurable) qualities such as self-awareness, independence and resilience.  
I might think I am simply focussing on building children's knowledge, but the way I work and the way I speak to learners, the time (or not) I allow for discussion, the value I place on independence are all there, in the background and can be read from the shape of each lesson. Do I jump in often when a pupil says they have a problem or they don't understand? Do I ask them what they think and see as well as telling them what I do? How much time do I allow for simply 'wallowing' in a maths problem? and do I alter tomorrow's plans because of what I have seen today ... and tell them why I have?
These qualities will be 'taught', just maybe not in the way I may want. Just as well to be explicit about it. 

Videos of classrooms: Teaching as if no-one's watching

Videos of classrooms: Teaching as if no-one's watching.

Yesterday I was shown a video of a Y6 classroom working on some maths, reasoning about fractions to be precise. The extracts from the classroom were interspersed with comment from their teacher.
It was a joy to watch. The relationship between the teacher and the pupils was tangible; the pupils were (dare I use the word) engaged, there was plenty of useful and informative discussion amongst one another, the teacher listened in but didn't overpower and gave children time to work on their ideas. Surprise surprise; children answered in whole sentences (!) and paid attention to the teacher (without 'tracking'), they took responsibility for their task and their learning. There was plenty of teaching. And, shock horror, there was laughter.
It was all a Y6 maths lesson should be; content rich, enjoyable, puzzling, memorable and collaborative: building a community of mathematicians. And Mr Malyn of St Margaret's C of E Primary School taught as if no-one was watching (thank you @EnserMark for this phrase).

Now some of you might know where I am going with this.
(Deep breath) So there are plenty of videos lessons out there, in particular on the NCETM website, purporting to demonstrate 'good' maths lessons. Some of these are of teachers brought over from Singapore as part of the government's push to adopt Chinese teaching methods in mathematics to raise our position in the. PISA and TIMMS league tables. My problem with these videos that I have seen is this. This is a visiting teacher, often encountering this class once and only once. Thus the culture of the classroom and the relationships between the learners and the adult are all missing. This is not unimportant. The reliance on 'from the front' instruction and the underplay (even elimination) of talk, discussion and the role of problems to situate and add context to the learning displays a particular type of lesson. And one I have worked hard to break down over 30 years because research has shown us how ineffective this is for many learners. Importantly, it is the teacher who is doing the maths, rather than the learners. I used to ask myself at the end of a lesson "who did most of the work there?" if the answer was me - well that's not really what should be happening, is it?

My question is this. If it was fairly straightforward for this publisher to find this English Y6 class to film (and in a school that has been in and out of challenging circumstances), how difficult would it be for NCETM to video the expertise and skill around in our UK classrooms? In a situation where a visiting teacher teaches an unknown group of children it is easy to slip into 'instruction' mode (let's leave aside here considerations of cultural differences). I know this as I have taught a fair few lessons in other's classrooms over a number of years.

But I realise what this is about. It is about our current government peddling one particular approach in our primary mathematics classrooms and the NCETM being part of that push.
So let's watch these videos with a critical eye. What has it got to say to us, with what we know about our students' learning? What am I persuaded about? What am I left wondering about?
In short - let's look nearer home and remember what it is we already know about learning maths. And let's all teach like no one's watching.

This video is in the public domain and is part of the package: "No Nonsense Number Facts: Teaching for mastery: Fluency through reasoning with number facts Y1-Y6" Published by Raintree and Babcock https://www.raintree.co.uk/products/9781474749541

My academic paper

I am trying to write an academic paper. 
I have been trying to write an academic paper for two years. 
What's stopping me? (In truth, I am writing at the moment and aim to have it submitted by Christmas.) But what has been stopping me is not the writing, which I like, but the hoops I see me having to fall through to be published in a refereed journal. 
I read this in the TES at the weekend:

 "... most educational research is not written up in a way that is designed to meet teachers' needs. (...) the teacher doesn't want something generalisable. They want something for their context and their pupils." ( TES 11 November 2016, 'TES talks to Philippa Cordingley')

The interview talks about making research 'particularisable' and suggests ways we might do this when using research in CPD sessions (start with the outcomes, then tell the story of the findings and finish with the methods). Philippa Cordingley talks sense. My problem is that in order for my article to be accepted I have to not only write the other way around (method, story, findings) but generalise my language and formalise my style. But I am writing about a small case study that, I am told, is strong on detail and presents a carefully analysed case.

"Your academic writing style is probably perceived to be too informal, writing in the first person can be mis-construed as being subjective."

Hmmm, subjective. Surely in order for any of us to hear and act on anything, it has to be subjectified? I need to hear a voice. If I hear the voice I can reach a decision about what this might mean to me.

For me, a major problem with many research papers I read is that they try too hard to speak generally, and in this I am unable to see my particular; and try too hard to speak 'objectively' (whatever this means), and in this I am unable to hear a voice that might speak to me.

I'll have another go, I guess.
And I wish Philippa Cordingly would contact BERA (many other research organisations are of course available) 

Just because they can does that mean they should?

I sent the following email about the KS2 arithmetic SATs paper to some people and it was suggested I blogged about it. So here it is, as my opener as a novice blogger.

Thank you Justine Greening for calling a temporary halt to the indecent rate of change in primary assessment. However, as I ponder  the fallout from this summers' KS2 tests, I would like to share this small piece of anecdotal evidence from Ben, a Y10 pupil (15 years of age) in the "top set" for maths, reported to be working at "level 8" (?) and on target to achieve A* in maths at GCSE. He last week volunteered to sit this summer's KS2 arithmetic paper for 11 year-olds: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/524052/2016_ks2_mathematics_paper1_arithmetic_PDFA.pdf

This is Ben's feedback.
 
It took him 1 minute off the full allotted half an hour to complete the paper. He thinks he got one question wrong. He started confidently but as the paper went on he felt "quite depressed". At the end he felt "demoralised". He wondered:
1.  What was the point of asking so many questions that tested the same thing: "It's the same stuff over and over, what is the point of that?" The first few pages were particularly depressing he said and he quickly became demoralised.
2.  Why you would even need to do most of the calculations without a calculator: "It's a complete waste of time".

In terms of the Select Committee's inquiry into assessment (deadline this Friday!: https://www.parliament.uk/business/committees/committees-a-z/commons-select/education-committee/news-parliament-2015/primary-assessment-launch-16-17/
And Greening's recently announced consultation on assessment in the New Year, I think the following points are pertinent.
The length of the arithmetic paper is unreasonable and contributes nothing to useful assessment. If we must have an arithmetic paper (and the question remains as to why we do, as no evidence-based answer has been put forward to support this) then it should consist of a few, well-chosen questions to assess not simply an arithmetic procedure, or something that is better done with a calculator, but the pupil's ability to reason through an answer. The current paper, by asking a pupil to repeatedly reproduce similar procedures, smacks of trying to catch an 11 year-old out. Currently the KS2 arithmetic paper tests stamina and not mathematics.
Finally, if a high-attaining Y10 pupil, who is successful at maths and intends taking this at A level, is demoralised by this paper, we must ask what it is doing to everyone else.