Louise Racher is a Primary Mathematics Adviser for Herts for Learning

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Having been lucky enough to be in the same room as the esteemed Jane Jones, Ofsted’s National Lead for Mathematics, I am going to attempt to order my thought succinctly. There were a lot of messages about Mathematics crammed into one day and many thoughts overlapped as is the tendency with this subject. At the end of the day when I looked back at my own scribbled notes I think I could see three general threads.  Overall, I was comforted that her messages aligned with my own and my colleagues therefore all of the training and subscription materials we are currently writing and producing to help and support teachers are steered towards the key messages.

Despite the conference being ordered from the headings from that of the Ofsted handbook my thoughts tend to be picked from different parts of the day, which I have attempted to put into three coherent themes. Therefore this is not a chronological recount, nor am I quoting word for word, it is simply my interpretation of the messages which follow.

Problem Solving

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Taken from ‘Ofsted Better Maths Presentation’ available via slide share

The key message here was that we need to make pupils think hard for themselves, and as Jane Jones presented a problem which was based on a problem from a Finnish textbook used with seven years olds the main thought was to “milk every problem for what it is worth” (there was a cow in the problem, Boom Boom!)

 

Jane Jones had a tendency to “get on her soap box” throughout the day, which I found really refreshing as I enjoyed hearing her own opinion which was gathered from being in the position where she observes many lessons across the country. One of her soap box moments was to abandon your RUCSAC.  Coming from someone who had a (very beautifully presented, if I do say so myself) display of just that in my own classroom it was a bit hard for me to swallow.  Since then I have been able to see the flaws in the acronym, that RUCSAC was really just teaching a procedure, and one with gaps in it too.  Newman’s Error Analysis research first carried out in the 1970s, found that most errors happen at the ‘transformation’ stage i.e. the stage where pupils transform their understanding of the problem into the calculation that will begin to provide a solution. In RUCSAC this would be between the U and the C.  Whereas, looking at the problem represented for KS2 pupils on Paper 3 this year we can see that the pupils need to recognise their starting point, so talking  to pupils about where they must start, where can’t they start and why is crucial to help them refine their problem solving skills and to essentially think independently.  RUCSAC certainly wouldn’t have helped pupils solve the problem presented.

Delegates were also provided with a worksheet where there were some steps to success which told pupils a procedure to follow, and in effect in following those steps the pupils were not being successful as it promoted a complete lack of independence. So instead, the attention and focus of the classroom needs to be on the problem solving strategies.  At this point, one of my colleagues retrieved the HfL working mathematically document (from her handbag no less), which was then passed to Jane during this section, she agreed it would be helpful to consider those skills and ensure that they are explicitly taught as well as opportunities given through the sequence of learning.  As I will be writing new training materials over the summer I think this will shift my focus slightly, we want pupils to really be good identifying the strategy desired to solve a problem.  This is what the 2016 KS1 and 2 test demonstrated, it required the pupils to assimilate a great amount of information and apply it in specific ways.  That may have been ordering information, or choosing a starting point, perhaps deciding on the order of operations, working backwards … the list goes on.  Pupils need to identify the strategy, then they can use the skills taught during that application.  Jane Jones is clearly a fan of George Polya (as are we), whose first principle was; Understand the problem.  He taught teachers to ask pupils questions such as:

  • Can you restate the problem?
  • Can you think of a picture or a diagram that might help you understand the problem?
  • Do you understand all of the words and phrases in the problem?

After this his second principle is to make a plan – to choose the heuristic or problem solving strategy that will best suit the problem.   For pupils to able to do this, they need to have an extensive set of problems to act on, only then will they begin to select the correct heuristic for the problem.

There was a section on attainment, and looking at gaps between pupil groups.  The message here was catch them early so the gap doesn’t widen, and Jane made the point that often we widen the gap without meaning to, such as giving the harder problem solving activities to the pupils who are the highest attaining, while the pupils who are lower attaining may be rehearsing skills, this leads to those pupils finding it even harder to apply those skills.  If we think about Polya’s work then we can see that by restricting access to problems or over scaffolding them, even with the best of intentions, we do not provide pupils with the experiences and skill set to tackle problems.

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Reasoning

The next message was about reasoning, I liked the way Jane saw this has the overlapping aim which linked the other two National Curriculum aims. Without reasoning you can’t solve problems and you can’t be fluent.  Paul Tomkow, HMI, also interjected with his own experiences of what he sees in schools upon inspection.  He was aware he was generalising, but I found his comments helpful in considering my own classroom and where I might have fitted into the comments he made.  One such comment was that he very rarely saw written statements in mathematics, the pupils might be asked about what they did, but not how.  Again, this resonated with me, as we have delivered training and often touched on the notion that reasoning does need guidance and support to develop this ability in pupils.  They are not always sure how to record ideas, or structure sentence when referring to mathematical concepts.  It is something we have worked on as a team through the concept of journaling and you can see a blog about developing pupils’ ‘Mathematical Voices here. I want to think more carefully about how we can continue to make this a reality in the classroom.  Another job for the summer school break.

Progress and progression – not the same

The final message I took away from the day was considering progress and progression. How they are very different, yet inextricably linked.  If you were to focus on one domain e.g. fractions and then look across the school in books or plans at how this delivered to pupils what would you notice?  How are the concepts being taught, what is being repeated and how does this build across the school.  I reflected this would have been really useful task to do with the whole staff, helping to see what is coming before and after what you are teaching.

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Soon to be released HfL Progression in Bar Modelling Document

There was the example of the formal methods being introduced to pupils, Jane Jones clarified that there is no statutory to teach content in a specific year groups, but as a Key Stage, how you structure this learning is up to a school.  It did become a running joke between colleagues as we gave each other sneaky smiles and thumbs up, as we found we either had written a document to support these ideas, or they were being written and coming soon.  To support progression there is a document which outlines bar modelling across the primary phase, in addition to a progression of mental methods across the school as well.

 

As a subject leader it was always a challenge to see that progression for all the different areas of mathematics and oversee it was being taught in a way to support and build on pupils understanding.  Jane Jones made the suggestion of helping pupils make links between previously taught methods, helping them notice what is the same and different about the formation of this method, rather than seeing each method as a different strategy but always building on the previous strategy until they reach a formal written method with sound conceptual understanding of the underlying structure behind the short hand notation.

The afternoon focused on pupils’ books, which helped to consider the main themes which ran throughout the morning. In the interests of trying to be succinct about this day I will leave that for another time …

 

Are you looking to make a real difference to mathematics learning in your school? Would you like to know how to undertake the activities and manage the challenges of leadership that can do this? Do the priorities in your mathematics improvement plan include actions to enhance all three of these areas: teaching & learning; curriculum; leadership & management?

If you are a mathematics subject leader and would like further training around any of these ideas, then Herts for Learning run a highly popular 5 day subject leadership course which you can find here.

Progression documents for Bar Modelling,  Mental Calculation and Written Calculation are all available here.

References

Newman, M. A. (1977a). An analysis of sixth-grade pupils’ errors on written

mathematical tasks. In M. A. Clements & J. Foyster (Eds.), Research in mathematics

educatiDn in Australia, 1977 (Vol. 2, pp. 269-287). Melbourne: Swinbume College

Press.

Jones, J and Tomkow, P; ‘Ofsted, Better Mathematics Conference’, 19th July 2016, Hertfordshire

G. Polya, “How to Solve It”, 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6