Tag Archive | new curriculum

New for Old – Introducing the new Primary Maths Curriculum

New curriculum resource tool

I’ve already blogged about some of my hopes and fears for the new curriculum here.  In this blog, I want to think more particularly about introducing the curriculum to schools and suggest some useful resources.

It’s important to plan the change carefully and make sure teachers are well prepared.  As the KS2 assessment arrangements don’t change until 2016, our current Years 3 and 4 will be the first to be assessed under the new curriculum at the end of KS2.  The expectations for them in some areas will be higher and it may well be that schools choose to start teaching at least some of the new content this year so that there is less for these children to catch up in Years 5 and 6.  This is particularly true in the areas of written calculations and fractions.  Similarly in KS1, the tests and reporting arrangements will remain the same until 2016.  This means that from September 2014, Years 2 and 6 should still continue to be taught using the current curriculum but all other year groups will need to move to the new curriculum.

Expectations for fluency with number facts and calculation methods will be raised and it may well be worth tackling this with some whole school initiatives.  Some schools are choosing to give an extra 10-20 minutes each day to focus on this in particular, outside of the maths lesson, rather in the way that phonics is often taught discretely.  For number bonds and tables, it would be well worth listing exactly which facts your school expects children to learn in each year group and sharing this with parents.  It’s also worth tracking the facts that children know so that children who are falling behind in learning these can be given extra support.  It would be good to discuss as a staff just what you all understand by ‘rapid recall’ of facts.  You may find that some teachers feel children know their two times tables if they can chant the table, whereas others would expect them to be able to answer mixed 2 times tables questions, answering 20-30 or more in a minute.  I have suggested some ideas and resources for teaching number facts and tables here.

The NCTM has a growing library of resources to support introducing the new curriculum.  In particular, their Resource Tool  could be a useful starting point.  So far, only material for Years 5 and 6 have been added, but we are promised other year groups’ material before too long.  For each year group, the content has been divided into several different strands.  Selecting a particular strand and year group and choosing ‘Show Selection’ brings up the information below the tool.  So for each of strand and year group, there is information on subject knowledge, connections (to content in other year groups, to other mathematical topics and to other subject areas), articles about good practice in teaching that strand, some suggested activities that could be used in teaching it, exemplification of the expectations and videos that support aspects of the strand.

The subject knowledge resources may be particularly useful for teachers in UKS2 where raised expectations may mean that they need a refresher in eg. calculating with fractions.

 

For more information about the new curriculum and some resources which might prove helpful when introducing it, my New Curriculum Pinterest board may be helpful.  For subject leaders or senior leaders based in the Midlands, you may be interested in a course I am running next month on preparing for the new curriculum.  I have lots of ideas and resources to share!

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Higher, Faster, Harder? Supporting More Able Mathematical Learners

Using and applying word cloud

Harder, Faster, Higher? – Supporting More Able Mathematical Learners

The new curriculum, we are told, is a mastery curriculum.  This means there is an expectation that instead of pushing our more able learners on to ever higher level curriculum content, the focus is much more on making sure all our children are secure with the core content for each year group.  This leaves us with a challenge for our more able learners, but also with a great opportunity.  With less pressure (we assume – the assessment procedures are not yet clear) to push these children through the levels, we have to think of different ways to challenge them – not so much higher and faster as broader and richer content.  These are a few ideas about how we can support these children.

Open ended questions

Challenging more able children should not be primarily about moving them on to ‘harder’ questions with higher numbers.   We want to extend their thinking by asking more open ended questions which challenge them to apply their knowledge in new ways.   We also want to develop their reasoning skills by asking them to explain their reasoning.   Using Bloom’s question stems can be helpful in planning this.  Ask children to explain how to find the answer to a problem and decide which approaches would be best to use.  Ask them to explain the rule for a growing pattern or to explain what would happen if …  Get them to think of other ways of doing things and compare approaches to decide which is best.  Challenge them to explain their reasoning so that a younger child could understand it.

Mathematically rich activities

Children need to learn to think mathematically and to apply their skills.   The Nrich website provides lots of games, challenges and activities to encourage this.  They aim for activities to be ‘low threshold, high ceiling’ ie.  accessible to as many children as possible but with enough to challenge more able children.  Their curriculum mapping documents are very useful in identifying activities which link to different curriculum areas.

Investigations

Investigations can help children to extend their mathematical thinking in a more open-ended way.  Typically in an investigation, children are given a starting-point and some ideas of how to get started, but they won’t know what the answer will look like.  They need to look for patterns and identify what is happening.  The Maths Warriors site has a number of interesting investigations suitable for primary aged children.

Challenges

More able children often respond well to challenges.   The ‘Mathematical Challenges for more able pupils’   have a number of challenges divided by age group.  Another good source of challenges for KS2 are the Challenge cards on the Maths Warriors site.

Problem Solving

Whenever a new skills is taught and learned, make sure the children have the opportunity to practise their skills in a real context by applying them to solving problems.  It can be particularly meaningful to give the problems a context from another curricular area.   As well as regular opportunities to solve problems as part of their maths lessons, children often also respond well to the challenge of a ‘Problem of the Week’ which can be displayed in class for a set time.   The Nrich site is a good source of suitable problems, some of which are available as posters.  The Numeracy Strategy Logic Problems also have problems at a range of levels.

Missing Number questions

For calculation in particular, once a calculation process is learned (eg. column addition), presenting questions with missing digits can extend children’s thinking about the process they have been using.

Other useful websites

Mathpickle has some interesting videos and other activities.

Mathsticks has lots of useful resources.  There are lots of great activities which are free to download, and some premium resources if you can stretch to a membership.

7puzzle  posts a new puzzle every day.   The site also categorises the archived puzzles into Easy, Medium and Hard etc.

My Pinterest board has lots of other ideas for investigations, puzzles and challenges.

In with the New – The New Primary Maths Curriculum

New curriculum main aims

Like it or loathe it, the time is coming when it will be impossible to ignore the new curriculum (unless of course you teach in an academy).  Year 6 will have another year to continue with the old curriculum but other year groups need to start teaching from it from next September.

I am currently taking the NCETM Professional Development Lead Support course (which I would so far highly recommend) and had my first residential training at the end of last week.  In the main I found this somewhat reassuring.  I am sure that Michael Gove had a heavy influence in determining much of the content and in particular the emphasis on the aim of fluency with recalling facts and using procedures, and generally higher expectations by the end of the primary years.  Despite this, the three overarching aims are difficult to argue with, focusing on fluency, reasoning and problem solving.  The NCETM approach is to emphasise that fluency can only be achieved, and should only be achieved by building on a foundation of good conceptual understanding.  Their training and the training that we in turn will be passing onto schools explores the key role that representation and the use of concrete apparatus has in building up this conceptual understanding.  They are also keen to encourage teachers to make connections between different mathematical ideas in their teaching.

My worry is about how well this message will be conveyed to schools.  I have had two years of training as a Primary Maths Specialist, another year of work towards my masters in primary maths education, training as a Numbers Count teacher and have done lots of reading and research in addition to this.  I understand the importance of representation and of making connections.  I have seen the damage that can be done when children are moved too quickly to working with abstract mathematical procedures before they have been able to build up their conceptual understanding to support this.  I have experienced those wonderful ‘light bulb’ moments with KS2 children who have fallen well behind and lost all confidence in their mathematical ability, but given the chance to step back a little and revisit concepts of place value or calculation using concrete apparatus, suddenly see how it works.  Many of my colleagues however have not had these opportunities.  I’ve learned so much from the high quality professional development I’ve received in the last few years and could probably fill at least a year’s worth of weekly staff meetings by sharing all of this.

In most schools, professional development time is very limited.  Maths has to vie with many other subjects and priorities for staff meeting and Teacher day time.  Courses can be expensive and require teachers to be covered which adds to the expense, and budgets are limited.  In my opinion, however, it is good quality professional development which has the potential to make a huge difference to the quality of teaching and learning in schools.  If even half the time and money which is currently spent on inspecting, monitoring, evaluating, tracking data and gathering evidence was spent instead on good quality CPD, I believe the impact would be incredible.

The introduction of the new curriculum could be a great opportunity for schools to revisit their teaching approaches, to ensure teachers are clear about progression and route ways, to explore the range of concrete apparatus and representations which will support conceptual understanding, to explore the links between different mathematical ideas and to share approaches and ideas.  But this will require significant investment of time and money.  I suspect, however that many schools will not find the resources to do this and instead the new curriculum will be presented as a list of requirements with the result that many teachers will feel under pressure to move children on too quickly, which could lead to even less conceptual understanding.

In his (always helpful) blog yesterday, Derek Haylock also made the very important point that the format of the new assessments (currently being developed) will have a great influence on what is actually taught in schools.  Will these assess children’s understanding of underlying concepts, their ability to reason mathematically, their ability to apply their skills to problems?  Or will they focus on assessing the children’s ability to use mathematical procedures fluently?

For more information about the new curriculum and some resources which might prove helpful when introducing it, my New Curriculum Pinterest board may be helpful.

Rich List – Using Rich Tasks in Maths Lessons

Growing triangles

The new primary maths curriculum has been criticised for its focus on fact fluency and traditional written methods.  However, of the three key aims at the beginning of the document, only one focuses on fluency.  The other two are that we should ensure that all pupils:

reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.”

and

“ can solve problems by applying their mathematic to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.”

It’s very important that we don’t lose sight of these very important aims in the new drive for increased fluency in recall and calculation.  Regular use of rich mathematical tasks in our maths classes can really contribute to both of these.

So what is a rich task?  In her very helpful Nrich article, Jennifer Piggott describes the characteristics in some detail and some of these are:

  • accessibility – they should offer different levels of challenge to learners of different ability, giving opportunities for early success but also scope to extend learning for the more able (low threshold, high ceiling)
  • encouraging growing confidence and independence, often by working collaboratively
  • potential to link with other areas of maths or to introduce entirely new areas of maths
  • encouraging different approaches and creative solutions to problems
  • allow learners to pose their own problems and ask questions

Jennifer Piggott also makes the important point that a mathematical task, although it may have the potential to do many of these things, does not become rich unless it is well led by the teacher, asking timely questions and supporting the children just enough to start to construct their own mathematical understanding whilst avoiding ‘spoon-feeding’ them.  In practice, this can be difficult to do.  In a busy classroom, it can be very tempting to wade in when a child is stuck and show them how to do it, but if we can restrain ourselves and instead offer a hint or a question that might open up a new avenue to explore, the experience will ultimately be much more satisfying and beneficial to our learners.

One good example of the sort of activity that could be used in this way is the ‘Sticky Triangles’ activity from Nrich.  Children are presented with a growing pattern of triangles as above.  These can be made from lolly sticks or pencils or similar or just sketched.  You might like to present just the first two steps to start with and see if the children can suggest how to extend the pattern.  Then get them to work on their own or in pairs or groups to explore the patterns.  It’s probably best not to ask too many questions to start with.  Children often naturally start to notice things about eg. how many triangles are in each row, how many lolly sticks are needed to make each pattern.  It can be very interesting to watch the children and see how they approach things.  Do they work systematically?  Do they record anything?  After a while, you might want to suggest some possible avenues for exploration.  Can you see any patterns in the way the number of lolly sticks increases with each new row?  Can you predict how many triangles will be in the next row?  How many triangles would be in the tenth row?  How many lolly sticks would be needed by this stage?  What about the 100th row?  Can you suggest any good ways of recording your findings?  Encourage children to explain the patterns they see to each other and to you, and encourage the use of accurate mathematical vocabulary as they do this.  The notes on the activity on the Nrich site also offers some other possible ways of extending the task even further.

The Nrich site offers lots of these sorts of activities at all sorts of different levels.  As a teacher, I’ve found their curriculum mapping documents for KS1 and KS2 very helpful in identifying activities which might be linked to our other current work.  Another source of helpful activities is the BEAM resources which can now be found in the elibrary of the National STEM Centre.   You do need to register to access these resources, but registration is free and well worth while as there are a great wealth of resources in the elibrary.

For other suggestions for mathematical investigations, puzzles and challenges, have a look at my Pinterest board.