Tag Archives: maths

Key Instant Recall Facts for mathematics

I am a massive fan of drilling and practice for children who need to learn number facts. And the reality is that that’s all children. Whether it’s the earliest number bonds, or the prime numbers, the new curriculum is very clear that fluency in these areas underpins much of what else is done in mathematics – and it’s right to do so, in my opinion.

Key Instant Recall Facts (Y2 example)

Key Instant Recall Facts (Y2 example)

I was, consequently, thrilled when the documents below were sent to me by Jo Harbour (@joharbour) of Mayfield Primary School. As a maths subject leader she has taken the time to set out a programme of teaching and learning to secure those essential number facts that runs from Year 1 through to Year 6. Beginning with the basic number bonds to 6, and developing to the knowledge of equivalent fractions and decimals by the end of KS2 they set out a useful progression for schools, and an excellent support for parents wishing to help at home.

Jo has kindly said that I can share these here, and so I am delighted to do so. They are created in Powerpoint format, which means that most schools can edit them. Note that some of the core elements are saved in the master slide, so to change the logo, for example, you’ll need to edit the slide master (accessed via the View menu on recent editions of Publisher). I have also uploaded a PDF version for those schools who cannot access the originals, but might want to follow the model.

Thanks must go to Jo Harbour for both creating and sharing these excellent resources (here contact details are contained within the files).

Key Instant Recall Facts (editable PowerPoint)

Key Instant Recall Facts (PDF)

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What should the primary curriculum really look like?

Or: What is the point of teaching them all this stuff anyway?

I’m firmly of the belief that a majority (perhaps the large majority) of primary teachers share the same view: that we force-feed the kids in our classes a diet of breadth over depth because the curriculum, or the tests, or Ofsted, or SLT’s demand it. I think most primary teachers – particularly in infants and lower juniors – find themselves teaching things that they think are being delivered ‘too soon’ for the children in their care.

This is not an argument for the molly-coddling of children, or the lowering of standards. Rather it is an argument for a rationalisation of what we try to teach.

Coming from a middle school background, I have long wished that the 9-13 Middle Schools of the 70s had really taken off. I wish that the National Curriculum from its first inception had been built around the three main phases of first, middle and upper schools. Then, we might perhaps have had a different approach. Perhaps not in 1988, but maybe by now we might have recognised that very little really matters in the curriculum for children under 9 unless they are already confident with number and language.

I raise this point because of a brief discussion I had with Heather () on Twitter this evening. She quite rightly pointed out that starting to teaching persuasive writing in Year 1 didn’t seem to be contributing to a significant growth in the transferability of such skill at GCSE level. And if the skills aren’t transferable after 10 or 11 years’ teaching, then what’s the point? My response was both complete agreement and disagreement.

I disagreed because I think the point of teaching persuasive writing at KS1 is not to enhance the persuasive writing skills of 16-year-olds. In fact, I think the only purpose for any form of writing at KS1 is the practice of the basic skills of writing itself: the building of sentences; the use of capital letters; the simple formation of the symbols. However, I agree that expecting the teaching of varied genres at KS1 to have much impact on the ability of children to write for different purposes is frankly erroneous.

So, what then, is the point of any such work?

Looking back at the three-tier model, I’d be quite happy to see a curriculum substantially different to the one we have in place at the moment. This links in with Michael Fordham’s (@mfordhamhistorypost on an altered Secondary curriculum (which is well worth a read). In it, Fordham argues that English as a separate subject (as distinct from Literature) ought to be removed from the curriculum and its various aspects be properly addressed in domain-specific subject lessons. A genuine approach to Literacy across the curriculum. I’d be happy with that model, and what’s more, I think that it should be balanced by the inverse approach at first school age.

Given the choice, I’d happily see a three-tier curriculum (as in first, middle and upper stages) that broadly followed this pattern:

First School (age 5-9): Only English, Maths and Modern Languages would be statutorily prescribed programmes of study. All other subjects currently in the National Curriculum would become part of required areas of study (Arts, Humanities, Sciences, etc.) which were intended to provide breadth of experience and support the core subjects. Physical Education would also remain statutory, with no programme of study.

English and Maths programmes of study would be re-shaped to focus on Literacy and Numeracy. That is, all children would be expected to focus on developing oracy, and reading and writing basics (comprehension, building sentences, vocabulary, paragraphs, etc.), without concern for genres or required areas of study.That’s not to say that children wouldn’t meet other genres, or contexts, but that these would merely be to support the core teaching aims, rather than becoming additional goals in their own right.

Similarly, in Maths the requirements would focus largely on number work with relatively brief forays into shape as appropriate. To be fair, the new Maths curriculum has moved a good way towards this. I have often heard many secondary maths teachers say they’d be happy to teach Y7s who came to secondary secure with number bonds and tables and relatively little else. I’d agree, but think we could move to that sooner. Let’s have all 9-year-olds ready for the next level.

By removing the requirements to study particular programmes of study in all areas, it ought to be possible to move towards a system where the current Level 4 expectations could be met by the majority of 9-year-olds, rather than 11-year-olds. As Mark McCourt (@EmathsUK) said this weekend at the maths conference: Maths is like Jenga – pupils don’t fail because of weaknesses in the blocks at the top!

Middle School (age 9-13): The current subjects of the National Curriculum would remain, although English and Maths would be radically re-shaped to reflect the changes in the first school range. English could now begin to focus more on literature, although as Michael Fordham suggests, ought not to need as much curriculum time as at present (often 7.5+ hours a week in primary schools) as literacy should be mastered by age 9. There would still be study of language and some genre-linked ideas, but the shift towards domain-specific writing should be reflected in a shift in timetabled hours. I would argue that Middle Schools used to do this, until the KS2 SATs demanded that they narrow their timetables to focus on meeting the odd demands of the tests.

This model should leave more time in this phase for the study of subject knowledge. It would be far more sensible, for example, to begin a study of chronological history at age 9 and maintain it until at least age 16, rather than the current 7-14, and would be far more successful if students had already mastered the required literacy skill. Of course, this also would be combined with the middle school approach to specialism. We should expect all teachers of first school-age children to be expert in the teaching of early reading, writing and mathematics. We simply cannot expect that to apply right up to the age of 11 any more. It isn’t working.

Upper School (13+): The model that Michael Fordham suggests seems to make a good deal of sense to me here. By this stage children should have a broad experience of all the subjects, underpinned by their ability to access and use texts and a secure knowledge of number work. Ideally I’d argue for greater breadth until the age of 18 as well

 

Of course, none of this is rocket science. Indeed, most of it fits with what many primary teachers already think: if we spent less time ploughing through genres, or tackling history concepts with 8-year-olds, we could focus more on the things that really matter, and give those kids the freedom to access all matter of higher level material as they got older. Surely that’s got to be better than the current system which tries to build all curriculum areas from age 5… and too often leaves interventions at 16 to try to plug the gaps the system leaves?


Addendum: I ought to note that it wouldn’t necessarily be a requirement to change the whole system to a three-tier model. But I would argue quite strongly that expecting any primary teacher to be an expert in all areas of the curriculum up to Y6 level is never going to provide us with the best system; middle schools present a good solution to this; specialisation in small primaries is much harder.

 

The importance of curriculum design

I’ve been thinking about this blog for a while, sitting on drafts, deleting sections and re-writing parts. Then, this weekend, a conversation with @ClassroomTruths, @imagineinquiry, @misshorsfall and @rpd1972 among others, led to an impromptu decision for us each to publish blogs on the loosely-linked theme of topic planning.

I’ve spoken in the past about the importance of getting curriculum right for children, focussing particularly on writing, but increasingly I’m coming to feel that we wildly underestimate the importance of curriculum sequencing and design. This is probably partly because for a long time primary schools had that responsibility removed from them and usurped by the national strategies. But I don’t think the strategies got it right.

What’s more, I think the arguments are more subtle and more pressing than the choice between cross-curricular and subject-specific approaches. There are arguments on either side about the benefits of each approach, but I’m coming to feel that it’s rather like the choice between cooking on electric and gas. Personally, I prefer a gas hob and electric oven, but I don’t have any evidence to suggest that these lead to better cooking; just that I have a preference. Similarly, I’m yet to be persuaded by any argument that topic-led or discrete subject-led teaching is inherently better for learning.

So if it’s not that the bothers me, then what? I’m increasingly concerned about the choices we make to bind together the various elements of the curriculum, both within and across subjects. I’m certainly not against cross-curricular work. In fact, as a middle school teacher, I was always astounded how students in secondary schools would find a History department teaching medieval history in Year 7, but English departments keeping Chaucer back for Year 9; or Science departments trying to get children to interpret graphs without first checking whether it had been covered in maths! There is much to be said for an ‘inter-disciplinary’ relationship, whether taught by a common teacher or different ones. However, I’m not convinced that cross-curricular teaching is automatically a Good Thing.

Tim Taylor’s blog already covers some of the challenges of topic-based teaching. What I particularly want to consider is an issue that is significant even when subjects are taught discretely. After all, in many schools mathematics is taught discretely from most topics, and yet this is one of the areas I feel needs most attention. For too long the decisions about teaching of core subjects have been taken out of teachers’ hands and handed over to folders from the department. While the National Numeracy Strategy file had its strengths (the exemplification particularly), the centralised directing of objectives on a micro level absolved teachers of the responsibility for designing the curriculum other than in the narrowest sense. In both English and Maths, teachers have been told what to teach, and when to teach it, and so have given relatively little thought to sequencing the curriculum for their own students.

In some ways, teachers have attempted to develop cohesion through topic-led teaching, but the coherence that this offers can be illusory. While planning out a whole unit on the theme of Chocolate might seem attractive, does the content we incorporate provide the best possible teaching sequence for the children to learn? It’s common to jump from genre to genre as we find writing opportunities and reading texts that suit the topic, rather than finding topics that support the gradual progression of teaching. To return to the kitchen analogy, this seems to me rather like taking the ingredients of a good cake recipe, throwing it all in a bowl and hoping. Teachers need to take on the role of chef and cultivate the best combination of those ingredients, in the right order, and combined with the right techniques to create the most effect outcome.

Dan Willingham and others have explained how focussing on context can sometimes distract from content. We need to ensure that what our children are thinking about is the material we’re hoping they’ll learn. By building our focus entirely round a single idea, do we sometimes risk elevating the importance of the topic above that of the learning context.

But as I’ve said, the problem is not unique to topic-led curricula. At present our maths curriculum seems to be largely built around short blocks of content before skipping on to something else. As with other things, we find ourselves facing children who cannot remember things taught earlier in the same year, when we attempt to revisit in the second half of the year.

But as we move towards the new curriculum, teachers are going to have to take back some ownership for designing the curriculum. The old frameworks won’t cut it, not least because of the new content in areas such as fractions. What’s more, the old approach of a few weeks on fractions  each year, simply hasn’t proven enough to get children to really grasp their use. If we are to be able to raise children’s understanding and knowledge about fractions, then we need to have a clear pathway through that allows children to progress by embedding learning at each stage.

So, what am I proposing?

Well, firstly, not necessarily the scrapping of topics. After all, some humanities themes lend themselves to teaching particular genres of writing, or other aspects of the curriculum. However, I am suggesting that the starting point for all of our planning, at every level, should be the key learning objectives. And I don’t mean, selecting them from an annual list to tie into a topic, but selecting, grouping and sequencing the objectives first, and then seeing if their is any scope for linking ideas together across subjects. If a school gets its long-term plan right, then it can select themes which complement the central learning, rather than lead it.

I have shown in my previous post how I’ve used the Victorians theme to support the teaching of certain techniques in Writing. I can also see how many well-planned topics can lead to effective learning. But I also see many topic titles set out for a 6-week block (or longer!), with the topic acting as the main form of cohesion. That can’t be right? If we are planning in long blocks, then there ought to be a reason for that, and one which links to the core objectives we’re aiming to teach, not to the over-arching label which provides a title for displays.

The new curriculum provides an exciting opportunity for schools to really think deeply about how they organise their curriculum across the whole school, ensuring progression and cohesion through the core subjects as a priority. Go and grab it!

 

Other blogs on the matter of planning and topics are listed at http://primaryblogger1.wordpress.com/2014/02/26/blogs-on-topic-planning-for-and-against/