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Maths in Primary Schools

Discussion in 'Primary' started by mrjoemaths, Jun 20, 2018.

  1. mrjoemaths

    mrjoemaths New commenter

    Hi everyone,

    I love maths, but I'm getting really confused messages. I'm currently based in Hong Kong and have been teaching internationally since before 2014, so all of my information regarding the implementation and strategies has been second hand or from reading. I was wondering if there is anyone out there in a similar situation?

    I've done quite a bit of reading around it and have come to these conclusions. I would love to open up a bit of a debate about some of these, because I am definitely open to changing my mindset and would love to find new ways of making it work. Here's what I believe from what I have read, if I am wrong or in any way misguided, please do let me know!

    The 2014 curriculum is not a mastery curriculum, but alongside the implementation of the curriculum, a mastery approach is also being shown as one way of delivering it.

    With regards to mastery, I still have a few questions. I have read all the material from the NCETM and watched the videos and sample lessons, I've trialled a version of mastery style lessons in class and I did not get it right at all. My understanding is:
    • The whole class are working on the same thing - I get how this can work in terms of all working on the same learning objective (as opposed to the old APP nightmare of different children on different things), but I found my lessons do not work without differentiation. I now differentiate by depth, which I know is not popular. All children are exposed to reasoning through the starters and plenaries of lessons and problem solving is inherent throughout the curriculum, but if I'm teaching Year 1 addition to 10, then I believe that some children will need to develop their conceptual understanding using physical resources, whilst others are ready to solve missing number problems, or uncover patterns. I would welcome challenges to my ideas as I do not think I've got this right, but have not been able to find a workable way to get the children all working on the same problems.
    • Same day intervention (or rapid intervention) - all of the videos suggest that more time is given to maths for this. I do not have control over the timetable and we cannot just find more time. How are others working this in their school? We can implement booster groups, or do some pre-teaching, but it is not the same thing and not in the spirit of mastery.
    In terms of curricular approach, we are currently using the Lancashire grids for learning which has a spiral curricular approach, but I am a big fan of the White Rose modular approach. I have been listening to Craig Barton's excellent podcast. Although it is aimed at Secondary, lots of the discussion is relevant, but it seems that there are still huge arguments as to whether it is better to go with a spiral curriculum, or to 'master' one aspect before moving on. A lot of the guests take issue at the idea that you CAN 'master' an aspect of maths. What have people implemented in their schools and what have been the pros and cons?

    I guess my personal ideal would be:
    • Modular lessons, but carrying on the number throughout the year in the form of games, or puzzles in order to revisit the essentials.
    • Assessment of fluency at the beginning of the module to see who is already fluent and who will need more support.
    • Differentiation in lessons by depth not content, but all children exposed to reasoning and problem solving, but just some children will do more practice to become fluent, whilst others take the concepts and explore it more (not ideal I know).
    • Assessment (possibly diagnostic questions syle) a few weeks after the module to assess retention of information and planning in some sessions/starters/booster groups if necessary.
    • I would love each module to be based on the excellent outline in the White Rose, but it would be great if we could, as a class build towards solving a problem rooted in some kind of context. The first stage would be developing the skills needed, and then guided exploration of the problem, before the whole class explores and presents their findings.
    • Most of the lessons would be building essential skills as outlined by the White Rose guidance, but some lessons would be given over to problem solving or reasoning tasks.
    I can imagine that people have quite a bit to say, including criticisms of this, and I would really welcome it. This is not what I currently do, but based on my reading, this seems like a decent solution. I would welcome links to reading/blogs/websites with any relevant information on this.

    Thanks to anyone who does help, I've posted on TES before and got some quite rude responses. I just want to say, I know these ideas need work and may be wrong. I am just looking for advice and any would be greatly appreciated!

    Kind regards,

    Joe

    TL/DR: From an outside perspective there seems to be mixed signals coming from the UK over maths teaching. How are people in the mix finding it and do they have any advice?
     
  2. snitzelvonkrumm

    snitzelvonkrumm Occasional commenter

    Whichever version of a Primary Numeracy curriculum you look at, older, newer, international, the coverage is all but the same. It is a cyclic curriculum where almost all subject matter is built upon within a year and over the years. I set myself to assess where is child's level of understanding/knowledge is and do my best to move the learning forward. This might mean teaching the children the same content at the same time, but usually, it will mean fine-tuning the challenges to engage individuals and groups. It may mean some are revisiting and others having new work. I find it necessitates the setting up of a peer tutoring system. I have also found the use of a quality Maths software program that can free me up to work extensively with small groups. Yes, I look at expectations for a given year level but only as a guide. Importantly the children must experience progress and believe they are making progress. It can be damaging to push some children at the wrong time past their maturity level. Setting up a positive can-do attitude /culture is a key. Setting up the peer tutoring where the emphasis is on being a team and where the concept that teaching someone else is the final step in mastery. Mastery can be a transient concept for many in Primary Maths. It's there one day and gone after next next concept has sunk in or the next holiday. Lots of revisiting is needed, exposure in new circumstance and being put into practical use. A fluid recording system, chances to be reassessed and seeing a mistake as an opportunity need to be embraced.
    Perhaps my main point - to hell with the 2014 changes/ expectations. You enjoy Maths, pass that onto your students, find what works for you and your students, don't be restricted by the doctrine. A mathematical formula is a constant but your teaching of Maths is constantly changing as you find what is most effective for you and your children.
     
  3. squashball

    squashball Occasional commenter

    Hi Joe, I think your post is very interesting but it's also very LONG which makes answering your multitudinous questions a bit of a slog. It strikes me you have a really good grip on how to deliver a "mastery" curriculum with lots of open ended questions and problems for those fast finishers to move on to: I think NCETM refer to allowing children to use the "dong nau xing" (don't quote me on spelling here) - applying their knowledge independently in lots of different ways; meanwhile the plodders plod on using lots of resources and relying a bit more on support. But that way, the class stays together on the same LO (albeit with children modelling lots of different ways of getting there).

    Intervention for those who don't grasp concepts takes place during assembly or playtime or lunchtime in my class (I know... don't say anything) but pre-teaching is also entirely in the spirit of a mastery curriculum: I'm not sure why you say it isn't. There is something really lovely about having that group of children who normally lack confidence be the experts in the following maths lesson.

    You really can't go wrong if you use White Rose planning - context is provided (which you rightly say is important to you). But why do you want to do more than is suggested in the WR planning, unless you judge your class to need it? WR planning is put together by folk who know their stuff and I don't see the need to add or change very much at all. You say the Number element has to be maintained outside of the modular maths lessons and I do agree - I'm sure we all chant times tables outside of maths lessons, or have quick fire line up questions or whatever. I too was worried by the plans which indicated long stretches away from calculation. However there are lots of number and calculation opportunities within the shape, time, place value, data units so it's not as big a concern as I first anticipated.

    snitzelvonkrumm has some very valid points too about paired work, team work and the need to keep going in lots of different contexts, checking these repeatedly. OH the frustration of children being able to count in 10s and 1s using Dienes but not coins only today!

    I have no idea if this is any help but good luck anyway.
     
    snitzelvonkrumm likes this.
  4. mrjoemaths

    mrjoemaths New commenter

    Hi Snitzelvonkrumm,

    Thanks for the reply, I completely agree with many of your points and love the idea of peer mentoring. I hadn't considered the White Rose to by cyclical, but I see now how it is revisited over the time the child is in school.

    I'm glad to hear you talk about fine-tuning the content. My experience of looking at the NCETM and the maths hubs has been that all children literally get the same work and the same tasks. I'm completely on board that we are all looking at the same objective, but feel strongly that children may need to approach it in different ways in order to have an appropriate level of challenge/support for them. This doesn't mean that children who find it tougher miss out on reasoning and problem solving, we still would look at examples as a class as well as have some lessons devoted to developing these skills, but for them they would spend more time on consolidating and becoming fluent in a subject before they apply it to contextual problems.

    Which maths programmes do you use? We are signed up to Mymaths which I'm not the biggest fan of. Other such ones as mathletics or matholia are brilliant for homework, but we found a little limited in the classroom. It would be great to see what is out there.
     
    snitzelvonkrumm likes this.
  5. mrjoemaths

    mrjoemaths New commenter

    Hi Squashball,

    This is indeed very helpful! Apologies for the rambling tone of my original message! So many questions buzzing around my brain!

    I'm glad I haven't misunderstood the point of mastery and that there is space for differentiated tasks within a session. I agree we want to be on the same learning objective, but looking at developing deeper understanding.

    Looking back, I have no idea what I was on about with the pre-teaching. I agree it would be lovely to have the children coming into the lessons confident. I think my main issue was when this would take place. My school already are trying to implement an 80% curriculum because of the extra enrichment activities and opportunities that take place (out of my control) so finding time is tough. I like your idea of taking children out during other sessions. It might be a bit of a losing battle to ask for that at my school, but definitely worth a go!

    I am a bit fan of the WR scheme, I think the main thing I would want to add is rigorous assessment to go along with this. I would like to know before the lessons which children will need more support becoming fluent and which children can already cover the material. At our school, we get a lot of very high achieving children who can already complete the year group objectives, but there are gaps in their depth of understanding of these topics. I would like to assess to see who I need to challenge further as sometimes these mathematicians would choose an easy path, being what I've heard Andrew Jeffrey refer to as 'tick hunters'.

    I must admit the idea of building up to a contextual problem is quite far-fetched and would be a nightmare to implement, plan, resource and assess. I think I was just thinking about the work of Hans Freudenthal and wanting to generate a meaningful context in which children would have to use maths to find success. This is not something I currently do or can see happening anytime soon because of the tracking and implementation issues, but in an ideal world, I'd love a bit of this!

    With the idea of giving some lessons over to whole class problem solving tasks, my thinking was: If I am differentiating so that some students are mainly consolidating their fluency in maths, I want to add in some opportunities for low threshold high ceiling tasks so they still get the chance to develop skills like systematic thinking, linking areas of maths and application.

    I hadn't looked in enough detail at the non calculation based areas of the curriculum, but it is great to see that there are opportunities for calculation. In a previous school, we set up 'building blocks' maths in Year 1, which ran like a guided reading session, with 4 or so activities around the class using physical resources which supported the children in one aspect of their calculation. This worked well, but again it is about finding the time in the day!

    Thanks again for your reply, sorry again for my long rambling reply too - I do need to learn how to be concise. You've given me some wonderful ideas to think about!
     
    squashball likes this.
  6. ElizaMorrell

    ElizaMorrell Occasional commenter

    Don't apologise for the rambling. Wanting to understand something in depth is nothing to apologise for.

    I've been teaching in Lancashire for the past year, and I was in Nottingham before that. My school in Nottingham used a modular based approach and, by the time I started y2 SATs revision lessons, they were pretty woolly. My current year 1s have a decent grasp of pretty much everything at this point and I'm putting that down to the cyclical nature of the planning. I don't follow the activities to the letter (big fan of NCETM activities), but I teach the topics in the order and frequency they recommend.

    Same day intervention is ridiculous in our school system. The idea is mainly based on schools in countries where they have 15-20 minute transitions between lessons, so the teacher can work with pupils who have struggled in the lessons. Teachers in these countries also have much less class time than we do, so they have more free time to deliver same day interventions (Clever Lands by Lucy Crehan is amazing for country contrasts). I use continuous provision for the last 30ish minutes of my day to work with the children who need extra help as we are expected to attend assemblies.

    To incorporate mastery into my year 1 class, I completely rearranged my timetable. I have maths mornings and English mornings. I have 3 tables of 10 children, each with a different activity. One table is skill practice, one is a mastery/reasoning activity and one is independent practice. My TA and I alternate who runs the reasoning table and who runs the skills table. We work at one activity for 20/25 minutes, then rotate. Every child accesses every table.

    The skill practice is always based around the same topic, but the questions get progressively harder. My tables tend to be mixed ability and all children start at the same point. Those who show understanding are moved to the more complex questions.

    The reasoning/mastery activity is the same for all children, the differentiation comes from how much support they get and which methods they use (manipulatives, pictorial, mental). This table always has an adult, so discussion is responsive to understanding.

    Independent work varies depending on the children's needs. For some, it is more practice following on from the skills table (love the idea of 'plodders'! Never heard this before and it made me chuckle). For some it is word problems. For some it is fluency practice. For some it is missing numbers, puzzles or in depth exploration of an idea.

    Starter activities or morning work is amazing for assessment of previous learning. Quickfire questions, note down who can do it, then quickly reteach and work a couple out together before moving on.

    Having said all this, it depends a lot on your year group and cohort. In year 1, the ability differences aren't anywhere near as pronounced as they can become higher up, so what works for my current littlies may not work for my incoming littlies.
     
  7. hammie

    hammie Lead commenter

    regarding "differentiation"
    something overlooked is that very few of the most successful countries internationally regarding Maths learning do any differentiation at all. They almost all teach mixed ability and expect all pupils to learn the work.
     

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