Mathematics: here is the answer

Instead of giving credibility to the shabby NZ Initiative report on mathematics by criticising it and similarly the shabby Hekia Parata decision to sponsor it (all designed to shore up the failing IES project and the anti-democratic EDUCANZ one), this posting is a positive one highlighting a different way, the holistic way, to take mathematics. The intention is also to highlight there being a different way, an holistic way, for all parts of the curriculum (and clearly a better way given the falling performance in mathematics, science, and writing and most else, leaving aside junior reading).

I want to put mathematics into the wider context.

I know many of you hardly listen to me when I write about there being a different way, but if it is true there isn’t a different way, we’re in deep trouble – but there is, of course. It’s one that puts the curriculum and children’s learning first, not bureaucratic control and political ideology.

The Primary School Diaries, in general, have the answer. That is not to pat myself on the back but to point to the principals and teachers I have learnt from in nearly fifty years of visiting them in their classrooms. I am pleading to you to be a wise leader and to put an effort into bringing along some wise teachers with you.

If we criticise the present nature of the curriculum we must have a better approach in our minds or we are just carping. And our leaders in making statements about the system, to be credible, should speak from the basis of that different and better curriculum.

I am not suggesting you act on what you read, though there may be parts you can without too much difficulty; all I’m suggesting is that you hold on to the idea that there is, indeed, a different way and better one; and one that, in the right environment, is eminently practicable.

The following is some of the things the Primary School Diaries: Curriculum 3 and 4 have to say about the numeracy programme.

Under managerialism (the Tomorrow’s Schools’ period), no curriculum initiative has succeeded, and no curriculum initiative will succeed. (Consider, for example, what happened to the new curriculum.) For a time, managerialist structures might prop up the initiative, hiding the extent of any failure, but to no ultimate avail.  How could any curriculum initiative succeed given the curriculum knowledge, or lack of it, of its developers and sponsors? How could it succeed given that the group whose task it is to put it into practice – that is teachers – is excluded from its development on the grounds of self-interest?

This brings this sad story to the nub: any curriculum initiative, for instance, the numeracy project, comes loaded with unworkable and undesirable features. The only way it could have been made to work was if teachers felt free enough to colonise it, but teachers, for reasons explained above, did not feel free enough to colonise it, are not freed enough to colonise it. Under managerialism, it is not teachers who colonise curriculum initiatives (and the curriculum generally for that matter), but the education review office.

My reasons why I think numeracy is on the slide:

  • The common practice of cross-grouping cutting maths off from the rest of the class programme
  • The resentment by children of the cross-grouping
  • The heavy emphasis on grouping in the first place
  • The way children in the top group receive a better deal than children in the other groups, thus making ability grouping a self-fulfilling placement of children
  • The way grouping and cross-grouping impede relating maths to real life applications
  • The teaching becoming routine because of a lack of attention to problem solving
  • A sense of teachers not being sufficiently on top of things to be able to provide cohesion – not being able to go backward (to concepts taken) and forward (to concepts to be taken) in mathematical references
  • Strategies being used in heavy-handed manner
  • The lack of integration of numeracy with curriculum maths
  • A severe drop in lively discussion – time pressures, you see
  • The use of unmediated, downloaded teaching units
  • The need for more ancillary aide help (the recent  review office criticism of the use of teacher aides can be interpreted as providing support for the government policy of cutting back on funding for them)
  • National standards.

Significantly, the best numeracy teaching I see now is in the stingily funded ministry remedial programme ALiM (Accelerating Learning in Mathematics) in which discussion is at the heart of the programme.

I featured Dan Murphy principal of Winchester School to demonstrate one way to take holistic maths.

This is what Dan wrote to me.

Hi Kelvin

I view the numeracy programme as a good teacher in-service largely because primary teachers generally have a poor grasp of mathematics and need some guidance. As for it being a teaching programme for children, I think it misses the mark badly. It creates what I call an ‘excluding curriculum’ in that like the old multi-level maths programmes (and Vince Wright was behind those as well), children are grouped according to achievement of rather trivial objectives (jigsaw-puzzle approach). Unfortunately, they don’t move on until they have achieved particular objectives, meaning many finish primary school without having covered even half the intended material and they certainly never make satisfactory mathematical connections. It is a recipe for failure.

At Winchester School we have abolished ability grouping, and following the levels and stages of the numeracy project, in favour of working on rich mathematical activities and in meaningful contexts. We call this the ‘big picture’ approach where making connections between mathematical ideas occurs. We have recently worked with Charles Lovitt from Melbourne, famous for the MCTP books and other such work in Australia.  More importantly, the approach we have taken with maths is a model for good teaching in other curriculum areas. I mean, can you imagine having science broken into levels and stages and putting children into ability groups for it? It is unimaginable and yet we will let programmes like numeracy destroy good maths teaching. Ability grouping guarantees the lower achieving children are labelled forever.

I see the numeracy programme every bit as bad as national standards. It has the same effect, that is, it puts children into little boxes and labels them. I find it amazing that opponents of national standards are not also opponents of numeracy teaching programme. It is the narrow measuring regime that restricts kids learning.

I would be interested in your thoughts.


Dan Murphy

To set up the maths programme, the following is the first letter Dan sent to parents:

The following articles are a series published to help you understand the deliberate approach we are taking at Winchester School to teach children meaningful and memorable mathematics.

Children need to engage in mathematics that is purposeful to create meaning.

To do this teachers use a range of elements to create success, including:

  • Stories
  • History
  • Discussion
  • Kinaesthetic physical experiences
  • Reasoning
  • Geography
  • Open investigations
  • Problem solving
  • Skill development.

Article 1

During the holidays, all teachers participated in mathematics training. We are going to be trialling different ideas between now and the end of the year to make mathematics more appealing to children, to give them more successful experiences.

When teachers have low expectations for students they respond by teaching them low-level mathematics. This is the reason why ability grouping in schools is not allowed in many countries, including Finland, the country that topped the world in the latest international achievement tests.

Researchers in England found 88% of children placed into ability groups at age 4 remain in the same groupings until they leave school.

All the research and messages we have been hearing demonstrate that using ability groupings to teach children is a recipe for failure. Children learn mathematics by engaging in meaningful activities, by talking, by reasoning, and explaining their thinking. Placing children in ability groups tends to restrict their progress and limit their learning.

We are trying to avoid making mathematics a bitsy process that impedes children putting together the big picture.

When there is a problem to be solved, one of the lovely things about mathematics is, by using different levels of mathematics, it can be accessible to all ages.

This week’s problem:

  • Suzie and Tommie went to the ice-cream shop. There were five flavours to choose from: apricot, banana, caramel, dark chocolate, and elderberry.
  • What different double scoop ice creams could they have ordered?
  • Talk about what things you could do to solve this problem. Let children try different ideas even if they don’t work.

Look for the answer and some strategies in next week’s newsletter.

Before Tomorrow’s Schools, the sort of thing that happened at Winchester School would have happened throughout the system; the numeracy programme would have been talked about and the ideas would have spread and been adapted and added to as they were. 

 But we are no longer inclined to talk to each other, what would be the point?

The above is a different way, the holistic way, and surely a better way. It doesn’t have to be exactly the way set out, of course, but in not being, is in itself, the holistic way. 

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4 Responses to Mathematics: here is the answer

  1. Bruce Hammonds says:

    Great read Kelvin. I will link it the blog I posted earlier today on the same subject.

  2. Kelvin says:

    I laughed when I read your account. Two minds alike. Re quote of mine, I can’t even remember writing that. Keep up the valuable work.

  3. Kelvin says:

    Hi Kelvin

    Loved reading your thoughts about the Numeracy project. I was persecuted at my previous school for not following the script … As you know, I am now teaching at … I have been given a good amount of freedom this year to work with the children, especially the boys, on ‘ making sense of maths around them ‘(most of the boys in previous years have given up on maths).

    It’s not easy, but at least my professional judgements are trusted and I can get with the job.


  4. Rex Morris says:

    Brilliant stuff – certainly great to see a Principal taking the lead and introducing a whole school initiative that is not tied to the numeracy project.

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