So the UK government wants "harder sums". (Part of a drive to raise standards - see Michael Tidd on The Level 4b myth for thoughts on this.) And they want to have kids learning their eleven and twelve times tables, instead of the tables from one to ten.

To me, this is not the way to go. Not because I don't want a challenge. I do.

Steep paths - even rocky cliffs - are fine,

Take the twelve times table. Not a big thing. But

So how would I like there to be more challenge? I really want kids to go further, rather than that their work is harder. I'm trying to make it as easy as possible to learn as much as possible. Anyway I'm trying to get my ideas on this spelled out, so here's a beginning of a list:

I'd really love to hear other people's ideas on all this, whether it be connected with the first three items in my list, or about any successful ways to extend children's learning.

To me, this is not the way to go. Not because I don't want a challenge. I do.

Steep paths - even rocky cliffs - are fine,

*if they lead somewhere*. If they are just a demanding rock face that leads to... more demanding rock face, without opening up onto a fertile and beautiful landscape, then maybe children develop grit or obedience or something, but they're not making the most of their maths learning.Take the twelve times table. Not a big thing. But

*really*, is that taking us somewhere?? Read Jon McLoone on*Is There Any Point to the 12 Times Table?*for his interesting thoughts on this.Creating their own pattern |

**Pick subjects that give power.**The same sums with more digits, rarely-used algorithms like long division (on this, see Owen Elton's*Why Gove is Wrong about Long Division*) or dividing fractions don't seem to me to lead anywhere much. Beginning algebra (in a fun and appropriate way - see my Year 4 lessons this year for example) on the other hand gives a really powerful tool for making generalisations.**Find the subjects where kids can be creative**, make something of their own. Get them up on the top of Bloom's taxonomy. An example is getting kids to generate their own patterns with manipulatives, and then describe and explain the pattern with numbers (example). As Keith Devlin said in his recent blog post,*Most Math Problems Do Not Have a Unique Right Answer.*In the real world, creativity is going to be very useful.**Go into history and biography**.The new maths curriculum for England has added Roman numbers . This could be just a dull dead-end, or it could be part of a sequence of lessons looking at how number systems developed that could really grab some children. Telling the story of a maths idea by talking about its discoverer will help the kids to go further with it. Take our work where we talked about Euler. The kids are prepared to go further because there's a narrative to engage them. (I'll probably do the Euler work again next year, but add something on graphing, maybe using Joel David Hamkins' great booklet on*graph coloring, chromatic numbers, and Eulerian paths and circuits*) In Primary we have a bit more freedom - we teach the whole curriculum, so it's easier to make links - between maths and history, or,as in the case of our work on Galileo with science and English too.

Rolling like Galileo |

I'd really love to hear other people's ideas on all this, whether it be connected with the first three items in my list, or about any successful ways to extend children's learning.

I strongly endorse the history and biography idea. Everything primary and secondary school students learn was discovered or created by someone who, at the time, thought what they were doing was really useful/exciting/novel/unusual/threatening/etc. Providing more of that context makes learning more interesting, easier, and also deeper.

ReplyDeleteFor example: roman numerals have no zero and no place value. So, what implications does that have? How long did it take for these ideas to get introduced into Europe and what reception did they find?