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oldandrew:

sideshow:

Does it matter if our children can't remember facts?

Yes.

sideshow:

I thought that thinking skills and learning behaviours were more important than facts?

No. These things are just excuses for dumbing down.

There are no generic thinking skills. We think effectively when we know a lot about a topic.

The approach also undermines teachers.

The world is far too complicated to understand excessively in terms of first princples. Outside school is not a New Stone Age; a teacher should have a duty to confer to children, society's 'garthered' knowledge, and children should understand that this is also a teacher's purpose. By reducing everything to self-understanding you effectively undermined the role of the teacher.

In isolation a child can easily think that their thinking is as valid as their teachers. Without the cultural knowledge transferance why think differently, especially knowledge when if ever required, can be found via the interent - as many children tend to think.

Although I would accept that overall the 'Little Mathematics' approach to modern maths teaching benefits more children than previous more formal approaches, I believe the general consequence is an overall dumbing down of the subject. It can hardly be otherwise when the delivered product at 16 - on average - has no more mathematically knowledge than the best the Ancient Greeks could offer.

sideshow:

Andrew, there is a big difference in being able to remember stuff and knowing how to work it out.

There is a distinction, but the latter is highly dependent on the former.

sideshow:

I teach chemistry now and again and I can just remember how many neutrons certain elements are and their symbols, or the molar mass of water etc. I don't expect my students to remember, I expect them to have the learning skills of perseverance and resourcefulness and the thinking skill of dealing with variables to help them work it out.

Since when was perseverence a "skill"?

Since when were there any "thinking skills" that didn't involve use of knowledge?

We can all think of examples where we might muddle through not being able to recall all the relevant information, but to get good at something you need a firm grounding in knowledge. 

sideshow:

For most kids working out proton number or number of moles is not something they will ever need, it is developing the learning skills and thinking ability that they will need when faced with a real life problem they don't know the answer to.

If there were such generic skills, and we knew we could teach them, that might make sense as an argument. The trouble is that there is no mysterious technique to learning; it is more effort and attention than "skills". As for thinking ability, it depends largely on knowledge. Nobody has yet found any measure of "thinking ability" that couldn't be improved by the acquisition of more knowledge.

blazer:

I look forward to the day when there will be no need to take driving lessons, students will just be able to think their way through the process of making the car move and then doing it on the road!

I don't understand why kids weren't expected to know times tables. After all it is only learning about 50 relationships, if that.

It could be got over with by about the age of six and would be there for ever. What harm would it do?

My younger daughter seemed to get through school without learning to spell or to estimate numerically. It has taken her years to remedy the situation.

oldandrew:

My point was that if you want to answer that question it really would take a long time if you had no ideas about the factors of 56. The more fluent you are at times tables the easier it is, and I find it hard to imagine somebody progressing to maths at degree level without at least the level of times table knowledge to think "7 times 8" when they see 56.

Does it help, oldandrew, if to 'knowledge' and 'understanding' we add 'mastery' which assumes both?

I find the introduction of the third term helps us move more effectively beyond the either/or debate.

weebecka:

shalteir:

As I posted earlier, tables were set back a bit, in earlier days, pre NC, certainly the majority would have learnt them by Y4, sure bright kids by Y2. the NC seemed to have set this back to expectancy by Y6, (and many were poor) but the last few years schools have been trying to get complete tables knowledge by Y4.

 

 

But multiplication seems to be an issue which stands apart from others. 

 

I have quite an unusual perspective on why this is so.

My perspective is that just as we have two primitives for division (splitting and chunking) and division is much better taught by teachers who understand that there are these two separate images,

so there are also two primitives for multiplication, which are repeated addition (which is taught exclusively in UK schools) and scaling (which is completely neglected).  

I suspect the discipline of reciting tables in unison voice is actually one of the best proxies we have which develops the scaling skills of students in a society where we are unaware of the existance of a scaling primitive for multiplication.

I am currently writing a PhD proposal on this and one of the papers I have to research to do this is one which compared Chinese and western teaching of multiplication.  The person who introduced me to it suggested that Chinese teachers do have explicit models for scaling which they teach their student and that I might find some evidence of it in that paper.

I'll get back to you when I've tracked down the paper and analsyed it.

 

Never in my full time career, did my class ever "recite" tables. On supply I've followed a few plans to do this. On supply, of late, I've found children run through the sequence: 4,8,12,16,20,24 etc. Then I've asked them what is, say, 4x4, and I got blank faces. 

I agree about teaching the different aspects of the rules. I did the OU Ad Dip in Ed "Developing Mathematical Thinking", and it was very thorough in all these aspects.