This debate has been had before but let's go. FIrst - I am really tired of people saying "We don't do times tables". Let me assure that every primary school I have worked in, tables has been key and has been taught in a variety of ways including daily repetition, songs, inverse - here's 20 - how do I make it etc. A whole lot of different ways so children become familiar with them. I am quite good at maths but I did find it hard at primary - especially long division. I just did not get it. We were shown a method but still did not get it. I would bet there are children who still do not get it - but chunking is another perfectly good way and the idea of counting up e.g. 10 tickets cost £60 so 20 cost £120 then 4 more cost another £24 so thats £144 buys you 24 tickets is a useful idea. Same for multiplication - I have so many tutees who struggle to work out 34 x 6 without resorting to a method like the grid method. Both short multiplication and the grid method reinforce the concept of partitioning to multiply and it's not the world's hardest sum to work out mentally. Numberlines, practical equipments etc - personally I think they are fantastic and very visual ways of seeing difference between, take away and addition. Not everyone is a numbers person so they do serve a purpose. This can then lead to columns. A lot of people in this country lack numeracy skills - is this down to "trendy modern teaching methods in the 60s, 70s and 80s" or is it a problem spread through the entire generation including those who went to school in the 40s and 50s?