## In praise of Sudoku

A few weeks ago my nine year-old granddaughter showed me a Sudoku puzzle and asked me what it was and how you solved it.

In the unlikely event that readers don't know what a Sudoku puzzle is I will explain.

It is a square 9 x 9 grid containing 81 squares. Within this there are 9 smaller 3 x 3 grids. Some of the squares are filled in with numbers from 1 - 9.

The task is to complete the grid by writing numbers in all the blank spaces such that every row, every column and every 3 x 3 box contains all the numbers from 1 - 9. There is only one solution to each puzzle.

Without my help it was clear that my granddaughter would not only have no idea where to start, she was also unable to understand what the task was, however she was excited about trying to solve it. Children that age love puzzles.

This was quite an easy puzzle and we soon solved it together. She enjoyed this so I bought here a Sudoku puzzle book with 120 puzzles for £1.70 from Aldi (I love Aldi). These were in a large format with one puzzle on each page that was not much smaller than A4. These puzzles were much harder.

I gave her a sharp pencil and an eraser and we sat down to look at the puzzle. I suggested to her that she could start with any row, column or 3 x 3 box and write in pencil (at the end of each row and column or in the corner of squares) what the missing numbers could be (ie. the numbers from 1 - 9 not already in that row, column or 3 x 3 box. I further suggested that it might be best to start with the rows, columns or 3 x 3 boxes with least blank squares.

That is all the help I gave her. She soon got the idea and has become increasingly competent in solving the puzzles, which get harder as you progress through the book. She loves doing these puzzles and gets tremendous pleasure from the way the missing numbers rapidly fall into place as you get near the end of the puzzle.

Although I never described it as such, she soon understood the following general method for solving a Sudoku grid puzzle.

1. Start with a row, column or 3 x 3 box with the least numbers of blank squares.

2. Write in pencil all the possible missing numbers.

3. By inspecting the numbers already in the row, column or 3 x 3 box discount the numbers that do not fit (because they are already there).

4. If/when you get a unique solution for a blank square then write it in the grid.

5. When one row, column or 3 x 3 square has been fully completed tackle the next one with the least blank squares until the whole puzzle is completed.

I am a Sudoku novice. This method may not work for very hard puzzles.

My granddaughter is now very quick at solving the puzzles. Her working memory is now such that she can hold the possible numbers in her head. Not so me. She can now solve the puzzles faster than I can but she still takes delight in us doing them together even though I just watch.

So what has been gained here? Not useful knowledge for sure. Who needs to know how to solve a Sudoku puzzle?

This is what has actually been understood by my granddaughter.

1. What an algorithm is - a sequential formula for solving a problem.

2. The logical operators NOT, AND and OR.

3. The programming instruction equivalent to IF ... THEN in BASIC

She is not aware that she understands these things in these terms (she does not know what an algorithm or a logical operator is), but I am certain that there has been significant cognitive development.

To me this has been confirmation of some of Vygotsky's fundamental tenets including the following.

1. The Zone of Proximal Development (ZPD) - what the child can do with the help of a more knowledgeable adult or peer, that cannot be achieved without such help and which facilitates cognitive development.

2. That the help provided should be minimal - just suggesting things to try.

3. That by such means children can understand and solve problems of surprising complexity.

4. That permanent cognitive development results, which is transferable to other subjects and contexts.

This is the sort of learning experience that children/pupils/students should meet and enjoy regularly (but of course not exclusively) in all Key Stages.

By these means students may progress in developing their cognitive sophistication levels (they are NOT skills) so as to ascend the cognitive grade hierarchy that I propose in my last post.

In the unlikely event that readers don't know what a Sudoku puzzle is I will explain.

It is a square 9 x 9 grid containing 81 squares. Within this there are 9 smaller 3 x 3 grids. Some of the squares are filled in with numbers from 1 - 9.

The task is to complete the grid by writing numbers in all the blank spaces such that every row, every column and every 3 x 3 box contains all the numbers from 1 - 9. There is only one solution to each puzzle.

Without my help it was clear that my granddaughter would not only have no idea where to start, she was also unable to understand what the task was, however she was excited about trying to solve it. Children that age love puzzles.

This was quite an easy puzzle and we soon solved it together. She enjoyed this so I bought here a Sudoku puzzle book with 120 puzzles for £1.70 from Aldi (I love Aldi). These were in a large format with one puzzle on each page that was not much smaller than A4. These puzzles were much harder.

I gave her a sharp pencil and an eraser and we sat down to look at the puzzle. I suggested to her that she could start with any row, column or 3 x 3 box and write in pencil (at the end of each row and column or in the corner of squares) what the missing numbers could be (ie. the numbers from 1 - 9 not already in that row, column or 3 x 3 box. I further suggested that it might be best to start with the rows, columns or 3 x 3 boxes with least blank squares.

That is all the help I gave her. She soon got the idea and has become increasingly competent in solving the puzzles, which get harder as you progress through the book. She loves doing these puzzles and gets tremendous pleasure from the way the missing numbers rapidly fall into place as you get near the end of the puzzle.

Although I never described it as such, she soon understood the following general method for solving a Sudoku grid puzzle.

1. Start with a row, column or 3 x 3 box with the least numbers of blank squares.

2. Write in pencil all the possible missing numbers.

3. By inspecting the numbers already in the row, column or 3 x 3 box discount the numbers that do not fit (because they are already there).

4. If/when you get a unique solution for a blank square then write it in the grid.

5. When one row, column or 3 x 3 square has been fully completed tackle the next one with the least blank squares until the whole puzzle is completed.

I am a Sudoku novice. This method may not work for very hard puzzles.

My granddaughter is now very quick at solving the puzzles. Her working memory is now such that she can hold the possible numbers in her head. Not so me. She can now solve the puzzles faster than I can but she still takes delight in us doing them together even though I just watch.

So what has been gained here? Not useful knowledge for sure. Who needs to know how to solve a Sudoku puzzle?

This is what has actually been understood by my granddaughter.

1. What an algorithm is - a sequential formula for solving a problem.

2. The logical operators NOT, AND and OR.

3. The programming instruction equivalent to IF ... THEN in BASIC

She is not aware that she understands these things in these terms (she does not know what an algorithm or a logical operator is), but I am certain that there has been significant cognitive development.

To me this has been confirmation of some of Vygotsky's fundamental tenets including the following.

1. The Zone of Proximal Development (ZPD) - what the child can do with the help of a more knowledgeable adult or peer, that cannot be achieved without such help and which facilitates cognitive development.

2. That the help provided should be minimal - just suggesting things to try.

3. That by such means children can understand and solve problems of surprising complexity.

4. That permanent cognitive development results, which is transferable to other subjects and contexts.

This is the sort of learning experience that children/pupils/students should meet and enjoy regularly (but of course not exclusively) in all Key Stages.

By these means students may progress in developing their cognitive sophistication levels (they are NOT skills) so as to ascend the cognitive grade hierarchy that I propose in my last post.

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## Comments

I agree Suduku rocks .......I despair of the numerous and tedious wordsearches that my child comes home with.

In the absence of such, pupils will feel terrible failures and the teacher will have the dilemma of how to respond to homework not done. In the increasing number of 'zero tolerance behaviour policy schools' this will trigger a 'no homework' detention.

However this won't help either because the pupil still won't be able to do it no matter how long the detention lasts or how often it is repeated - unless of course the pupils in detention are encouraged to talk to each other about their detention tasks and solve them together. However 'zero tolerance' schools don't usually run those kinds of detentions.

In such schools teachers are forced to set homeworks by the line management policy of the school (and be checked up on) so the result is wordsearches or similar wastes of time. The key property of a 'homework policy' homework must be that the pupil can do it without help - the exact opposite of Vygotsky's ZPD.

If the school really wants to impress pushy parents then the solution is to set homework that the pupil can easily do but which takes a very long time which has the added benefit of making the pupil feel as miserable as possible about school, thus preparing them for 'the world of work' in terms of Osborne's 'full employment'.

Even 'research homeworks' are a waste of time because the results of Google searches are unlikely to make much sense unless they are trivial and therefore of little learning value. Then there are 'consolidation' homeworks - eg practising lots of easy maths examples. But this is Kahneman System 1 isn't it? Don't we want to encourage Kahneman System 2 thinking in our children? But if you set those sorts of homeworks pupils need help to do them ... which is back where we started.

So what's the solution? It's simple, ban compulsory homework! Shock, Horror! (But joy for teachers). Instead, encourage pupils to follow up the interesting things that really gripped them in the System 2 lessons they did at school - but no compulsion - inspiration instead.

The other attraction of homework for parents is that it keeps their children at home where they see them rather than out on their own playing with other kids out of sight where paedophiles lurk behind every tree.

What I find odd about wordsearches is that they seem to be accompanied by the words themselves, so require nothing beyond the ability to find patterns of letters. If the words are not given, but instead questions whose answers are to be found in the grid, they can be quite useful, enlivening what otherwise might be quite dry. Unfortunately, they do get overused and can produces groans of the 'not another power point/word search/poster/etc' type. So many commercially available worksheets are of the fill-in-the-gaps type and, with word processing and other IT, I prefer to make my own question sheets. As for the poor quality of text books, don't get me started.

Your grand daughter's experience shows the case for CASE.

FJM - Yes, which links to my previous post about the new GCSE grading system.

http://www.localschoolsnetwork.org.uk/2014/04/80-of-english-schools-good...

I know what Ofsted would think about it. The paradox is that schools do need to be much more challenging of pupils - but in a good way. That is why I ask how a good school can be recognised. It is not a trivial question because 'good' is often 'bad' (despite Ofsted judgements) and how are parent to know the difference?

When I began my primary teaching career forty years ago it was a different world. I had views about homework that were shared with parents at a meeting soon after taking on a new class in September. (In those distant days, I always felt the need to know what they believed about their child, what expectations they had, etc, etc, before I gave my undivided attention to the 'stuff' on record, produced by their previous class teacher!!!) Obviously, this was pre-Ofsted, pre-National Curriculum, per-the present paraphernalia of testing with its, in my view, unnecessary impact on the lives of children and teachers. It was so long ago that we weren't even required to have a homework policy!

It sounds like I'm saying that everything was better without all the accountability, but it clearly wasn't, which brings us back to your paradox over 'good' schools and 'challenge'.

At this first meeting with parents (not so many diverse carers in those days) my message was that whatever I sent home was intended to be seen as an opportunity for them to share the activity and one where 'right' answers were not the highest currency. It wasn't truly Vygotsky's ZPD, but it was as close as they might get to it and as good as I could do at the time.

Today, I too am very joyously involved in my grandson's life, including his education. Left to our own devices, we do everything together, from woodwork to practical science 'experiments' but the bane of his life is homework. I don't care what has changed over time, I have to agree with him, homework is not cool. In my view it sucks. Clearly it is of the 'required' variety, required that is to fill another slot in our worryingly 'slot-machine' view of accountability in education.

At eight years of age, I believe the little chap has a point when he asks, "Do I have to do it?" I have managed to resist the temptation to answer his question with a question, "Who is it really for?"

Primary school homework should be limited to learning a few spellings and a reading book.

Teachers of English could always set homework such as producing a first draft for a topic to be presented in class or completing coursework (before controlled assessment came in). Sometimes I'd set reading (say, at least a chapter) or even watching a particular TV programme ready for follow-up discussion. But that's not "proper" homework, is it?

But setting homework must be a nightmare for teachers of other subjects.

Good idea from FJM - producing his own question sheets. These have the advantage of being targeted accurately. And the excellent "Bang Goes the Theory" programme now airing on BBC 1 could be set as homework - not just in science but for English, Geography (only it's not "proper" homework, is it?).

There could be a lot of mileage in getting pupils to do something on a particular website but this has the serious downside of further disadvantaging disadvantaged children.

On the more general question of HW, it should test and reinforce classwork, and marking it (peer assessment from time to time, not just the teacher marking it every week) can identify problems to follow up.

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