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.