# PATTERNS AND PROBLEM SOLVING

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```					PATTERNS AND
PROBLEM SOLVING
Tom O’Brien working with Chris Wallach document their
experience of working with 6-year-olds over several weeks.

These observations arise from weekly sessions           were handed out, children went to work, and this
conducted jointly by a university professor and a       is what happened.
classroom teacher, sessions which have been under           All but one of the sixteen children went eagerly
way for several years and which have been widely        to work. The exception was a lad who broke down
reported. (See Notes.)                                  in tears. He cried with vigour until Chris went to
In our latest effort we worked with Chris’s first   him, asking what was wrong. “I can’t do this. It’s
grade children for an hour in early January. The        too hard.”
children were age 6.                                        “Of course you can do it. Let’s get started. You
The task, invented by the late Kathy Feely          were asked to put the numbers 1 to 9 on this grid.
during a course taught by Tom at Ralph Captain          Start with the number 1 and just keep going,” and
School, Clayton MO, in the late 1990s, was this:        she gave the boy a long reassuring hug. He put the
number 1 on his grid and quickly found a place to
Here is a 3-by-3 grid. Write the numbers 1 to 9 in      put a 2. He continued working successfully in a
the boxes in such a way that they make a pattern.       horizontal pattern. No more intervention was
needed and Chris left him to continue his work
independently.
The children worked for about 20 minutes.
They generated so many grids early in the session
that Chris had to leave the room to make more
handouts. When those were filled, they turned
their pages over and created grids of their own.
At a certain point Chris asked individual
children to draw one of their grids on a large dry
Chris had prepared handouts – three empty           erase board and explain it to the rest of the class.
grids to a sheet – to give out to children. These           Here are some of the grids they showed.

(1)                           (2)                        (3)                          (4)

1       2      3              1       2      3           9       8      7             3       2      1
4       5      6              6       5      4           6       5      4             6       5      4
7       8      9              7       8      9           3       2      1             9       8      7
(5)                           (6)                        (7)                          (8)

7       6      5              1       2      3           7       6      5             1       3      2
8       9      4              8       9      4           8       4      2             4       6      5
1       2      3              7       6      5           9       1      3             7       9      8

MATHEMATICS TEACHING 213 / MARCH 2009                                                                          3