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A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).
Students may ask for 'the answers' but this supposes that the activity is
closed. Investigations can always be extended by varying the initial
instructions or asking the question 'what if...?'. Sometimes students point out
that the instructions are ambiguous and can be interpreted in different ways.
This is fine and the students are encouraged to explain how they interpreted the
instructions in their report.
Some students may benefit from a writing frame when producing the reports
of their investigations. Teachers may suggest sections or headings such as
Introduction, Interpretation, Research, Working and Conclusion or something
similar.
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Vijaya, Jodh
Friday, April 30, 2010
"There are eleven rectangle."
Mark, Holland
Friday, September 24, 2010
"Every square here contains 9 rectangles."
Class 4T, Kaimes School
Wednesday, January 12, 2011
"We had a go and we got various answers. When we discussed the rules and the boundaries of the shapes we found that allowed more. We also concluded that squares are also rectangles. We are going with 232. But there is probably more."
Wonhang Lee, Korea
Friday, January 27, 2012
""There are forty-one rectangles."brown color 33 &yellow color 8."
Callum , Year 8, Carisbrooke, Isle Of Wight
Friday, May 4, 2012
"We have reached 206 rectangles of various sizes and there are still a few more!"
Spruce Class - Year 5, East Borough Primary , Kent
Tuesday, March 19, 2013
"We found 173 at most, but we are still looking! Does anyone have an accurate answer?"
Jill, Twitter
Wednesday, March 4, 2020