Apr 222015

Assumptions can be a major issue with gifted students, and a tutor may need to not only teach students to sometimes make assumptions, but also teach them which assumptions people will assume they should make. As an example (and for your amusement) here is a word problem, from an actual math textbook currently in use, with gifted-student commentary in italics. The commentary is derived from several different gifted students.

There are 12 flowers in the first row of a garden. Just flowers? Maybe there’s other stuff in the row. The second row has 20 flowers, the third row has 30 flowers, and the fourth row has 42 flowers. This is a weird shaped garden. Are all the flowers the same size? Maybe the first row has bigger flowers so it’s the same length as the second. How many flowers are likely in the 6th row? We can’t really know that- but it did say “likely.” O.K., this already sounds like a really long, skinny garden- they probably wouldn’t want to make it any longer, so they would probably start making the rows shorter again soon. Symmetrical things are pretty, so they’d probably make the new rows match the old ones, so the fifth row would be 30 flowers again, and the sixth row would be 20 flowers again. So the answer is 20 flowers.

Of course, the textbook writer wanted the answer to be 72 flowers, based on a sequence of +8, +10, +12 . . . but a gifted student might have real trouble seeing that, because it not only requires assumptions without evidence, but specific assumptions.

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