Reasoning About Problems ◆ 103Convince Me Problems
Convince me problems are set up so that students can actually prove their think-
ing in a logical format. These problems require students to use numbers, words
and pictures to explain their thinking. They demand that students justify what
they know and how they know it. They require students to lay out that jus-
tification in an organized manner. Here is an example (see Figure 6.24):
Adapted from http://mason.gmu.edu/~jsuh4/teaching/convince.htm
Figure 6.24 Use Manipulative, Sketches or Diagrams
Dan said that ¼ was greater than^1 ⁄ 5. Discuss his thinking.
(Convince me with words.)
I know that. __________________________________________________
______________________________________________________________
_____________________________________________________________
______________________________________________________________
(Convince me with drawings or a diagram.)
I can prove my thinking with a model.(Convince me with numbers.)
I can verify the answer another way:
Therefore,Find and Fix the Error
In this activity you give the students a problem with an error. The students
have to find and fix the error. This develops what research calls “a nose
for quality.” Students are able to think about, analyze and reason to them-
selves and with others about the nature of the solution. They ponder, is
it correct? They think about where the error might be and then how they
might fix it. This can occur across mathematical topics and should because
there are specific errors that students consistently make (like adding
denominators). The find and fix the error activity spotlights these common
errors and asks students to catch them and throw them back fixed. For
example: