The teacher had the manipulatives to teach math and it was a well-organized lesson on fractions for grade 8s: computer with visuals and moveable shapes on the screen, handouts, blocks for students to manipulate and a clear learning goal. The lesson was unfolding seamlessly until she realized that the demonstration of adding fractions using the blocks did not yield the right answer! She carried on by saying "I've done something wrong here" and then refocused the lesson by asking the students to solve the problem: "why didn't my operation using the manipulatives work?" A couple of thoughtful boys came up with the solution: the base, or denominator has to be the same even using blocks, which means that you can't just separate the blocks and add them up separately and get the same result as when they are joined together.
Example: a six inch plus a one inch over two five inch blocks joined together is 7/10, but a six inch over a five inch block plus a one inch over a five inch block understood as 6/5 + 1/5 does not equal 7/10, but 7/5 or 14/10! The problem to solve in math became the teacher's problem for the students to solve, and it worked! Nice recovery for the purpose of learning! Instead of a wounded ego trying to cover up, deflect or deceive, this teacher used her mistake to help students learn!
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