the time) I use when I teach fractions to children. I would like to use the blocks with you, but I don’t want to offend you. What do you want me to do?”
The men discussed his wish and arrived at a consensus:
“Bring the blocks. Just close the door to the classroom.”
Paul brought the blocks for two sessions. The result was SUCCESS!
The following is a list of the vocabulary pertaining to Fair Lands that was used in this booklet. It is all right to invent your own in working with the Fair Lands blocks. The blocks and the way they are made does most of the teaching, not the talk.
Modeling subtraction as a business transaction—a sale—in Fair Lands. The blocks or counters already on a Fair Lands activity board show what is in inventory before the sale. Those on the invoice show what is to be taken out of inventory to fulfill the sale.
He addressed the error with chalk-and-talk and explained that if working with, say, eighths, that they had to borrow eight eighths, not ten eighths as they were doing when they just stuck a one in front of a numerator like the 3 in the example above, but old habits die hard, and they didn’t get it. What they got was another rote, meaningless procedure to replace the rote, meaningless one they had been using, and pretty soon they were back to doing what they had been doing. They did not grasp that fractions were in “lands” determined by their denominators and that the lands governed the trades that could be made.
Paul was beside himself. He reckoned the men needed to work with the Fair Lands blocks but dared not offend them by thrust-ing upon them what looked like children’s building blocks. Although none of the men had ever confronted him in the slightest, a prison is a dangerous place, and when tempers flare, men die, so he explained his angst to them and sought their permission to teach them with the blocks.
“Gentlemen, I see the problem you’re having with fractions. I gave you my best lecture when I talked about what you were doing wrong, but it didn’t connect with you. The only way I know to make it connect is with some colored blocks (Cuisenaire multi-base arithmetic blocks at
He was surprised, though, when afterward the men said thank you. Thank you! These tough men in a tough place THANKED him for a math lesson for kids.