After Monday's frustrations, I had some better sessions. Miki showed remarkable progress. She won't speak English to me, but she has demonstrated that she can understand some of the commands I give in English. If I say something like "What's the answer to #3?" and she gives me the answer, even in Japanese, I think it's okay to consider that progress. It's much better than getting a blank stare.
Miki also demonstrated some ability with proportions. Previously, all types of math problems had been difficult for her. This week, she had a worksheet filled with proportion problems, front and back... all word problems. As soon as I saw this, my heart sunk and I knew it would be a long session. But Miki really surprised me!
All the problems were basically the same. Two sentences - the first one allows you to set up a proportion, and the second one asks you for an unknown. For example, "Every year, 10 people die from dog bites. How many people have died of dog bites during your lifetime?" So you use the first sentence to make a proportion... 10 deaths/1 year. Then you get the unknown from the second sentence and solve.
Once I taught Miki the basic set-up, she was remarkably good at picking out the important parts and making the equations, despite not understanding the meaning of the sentences. She couldn't always solve them correctly - she often didn't know whether to multiply or divide - but she was much better than usual. It was quite refreshing.
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