I have been blown away by Ben's math ability. Just last night I cut some circles into halfs, thirds, quarters, sixths and eights. Then I wrote some mixed numerals down and some improper fractions. Before I had time to explain them, Ben had converted the mixed numerals into improper fractions and the improper fractions into mixed numerals. I couldn't believe he really understood it so I had him explain it to me using the fractions of circles I had cut out. He could have taught a lesson on it.
Then I thought I'd be really clever. I knew he understood that 5/6 > 4/6 > 3/6, so I changed it around. I asked him to put the fractions in order from greatest to least using the same numerator and different denominators. (3/8, 3/4, 3/6) He did it immediately saying it was easy and rolling his eyes when I wanted to show him using my paper circle cutouts.
Guess I spent 20 minutes cutting out fractions for nothing. Except at least I know he understands what he is doing.
What makes this all the more amazing is that I thought math was a trouble area for Ben at this time last year. He had been having to memorize his math facts at school using flashcards and answering them in 3 seconds each. He found this stressful and said he couldn't do math. He was so stressed by it that he had reflux and migraines. He would often be sent home from school just before math class. So he missed math instruction in first grade. In second grade when we were given flashcards to work on at home, I said that Ben would not be doing them. Somehow he mastered his addition and subtraction facts without flashcards. His 2nd grade teacher picked up on the fact that he was good at math. He was evaluated and given some more advanced work. This summer Ben begged me to sign him up for the Aleks math program. I signed him up on July 1st. He loves it and works on it for 5 to 20 minutes a day. In just one week, he has completed 69% of the third grade course work. With doubts that anyone could master material that quickly, I felt a need to teach him some of the skills it said he had learned or was ready to learn. That is why I spent all that time cutting out fractions. But Ben already understood the concepts and could explain them to me, even the ones it said he was ready to learn next. Where did this child learn these skills? I have no idea. He just loves math.