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Sunday, June 3, 2012
Saturday, February 4, 2012
Week in Review--February 4, 2012
We're now at the end of the fourth week of the winter quarter at the university and have settled into the new routine, though I've now added a new job to my list: I'm student teaching math to fifth-graders from extremely low-income and otherwise unfortunate/tragic family backgrounds. It's a very different experience from homeschooling, obviously, but the pedagogical tools and the variety of mathematical approaches I've learned from homeschooling have been absolutely invaluable. I've worked with two small groups of students, one at the just-below-average skill point and one well-below-average, and covered different topics with each. On Monday, the first group worked on simplification of fractions. Most of the students were fairly strong on their lower multiplication tables, but one didn't actually know that multiplication is just serial addition. Once he knew that, he could (slowly) solve anything I threw at him. I'm letting him play with that for a while (he's sorted out that counting by twos and threes is equivalent to and faster than adding them over and over--well done him!), and I plan to start working on the multiplication tables with him this week. It's well-timed, actually, because Oscar's going to begin memorizing his twos and threes on Monday as well (more on that below). The other students in that group were very close to full understanding before they came to me, and they'd achieved mastery by the end of our session.
The second group was more challenging, because one student speaks Spanish exclusively (my own Spanish is limited and rusty, but the goblins and I start back with our Spanish tutor this week so I'll be improving), and another student is reported to have an IQ of 70 and to be clinically retarded. That one is mysterious to me, because while he did certainly need remediation in topics well below fifth-grade level (we were using manipulatives to illustrate the concept of multiplication), he picked it up easily and is also thoroughly bilingual. He's apparently about to turn 13, but it's difficult to tell whether there really is an intelligence deficit or some kind of learning disorder (or disorders) muddying the waters.
On Wednesday I arrived with my own manipulatives and ready to pick up where we'd left off, but to my dismay we were moving on to long division (!). Their teacher has to move the rest of the class along, of course, and because we're working during class time we have to at least attempt to keep up. After the teacher's lesson, my first group of students made their way back to my table, and sat down not with the excited and proud faces they'd left me with on Monday, but with expressions of deep frustration and self-doubt. Still, even though we'd skipped some very important steps and they'd been terribly discouraged by trying to follow along with the lesson, they did get it working after we discussed it some as a group, and by the end of our time three ten year-old boys asked me if they could skip lunch and do more math with me. I'm taking that as a sign of success. I tried to make it clear to them that far from being dumb, they'd essentially skipped two grade levels (without mentioning the grade levels themselves) in 48 hours and still managed to succeed. I've also arranged to set up an after-school program two days a week so I can work with these students on the topics they really need to be working on so that they can follow the class lessons without frustration. The teacher asked if I could teach reading as well, and my groups are small so it's actually starting to feel a bit like homeschooling after all.
I mentioned earlier that Ozzy's working on multiplication himself. Singapore Math teaches operations and their inverses together, so the unit he's just finished in 2A covered the introduction to the concepts of both multiplication and division. When we're discussing a new topic, I always make the first few lessons a leaderless collaborative effort, the next ones a student-led collaboration, and the final ones I let him work through on his own with the option to ask questions. When he's going to be working on his own, I flip through what he'll be doing to make sure he'll be comfortable with it, but on Tuesday I somehow missed that the last two pages I'd set out for him were division, which we hadn't discussed at all yet. I'd gone down the hall to brush Sofie's hair, and when I came back five minutes later he was done, having apparently fully understood what the one-word instruction ("Divide:" followed by a list of equations) ought to mean and completed both pages without error. We've since discussed and played with division just to be thorough, but that was a fun moment.
Ozzy does have a tendency to despair if he doesn't fully assimilate a concept the first time he hears it, and working on difficult problems from multiple angles feels like cheating to him, so last night we watched the NOVA documentary on the process of proving Fermat's Last Theorem. Seeing that the world's top mathematicians struggled with that one problem for centuries, and that solving it absolutely required thinking about it from many different angles and using different approaches, seemed to help Ozzy relax and believe me that math is not a race and that part of the joy of math is the struggle and the insights that are developed during that struggle. It was also very interesting for me, because one of the classes I'm taking this quarter introduces proof techniques, which I could recognize in an extremely primitive way in the work in the film.
In my last weekly review, I mentioned that we'll begin MCT's Grammar Island in the next month or so, and I expect to transition into it's being our primary grammar curriculum instead of First Language Lessons. I had already ordered FLL3 when I discovered MCT, and from what I've read the combination of the two is rather ideal for the first level or two of MCT so that worked out fine. I haven't ordered MCT yet, but FLL arrived last week and confirmed something else I'd read about FLL: that FLL2 is unnecessary for most students. Oscar's over halfway through, and we'd been taking the lessons two or three at a time because they were fairly repetitive and moved forward in rather small increments, which might be very good for a student for whom language or memorization are not major strengths. FLL2 repeats everything covered in FLL1, and the new material in FLL2 is repeated in FLL3, so unless a student needs the repetition or some extra time to mature, it's very feasible to go from FLL1 directly into FLL3, which is what I plan to do with Sofie. In any case, Ozzy's started on FLL3 now and is doing very well with it.
The second group was more challenging, because one student speaks Spanish exclusively (my own Spanish is limited and rusty, but the goblins and I start back with our Spanish tutor this week so I'll be improving), and another student is reported to have an IQ of 70 and to be clinically retarded. That one is mysterious to me, because while he did certainly need remediation in topics well below fifth-grade level (we were using manipulatives to illustrate the concept of multiplication), he picked it up easily and is also thoroughly bilingual. He's apparently about to turn 13, but it's difficult to tell whether there really is an intelligence deficit or some kind of learning disorder (or disorders) muddying the waters.
On Wednesday I arrived with my own manipulatives and ready to pick up where we'd left off, but to my dismay we were moving on to long division (!). Their teacher has to move the rest of the class along, of course, and because we're working during class time we have to at least attempt to keep up. After the teacher's lesson, my first group of students made their way back to my table, and sat down not with the excited and proud faces they'd left me with on Monday, but with expressions of deep frustration and self-doubt. Still, even though we'd skipped some very important steps and they'd been terribly discouraged by trying to follow along with the lesson, they did get it working after we discussed it some as a group, and by the end of our time three ten year-old boys asked me if they could skip lunch and do more math with me. I'm taking that as a sign of success. I tried to make it clear to them that far from being dumb, they'd essentially skipped two grade levels (without mentioning the grade levels themselves) in 48 hours and still managed to succeed. I've also arranged to set up an after-school program two days a week so I can work with these students on the topics they really need to be working on so that they can follow the class lessons without frustration. The teacher asked if I could teach reading as well, and my groups are small so it's actually starting to feel a bit like homeschooling after all.
I mentioned earlier that Ozzy's working on multiplication himself. Singapore Math teaches operations and their inverses together, so the unit he's just finished in 2A covered the introduction to the concepts of both multiplication and division. When we're discussing a new topic, I always make the first few lessons a leaderless collaborative effort, the next ones a student-led collaboration, and the final ones I let him work through on his own with the option to ask questions. When he's going to be working on his own, I flip through what he'll be doing to make sure he'll be comfortable with it, but on Tuesday I somehow missed that the last two pages I'd set out for him were division, which we hadn't discussed at all yet. I'd gone down the hall to brush Sofie's hair, and when I came back five minutes later he was done, having apparently fully understood what the one-word instruction ("Divide:" followed by a list of equations) ought to mean and completed both pages without error. We've since discussed and played with division just to be thorough, but that was a fun moment.
Ozzy does have a tendency to despair if he doesn't fully assimilate a concept the first time he hears it, and working on difficult problems from multiple angles feels like cheating to him, so last night we watched the NOVA documentary on the process of proving Fermat's Last Theorem. Seeing that the world's top mathematicians struggled with that one problem for centuries, and that solving it absolutely required thinking about it from many different angles and using different approaches, seemed to help Ozzy relax and believe me that math is not a race and that part of the joy of math is the struggle and the insights that are developed during that struggle. It was also very interesting for me, because one of the classes I'm taking this quarter introduces proof techniques, which I could recognize in an extremely primitive way in the work in the film.
In my last weekly review, I mentioned that we'll begin MCT's Grammar Island in the next month or so, and I expect to transition into it's being our primary grammar curriculum instead of First Language Lessons. I had already ordered FLL3 when I discovered MCT, and from what I've read the combination of the two is rather ideal for the first level or two of MCT so that worked out fine. I haven't ordered MCT yet, but FLL arrived last week and confirmed something else I'd read about FLL: that FLL2 is unnecessary for most students. Oscar's over halfway through, and we'd been taking the lessons two or three at a time because they were fairly repetitive and moved forward in rather small increments, which might be very good for a student for whom language or memorization are not major strengths. FLL2 repeats everything covered in FLL1, and the new material in FLL2 is repeated in FLL3, so unless a student needs the repetition or some extra time to mature, it's very feasible to go from FLL1 directly into FLL3, which is what I plan to do with Sofie. In any case, Ozzy's started on FLL3 now and is doing very well with it.
Friday, January 13, 2012
Week in Review--January 13, 2012
Perhaps I should change these posts to "Month in Review" posts, because that's about how often I'm actually doing them. In any case, this was our first week back at the university, and our first week using our new lesson schedule. It went very well, although I did realize there were a few changes I needed to make to our schedule to reflect the change that will happen to our Thursdays when Ozzy's ballet class starts in February. I had planned to do full math lessons Tuesday, Thursday, and Friday, but they won't be getting home until 7:30 on Thursday nights once the ballet class starts, so it'll be getting a bit late for a full math lesson (which usually takes about 45 minutes per goblin). It's enough time for each goblin to have ten to fifteen minutes on the math software, though, while I do a full spelling lesson with the other (spelling lessons are only about twenty minutes each, once a week, with a five-minute review four days a week). Also, since Sofie's ballet class is a different day, Richard will do her reading and penmanship with her during Ozzy's class so that'll be out of the way when they get home. So I ended up moving Thursday's full math lesson to Monday nights, when we're home at 7:00 instead of 7:30. It must sound like the goblins are constantly on the go, but they're really not. It's just that instead of having their less-busy hours at the end of every day, sometimes the quieter hours are in the morning or afternoon. Thursdays are, unequivocally, a bit busy though now that their Lego engineering class is Thursday mornings instead of Fridays, but it means Friday mornings are less busy, so it evens out.
Ozzy and I have really been enjoying the switch in his math lineup. He likes the change of pace and the fact that the bar has been moved higher, but because Singapore Math seems to be more evenly incremented one topics are introduced, the trajectory is smoother. I've heard the opposite about SM, and I can easily imagine that that might be true if SM were used as a solo curriculum--which it's intended to be--but since we're still using RightStart to introduce new topics, we seem to have avoided that issue.
Sofie's math has been a challenge, though. I think I mentioned in my last Week in Review that she'd reached a point in RS B at which she could no longer make real progress until she could achieve instant recall of addition and subtraction facts. To improve that for her we've taken the last month or so off from formal math curricula and just played math games like Go Fish (in which a number is chosen at the start, and the "pairs" are two numbers whose sum is that number, instead of two numbers that are the same), Addition War (in which both players play two cards at once and whoever has the higher sum gets all four cards), and some other games. She's made some progress and has been enjoying it, but the part of math that appeals most to her (and to me) is the discovery aspect and the joy in seeing how all the concepts relate to one another, so she's started to get bored and keeps getting out the RS B manual in hopes that we'll get back some "real math," as she calls it. She's very strong on mathematical thinking and makes connections that I wouldn't have thought to point out to her yet, so I'm not concerned (am actually secretly thrilled, because my bias favors conceptual understanding over procedural understanding), and have decided to take this as an opportunity to try Miquon Math. Miquon is discovery-based (an exploration, rather than a guided tour), and uses cuisinaire rods instead of the abacus, which will be a fun change of scenery. Miquon is very inexpensive, so I ordered the first through third-grade books so that Ozzy can play, too. We might also add in some MEP math, which is a (free!) British program based on a Hungarian one, and is one I've heard wonderful things about.
Sofie's also had a breakthrough in her reading, and as of this week is reading short picture books that aren't phonetically-controlled, for the first time. Last night she was reading The Runaway Bunny, and I'd planned to do her next lesson in The Ordinary Parent's Guide to Teaching Reading when she finished, but it turned out that everything in the lesson appeared in the story itself, so we skipped the lesson. I flipped through the rest of the book, and I think we'll actually put it on hold indefinitely. With Oscar I definitely wanted to hit every lesson, but now that we're using All About Spelling, which covers almost all of the same concepts, and since she's doing so well regardless, I think we'll just keep on reading living books and practicing the rules with the spelling program, checking OPGTR every few weeks to make sure we haven't missed anything. It was at about this point that Oscar took off with reading, as well, and in the space of one year went from not reading at all to reading Sherlock Holmes unabridged. I'm relieved to see that milestone on the horizon for Sofie, because it'll open up some more interesting curricula for her and will allow her to be slightly more independent in her work (total independence is most certainly not a goal for us, however, at this age). Oh, and it also means that she can start doing the copywork in Writing With Ease instead of my having to make up copywork for her.
I'm almost totally convinced to switch Oscar to MCT grammar when he finishes grade 2 in First Language Lessons, because FLL3 apparently uses its own conventions in some areas, whereas MCT uses traditional ones less likely to cause confusion later on. MCT also includes poetry and Latin-based vocabulary study, which would be nice additions. I've actually already ordered FLL3, though, so I'll probably go through both programs and combine them in much the same way that I did with SM and RS.
And I think that's about it for us this week/month. We're having our first Field Trip Friday in several months today; it's nice to be back to it. Have a great weekend!
Ozzy and I have really been enjoying the switch in his math lineup. He likes the change of pace and the fact that the bar has been moved higher, but because Singapore Math seems to be more evenly incremented one topics are introduced, the trajectory is smoother. I've heard the opposite about SM, and I can easily imagine that that might be true if SM were used as a solo curriculum--which it's intended to be--but since we're still using RightStart to introduce new topics, we seem to have avoided that issue.
Sofie's math has been a challenge, though. I think I mentioned in my last Week in Review that she'd reached a point in RS B at which she could no longer make real progress until she could achieve instant recall of addition and subtraction facts. To improve that for her we've taken the last month or so off from formal math curricula and just played math games like Go Fish (in which a number is chosen at the start, and the "pairs" are two numbers whose sum is that number, instead of two numbers that are the same), Addition War (in which both players play two cards at once and whoever has the higher sum gets all four cards), and some other games. She's made some progress and has been enjoying it, but the part of math that appeals most to her (and to me) is the discovery aspect and the joy in seeing how all the concepts relate to one another, so she's started to get bored and keeps getting out the RS B manual in hopes that we'll get back some "real math," as she calls it. She's very strong on mathematical thinking and makes connections that I wouldn't have thought to point out to her yet, so I'm not concerned (am actually secretly thrilled, because my bias favors conceptual understanding over procedural understanding), and have decided to take this as an opportunity to try Miquon Math. Miquon is discovery-based (an exploration, rather than a guided tour), and uses cuisinaire rods instead of the abacus, which will be a fun change of scenery. Miquon is very inexpensive, so I ordered the first through third-grade books so that Ozzy can play, too. We might also add in some MEP math, which is a (free!) British program based on a Hungarian one, and is one I've heard wonderful things about.
Sofie's also had a breakthrough in her reading, and as of this week is reading short picture books that aren't phonetically-controlled, for the first time. Last night she was reading The Runaway Bunny, and I'd planned to do her next lesson in The Ordinary Parent's Guide to Teaching Reading when she finished, but it turned out that everything in the lesson appeared in the story itself, so we skipped the lesson. I flipped through the rest of the book, and I think we'll actually put it on hold indefinitely. With Oscar I definitely wanted to hit every lesson, but now that we're using All About Spelling, which covers almost all of the same concepts, and since she's doing so well regardless, I think we'll just keep on reading living books and practicing the rules with the spelling program, checking OPGTR every few weeks to make sure we haven't missed anything. It was at about this point that Oscar took off with reading, as well, and in the space of one year went from not reading at all to reading Sherlock Holmes unabridged. I'm relieved to see that milestone on the horizon for Sofie, because it'll open up some more interesting curricula for her and will allow her to be slightly more independent in her work (total independence is most certainly not a goal for us, however, at this age). Oh, and it also means that she can start doing the copywork in Writing With Ease instead of my having to make up copywork for her.
I'm almost totally convinced to switch Oscar to MCT grammar when he finishes grade 2 in First Language Lessons, because FLL3 apparently uses its own conventions in some areas, whereas MCT uses traditional ones less likely to cause confusion later on. MCT also includes poetry and Latin-based vocabulary study, which would be nice additions. I've actually already ordered FLL3, though, so I'll probably go through both programs and combine them in much the same way that I did with SM and RS.
And I think that's about it for us this week/month. We're having our first Field Trip Friday in several months today; it's nice to be back to it. Have a great weekend!
Thursday, January 5, 2012
How We Do It
Due to the fact that both Brandon and I are full-time students ourselves, we're frequently asked how we manage to homeschool as well. I touched on our method a bit tangentially in this post on our current schedule, but given the interest that that topic tends to generate, a dedicated post seems to be indicated.
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