March 2006 Archives
I talk a lot these days about Singapore Math because that's the curriculum I'm getting to know up close and personal. REAL up close and personal. I just home schooled three kids yesterday in Singapore math. We're on our way.
For those of you new to my blog--no, I'm not a homeschooler. My kids are public schooled in Ridgewood, New Jersey. Our school district is a mystifying blend of good teaching, high standards, and misguided experiments. I've always said, "I'm a homeschooler wanna-be but my school district is too good."
I still say that, even though I'm replacing their math instruction at home. Search around my other blog entries to find out what I like about our school district, and the history of how I came to be home schooling my kids in math. But in a nutshell--they're getting TERC Investigations in school.
This entry today is about home schooling my kids in Singapore Math.
In the last few weeks, I did this prep:
1. Researched which curriculum I'd like to use
2. Ordered the books
3. Started reading Liping Ma's book about a comparison between American and Chinese understanding of math concepts, and its effect on students
4. Ordered some manipulatives from the Singapore Math site
5. Made some manipulatives with paper, markers, photocopies, and clear contact paper (the poor man's version of laminating). They're pretty creased, but they work
6. Went shopping at Office Depot for a few items such as a meter stick, gram scale, triangle, and protractor
7. Unpacked my thinking with my husband, who will be teaching, too
8. Meditated upon math teaching, and what my goals really are
9. Rearranged some shelves in my dining room to make room for all this new stuff. The dining room is now doubling as the math room
10. Talked to our kids about why we're doing this, our goals, and what they'll get out of it. For the second grader, that includes a Twizzler with every lesson
I've spent about $200 to $250 in supplies, but that's cheap compared with the expense of tutoring.
Does the choice of curriculum make or break good outcomes? Does curriculum reign supreme? No. There are many right curricula. Take Saxon, for example. I did not look into Saxon math, but I know it's widely used by homeschoolers and lauded by a lot of the folks on the web that would like to replace TERC.
Liping Ma also has a curriculum that's focused more on undoing some damage caused by bad teaching. Bad teaching is NOT our problem here in Ridgewood, however. The short version of our problem is lopsidedness.
Singapore math is more well-rounded, and also does some instruction in a different order. My main goal is to accelerate my kids so they're doing Singapore grade level work, which is two to three years ahead of grade level work here.
(Actually, Singapore is two years ahead of the U.S., but if you compare to individual states, Singapore Math is three years ahead of New Jersey. Which by some strange measure means my kids are doing okay, in that they are meeting New Jersey's expectations.)
I would strongly recommend to parents that they seek out a replacement curriculum for their kids that is right for their particular situation. A replacement curriculum can be administered by the parent, a tutor, a tutoring business, or a new school. Reactive tutoring, as opposed to replacement curriculum, isn't such a good idea. Read more about reactive teaching.
As a trained teacher myself, I have always known that good teaching involves discovery, personal connection, and any other way to engage the student in taking an active role of learner (and a teacher to others.)
Now that I've started working with my kids with a replacement curriculum, I'm tapping into my good teaching skills, and I'm really noticing them, especially because I'm simultaneously training my husband. Our plan is for him to teach the oldest one (for a variety of reasons I won't go into now.) Hubby's a fast learner.
As soon as I see my kids make a connection and really understand the concept, I move over a notch. For example, start with tens cubes to illustrate subtraction with decomposing (also called borrowing). Once they get the concept with the cubes, we can move to number disks, which are halfway between concrete and conceptual, since each disk has the numeral written on it but cannot be broken up into smaller units.
Actually, the disks haven't arrived in the mail yet, and I'm anxious to get them. I'm thinking they may prove to be an important tool.
Then when they see the concept with the disks, we can move to a few ways of working the algorithm. Then, in the final step, you help the student discover the quickest way for him to do the computation. After that, occasionally go back to the concrete, especially for new topics.
It's so simple. But in the long run, the kid needs to know any useful shortcuts so he can have something quick and effective in his pocket. He can also learn to use the calculator at that point.
The more I immerse myself, the more appalled I am that the school is vilifying direct instruction. Happily, though, this aspect of TERC Investigations is so misguided that it probably won't last. I predict it's the first thing that will fall away as they begin to attenuate the TERC Investigations program.
They will never admit the error, though. Instead, they'll find a fig leaf, in the form of "we've enriched TERC further." But that's okay with me. As long as they do it soon, for the sake of the other kids in the school.
The child should definitely participate in the learning process, but the teacher is the one who knows the goal and the bigger picture. Direct instruction can be done badly or well. With good teaching, direct instruction involves discovery.
Several years ago I taught my stubborn nephew to ride a bike. He was getting too old, and his parents had given up. I used a different approach. I handed him the wrench. Take off your own training wheels. This served to equip the child with ownership of both the problem and the solution. Constructivism? I guess so. I just call it good teaching. He learned that day to ride his bike.
Here's a summary of how it went the first weekend:
1. Our grade 2 kid: He responded well to the lesson. He recognized the manipulatives, and it quickly became clear that he has used manipulatives extensively for this level of math, which is a review for him.
So I touched lightly on the manipulatives, just making sure he knew the concrete. He's a wiz at mental math. I'll check in with him once in a while as we progress. At some point, we'll get ahead of the school, and he may need more help with the mental math from me.
2. Our grade 5 kid: For her, this was mostly a review, but next week will be new material already--she'll be doing metric length. It was an interesting lesson yesterday because the entire thing was on mental math. I found out she hasn't done much mental math since fourth grade, and was rusty.
As we discussed mental math, and our different strategies, she ended up learning one new strategy from me. I did not set out to teach a new strategy, but she liked my personal strategy better than one of her own.
Until this week, I did not even know I used mental math. And I'm learning some new strategies myself. Over the course of the session, she got quicker at mental math. I wonder why she hasn't been using it.
3. Our grade 7 kid: She went along swimmingly with the level 4 curriculum until they hit a section on mental math, at which time she had a complete breakdown. This is fitting for her personality.
But it also means she has some kind of mental block around mental math. Certainly, much of what I learn about my kids and math will be unrelated to the school. Every kid responds differently to math instruction, and they all have math personalities.
Apparently, she never felt she could do mental math. We can't really tell how much instruction she's received, but we suspect that mental math has been emphasized more in our district in only the last few years, so she got less of it than our other two.
Summary: Everyone is cooperative (or at least resigned) and willing. The Singapore instructions are pretty choppy, though, so the plan will be Saturdays: use the home guide and the text, Sundays they do independent work in the workbook. Less choppy that way, and we get to do the dishes on Sunday.
My plans: I think I will plan all curriculum during the week. Then on Friday or so, I'll take a half hour to transfer plans to my husband for our oldest child. I'll show him the manipulatives, the material, and any notes I've written on what to emphasize, some teaching tips, and so on.
Linda Moran is LensMaster of the TERC math lens, titled Beyond Terc Math.
Moran is also LensMaster of the teens and tweens lens and the owner of the teens and tweens message board on Yahoo.
I received my Singapore Math books in the mail yesterday, and am getting very excited about teaching my kids math. This is a popular program among homeschoolers, which is telling when you consider that home schooled kids consistently score higher on standardized tests than do public school students in our country.
In fact, the country of Singapore once again scored number one for the 2003 TIMSS (a study based in Massachusetts that looks at how countries score in math achievement.) In Singapore, they use the Singapore Math Curriculum. 
The materials look very thorough, and they move nicely from the concrete to the conceptual. For each unit of study I will, as always with good teaching, start with a constructivist approach, and then move beyond to direct instruction.
The kids' textbooks and workbooks are appealing-looking, and the home guides are great. Instead of buying the teacher's guides, I bought the home schooler's guides, because they're more oriented toward one-on-one teaching.
Someday I hope my district decides to learn from homeschoolers. Now that would be a wise move. I'd be so impressed. But they're not there yet. Imagine--best practices from home schoolers. They're a wealth of knowledge.
I've resigned myself to the time and expense (mostly time) it will take to home school my kids in math. The reason it's okay with me is because in the bigger picture, they're getting a great education. I shall always hold these things dear to my heart:
1. Reader's Workshop (language-intensive reading program)
2. Writer's Workshop (thought-provoking constructivist-based writing program that produces middle school and even high school level writing in an elementary school).
3. Open Circle (social skills program that has served my children well.) To find out something wonderful that happened to my daughter in Open Circle, read my story called "Outing My Kids." This story was published in Exceptional Parent magazine. I've thought to send this article to Wellesley, but haven't gotten around to it.
I'm thinking that I probably won't need to say anything at all to my principal or teacher(s) in the next few years. That's because TERC Investigations and Singapore Math can reside nicely side by side in my son's brain. He's a smart kid. I've already begun to tell him that he can do math the TERC way at school, and any way he wants to at home. He understands this.
He also understands that the school can't be perfect. He's used to this, as we've had such discussions before. When the school nurse was teaching the old food pyramid, I helped all of my kids understand that the food pyramid was faulty, but that it wasn't the nurse's fault--she was required by the state to teach it.
So they knew to answer the questions on the test the way the teacher wanted. They knew to spit back that fats and sweets are bad, and that you should have ten zillion servings of carbs per day. (Okay that's an exaggeration, but it really was wacky.)
And they also learned from me the truth about food balance. They can live with this dichotomy and still respect their teachers and school.
Another topic I discuss with all my kids is the difference between education and indoctrination. Education allows for critical thinking, and arises from a teacher who thinks critically. Indoctrination is a replacement for thinking. The artificial divide between "good foods" and "bad foods" is an example of indoctrination instead of critical thinking. Another is the teaching that all drugs are bad, without mention that heroin is used as a base in some pharmaceuticals.
They can live with this too. They're smart kids. They've learned from me to be active, savvy consumers of their own education.
I think my child will benefit from TERC Investigations. It's just that it's not math. Rather, it's an interesting extended language program. We can laugh about it at home. And my child will be laughing all the way to higher mathematics.
I'm so glad I started my kids young in handling dichotomy, in thinking critically about their school environment, and in discerning between indoctrination and education. It's the reason that doing Singapore Math at home, while doing TERC Investigations at school, will work nicely for my remaining child in elementary school.
I feel bad for those parents who don't have the time, courage, or background to tutor their kids. I know that lots of parents are paying a bundle to get formal tutoring for their kids. Others can't afford it. No Rich Child Left Behind.
It's nice that I'm a licensed elementary teacher with a 7-9 math extension. However, home schoolers produce high-achieving students with no teaching license at all. I'm hoping other parents will take the advice to heart that if you want to home school your kids, all day or in just one subject, you can figure it out.
I call this home schooling instead of tutoring because tutoring implies the kid needs extra help. Home schooling implies more of a full curriculum, and that's what I've chosen. That's why I selected Singapore Math, which is a far cry from raw drill. In fact, its biggest criticism is that for some kids it doesn't offer enough drill, but that can be supplemented.
It's interesting that in Singapore, the kids do receive drill, but it's after school. I call that well-rounded!
Tomorrow I'll go shopping for my manipulatives. My list is about 30 items long, and includes metric weights, base ten blocks, linking cubes, hundreds chart, place value cards, and much more.
Redundant? Nope. The idea is to get them ahead of where they are in school, then keep them there. That's why I'm teaching my middle schoolers, too, even though they're not getting TERC Investigations anymore. They're just plain behind in math, and that's more the fault of the NJ State Standards than anything else. The New Jersey state standards are heavily constructivist-based.
Besides, there are problems with what is known as reactive teaching.
Actually, according to the Federal Department of Education, it's my fault my kids are behind in math. According to our government, the education of our children is the ultimate responsibility of the parents. So I should have been getting them tutoring earlier, like some other parents I know have done. But I was trusting my school. Silly me.
When my kids get to college, I want them to have all majors open to them, not just the ones that are light on the math requirement. That's my bottom line.
Sign up for the free Yahoo! Beyond TERC group
Moran is also LensMaster of the teens and tweens lens and the owner of the teens and tweens message board on Yahoo.
