Thursday, January 28, 2010

Unschooling Math - sort of, so far

Unschooling math isn't something I'm completely comfortable with, yet I find it preferable to the alternative of using a math program or curriculum. Perhaps no parent is ever completely comfortable with how their child is learning math -- every program has deficiencies and we always wonder if there is something better suited to our children out there. I'm not offering any insights or advocating my way of seeing things. I'm just documenting why I'm taking the approach I take so that in the future when I ask myself what the hell I was thinking, I can come back and see this post and say "ohhhhh...."

I don't think I'm having any new epiphanies on the matter, so maybe this is a progress report. Also, since I started this blog, Blogger has added tags, so maybe I can tag this and find it more easily than my older posts on the subject. Someday I will get around to tagging those, but for now, this will be a recap and an update of how math is going in our homeschool.

I'm a collector/hoarder of books and educational paraphernalia. I suppose that what I'm thinking is that if we have everything we could possibly need, my kids will find it and use to as it helps them best. I'm also a big believer in natural learning - that so many needed skills can be learned just through the normal course of life and that this knowledge learned through application will stick better.

Back when I first started to homeschool, I read alot about homeschooling and education. Some things that stick out in my mind were reading Mary Pride mention that her father taught her all of elementary math in one summer. Well, that sort of takes care of my concern about elementary school and it reinforces my feeling from school that most of the math seemed to just repeat itself year in/year out. I always liked math, found it to be a game and I enjoyed it. I was never in the highest math group but always did well where I was. What sticks out most in my mind was how much I loved algebra and geometry. Most interesting, though, was that I truly found high school geometry to be a reiteration of what we had been learning up until then. I suppose there was the added element of proofs, but I recall that they were very simple and fun for me. Beginning with trigonometry, I found math tedious and uninteresting. Maybe I'm just not the math sort. Luckily, I have a husband who did not find it so and went further in math than I did, so I can balance my math thoughts with his, though his thinking is very similar to mine.

After Mary Pride seemed to confirm my suspicion that there is not all that much to elementary math (or perhaps math before algebra), we found Gareth Lewis. I admit I have not read One-to-One in years, but what my husband took from it was the importance of keeping math mental for as long as possible.

Since my older daughter is such a reader, we have lots of math books in our house. A few are text books from used book sales, but I don't think anyone looks at those. I have found the E.D. Hirsch books helpful. FUN books has a great selection of math books and I've heard good things about the Jacobs series. We've also acquired the first Life of Fred book, though we may not be ready for it, but it's on my radar. Just looking through his website, I found what probably best sums up my approach to education - "Let them have a happy childhood." What he writes for how to learn the times tables is true of our house -- my husband quizzes my daughter in the morning with the math fact of the day. It's a "fact family" - what is 5 x 3? 15. What is 15/3, what is 15/5 sort of thing. We have the multiplication charts on the back of the door of our downstairs bathroom. I have tried to interest my daughter in the multiplication grid without much interest. I should try again. Just playing around with the multiplication chart and a 100 chart (easy to find on an internet search) helps to learn the times tables. John Holt recommended in one of his books to learn the tables by using a multiplication chart with blank spaces and letting the child fill it out.

I suppose what is most important to me is that my children learn to add, subtract, multiply and divide, so that is what we are focussed on right now and it seems to be happening fairly seamlessly. I buy the placemats with the tables on them, they may be ignored. I hang the hundred chart and the multiplication tables. We talk to our kids, peppering then with questions throughout the day (it's easy to incorporate multiplication into many daily tasks, especially trips to the grocery store).

Up next....
Mathematicians lament.
American Girl books.
Freedom in education blog

Wednesday, January 27, 2010

Homeschooling 4th grade math

I'm an unschooler. It's not something I aspire to be, it's just who I am. Sometimes I think about homeschooling in some other way and I always decide against it - I really believe my children know how to learn best and they'll show me how best to help them. So, for most of the year, things are fine and dandy and we learn so seamlessly that I'm always hard pressed to demonstrate or describe what's going on in our homeschool. I guess it's like brushing my teeth, I do it every day, but I'd have to stop and think to describe exactly how I do it and I always seem to bore myself in the explanation. An odd analogy, perhaps, but perhaps I'm an odd person.

Our state requires that we give proof of progress annually. I don't mind this regulation as it seems reasonable and fairly unintrusive. To give proof, we use the California Achievement Test (CAT). We've also been using the Spectrum Test prep books, though they are far more intensive than necessary to prepare for the test. However, they give me the chance to see what my kids know (to a limited degree) and whether they understand how to take the test. I have found them very useful in the past, though I must say that their utility seems to be decreasing as my kids get older. Starting around 3rd grade, Spectrum does not seem well correlated to the CAT. If I remember correctly, Spectrum introduced long division and did not review subtraction with regrouping. The CAT at the same level did not have any long division and did have subtraction with regrouping. So now I'm careful to do more math review than the Spectrum offers and to use it as a way to introduce new math concepts without too much worry that it will be on the test.

My oldest is in 4th grade now and, as has been my habit, I ordered the Spectrum Test prep earlier this month. My youngest is in 1st grade. I pulled out the books and started the review. My oldest is learning long division. I don't use a math curriculum, an issue I am constantly reconsidering and so far have always decided against - I blame Mary Pride who wrote in her Big Book of Home Learning that her dad taught her six years of math in the summer after first grade. So, when it's time to prepare for testing, I need to cobble together material other than my own tutoring that can help my daughter. She is a strong reader and loves books, so I usually go the literature route. We have the whole E.D. Hirsch series, What Your X Grader Needs to Know. Like the Spectrum grade levels, it seems I have to consult two grades in Hirsch to get what we need. Two digit multiplication and division can be found in the third grade and fourth grade books. I have assorted other math books (text and otherwise) that I look at, but I think the Hirsch books do a nice job of displaying and explaining what is going on in the problems (how they are done). As you can tell, I am not into drill and kill, I want my child to understand what she is doing and why - not just spit back the procedure. I'm not advocating that this is the proper approach, just explaining that it's mine.

While at the library today, I also checked out some books on division that I also thought seemed to illustrate the procedure clearly. I got Division Made Easy is from the Making Math Easy series (one I was unfamiliar with). Hey, cool, there are reproducible worksheets for the book on-line. I also got Dazzling Division by Lynette Long, which looks much more games oriented but might be a way to extend the concept and make it more concrete. We shall see. As much as I love the idea of using games to learn math, I tend chafe at using a contrived "math game" and prefer to play real games. I don't know that it reaches long division, but most card and dice games at least offer a lot of practice in addition (thinking of my younger daughter here). Maybe it's time for me to try some math games.

I also picked up a couple of video tapes from the Math for Children series. I got Multiplication and Division and was very pleased with how entertaining and educational they are. My kids seemed to like them and perhaps they will even watch them a few more times. Can't hurt, right?