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?