Thursday, May 25, 2006

Unschooling Math?

Formal math is my last holdout. Everything else, I can SORT of see how to do in an unschooling format, and I am realizing more and more how the informal learning was the underwater bulk of the learning even though we had some minimal academic structure super-imposed. But math thinking and "numeracy" is still a mystery to me and a fearful one. I found school math easy and enjoyable, and never had a problem with text work in this area. It is difficult for me to see mathematical thinking in real life.

Consequently, we used math workbooks all last year while I deschooled everything else. I decided to use summer as my time to get comfortable with a more real approach to math. We don't usually do much formal math in the summer anyway, so I can use the time to think, and look for math in our day to day life, and observe how my kids learn.

So, some preliminary links:

Unschooling and Math
Developing a Math Non-Curriculum

I think I am going to start some math journaling, too -- not for the kids but for me as I watch the kids. This will give me a way to start thinking about how math is involved in our lives and maybe make a conscious move towards deschooling this last holdout.

And a couple of preliminary thoughts:

My oldest son loves math and excels at it. Yes, he went through a formal though relatively light curriculum. His first couple of years homeschooling, grades 3 -4, we did very little in math at all. In fact, I have forgotten what we used, so it must not have been memorable! Oh, I think we went through some of the Core Knowledge math sections. I remember that the times table was a big issue. He took a long time to learn it and an even longer time to become quick and automatic.

In 5th grade we used Saxon 65 and a storebought 5th grade workbook -- I think it was Spectrum. He never finished either. I was pregnant that year and lost twins. In 6th he did Saxon Algebra 1/2. Again, we did not finish the book. I was pregnant again. Still, I was noticing a change in his attitude. He had begun adolescence and was developing more focus than he had had in the past. He was able to work harder and more diligently than he had in the past. He had always been both conscientious AND a daydreamer, and still is, but was now able to use one trait to benefit the other one, where previously they were sometimes in seeming conflict.

In his 7th grade year we were suddenly relocated to San Francisco when his little brother was born ill. He was ready for Algebra, but I didn't have the time to focus on working through it with him. So I got him Mathematics made Simple from a local bookstore -- a review of basic math and intro to higher level math, hoping he could work through it on his own. He finished about 2/3rds of the book. I recommend it as a survey and consolidation of arithmetic but the introduction to Algebra and Geometry was inadequate for our purposes and we ended up dropping it because it was confusing.

Then, back home, I bought him Saxon Algebra 1. This was the first time he really protested a math text decision. He wanted to learn geometry and disliked the Saxon incremental approach for this subject. I cast around frantically and discovered Jacob's Geometry. It worked just beautifully for him. He could do some of the algebra reviews at the end of each chapter, but not all of them. So I got Jacob's Algebra 1 and he found the first half of the book too easy. I allowed him to test out until he came to a stopping point, which was just after the midterm exam in the book. The rest of it he did entirely. By now he was in 10th grade.

From there we went to Foerster's Algebra 2/Trigonometry. He took 2.5 years to work mostly through this book. At some point I realized he was getting near-perfect scores and yet doing Every. Single.Problem. So I suggested that he do alternate problems when he felt he knew the material well. He started working this way and was able to finish the book before he graduated.

He used Apologia for Chemistry and Physics. He was also teaching himself to program during this time but I have no idea how he taught himself because I know nothing about programming myself. I will have to ask him for the details, but I am mentioning it because I think it probably helped him get comfortable with math thinking. I know that both he and my computer programmer husband like Python.

This year was his freshman year in college. He is doing Euclid for math and getting A's.

So this is one child's experience. The next two children are quite different and the next two after that are different again. The formal aspect of his math experience was quite light, as you see. But I am wondering if this was partly an advantage, not purely a drawback as I had thought in the past. I wonder if there was a natural talent and a cultivated interest in informal math -- through programming, logic puzzles, electronic science kits, and computer and board games -- which allowed him to feel comfortable with math concepts.

He was slow to develop automaticity in math memorization. I think he was in 6th grade before he had all his arithmetic facts down pat. I think if we could do it over again he would have preferred a bit more focused drill of some kind. Workbook drills don't seem quite adequate for this, in my experience with my kids, though they can be partly helpful. You can do them and still not be able to apply them in more complex operations. We have the same problem with handwriting workbooks. I think maybe some mental math problems as in Ray's Arithmetic might have been more helpful. Ruth Beechick has some good practical suggestions. Exploring his interests in an unschool format might have been even more effective.


Andrea said...

Math workboosk were one of our last holdouts as well, but mainly becaue we *like* math here. :D Except for Saxon. My kids really liked the Key To math series.

I should probably blog this, but our middle daughter Meaghan asked me, "What is algebra?" so I tried to think of an example she would understand. (although all algebra really is, is an equation with a missing piece or two)

She really loves cooking and the food network, so my question was this, "Alton Brown recommends 2 tablespoons of coffee per 4 ounces of water. Dad needs his 12 ouce pot filled. How much cof..." and here she yelled out "6!"

See? Real-life algebra. :D
(okay, incredibly simplified algebra, but still...)

Karen E. said...

Hey, any algebra involving Alton Brown is terrific in my book ....

Great links, Willa. Thanks.

WJFR said...

I like the Key to... series, too. Didn't discover those until later, though.

My 13yo just loved football problems and I still use them to help with negative numbers. A 3 yd gain and then a 9 yd loss -- what's the result?

JoVE said...

This is really helpful. I hope you get around to writing similar posts about how some of your other kids did math. I find that the process of unschooling is, for me, about learning to let go. And math is the hardest thing to let go, I guess. Following some of those links helped me with that.

I've seen good things about that Key to ... series. I am thinking that maybe we should have that lying around.


Dawn said...

Willa, I really enjoyed this post. We are getting tired of Saxon (really tired) and I'm casting about for a new approach. Lots of food or thought here ~ thanks! :)

Theresa said...

Great post, Willa. What is it about math that makes even the most die-hard unschoolers head for the workbooks!LOL!
Seriously, I am most likely going to do the Keys to.. series for middle school and then move on to Jacobs, etc for hs. I detest Saxon. We've used a pretty eclectic mix so far and it seems to have worked well. At least ds likes math, which is half the battle.