Math - the bane of many unschoolers. I'm still not sure how to go about covering it, so I kind of ignore it, figuring it will all work out in the end. My husband does not exactly share my outlook, though he does understand the downside of drill and kill. Honestly, if you know how to add or subtract or multiply or divide, do you really need to practice it with endless worksheets? Maybe, for speed and accuracy. But we don't. And I would have to say my daughter's speed shows it. But does it matter? Will she eventually build up speed? Does it matter if she doesn't?
I can probably thank John Holt for my outlook on math, especially his books Teach Your Own and Learning All the Time. I feel there is no necessity that it be sequential and routine. I think math opportunities abound in the real world and if a child wants to learn the multiplication tables, should I really put her off and insist she practice addition and subtraction ad nauseum first? Is it possible that by learning her multiplication tables, she'll figure out that they are really like speed addition of the same number and her synapses will fire and it will all make sense to her in ways it never made sense to me in school? (Thanks to Stephanie, who was the first person to vocalize that to me, I'd link to her post on it, but got side-tracked with all her math posts, which are awesome! Why am I even writing this?) It seems to me that math is about discreet skills of addition, subtraction, multiplication, and division, applied in different ways for different reasons and that these are merely ways of manipulating and expressing relationships of numbers. Doesn't allowing her to explore these freely rather than doling them out to her piecemeal at slow pace make it more likely she'll think mathematically?
Well, I am not a mathematician (obviously), but I always enjoyed math class. Math seemed incredibly repetitive to me. Perhaps I was not challenged enough in my math classes, but I really couldn't see how high school geometry varied that much from the geometry I'd been exposed to throughout my earlier schooling. I suppose they added the element of doing proofs, but the rest seemed review. Regardless, it was super easy for me and I sailed through it with great grades. I loved the puzzles that algebra provided. It wasn't until trigonmetry, algebra 2, and analytic geometry that I began to get bored. I did okay, I don't remember being confused, I just didn't really like it anymore. I did love physics and the math we used in there. Maybe I'm just an applied math kind of gal. It doesn't really matter and this is supposed to be about my child learning math, not about how I learned. But perhaps how I learned does play a part in all this.
I'm the visual/aural type, so I'm attracted to learning through reading. It's how I learn best and my eldest, Suzanne, seems to be similar to me in that way. I've acquired a lot of picture books that deal with mathematical concepts. Stuart Murphy has a series; I'd never call it great literature, but it's not bad for introducing a mathematical concept and each book includes a few other titles that demonstrate the principle. I also found a great article in Book Links, a publication by the American Library Association, that lists and summarizes a number of books that help preschoolers through elementary aged kids learn about math.
I collect inexpensive workbooks which include math and leave those around. Suzanne will sometimes work in them, sometimes not. When she does work in them, she tends to do a lot of work in them before setting them aside. Sometime after she's done, I take a look at her work to see what she understands and what she doesn't. When she doesn't understand something, I explain it to her, but I realize that if she isn't paying attention or if she simply isn't getting it, that it's best to leave the matter for another time.
Another influence on our approach to learning math we credit to Gareth Lewis, author of One-to-One (scroll down on that link to find his book. If you have an older child, you may want to look at this book of his). Lewis was a maths teacher in a Waldorf school (don't you just love Europeans and how they pluralize 'math,' opps, I mean pluralise). His on-line article includes much of what he wrote in his book on the matter. What my husband really took from his book was to try to stay with mental math for as long as possible, before getting down to pencil and paper. Granted, Tom has been known to write out some math problems for Suzanne to work on when she shows an interest, but he also asks her a lot of math questions -- basically, word problems. To improve her speed, I'll answer them first sometimes -- it sounds mean and I'm willing to accept the label, but it works. I also credit Tom for having found the Jefferson Lab. While I was away from the computer just now, Suzanne jumped on and was working on speed math.
When Suzanne was younger, we worked on math concepts simply by playing. Manipulatives haven't really worked for us. I dutifully collected milk jug tops for counting practice and was never able to interest the kids in that, though they love playing with the tops and will often sort them by color or use them in their story-telling. I was interested in Holt's explanation of math manipulatives. They may help some kids, but for others, they may be confusing or get in the way (perhaps if the child is an abstract thinker to begin with). Holt explained that sometimes manipulatives seem like a great way to teach a concept but that may be because we adults already understand the concept and can see the illustration. Since the child doesn't know the concept yet, the manipulative may not work in the way we would expect. At least that's my understanding of what I read - I realize sometimes I take something from my reading that isn't necessarily there! I wrote a post on unclimber about 'teaching math' to my daughter when she was preschool aged. I highly recommend the use of dice and card games.
Another thing that struck me in my reading about homeschooling and math was what Mary Pride said in her curriculum guide (I think that's where I read it), and which I found here. She talks about her father, a college professor, and says, " I also had the tremendous experience of him teaching me six grades of math (from grade 2 through grade 7) in the summer after first grade." Reading that seemed to lift all the pressure about 'teaching' math from my shoulders and it confirmed what I had suspected, that much of elementary school math is repetitive, and needlessly so.
While we are satisfied with how our eldest is learning math (and obviously don't spend as much time worrying about our youngest!), we are not immune to worries about math or the lure of prepackaged curriculum. At the last homeschool conference we attended, Tom was tempted by Right Start Math. I found the sample DVD for Math-U-See intriguing. Tom wonders whether and which program he should get - Singapore vs. Saxon. So we decided to ask Suzanne if she wanted a curriculum, if she'd enjoy it. "Probably not," was her response. So we'll keep that money in our pockets for the moment.
Marjorie is homeschooling her two young daughters, a second-grader and a kindergartner. Her family chose homeschooling without ever having sent the kids to school for the freedom it afforded them -- freedom from the school schedule and calendar; freedom to follow her children's interests; freedom from labeling and categorizing her children; and freedom from testing and homework. She enjoys volunteering with her state's inclusive homeschool association, knitting, shuttling her kids to playdates and a limited number of activities, and writing on her blog, unclimber.