I’ve been doing a lot of reading recently and have really appreciated some of the posts by Julie Brennan, the founder of the Living Math website. She encapsulates some of what I’m thinking at the moment and also seems to have had children who are similar to Edward in terms of their orientation to language, rather than maths. I’m copying two of her recent posts on the Living Math yahoo group here to remind me of these thoughts as I continue to mull these things over!
“I wanted to share something about the idea of “doing math.” When my kids were in early elementary, I followed the Charlotte Mason idea of not pushing any more than 15-20minutes of *structured* math time daily, although if we were on a roll, we’d keep on going. But part of the reason I could be very comfortable with that was the realization that we “did” a lot more math than that throughout the week and weekend, because reading math readers, playing games, and activities using math are just as valuable learning times as formal, sit-down math lessons. These activities are often even more efficient than formal lessons at this age. We spent many, many hours learning math this way in the evenings, weekends and summers beyond a typical “school” day. We would have as long as an hour and a half long math sessions at night sometimes, with them begging to keep going and me having to say no more because it was past bed time. I didn’t let the time we did the activity take away from the fact it was learning time.
Virtually all of us parents grew up in school where learning was compartmentalized. You learned at school, you played at home, and because we were “schooled” we often resisted learning at home after school, unless we were fortunate enough to have an inspiring school experience or parents who were able to inspire us even after a long school day. It can be easy to retain this compartmentalized view of learning when we are homeschooling, and it sometimes takes work to shift our way of thinking and recognize just how much learning can be accomplished beyond the formal, sit-down lessons, particularly BECAUSE we are homeschooling and can provide our kids with lots of opportunities to do so, without burning them out with formal lessons to the point they resist learning any other time.
Homeschooling means we don’t have to compartmentalize, schedule or define learning times, and so our family “did math” 7 days a week, as many times a day as we wanted to, without counting the minutes or the times, because I already knew we were well over the few hours a week that school kids might be spending, and even that would be in a classroom without the efficiency of one-on-one interaction.
So don’t downplay those times when you play games, when you skip count in the car in a game-like manner (most of my kids learned skip counting by us “skip” skip counting, I’d say 2, they’d say 4, I’d say 6 and so on, it was fun). Those are as valuable and “countable” learning hours as the formal lessons.
Over time, I learned to use curricula as a tool, not a taskmaster, and to celebrate what I saw that they were learning, the progress, not worrying about all the benchmarks. They all did hit them in their own time, and not one of our kids was “behind” by late middle school, in fact the youngest is now taking algebra as an 8th grader and I thought she’d be the one to take the most time getting there based on her pace of learning in her earlier years. But when she was ready, wow, she took off. Again I reiterate, we did not avoid math, we didn’t “not” do math, but we were able to infuse our lives with many, many hours of math by weaving it in our daily lives through games, activities, oral math (which takes away the burden especially to boys of having to master the physical skill of writing at the same time they are trying to learn math concepts), and reading any time of the day, but especially at bed time. It’s amazing how much math you can cover on a Friday night when they know they can stay up longer if they keep asking for more stories. I wrote up some of our reading time math sessions a number of years ago here:http://www.livingmath.net/LearningIdeas/JustReadIt/tabid/269/Default.aspx and you can see just how much math is actually being covered when they don’t even perceive it as work or effort.”
“The difference I found was that at younger ages, two of my kids had a very strong drive to learn language-oriented things, and this is where they were willingly challenging themselves. I could have tried to challenge them with more math at the expense of their self-motivated language learning activities, and in fact I tried with my oldest, but it was a failure in the elementary years. I needed to find ways for these kids to learn math that could “hook” on their current drive to learn language and their need for context, which is why we went the way of lots of math literature, math history, games and lots of “talking math” problem solving, etc.
For both of these kids, their arithmetic development was behind their language development all during their elementary years, until about 7th to 8th grade when it radically caught up to their language development. I said arithmetic, because they did learn a lot of math in those years, it was just off the beaten traditional path. Both now are very good at math and enjoy it intrinsically, willingly learn it, even my 21 year old who just does math for fun.
I cannot tell how much of their faster language development / slower math development had to do with their internal drive and motivation, and how much of it was natural aptitude. It had to be a combination of both. But as they grew and matured, their overall capacity to learn more complex things grew, and their drive and motivation to learn increased. It was kind of like how young kids may not like a certain food even though it is frequently on the family table, and then suddenly they begin to start eating it, their “palate” expands. In the research she cites with the London cab drivers and the bus drivers, there is a huge difference to childhood math learning – the cab drivers CHOSE to learn the complex routes to achieve a personal goal. In the case of compulsory childhood mathematics education, the choice factor and personal goals are missing, so the motivation has to be supplied in some other way. A really great teacher can motivate a lot of students to learn something they might otherwise have not wanted to learn, but even then, a student who does not want to learn simply won’t.”