My daughter was positively thrilled with her own discovery, with her new-felt math prowess. With the first-grade book in Right Start Math, she was solving word-problems that would normally involve "carrying" in the usual algorithm. However, not yet knowing the algorithm or the concept of "carrying," she gleefully solved the problem in her head using an abacus. She thought it was as fun as anything.
I call that age-appropriate math play. The student is using her mind to form concepts and figure out creative solutions to challenging, hands-on problems. I like that there are lots of this type of figure-it-out, thinking activities in Right Start Math and that there are hardly any worksheets.
We've also been enjoying the TOPS Get a Grip kit which operates on a similar philosophy. Using guided discovery, Get a Grip develops math and science understanding through measuring play with a bunch of different sized containers and a big box of . . . lentils!
Sometimes my Kindergartener likes to complete the TOPS activity booklets, and sometimes he prefers to free-play with the lentils. Since kinetic free play is as important as any structured learning, especially at his age, I am just fine with that!
My older scholar likes to free-play but also enjoys the increasing difficulty of the activity booklets which will gradually guide her from easy comparison activities to "sneaky algebra." And the physical, hands-on element is important for her, too. With it's progression to more advanced concepts, the kit can meet the needs of students up to sixth grade.
But my hope here is not so much to recommend particular math and science programs as it is to highlight a kind of learning that tends to be highly effective for most students. And that is play.
With math as with other subjects, students at every grade level tend to learn and retain concepts well through interactive learning. At least this is what I've observed and read.
There is no sound dichotomy between "play" and "real learning."
For example, we might think of a good Socratic discussion of a classic text as age-appropriate play for highschool and college students. Some skeptics might suspect that less learning is happening in such a discussion than in a traditional lecture situation because prescribed content is not being "delivered" in a controlled way. But you and I know that deeper, more substantial learning does take place in a Socratic dialog, even if it might sometimes feel more like play to the participants. (And if you don't know this, perhaps you should give the dialectic a try!) There's a place for lecture, but there is at least an equally important place for the dialectic.
In the same way, real learning often happens in the primary grades through play, especially certain kinds of educational play. That kind of authentic, active learning sometimes sticks better than many "traditional" educational approaches which can devolve into "in one ear, out the other."
Since later is better, I like to start in on a formal math program no sooner than first grade, maybe even second grade. Sometimes we fly first with only the free, custom printables—mostly the time and money worksheets—from MathFactCafe.com. But first we get hands-on with actual coins and clocks around the home.
For other tips on getting started with math play in the early years, I liked Ruth Beechick's Arithmetic booklet. Inexpensive and brief, it covers both foundational theory as well as practical applications for homeschooling the early years.
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| By Galilea at de.wikipedia [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], from Wikimedia Commons |
Here's a final angle to consider: Who is the "real" mathematician doing "real" math? Is it the folks who successfully apply the symbolic algorithms like the Pythagorean theorem? Is it the people like Pythagoras who play with shape, measurement, and relation in order to discover the principles and create the symbolic algorithmic formulas that the rest of us use as ready-made tools? How can we best prepare students to think like a mathematician?
Do you play math with your budding mathematicians? What works well in your home?
I mentioned the wrong math program to you earlier. It was Miquon Math not Math Mammoth that is exploratory based math. T.S. is asking to do math, so though I wasn't planning on doing anything formal this year, it seems he finds is relaxing and fun and so started a math game shelf this week in his playroom.
ReplyDeleteI also just purchased the Miquon Math series....I found all 6 workbooks and manual (K-3) for $40 used. They also have a cool "lab book" of what play games they used with cuisenaire rods in their first grade class. A friend recommended to us http://www.educationunboxed.com/ as a good reference for playing with cuisenaire rods as well. The rods were one of the few toys we took to Greece this summer, b/c they were small and easy to fit in the suitcase.
Sorry to through out more resources....sometimes that becomes more overwhelming than helpful.
It sounds like you have a great understanding of where you are going and how to teach students to think like a mathematician.