I came across this article online at the American Physical Society that I found thoroughly fascinating and it seemed to reflect an experience I'd had early on in my (Information Technology) career - but I'll get back to that.
If you have school-age children, the full article is worth a read. A Math Paradox: The Widening Gap Between High School and College Math written by Joseph Ganem. In it, he describes a finding where despite getting more challenging work in high school and being tested more, kids are getting to college with gaps in their Mathematics understanding. In his opinion, Mr. Ganem saw three problems (and here I am paraphrasing my perspective on the explanations):
Even though I want Lucas to be challenged in Maths, I want him to understand how everything fits together. I am fortunate in that Lucas "gets" Math, and I just check that he is "getting" the understanding clear in his head.
Check out the article, A Math Paradox: The Widening Gap Between High School and College Math written by Joseph Ganem, I highly recommend it.
If you have school-age children, the full article is worth a read. A Math Paradox: The Widening Gap Between High School and College Math written by Joseph Ganem. In it, he describes a finding where despite getting more challenging work in high school and being tested more, kids are getting to college with gaps in their Mathematics understanding. In his opinion, Mr. Ganem saw three problems (and here I am paraphrasing my perspective on the explanations):
- "Confusing difficulty with rigor". Harder problems do not necessarily help with understanding - you have to use concepts children understand to help them develop their own reasoning abilities but the problems must not be so difficult that they always have to ask for help.
- "Mistaking process for understanding". Just because a student follows the rules on how to solve a problem doesn't mean they understand either the problem or the solution. I remember a colleague of mine made a comment that made me think he didn't understand the "why" of what he was doing, but he knew the "how". If he knew why this process worked, he wouldn't make the statement he did. (I wish I could remember what it was!) In Trinidad, I found the opposite problem. My school work was almost totally focused on theoretical learning - the "why" but not so much the practical application (the "how").
- "Teaching concepts that are developmentally inappropriate". This suggested to me that each new Mathematical concept needs to build on previous ones appropriate to what they can understand. Teaching a concept in order to solve a problem without a context and relation to what they've learnt and understood before, doesn't seem like a good idea.
Even though I want Lucas to be challenged in Maths, I want him to understand how everything fits together. I am fortunate in that Lucas "gets" Math, and I just check that he is "getting" the understanding clear in his head.
Check out the article, A Math Paradox: The Widening Gap Between High School and College Math written by Joseph Ganem, I highly recommend it.
I'd be interested to hear your thoughts on this.
Comments
Coincidentally, i've been having conversations with other parents about gaps in the education our children are receiving in elementary school. With regard to Math, we all agree that more attention should be paid to Math drills and problem solving.
While some parents differ as to which area should be given more emphasis at this stage, the consensus is parents need to work with their children at home.
I had to smile when I read the part of the article where Joseph Ganem's wife wondered how do other parents help their children if they don't have the expertise of her husband, who is a college Physics professor. It reminds me of a story one of my friends told me. Her son is currently in 7th Grade at one of the best high schools in NYC, and he had some trouble figuring out some of his Math. His dad is very good at Math, but he could not figure it out either. They had to spend a couple hours on an overseas phone call getting help from his grandmother who is a Math professor :-)
Re your little anecdote about your friend, it does make me smile too, I can only hope that my undergrad Math courses will see me through 4th grade!
I actually found Ganem's article a little difficult to believe, though I'm sure he is describing the truth of his experience. But what he described sounds like a very old-fashioned way of teaching maths, more like the way we were taught back in primary school. I remember, at age 7 or 8, being taught how to do long division, and feeling very confused because, even if I could follow the steps mechanically and get the answer, I didn't understand why the process was correct.
From what I've seen of my kids' primary school experience, maths teaching is done very differently nowadays (at least here in the UK). The focus is much more on understanding the concepts, and less on rote learning of facts and procedures. In some ways my kids are very "behind", as I don't think my 11-year old can has met long division yet. But I'm not sure how much that matters in these days of calculators.
Anyway, my experience of maths teaching (at primary level) is very different from what Ganem describes!
I think your comments have made me realize that I should just wait and see rather than assuming my past experiences and those of the author necessarily reflect what my children will encounter. From what I see with how Lucas is being taught addition and subtraction now, it is different from how I was taught.
I need to pay attention that any parental "help" has to be done in the context of the way they are being taught and not the way I was.
Thanks for your comments!
I will add Tony Wagner's book to my list of parenting books (short list - only 2 right now).
Take care!