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My kids do learn multiplication tables. They present it a little differently than they did when I was a kid, but they are still expected to know the math facts.
I would teach her. Dh and I are both in education and I think the idea that there is intrinsically something evil about memorization is nonsense. 
What are families supposed to do when both parents have to work full time jobs, come home at 5pm, cook, do the homework with their children and in addition teach them maths? . 
Well, dh and I work full time, too. I don't have any problem at all with supplementing and reinforcing my kids' education at home. My parents did it with me, back when the earth was cooling. I view it as a perfectly normal part of parenting.

Okay, I already stated my biases up front previously, so please take that into consideration.:
That said, though, don't you think there's a crucial difference between "supplementing and reinforcing" your kids' education at home and having to teach them a fundamental concept the school is not addressing? For example, I think we'd all agree that it's totally reasonable to help your child with his or her English homework, let's say  reasonable to provide insight or clarify an ambiguous direction or to give additional examples. However, isn't it one thing to say, "Well, Jimmy, where do you think the verb in this sentence is?" and another thing altogether to have to teach the parts of speech because your child's school decides that's not a skill they need? 
A few years ago when I substitute taught, the kids in the middle school math class couldn't do basic operations (6x7) without calculators. Scary.

I used to teach accounting at a technical college and I was horrified at the vast number of students who could not calculate percentages at all, could not add two 2digit numbers without whipping out a calculator, didn't know what a numerator/denominator was, etc.

Ugh.. Please do your daughter a favor and teach her multiplication tables... As a 6th grade math teacher, I can't tell you how frustrating it is to have kids spending time counting by 6 to get to 42 :
I took classroom time to do it in middle school, and I personally think it is a ridiculous thing to have to do. They should have learned it in 3rd grade, right after they learned what multiplication means and how it works. This should not be happening! 
another teacher here
Please make her learn them! The argument for not teaching them at my school is that we have so much content to teach that we shouldn't "waste time" on memorization. They ask parents to work on them at home. All future math builds on this! Argh. Pet peeve, can you tell? 
I have never ever been able to memorize my multiplication tables. Oh sure I MIGHT have been able to manage it for a test.. then it just fell out of my head later. I can't spell either. Same thing.

No kidding! Isn't one of the virtues of school supposed to be that they teach children the fundamental bases of the knowledge they will use? Isn't the role of the parent supposed to be to reinforce those knowledge bases, provide support and time in which homework can be done, work as a partner with their child's teacher, et cetera, but not have to be compelled to fill in a crucial gap the school is not addressing?
SO not fair. 
Well, whatever. I figure a teacher's competitive advantage is going to be in teaching concepts and getting a kid to really understand how, as in this example, math WORKS. If you'd rather they skimp on concepts in favor of spending time on rote memorization, so that you can get out of any teaching function at home ... I guess that's OK for you. But don't complain when your kid ends up not really understanding the concepts behind the basic facts he or she has memorized.
School time is finite. So is parent time  but it's a lot easier to coach a kid through a bit of rote memorization than it is to get them to learn the concepts underpinning arithmatic (and higher level maths as well, of course). 
If you'd rather they skimp on concepts in favor of spending time on rote memorization, so that you can get out of any teaching function at home ... I guess that's OK for you.

School time is finite. So is parent time  but it's a lot easier to coach a kid through a bit of rote memorization than it is to get them to learn the concepts underpinning arithmatic (and higher level maths as well, of course). 
Part of the problem is that far too many math teachers, especially at the elementary level, do NOT understand "how math works" and therefore aren't particularly adept at teaching what they don't particularly understand.
Since many of them also now do not teach rote memorization, we now have far too many students who don't know either how math works or their multiplication tables. 
I have never ever been able to memorize my multiplication tables. Oh sure I MIGHT have been able to manage it for a test.. then it just fell out of my head later. I can't spell either. Same thing.

I hope you are not suggesting that just because you struggle with spelling we should stop teaching kids how to write well, and to spell correctly?
Same goes for math... I respect people who struggle, but I don't understand the argument "I wasn't able to, so who cares if the rest of the kids are taught math facts..." 

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