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, I plan to teach it to my kids. My dd is almost 8, and we haven't done any mandatory memorization. She likes to memorize, though, and does it without really having to try. She's discovered acting, which is promoting an interest in memorizing. She learned Jabberwocky the other day...it's awfully cute to hear her recite it, except that she'll do it for anybody whether they want to hear it or not. This to say, if it's fun then go for it. 
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We are unschoolers, but I do see value in memorization. I think that there are bound to be times in a person's life when memorization of a large quantity of information is necessary (passing the written component of a drivers' test, memorizing product codes for a parttime job as a supermarket cashier, learning everyone's name at a meeting, eg.) and I think that by having had experience in the past, a child will better understand the strategies that suit him or her best.

If I had just memorized the dang times tables, math would have been a whole lot easier for me. The ability to think conceptually and problem solve was never an issue for me, but I kept getting hung up on the stupid basic stuff because I didn't have it at the ready in my mind. Yes, there is definitely a reason to memorize *some* things.

Single mom to Rain (1/93) , grad student, and world traveler
Saamy Student mama to and and
The algebra teachers at my school struggle daily to help students who don't know the multiplication tables learn how to factor so they can do quadratic equations. Calculators do not factor for you. I'm a fan of knowing the multiplication tables.

Single mom to Rain (1/93) , grad student, and world traveler
I've found the opposite... the higher you go in math, the less useful arithmetic skills are, and the more critical it is to be able to think logically. I regularly tutor high school kids in Calc II and Stats who don't know their multiplication facts from memory, but they all have calculators so it's never an issue...
dar 
Algebra is still pretty basic stuff... and there are some simple little programs that kids can download to their calculators that will solve quadratics for them... or you can use a chart... but really, solving quadratics is something computers do easily and human have to work at  it's computation, not thinking.

Mom to 10yo Autistic Wonder Boy and 6yo Inquisitive Fireball Girl . December birthdays.
Single mom to Rain (1/93) , grad student, and world traveler
It is unlikely you are ever going to GET to higher math without the basics being so ingrained you don't even have to think about them. That process starts with memorizing addition and multiplication tables.
It is along the same lines as people thinking that they don't have to know the material as well for an open book test. Most of the time, if a prof offers to let you have the book open, the test is going to assume you know the book already. Those people who understand the book (have it "memorized") are the only ones who are going to do well on the test because it assumes the base knowledge and is asking you to think. If you are still having to figure out the basics to even understand the question, you are not going to be able to finish the test in time. 
My husband (biomechatronics, Ph.D. in Physics) would strongly disagree. So would I, though he uses higher math everyday, hence my including him and his qualifications.
The higher you go in math, the MORE useful both arithmetic AND logical thinking are. One does not cancel out the other. You need both. Not knowing your basics prevents you from logically contemplating/exploring the mathematical topic at hand. (Calc and Stats are considered an extension of basic math, by the way...higher math includes linear algebra, complexity of vector spaces, mathematical biology, etc...that was considered the case at both my Ivy grad school and my very unIvy undergrad institution). 
Dar, so you're agreeing that memorization IS important. What you're describing is a different (longer) way of getting there. 
Single mom to Rain (1/93) , grad student, and world traveler

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