Recently I was looking through a second or third grade math text and was pretty amazed to find that it contained about four months worth of calculator lessons. Well, they called it something cooler than that but it was basically lessons on how to operate a calculator.” So really, how many seven-year-olds need four months worth of lessons on how to operate a calculator? I teach several math games classes, so I thought I ?d do my own very informal test.
In my six- to eight-year-old class of 14 students, nearly all of the kids already knew how to operate a calculator. And I ?m pretty certain they didn ?t have four months of calculator lessons (they ?re homeschooled and probably wouldn ?t be using one of those textbooks.) The few kids who did not, learned with one minute of instruction, and two minutes of practice.
More disturbing than the fact that the textbook publisher felt the need for calculator lessons is the national trend this signifies. Why in the world would our children even need to be using a calculator when they almost certainly do not have their math facts memorized? This New New Math ? (yes, that ?s really what they call it, and nope, the old New Math didn't work either) says it ?s just fine for kids to depend on a calculator and not have the math facts memorized as long as they understand how they got the answer. Memorizing math facts got a bad rap initially, as many kids were learning the math facts by rote. ? In other words, they could memorize the numbers, but had no idea what it meant. Ideally, why not learn both?
And we wonder why America is falling behind in math test scores. This dependence on calculators is rather silly, when you consider several things:
- No one always has a calculator on them when they need it.
- If you memorize the facts, you ?ll be much faster than the calculator.
- Upper level math is a heck of a lot more difficult if you don ?t know your math facts. And using a calculator will slow you down.
- A calculator will only give you the answer to the problem you typed in. If you don ?t know your math facts, how will you know if the answer is right if you don ?t estimate it? I guess you could type it in a few times to make sure… (which of course takes more time.)
Children shouldn ?t be allowed to have a calculator for their math homework until sixth or seventh grade, upper level math like algebra and beyond, or until they can go three ?four times faster than the calculator (the calculations can be done almost instantaneously in your head with practice.) I don ?t care if they play with calculators, or write funny upside down messages (like 0.1134). And granted there have been a few math pages where it really was warranted to use a calculator (as it would ?ve taken them 56 hours to complete if doing by hand). But it ?s the dependency on the calculator that we need to watch out for. If the use of a calculator is allowed too much or even promoted too early, the kids will want to take what they see as the easy way out. ? As educational consultant Aimee Yermish said,
My private practice is full of kids whose parents thought that way (…why bother memorizing facts?), and now have to pay me lots of money to teach the kids what they could have been taught for free in second or third grade. They usually hit the wall some time in middle school or in algebra I, where you have to use these math facts rapidly on the fly.
Read the complete article Why Memorize Math Facts? ?
If your child is being allowed to use a calculator early on, you might want to talk to the teacher. The teacher may not be able to do anything about it as they might have to follow a certain program. If talking to the teacher doesn't help, you can always ban the calculator at home for math homework and work with your kids to improve speed. There are lots of great games to play with your child that are fun and really do help memorize those math facts (which, by the way, you should memorize up to 12×12 since we happen to still use an English measurement system and 12's abound in that.) And if you don't have your math facts down, no time like the present!
Just another thing to get worked up about, if the state of our nation isn ?t enough for you.
Great article! I completly agree that kids in 3rd and 4th grade shouldn’t be using calculators. But some kids will never pick up math, no matter how many tricks you try to teach them. I know, because I was one of them (still am!). I dreamed of the day I would be able to use a calculator (8th grade Algebra, taught the last two or thee months of the school year). I would hide my hands under my desk to count, because I couldn’t do math in my head. I still can’t. I try all the time, and when I am able to add something in my head, I am quite proud of myself, but it takes a long time, because my brain just doesn’t work that way. As a result of that, I am a huge proponent (spelling?) of really hitting the basics hard, and repeatedly throughout elementary and middle school/junior high. But teachers should be on the lookout for students that are trying, but really struggling, so they can help more, or help the parents set up a tutor or something. I only had a couple of understanding teachers when I was young, so by the time I got to 5th grade, I had given up trying to understand math at all. It was taught way to fast for me to keep up! Anyway, I guess my point is to be patient with the kids out there, and remember, not everybody “gets” math. Remember to praise every little accomplishment for them, it makes a huge difference!
Wow– that surprises me, too! I didn’t realize they were using calculators so young!
If memory regarding my son serves me correctly– they don’t start whipping out calculators here until 5th grade.
Gee- maybe it’s 6th. My daughter’s half way through 5th and she hasn’t used a calculator yet. ( I don’t mean ever– I mean in relation to math lessons)
It sounds similar to the problem with kids using computers as well, Molly. I remember reading an article a couple years back– I think it was on the news too– that kids’ spelling skills and penmenship had taken quite a dive, attributed to the use of computers and “spell check”. The kids weren’t paying attention to their spelling. There wasn’t even really an effort to spell correctly for many, because all they had to do was hit “spell check”, and in some cases, their programs automatically fixed spelling errors even WITHOUT the need to hit “spell check”.
And obviously, there isn’t a need for “penmenship” if your typing everything on a computer.
Yikes, it just dawned on me– this generation doesn’t even to write and pass “notes” in school, they just text each other!
Good article– I enjoyed it.
As a school teacher, I can say that there is much to be gained by “rote” learning as you called it. There has never been anything wrong with sitting down and memorizing something. I think there are just some things, like math facts, that need to be commited to memory. I remember my Grandma sitting down with me when I was about 9 years old and drilling me on my multiplication tables. I’m very thankful for that, because I was part of the first wave of “new math” students back in the 1970s, and my poor little brain didn’t get it, but it got memorization. And you are right, you never have a calculator when you really need one!
I wonder if I will be booed and hissed for this? I’m a big chalk and chalkboard fan. One of the things I know about the old people I hang out with is that they are well-educated in the basics. They can read. They can spell. They can write, and their penmanship is, just about without exception, legible and beautiful–because they PRACTICED. They know their math facts, and they can do essential, everyday math in their heads. We’ve sunk a lot of money into computers, and education about computers, and reams and reams and reams of paper–at what expense? If we were spending all that money, and our children were BETTER educated than our forebears, it would be progress. But it isn’t. We’re spending all that money, and we’re regressing.
The local principal would like to kick my pockets when I mention this, (and the superintendent of the school district agrees with me. ?????) One of those cases in which we call a spade a spade. A computer has its benefits, and I especially love that we can be connected to the world through it, but I think it is detrimental to use it to teach basic education.
I was involved in a revolutionary individualized math program when I was in elementary school. Educators from all over the world came to stare at us while we did our work. We were allowed to go at our own pace, and we learned from math packets instead of teachers. If we could pass the multiple-choice test with a 69%, we could move on to the next packet. I was not a great math genius, but I WAS a very lucky guesser, and I consistently moved up because I guessed well. I didn’t learn basic math until I made it to the eighth grade, at which time I had an old man for a teacher. He taught with a chalkboard and a piece of chalk. We played math baseball, and we literally moved around a diamond in the classroom by answering questions correctly. We loved it. He was such a smart old man, and I was so grateful to him. Math is still not my forte, but I learned it because of him.
Don’t even get me started on spelling. My children are allowed to do “creative writing” in their elementary school–and the only thing creative about it is the way they spell! The teacher doesn’t mark misspelled words wrong, because she doesn’t want to “inhibit creativity.” Here is a TEACHER standing at the front of the classroom saying, “Don’t worry about it; spell it like it sounds.” This was only supposed to pertain to creative writing, but what MY children remembered through the years was, “Spell it like it sounds.” They don’t cover spelling in their classrooms; my nine year-old does a word-sorting exercise for her spelling assignment each evening, and it has nothing to do with spelling. They aren’t tested on spelling for the state tests, so teachers feel they can’t spend time to address it, because there are so many other things the kids ARE tested on.
I have to giggle. The teachers send home notes filled with spelling errors. This is consistent. Are they typing too quickly to be accurate? Or possibly, do they not know and not care how to spell well? Seems like the height of hypocrisy to me. I feel like taking a red pencil to the notes they send home and sending them back corrected, just for consideration. (I know, be nice, Davidson.)
Are we modern-day Mulekites? Are we in danger of losing our language because we won’t do the work required to preserve it? Do you suppose we’ll be packing our laptops when we WALK back to Jackson County, Missouri? Possibly plug them into a currant bush to recharge them when the need arises?
Some might tell me that I could solve all this by homeschooling my kids. That is a viable alternative–
but if we are sinking our money into public schools, can’t we at least expect to get a basic education in return?
(Spray-painting “sopebox” on the side before I put it away.)
Sure, you can expect it, davidson. 🙂 The question is whether you are going to get it and I suspect the answer is: You’re not.
davidson, I get notes from my kids’ teachers with spelling and grammar errors all the time. I’ve often wanted to do the same thing… send it back “corrected”. 😉
Me, too! Red pencil corrections on the typos, with the desire to send them back. It drives me nuts! I know teachers are busy, but I wish everyone (including the PTC newsletter writer) would just take a few minutes to check their spelling and grammar.
But of course, I’m a crazy “triple check” everything kind of lady, so I usually catch any of my mistakes… (Now watch, the next thing I send out will have typos in it!)
The pendulum swings to the extremes constantly in education. “Throwing the baby out with the bath water” fits perfectly. I was in educational publishing sales for nearly ten years, and that was SO frustrating – to see schools change curricula and intervention programs almost yearly, without ANY real analysis of what worked and what didn’t.
Don’t get me started, or I will type a comment three times as long as davidson’s.
Thank you, Molly!
Shall I get out my giant soapbox now? :devil: I completely disagree. I can’t think of any advantage to rote memorization when compared to actually learning how an operation works. Rote is “the mechanical or habitual repetition of something” (also defined as “mechanically, automatically, unthinkingly, mindlessly; from memory). And the truth is, millions of kids learn to spout of their “math fact” when they have NO IDEA how to reach the correct answer.
Let me give you one example. In school, I was taught to divide fractions thusly:
The quintessential vote for rote. “Just do it, don’t ask me WHY!”
Now, for the shocker. I don’t drill my kids in math. And here’s the other shocker. They all score in the 99th percentile in math. Here’s the key: they know what they are DOING and they learn the so-called “facts” by USING the numbers, not by MEMORIZING the answers.
Full disclosure, when they get to about algebra level, if they have any speed issues at all with any so-called “facts” we do “bunny math” for about 30 minutes total. That could reasonably be called a “math drill.”
What, exactly, ARE the “math facts” and who decided?
Eden, this isn’t a slam on YOU, because I don’t know you well enough to make any claims about YOU. OK? But statistically, school teachers are almost the worst math students in colleges. The majority (according to research)choose education as a major IN ORDER TO AVOID UPPER MATH.
The problem with “new math” wasn’t primarily the “new math.” It was that we didn’t have new teachers who “get” math to teach it. You have people who don’t like math and don’t USE math, trying to teach real, practical, usable math to students. It just doesn’t work. So, truthfully, unless we change THAT, the only thing that can “work” in schools it to let the teachers teach at a level they understand. Memorize the “facts” and don’t ask why. FWIW, many years ago I did a little poll of schoolteachers about dividing fractions. Not one could tell me what the process does or why the algorithm works.
My sister’s math thesis was titled, “Scientists, schoolteachers, and the two cultures of mathematics.” When typesetting that about 18 years ago, I first became interested in pre-college math education and began researching more. Her research–and all her resources and all I researched later–discussed how scientists and others who USE math view it (as a tool to solve problems) whereas teachers see it as a bunch of rules and formulas and tricks to use to manipulate numbers. Plug and chug. Stick the right number into the right algorithm and the right answer magically pops out.
This mentality it seen often as kids struggle to apply math principles to REAL problems when they are not given the problem in a setup that obviously indicates the use of a particular algorithm to solve it.
This discussion has compelled me to (finally) repost this article from the old site to the new. It was first published in Super Learning Tools and later in Home Education Magazine and now it’s posted on many different sites on the web, but here you go anyway. My thoughts on math education.
Thanks again, Molly!
“Ours is not to question why, just invert and multiply.” HA! It would be fun to meet your dad, Alison. And your sister. And you.
By the way, I’m very careful to not point out to my children that I struggled with math. My dad was a real trouble-maker in school and proud of it. He likes to tell my children stories about his glory days. My husband often tells my children how he never took books home; he always did his homework at school. Guess what? This week I got to go to my son’s school and hear how he is the class clown, and how he is working beneath his potential because he will never finish and turn in homework assignments, or rarely. His state tests reveal that he is an “advanced” student, as far as smarts go, but he thinks he is smart enough to beat the system. I think we have to be careful what we say to kids who are too immature to reason about cause and effect.
Oh, Michelle! You are so right! I just realized that when you and I were talking about having a cemetary party, I spelled cemetery wrong! So much for being the Great Spelling Whiz! Just goes to show that when you point a finger at someone else, you point three others back at yourself. (I’m guilty of the mote and beam situation.)
:shamed: :shamed: :shamed: :shamed: :shamed: :shamed: :shamed:
Just wanted to let you no you’ve ben speling things rong.
:rolling: :rolling: :rolling: :rolling: :rolling:
HA! I kill myself. (Probably more often than I want to know.)
Thanks for being patient with me.
Actually, I was thinking about the “calculator issue” the other day. I generally agree with Molly on this, and can’t imagine anyone needing “calculator lessons” let alone 4 months of them, but I do wonder two things:
(1) If we’re advocating rote memorization (which I’m, obviously, not), then can’t using calculators be a reaonable method for encouraging memorization along with flash cards, computer games, speed drills, etc.?
(2) How much does this relates to other things that are occurring with advances in technology, etc.? For example, lots of us simply no longer know how to spin wool or harvest wheat, because we just buy them at the store. The idea that “we won’t always have a calculator” applies here, too. We won’t always have a Walmart close by when we need something. Aren’t we missing basic survival skills?
My kids do learn their “math facts” by using the numbers, but I’m not entirely convinced that they’d be incapacitated if they didn’t. Resources are limited. Do we spend the time drilling math facts or learning Python? I don’t know, but there is an opportunity cost for everything we do and I’m not really convinced that memorizing “match facts” is now (or always will be) the best use of time, given all the other things to do.
Handwriting is another example and even, gasp, spelling. I can’t recall the last time I sent a hand-written letter so, actually, I”m glad I did NOT spend as many hours as my parents did in penmanship. (And now I’m more likely to become a doctor…) And even though I used to be a champion speller, I can’t spell worth a hill of beans anymore. I don’t have to because spell check is there to save me…to my brain made room for other stuff.
On a side note, my oldest started coding web pages when she was nine. When she was in 9th grade (the traditional age to learn touch typing) it was too late. She had already established her typing mode and I could not get her to learn the “right” way. She has a really funny way of typing and never uses her little fingers or her ring fingers. And she types well over 120 words per minute.
I’m just waiting for the Dvorack keyboards to start gaining in popularity…
So we’re saying that math is valuable and spelling isn’t, Alison? :bigsmile: :bigsmile: :bigsmile: I’ll see YOU at recess!
Things like multiplication tables, and knowing how to add, subtract and multiply in your head. I don’t know who decided these were the facts, but when an 11th grader can’t do a simple sum, like 8 + 7 = 15 in their head, that’s a problem.
I don’t take what you said as a slam, but teaching in a real school, with kids whose parents don’t care to mentor them, as you do with your children, it comes down to memorizing things sometimes. I still stand by my opnion, there are some things you should just know, even if you have to memorize them.
As for penmanship and spelling….I love spell check and the computer, but with the ever increasing use of the keyboard and text messaging, penmanship and spelling are becoming a lost art, and there are still many kids who do not have access to computers, so they have to turn their work in hand written. I also can’t remember the time I acutually hand wrote anything, but it is important to know how to write, and to be able to read what you write. Again, I will use the 11th grader as an example…most kids in rural N-NM, do not know how to spell because they’ve never been taught the basics, and think turning in a paper that is written in text speach is ok. Not so much in my classroom, consequently the time spent re-teaching basic skills, is/was a huge time waster.
In the end, I’m not saying discount technology, but it does not hurt anyone to know how to do things the old fashioned way…that way then the school does change the cirriculum mid-stream, at least there is a foundation upon which to fall.
Alison’s comment about the math abilities of most elementary school teachers is spot-on and the real, core issue.
The VAST majority of elementary school teachers in our country are “language arts” people persons – NOT “mathematics” number people. They are more social workers than accountants. Therefore, our school face two specific problems in regard to math instruction:
1) Most of the teachers subconsciously don’t like the topic, and underlying attitudes manifest themselves in the way teachers teach. Think about it: I’ll bet most of your favorite teachers were passionate about the topic(s) they were teaching. If a teacher is ambivalent, the students pick up on it and more likely to be ambivalent.
2) Most of the teachers don’t “get” math intuitively, so they don’t “know” math deeply. They can teach how to memorize facts, but they have a hard time explaining the foundation concepts. Therefore, they tend to focus either on rote memorization OR on letting the textbook be the default teacher. Neither is a good model.
An example, and I don’t mean this to be condescending in any way: How many here can explain the concept behind the Pythagorian Theory – not the calculation used, but the reasoning behind the calculation – what the calculation means. How many here can draw a visual representation of it, so that visual learners can “get” it? It’s really quite simple once you see what it meant originally, but it can be brutal if you simply have to try to remember which formula applies to which theory.
Submitted too early:
Good instructional technology can bring math to life for kids who need to visualize something in order to get it. That, frankly, is priceless, but there are exceptional programs that don’t cost much for a school. Some of the visualization that technology can produce is phenomenal.
Well Ray, I can’t even give you the calculation of the Pythagorian Theory. For that matter, I can’t spell it either! 🙂
I do vaguely remember it. I took up through college pre-calculus, but freely admit I studied to the test and passed (never lower than a B- overall grade, either). I remember none of it now. But I do get by. I do know my addition and multiplication at least, and that’s been enough to shop and balance my checkbook.
I’m not saying I advocate being stupid like me. I really do hope my kids do a better job than I did – but unfortunately they won’t get their math brilliance from me.
agardner, I’m not sure if you are a visual learner or not, but what you describe is classic – someone who made it through the classes by memorizing what needed to be memorized. Obviously, if there was no mental “picture” to back up or explain the formula, that formula will be lost when not used.
Math is a language in a very real way, and when you don’t practice a language (especially one about which you weren’t excited in the first place) you lose it. I guarantee if I could draw you a picture of the Pythagorean Theory (spelled it wrong the first time and didn’t edit well enough) and show you how it was devised, you’d never forget it – no matter how “naturally” you understand or don’t understand math.
I think that’s the main point – that unless we understand something (what it means and how it works), we will never be able to master it and keep it active in our memory.
a^2 + b^2 = c^2 right? Then again, I have only been out of high school for almost 6 years, if that is right.
Enough with the darn languages, for pete’s sakes! hasn’t there been enough tears and anger over language barriers already? Now Math is a language that I need to be fluent in? Will the insanity ever end. Sob! Sniffle! (I warn you, I am NOT a cute crier):fierce:LOL
No, I’m saying memorization of “math facts” and spelling have become LESS crucial due to advancing technology.
My point was that while many insist that kids should memorize the “math facts,” most can’t articulate exactly what that means–except that it’s whatever they were forced to memorize as a child.
Ours is not to question why…
I question everything. 🙂
I agree, except that I don’t think it takes parents to mentor. If teachers knew how to do it, they could do it just as well. How do I know? Well, for one thing, the course I use with my elementary kids was created in a school for kids in a school.
But you only “just have to memorize them” if you don’t use them enough to learn them. Did you site down and do a drill to learn the way to your house? Or did you just GO to your house enough to get used to how to get there? My position is, that schools do it backwards. They drill and teach algorithms when they should be spending their time USING the numbers. Then there is almost no drill to do AND the algorithm is generally a snap because–particularly in arithmetic–it makes perfect SENSE. It isn’t a bunch of memorized gobbledy-gook. (Ok, there’re not enough to take away so I carry…no, I borrow, from….there, now I add the one–or do I multiply?–and I cross out the 8, where did the zero come from???) It’s a clear manipulation.
One of the funny things to me is that most people who think rote memorization in math is good, support PHONICS for reading. And most people who are into “new math” methods, promote WHOLE LANGUAGE (which is lots of memorizing shapes and words). It seems so inconsistent to me. I like “guided discover” for the many of the same reasons I like phonics.
Yea, but so? There are lost arts and then there are found arts to replace them. I’ve lost the art of cow milking and replaced it with a web-based business and buying milk in a carton. Don’t know why the “old way” is really preferable.
Sure, there are some kids who still don’t have computers. But just as the transition from cow to carton, that movement will likely continue. Some skills become less and less crucial and others more and more crucial.
FWIW, I don’t think reading is inherently valuable either. Wanna debate that one? :devil:
You kind of lost me on the teaching/reteaching thing. If they didn’t know, they aren’t being retaught, are they?
Actually, I think it does. It’s called opportunity cost and I think it’s an incredibly valid consideration. Probably THE SINGLE biggest reason my oldest is so successful now, at 20, is that she did NOT have to spend time doing stuff that would not serve her in the future JUST BECAUSE someone had it on their scope and sequence. Instead of spending 7 hours a day, 180 days per year (plus homework at night) doing what the school board said, she spent about 3 hours a day, about 150 days per year (spread out in between our vacations and holidays), and spent the other 810+++ hours doing things that she was passionate about. The big ones were: horses (English only, particularly jumping), dogs, ancient Greece, reading classics, and web design and other computer stuff.
As I mentioned earlier, one great example is that rather than taking a CLASS in typing, she just typed while DOING stuff she wanted to do. And she types about twice as fast as any of her coworkers (all computer geeks).
Ray, I can’t draw it on the computer very well, but I think I know the exact picture you’re referring to. My oldest three have all seen it. Easy as pie and NOT the way I was taught. (I was just told, “Here it is. It works. Trust me.”)
Let me see if I can find one. Everything is on the web.
Look at this page. It’s great. One of my kids and I just worked with the Chou Pei Suan Ching earlier this week. Love that. How clever. Scroll down to the animation.
Also, look at this page. We’ve messed with Proof #9 before, which is good, IMO, because you can really see that the two smaller squares really DO combine to make the larger. (That’s hard to tell visually.)
Well, I just get way too excited about this…
That’s the basic picture, Alison. Now imagine each square with liquid in it and an animated image showing how, when you pour the liquid from the squares on sides (a) and (b) into the square on the hypotenuse (c), the amount of liquid from combining the two squares perfectly fills up the other square. Hence, a^2 + b^2 = c^2. When you see it, it makes perfect sense – and you never forget it.
The opportunity to animate our instruction and appeal to multiple learning modalities simultaneously is astounding. Unfortunately, the (elementary) school classroom, especially, is the last bastion of anti-technology sentiment in our world – and I mean that sincerely. VERY little of the technology in our schools actually is instructional in nature. In far too many classes, the primary mode of instruction still is either lecture or reading from a textbook. Our kids might as well live in the 1800’s in many, many classrooms.
Sorry, I forgot to add the second link. It’s up there now.
Ray the problem I see with the liquid animation, is that you can’t tell if it really works. Pouring fake liquid into another shape doesn’t prove that it will actually fill the other space. Does that make sense You just have to believe the animator is actually good at geometry. 🙂
That’s why I like the real proofs. Some of them are pretty simple to understand.
Oh, the other thing that helps is when people understand that squaring numbers is like making a line of said length into a SQUARE with sides the same length. And the same with cubing. It’s very visual. Of course when you get to higher powers (as in exponents, not as in deity! :shocked:), it’s harder to visual the same way, but in my experience, by that time they “get it” anyway. No need to tap into the fourth dimension.
And you’re the one hocking books ? haha
I think we will have to agree to disagree Alison. I admire your progressive approach to edcuation, and you should consider yourself very blessed for the rescources and time you have to spend. However, here on the ground in rural Northern New Mexico — the real world, we don’t have these same advantages, so we do with what we have. I’m a big believer in the basics, and basic skills…and for what it’s worth, I loved Phonics, and I hope to get my fututre kids hooked on it!
You want to try to tell me why being able to read is valuable? I’m guessing you can’t do it outside of this very limited context:
Reading is only important because so much of our information is based in text.
If it were all audio, would you need to learn to read? Of course not.
Before you say that’s an inane point, it goes along with all those things we are talking about. A huge percentage of the things we learn in school are ONLY important in the context of our particular time and culture. (Did the pioneers need to know how to type? Would it have been a productive use of time to learn it?) Given that fact, as the culture changes we DO need to change what we teach. And we’ll only do that if we actually look at what we teach regularly and evaluate its usefulness.
While I do feel blessed, I feel that minimizes what is really happening. I’m not homeschooling and teaching my kids because I have nothing else to do and nothing else to spend money on. When we began homeschooling we were barely out of college with very little to get by on. The way I teach my kids math isn’t expensive nor is it exclusive. In fact, the materials are likely a fraction of what is spent annually on every public school kid. And I chose to spend my time to teach them at the same cost most people pay for that choice.
But given that kids in school are already given the resources and time to learn math, what precludes us from doing a better job of it?
What “advantages” are those other than a teacher (me) who’s willing to look for something better? Disadvantaged kids aren’t stupid and they can (and do) learn the same stuff with ease. I guess I see that like the NEA arguments against vouchers. The truth is, there are incredibly disadvantaged kids all over the country who are excelling in schools while spending markedly less than public schools. It’s not a resource problem.
As cultures change, “the basics” also change. Still, I’d say rote memorization in math was never a “basic skill” to begin with.
Like I said, that’s odd.
Rather than whole language, that requires “rote memorization” of shapes and words, you like a program that teaches a system. Phonics teaches WHY a word sounds like it does and how different letters work together to create new sounds. You allow kids to practice sounding out words and reading in context and then, if they get it wrong, you guide them back to the principle that is at work, phonetically, in a particular word.
Why not use the same approach with MATH??? Or maybe a better question is, why have two such markedly different teaching philosophies for two different subjects?
My favorite education quote: “We must educate our children for THEIR future, not for OUR past.”
I wish more school systems did that.
Love that, Ray.
I am going to bump this one up. Alison, I have a queestion about your phrase “using the numbers” (rather than just memorizing rote algorithms) I wonder if you could give me some examples. My 6th grader is needing some supplementing. I feel like in school they are not thoroughly and adequately teaching fractions (adding, dividing multiplying etc.) I correct their tests, and most of them are struggling. I think they are not familiar enough with what the answers mean, or why they are even doing various steps……anyway, I don’t consider myself a math person AT ALL…..but I have become pretty good lately at researching everything I can on the internet to help supplement and teach my daughter some of these basic math concepts that don’t seem to be cemented at school……Thoughts????
Fractions are a great example, Lisa. They really aren’t that hard, but FOCUSING on learning the algorithms–before learning what is going on–makes them utterly baffling IMO.
I love to use food for fractions. A six-year-old who seems stumped by fractions, is NEVER confused when fairly dividing up cookies. I kid you not. Change it to cookies or M&M or popcorn or anything (especially right before lunch :wink:) and the lightbulb flashes right on.
You can really just do lots of stuff messing around with fractions. Cooking, carpentry, sewing, construction.
If you’re looking for some kind of workbook, I really love the book Everything’s Coming Up Fractions. It uses a common manipulative called Cuisenaire rods, proportionally sized, colored, plastic blocks.
Hmmm… Won day wee may knot knead two no how too spell because of spell check, but I steel think kids kneed two no how too spell.
I’m a big advocate of playing with numbers to figure out how they work, but ALSO of memorizing the facts (yeah yeah alison, there are a standard set of facts that really are quite useful to know – addition facts to 10, and multiplication to 12.) The problem is that so many schools doing this “new new math” ONLY play with the numbers. They play with the numbers so much that they sometimes don’t ever even GET the understanding part, let alone memorizing the facts. There just comes a point where you’ve got to memorize simply to become efficient.
I am fast on all my math facts. And I use that knowledge ALL the time. I don’t think that many people even realize how handy it is until you have them all memorized! Yes, we have technological advances, but really – you never have a calculator when you need one, and even if you do, you’ve got to be able to estimate the approximate answer or it’s so easy to get the wrong on on the calculator! I know it’s harder for some people than others, but I know you can still learn it. It might just take you longer, or using a different method. Lots of kids got “left behind” in math because it’s such an individual thing and cumulative, and if you don’t mesh with the teacher or the teaching style and you miss out, it does make you way behind. But you can still learn it. Even if you’re not as smart as Alison’s kids.
Alison’s kids may be more intelligent than mine, because mine do need extra practice to get fast/efficient with their math facts. I have a nearly 14 year old who has an excellent mathematical mind but who just has not been very efficient with his math facts. He’d much rather be thinking about upper-level math problems that fiddling around memorizing stupid math facts. 30 minutes of bunny math definitely won’t get him “up to speed.” So we play games. Lots of games – board games or games specifically for math facts practice. And he has gotten faster. Once he’d moved to upper level math he realized that it would be nice to know his math facts, so he was more open learning them. I’ve put a bunch of cheap fun easy math games on my website at http://www.inspiremath.com (which unfortunately doesn’t work right now, but I am working on fixing it!)
I also agree that spelling is important! This same son hates spelling too (he’d rather be writing a novel.) But we still work on spelling, and because we homeschool, he can’t graduate till he can spell. Too bad the public schools can’t do that, ha! 🙂 Same with penmanship (this kid hates that too! He’s too much of a deep thinker to worry about those things, lol.) The great thing is that the older he gets, the more he realizes that not knowing these things really does hold him back, and he’s much more interested in learning them.
Fwiw, Yahtzee is great.
Honestly, I think the verbiage here is skewed. Using numbers a lot isn’t synonymous with “playing” of “fiddling.”
As I said, I don’t have a problem with having math facts memorized. I just have rarely needed much rote drill to do it. I’d rather spend my time elsewhere about 99% of the time.
Yes, I agree. We’ve discussed this for years, yes? My point in bringing it up is that in the past 16 years I’ve been looking at this issue, upwards of 95% of the people who demand memorization of “math facts” can’t even tell you what that means. That’s telling, IMO.
Not having analyzed any “new, new math” curriculum, I won’t speak to it directly. But in my experience often the complaints about math programs have much less to do with the actual program and a lot to do with the administration of the program. And until we have teachers who generally understand math, that’s not going to change.
In the context of this discussion, I think that implies: “There just comes a point where you’ve got to use rote drill to memorize…” And so I want to be clear that most of the time you really don’t need to do drill work much at all. And when I say not much, I’d say the MOST any of my kids has spent is…hmmm…I’m guessing two to three hours total in all of their schooling.
My point about technology wasn’t to make a case about NOT knowing math facts. It was more to bring up the idea that the value of particular skills DOES evolve. I don’t think I made any conclusive statements about any particular thing, just brought up some stuff to think about. What about handwriting, what about computers, what about…?
Just like the undefined set of “math facts” I think very often we simply impose certain standards that are familiar to us, without even stopping to think WHY we’re doing it and whether it even makes sense. The whole first habit in my book is really about that: getting people to think through why they do what they do.
Ever notice that most elementary school scope and sequence lists include an entire unit study on modes of transportation? Yeesh!
Actually I have a calculator with me about 99.7% of the time. It’s on my phone/PDA, which contains my entire brain. Which is kind of what I’m talking about. Will this kind of thing increase or decrease as time goes on?
OK, can we stop the cracks about my genius children? You know as well as I do that my kids are all very different. It’s not about IQ at all and I’d really like to present the idea that using numbers really can create the necessary repetition to learn the “math facts.”
Is it the QUICKEST way to learn them? Not by a long shot. So IMO the real consideration should be something along the lines of: how do you want to spend your time? If you find the drill works, it may well be that it allows you to move on to something else while we’re still “playing” with numbers. I PREFER to spend enough time using the math to get the “facts” ingrained and know it’s possible. But other models have advantages and disadvantages.
Still, I’ll always disagree with memorizing an algorithm before it’s understood, at least in arithmetic and quite a big beyond that.
One of the things I like about Harold Jacobs is that he’s big into going through proofs. He shows all sorts of ways that explain why the algorithms work. Kind of like the Pythagorean theorem we were discussing. When I learned it, I was given the formula and told to use it. Period. That’s so much more confusing than learning how it works. It’s easier to remember, when you know WHY it works.
Sorry I wasn’t clear about my point on this. I wasn’t trying to declare spelling unimportant. We actually do work on spelling. Not the way I learned it in school (here is a list of words to memorize for the test), but we do work on it. My point was to get you all to CONSIDER how things changes. In some box at my dad’s house are drawers of spelling awards, ribbons, etc. Sincerely, I can’t spell anymore. It’s ridiculous. But I’ve become dependent on the computer and haven’t HAD to spell for years.
That’s what I’m talking about. Will it REALLY hold him back? I don’t know. And I think it’s good to consider the idea that is might not.
I used to be able to spell. Now the only time it “holds me back” is if I’m teaching in church and want to right on the chalk board and can’t think of how to spell the stupid word. (I’m hoping for chalkboard spell check technology soon). Then I have to think of a reasonable synonym I can spell. (Which is, in itself, a great critical thinking activity that I’d miss if I could still spell!)
So, does it hold me back? Maybe. But lets see. The alternative would, seriously, probably have been for me to KEEP up my spelling skills instead of…hmmm…instead of learning to code websites? instead of reading a bunch of books? instead of… What is the cost for that knowledge?
Just something to consider.
Actually I wasn’t trying to disagree with you, you know we pretty much agree on this!
Playing with numbers, yeah probably poor word choice. I should’ve said using numbers. Still, even though my son uses numbers a lot (he LOVES to use numbers!), he still isn’t efficient. And just saying memorize them, it’s not advocating rote memorization (or memorization without understanding.) It’s just memorizing them after you understand them simply for efficiency. Why must you figure out what 3×6 is every single time you need to know? You don’t. (And I know you weren’t saying that.)
The “New New math” is similar to the old “new math” except this time around they do teach the algorithms after letting the kids play with the numbers. Except you never learn it efficiently enough to actually use it, well, efficiently. Like memorizing math facts, you do need that at some point to make life/math easier.
I’m not so organized to have a calculator with me all the time, and most people probably aren’t. I still think it’s worth the time to memorize them.
Of course all kids are different. Some of mine just happen to be the kind that need more practice, even though we do use numbers a lot. Some of mine probably won’t need all the extra game-playing. Yes, ray, Yahtzee is great!
Spelling – Alison, you still know how to spell. Yeah, you might have to think about it a little longer, but you’d still be able to spell. People who can’t spell still can’t get it all out correctly in print, as a spell-checker just doesn’t do it all. My son is learning all about that. 🙂
I understand you’re just trying to get people to think outside the box here. My opinion is that it’s worth the time to be efficient in those three areas. However, that doesn’t mean I think everyone should drill, drill, drill at the expense of learning other things. But it sure doesn’t hurt to practice if you’re having fun. Sometimes just TIME is all it takes to show great improvements, and sometimes you need the time to find a desire to learn it.
Isn’t it a good thing we aren’t all the same? All elbows? But rather, elbows and hands and feet and noses and shoulders in the body of Christ? I am thrilled to find people who are my friends who not only know their math facts, but understand the reasoning behind them. I wish I could learn that reasoning from you. I’d love to be a student in the Alison Moore Smith home! Your children are so greatly blessed. I’d also love to be a student in Molly’s home; your children are also greatly blessed!
I memorized math facts. Elementary school teachers tried to teach me the reasoning behind it, but I never understood it. “Story problems” were my worst nightmare. Brains are still forming at that age, and I feel that the logic part of my brain wasn’t very fully developed at a young age. Still isn’t! We laugh about it. My dad was a great mathematician and had a very successful career using it. And he couldn’t explain it worth a hill of beans! He used to get out a huge bottle of pennies and try to explain mathematical principles to my twin sister and me. We were even more confused after his “explanation” than we were before. It’s a family joke now. When he’s trying to explain something that he thinks is clear as a bell, and no one else understands it, we say, “GET OUT THE PENNIES!” It would be interesting to know, wouldn’t it, if the fault lay in my inability to understand, or his inability to explain. Being good at knowing doesn’t automatically presume being good at teaching what you know.
Nature or nurture? Would it have developed neuron pathways, enabling me to think more logically, if I had persisted? Or would I always be a little bit behind in that respect? Since people are so different in so many other ways, I tend to think that brains might be different, too. Some people are naturally logical thinkers, while others have to work hard at it. Some people are naturally gifted communicators, spoken and/or written, and others have to work at it. Both camps might be tempted to believe that since a specific skill is easy for them, it should be equally easy for everyone else. An elementary school teacher I know said the same thing about spelling. She said some children just had a knack for it, and she believed with all her heart that it was a skill that couldn’t be taught, in spite of effort. Either you could spell, or you could not. That was after 25 years of trying to teach children to spell, ( and she was a good teacher, revered in the educational community.)
I’ll tell you what I think, Alison, and it’s very possible you won’t agree with me. I think spelling and grammar are to nonverbal communication what makeup and grooming tools are to appearance. You never get a second chance to make a first impression. As Missbrown was trying to point out in her post above, spell check might spell words correctly for you, but it may correctly spell a word you weren’t intending to use! The error is still there, even though the word is spelled correctly. It interferes with the communication process, slows it down. And I don’t believe there is such a thing as “grammar check” yet. People might understand what you meant, but it will give them pause, as they try to understand what you were actually trying to say, and it doesn’t present you in the best manner possible. People will misunderstand the worth of what you have to say, judging by the way in which you say it–or possibly write it. That sounds harsh, but it is true. Aren’t we all told that one of the ways to spot a scam email, even if it looks professional, is to watch for the incorrect spelling of words? I have to laugh when I drive by marquees downtown. Go to all the work to climb a ladder in the freezing cold, place letters on a marquee, and spell the words incorrectly? It doesn’t make sense. It reveals laziness and doesn’t bode well for the business. Some may not be able to spell well, but if I were going to promote my business, I would certainly take time to look up words in the dictionary before I blared them to the world, especially if I felt that my spelling skills weren’t exceptional. You never get a second chance to make a first impression.
I sort of disagree with the idea that teachers become teachers by default. They aren’t good at math, so they go into education. My experience doesn’t reveal that. I think of some wonderful teachers at our local elementary school and middle school. They are good mathematicians. They are good communicators. They make learning fun. Their kids adore them. The kids are getting a well-rounded education from them. I see that more often than I see listless, useless teachers who should be in another profession. Just my experience, though. It could be different elsewhere in the world.
I’ll give an example, and then I’ll be quiet. We have a wonderful Sunday School teacher. He is a young married man and a very bright engineer, a very confident speaker. He’s an excellent Gospel Doctrine teacher, and he knows and communicates the gospel well verbally. He is full of the Spirit. An unusual thing happened to drive away the Spirit in a class recently. We were having a wonderful discussion on a gospel matter, and people were excited about the topic and discussing it well. He stood up to write on the chalkboard, and he wrote one word after another incorrectly. As people stared at the board, trying to understand what he had written, they started chuckling at his obvious errors. He heard the laughing and admitted that he wasn’t the greatest speller. So he erased the words and rewrote them, but he spelled them all incorrectly again in a different manner. People laughed harder. I was embarrassed and sad for him and a little peeved with the people around me. He tried to act like it didn’t bother him, but I know it hurt him. His confidence went down the drain, and the Spirit went with it. End of fantastic discussion. And now he is very reluctant to write on the board, but he keeps trying. If he’s going to use the chalkboard, I wish he would plan ahead and look up the words during his preparation, or ask someone else to write for him. It is causing an awkward situation in our class, an unnecessary detraction.
Hey, I ain’t perfect at spelling. I make it a point to not correct other people’s spelling and grammar, feeling that as soon as I do, I will make a stupid error myself–but I’ve noticed that math whizzes DON’T HESITATE to correct my mathematical errors. They are all facts. Misusing ALL facts has the potential for harm. This is an old soapbox for me. My dad is pretty quick to indicate what a lesser person I am because I’m not necessarily a logical thinker. He is lousy at spelling and grammar, and he doesn’t realize that his inability to communicate functionally in a written manner harms the way people perceive him a great deal. I do not point it out to him. He knows he has this difficulty, and sometimes he will ask for my advice, which I am glad to give. As elbows and hands and feet and noses in the body of Christ, we need each other. We can’t afford to disconnect.
Yea, I like what you said, Molly. Thanks for taking the time. Now as for learning the algorithms efficiently, that is a good point.
We do things in a different order than most schools. For example I learned to borrow and carry in 1st grade. Had NO clue what I was doing, but I memorized the “trick.” I never teach that in first grade, because place value is actually a really complex idea. (Sheesh, how long did it take adults to figure out using place value?) But my first graders can do just about anything with fractions. (Yea, the cookie thing.) Add, subtract, multiply. (We do division a bit later usually.) But it’s so easy for them to understand.
Monica is ten and I just taught her “long division” last week. She knows how to divide really well. She know the “basic division facts” from using them. But only once have I had a kid who “invented” an efficient long division algorithm. (And even then, it wasn’t quite as efficient as the standard model.) And doing division with very large numbers was getting cumbersome. So, we sat down and I showed her the standard algorithm and one other one I found online. The second one (I had never seen before) was more intuitive for her, made more sense. Almost every day since she’s asked me to write down some problems that she could practice the algorithm on. Then she multiplies to check her answer.
Like you said, being efficient at the steps takes some repetition. As long as it’s not painful, I don’t have a problem with that. She likes it and finds it useful. As I said in my article, “the algorithm comes last.” Learn the algorithms and get good at them. It’s doing them without understanding what’s going on that I find most problematic.
FWIW, I have some similar feelings about music and don’t really like Suzuki method for some of the same reasons.
davidson, again, I’m not advocating that people shouldn’t learn to spell or learn correct grammar. If you want to know the truth, in our homeschool we:
learn reading by phonics
read tons of classic literature
use a classics-based language arts program
practice spelling (again, not like schools)
take an eight-year italic handwriting course
take a five-year study of english roots
take three years of Latin
I’d guess that our language arts study is probably more rigorous than 90% of schooled kids get.
Still, you can’t argue the fact that penmenship is nothing like it used to be in the early part of the 20th century. My parents both have gorgeous handwriting and spend hours and hours and hours in school to learn it. Is it really a serious loss that we have replaced that with other courses? Only you can answer that for yourself, but I’m not mourning it any more than I’m mourning the fact that my kids don’t know how to hitch a horse to a buggy. (Is “hitch” even the right word?)
My mom also learned shorthand and it was a very valuable skill. Do ANY of you know shorthand? Is it a big loss in your life?
Again, all I’m suggesting is that you all THINK about education with a mind to opportunity cost. If you (or your child) spends time learning one thing, they cannot use that time to learn ANYTHING ELSE. Given limited resources (kind of like the immigration discussion), what is the best use of your/their time?
Thanks so much for resurrecting this topic again!
Alison: Thanks for the book recommendation, I’ll check it out. I never thought of using a manipulative like m & m’s to teach fractions–I am totally going to try that. I think *I* personally would have benefitted greatly from a “why does this algorithm work?” approach. I really stunk at Math. I am only slightly better now because I have had to teach my own kids and help with homework, so I’ve done the research and learned things myself that I am kind-of mad weren’t taught to me in a more logical way when I was struggling through Math in school.
Molly: When and where is your math class being held? I am interested in a little more information.
Davidson: Had to laugh (AGAIN!) at your Dad’s way of explaining with pennies. I find it funny that I am asked to tutor math kids at school on the days I volunteer. The kids tell their teachers I explain it in a way they can understand?????? It baffles me….but I *think* it may be that I don’t have a “naturally mathematical mind”, and struggled a lot (I could tell the math wizzes here stories that would make them cry at my utter stupidity!!) so…..for some reason I can see where the roadblocks are and help the kids maneuver around them??? That is partially why I am looking for more tools with fractions. I’ve been asked to help the 6th graders who are struggling. So I’ve been doing some more research.
I just tend to feel, since we spend so much of our time communicating, that it is worth slowing down enough to communicate well. I think penmanship is all about legibility, not necessarily aesthetics. Legibility doesn’t come without practice. (And I’d love to see the italic handwriting course!)
It’s such an obvious example, but I have been the recipient of the problems that come from a doctor’s notorious inability to communicate his directions through a legible written prescription, which you’ve already alluded to in an earlier post. Maybe this doctor didn’t learn to write legibly because he was too busy learning other crucially “important” things. I wonder how many people die or become ill from that “unimportant” aspect of his communication. All of his learning isn’t beneficial if he can’t communicate it functionally. Same thing with the written part of most exams. We have a world-reknowned music business in this area. They sell instruments and sheet music and everything pertaining to music you can imagine. It is a huge store. They won’t hire a person unless they have a musical background. They also won’t hire a person if he can’t pass their very basic math and spelling test and write it legibly enough to be understood. I knew a very talented musician who couldn’t get a job there because of that.
It’s a different world, isn’t it. I never learned shorthand, and I wish I had. In my last ward, there was an older sister who learned shorthand, and every fast Sunday, she jotted down the baby blessings in shorthand, typed them up later, and gave a copy to the parents. I thought that was a spiffy idea, and the parents loved it. I try to do it in my ward, but I don’t know shorthand, and I miss a lot of the words. I also wish I knew it when I’m taking notes in church meetings. I also wish I knew it when I’m receiving instructions from a doctor, or other important information that is being delivered quickly and spontaneously. Not knowing it is not a HUGE loss, but I bet the sisters who know shorthand still use it regularly, to their advantage.
And I have never in my life written a text message! Because I don’t own a cell phone! My husband does, and my daughter does, but I don’t–because I don’t WANT one! (Sometimes I go out of the house to get AWAY from the phone; why would I want to pack one with me?) (Whole ‘nuther can of worms.) I realize I am seriously behind the times, and I am content to be there. Cell phones also seem to facilitate the lack of prior planning. When my kids know they can’t call me at the last minute, it forces them to plan ahead. I also tend to believe that there is a danger of youth losing the limited communication skills they have because they rely so heavily on text messaging. (Yet another can of worms.) It doesn’t encourage correct spelling or grammar, that’s for sure.
We may not need horses and buggies in our day, but I think communicating on a basic level, minus electronic devices, still has a place in the world, no matter how technically advanced it becomes. It’s a good solid basis for other learning. Just my opinion.
feel not alone dear Lisa! I didn’t get math until I was in college at 26. I had been homeschooled and my mom and I would fight for hours over math.I would sit there crying. I took “dummy” math all through highschool, and into college. I never really got it. I decided to take it one more time, and go for the gusto. No remedial math for me this time! I took Math 101, intro to algebra. and guess what? for whatever reason, I think it was the teacher, it finally clicked. I got an A in the class,and found a new love for math. I knew I had to do something if I didn’t want my daughter to hate math too. If I was doing well, and was excited about it, then she would be too! and thus far it has worked. Now we shall see when I start teaching her myself!
I don’t fundamentally disagree with anything you said, davidson. I’m just trying to get people to think about what’s important and what’s not…to THEM.
So I have a question. Why don’t you learn shorthand since you find so much value in it?
Almost without question, your answer will have something to do with opportunity cost. I’m asking that we realize this applies to ALL learning, not just shorthand.
As for the doc who’s killed so many people with his handwriting? I guess you have to weigh that against all those he could NOT have saved if he’d spent more time in chirography and less in neurology.
Hee hee! I’m sufficiently humbled, Alison. I was thinking of the hippocratic oath doctors take to at least “do no harm.” Seems like a good commitment to take seriously.
Lisa, I think we posted at the same time. I really agree with you. I knew a woman who owned her own trampoline company, and she wouldn’t hire straight A students, because she said everything came too easily for them. They didn’t know how to solve a problem when one came up.
Just one woman’s viewpoint, but I thought it had SOME merit. Instructors who have struggled themselves know their students’ struggles intimately, and empathy opens the door for learning.
I sure found it to be true when I was teaching family history. My family history skills were self-taught, because our ward had never had a family history consultant before. It was really, really hard for me. I knew next to nothing about computers. I tried to attend classes at our regional family history center, but the instructors knew so much, they had a hard time distilling it down to the basics. They answered my questions with terms I’m certain were accurate, but they were way over my head at the time and helped me not at all. My “students” and I learned together. I love the books for “dummies.” Once you get over the label and humble yourself to buy one, it usually explains things in a clear and concise manner, and I really like that.
Must go! Late for shorthand class!
Kidding, Alison, and I am very, very proud of you for the way you’ve educated yourself and your children. The world needs more Alisons. And I will be thinking about the things you said for many days to come. I could do better in this area. Thank you.
Think about the implication there. Does it mean doctors must be expert in EVERYTHING? Handwriting, dictation, pharmacy protocol, equipment sterilization, insurance processing–in addition to all the medical info. ALL the medical info. If bad handwriting is a breach of the oath, then certainly not being an expert in EVERY area of medicine is. How many people die as a result of bad handwriting as opposed to being misdiagnosed or undiagnosed?
Due to all that must be learned to practice sound medicine, I just don’t see penmanship as being the most crucial aspect in reducing harm to patients. And I don’t think bad handwriting is any indication of someone who doesn’t take the commitment seriously.
I really did hope you’d answer the question above. Why don’t you learn shorthand since you find so much value in it?
Why do you want to know? I can’t hear your tone of voice.
Great way to phrase that, davidson. I mean that.
I want to know why, because I think it will show you my point better than I can explain it.
Can shorthand still be useful? Sure. Most ANY skill COULD be useful in SOME circumstances. But that doesn’t remove the issue of opportunity cost. You listed some great things about shorthand, but you’re STILL not running out to learn how. Why not? Almost certainly it’s because the COST of doing so outweighs the benefit in YOUR mind.
So, rather than just ACCEPT that we SHOULD learn “math facts,” or penmanship, or colors, or shorthand, or touch typing, or sewing, or spelling, modes of travel, or…. under the premise that they are good or valuable or could be useful or that they are familiar or that we had to learn them or that the teacher said so…I’d like people (especially parents) to THINK about WHY, particularly in light of the cost of learning a particular thing.
FWIW, one of the best thing about homeschooling is the ability to spend more time doing things that really meet our kids’ needs (assuming we’ve done the work described above) instead of some of the stuff that the schools require. Some of it is fine and some of it is a total waste of time. Yea, my kids really need to take a whole semester of “teen living” and “lifetime activities.”
I figured that was the point you were trying to make, but I wasn’t sure. You are right. While I think it would be useful to know shorthand, there are probably other things more worthy of my attention, my time, and my money (and it would be difficult to find someone to teach it.) However, I continue to believe that studying grammar, spelling, and learning to write legibly for those occasions when computers aren’t available, are pretty essential to basic, efficient communication, and I don’t consider them on a par with the more elective alternatives.
Incidentally, I love “teen living” classes at the middle school and high school. And I wish it weren’t just a semester; I wish it were a year-long class! My kids learn to cook and sew from professionals for just the cost of the materials. I can cook and sew, and I teach my children, but I am always interested in the opinions of experts. My kids have taught me tricks their teachers taught them. Sewing might be just an elective skill (this is debatable), but as long as we continue to need to eat every day, I think learning to cook is a pretty good idea. Can’t tell you how many times I’ve been asked to shorten a temple dress or sew a Halloween costume or mend a pair of pants for women who felt they didn’t “need” to learn how to sew. My children use the information they learn in this class a lot more than they use geography.
I guess you’re right. People have different needs, interests, and abilities. They place different values on opportunity costs. I think there is room in the world for all of us.
Here, for your mathematical enjoyment, (and with no hidden agenda), is “The Beauty of Math.” I thought the numbers were cool and the communication at its finest. My brother sent it to me in an email today.
The Beauty of Math!
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Brilliant, isn’t it?
And look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
Now, take a look at this…
From a strictly mathematical viewpoint:
What Equals 100%? What does it mean to give MORE than 100%?
Ever wonder about those people who say they are giving more than 100%?
We have all been in situations where someone wants you to GIVE OVER
How about ACHIEVING 101%?
What equals 100% in life?
Here’s a little mathematical formula that might help answer these
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.
8+1+18+4+23+15+18+11 = 98%
11+14+15+23+12+5+4+7+5 = 96%
1+20+20+9+20+21+4+5 = 100%
THEN, look how far the love of God will take you:
12+15+22+5+15+6+7+15+4 = 101%
Therefore, one can conclude with mathematical certainty that:
While Hard Work and Knowledge will get you close, and Attitude will
get you there, It’s the Love of God that will put you over the top!
fun stuff davidson! I love it!
We hold our classes in Pleasant Grove, UT. My website isn’t working now, which is very annoying as it’s the hosting company’s fault and they won’t fix it (and I’ve not got a clue how to.) All I do though, is try to bring in some of the “right-brained” stuff into math since historically math is usually taught to the left side of the brain. The orderly nature of workbooks & textbooks & flashcards appeal to the left side of the brain, and that’s usually what is used to teach mathematics. So I do jokes, poems, hands on stuff and games – humor, creativity and fun all appeal to the right side of the brain.
And Davidson, it IS great that we’re all different. We definitely all have our talents, and there are definitely ways of teaching/learning that come easier to us. But I think it’s most useful if we are taught using methods that appeal to both sides of our brains, which will help us to use both sides of our brain. We can get those neuron connectors firing all over the place if more than one method is used. Most people believe that to be good at math you have to be left-brained. But you absolutely have to use the right side of the brain just as much to see the patterns, picture the math and to do creative problem solving! This really goes for any subject, imo. (And btw, I loved that post of the beauty of numbers. I’ll pass that on to my class!)
Thanks, Molly. I agree that it’s a good idea to appeal to both sides of the brain to learn something new. When my brother sent The Beauty of Math to me, it was centered on the page, vertically and horizontally. It looked much nicer. When I added it here, everything was aligned with the left margin, and I couldn’t figure out how to center it. Just a thought before you share it.
I feel the need to point out the obvious from a previous comment. No ill-intent against you at all, Davidson; it’s just that this perception from the woman you mentioned raised my hackles a little…
“I knew a woman who owned her own trampoline company, and she wouldn’t hire straight A students, because she said everything came too easily for them. They didn’t know how to solve a problem when one came up. Just one woman’s viewpoint…”
Most of my kids are consistently straight A students. While this generalization might apply to some of them at times, it most certainly doesn’t apply to some of my other kids. They work HARD for the A’s they earn because it doesn’t always come naturally. They most certainly know how to problem-solve — they have figured out how to do difficult work in order to get a grade they desire.
I know there are good students who seem to have everything come too easily. I vividly remember the shock of realizing I would actually have to “work” to earn my own A’s, instead of getting them with minimal effort. But there are also those who work hard to get the top grades and it doesn’t come easily at all. I would hate for some of my kids to lose out on a possible job just because they work hard to get good grades at school.
Please, nobody take offense! I don’t mean it that way at all. I was just bothered by the assumption. As I said, this is a fairly obvious distinction. I think all of us here realize that not *all* straight A students have things handed to them too easily and can’t solve problems because of it — and that, on the other hand, there *are* some straight A students who really do fit that description.
Now, back to the topic at hand… That Beauty of Math is really beautiful! I love symmetry.
What my wife said.
Go to bed, babe.
Thanks, Molly. As it gets closer, if you’ll post details. I think I would like to check it out. Love the idea of both right and left brain teaching. I think I only have a smidgen of each left. But I’ll give it my best!
Thanks for your comments, Michelle. I can see your point! I hope I made it clear that it wasn’t necessarily MY viewpoint. When I said it was ONE woman’s viewpoint, and I thought it had SOME merit, I meant that I thought she was partially right in saying that SOME straight A students wouldn’t make good workers because they didn’t know how to solve problems; schoolwork came too easily for them. I’ve known a few like that. I am the mother of a bipolar daughter who was a straight A student. Because it was something she COULD do, she EARNED her grades. There were many things she couldn’t do, but studying hard wasn’t one of them. It was common for her to study six or seven hours a day.
I didn’t like it when the woman in my ward said that either. I only remembered it because she had such a strong conviction about it.
Yeah, Davidson, I knew it wasn’t your viewpoint. I’m glad you understood what I was trying to say!
I guess this example shows why it’s best not to make these types of judgments, to stereotype people based on just one criteria. (Or is that criterion, in the singular?)