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February 20, 2008

A Teachable Moment For Parents?

Interesting article in the WaPo yesterday:

Greg Barlow, an Air Force officer in the defense secretary's office at the Pentagon, was helping his 8-year-old son, Christian, one recent night with a vexing problem: What is 674 plus 249?

The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned. Applying lessons from his school's new math textbook, "Investigations in Number, Data, and Space," Christian tried breaking the problem into easier-to-digest numbers.

But after several seconds, he got stumped. He drew lines connecting digits, and his computation amounted to an upside-down pyramid with numbers at the bottom. His father, in a teacherly tone, nudged him toward the old-fashioned method. "How would you do that another way?" Barlow asked.

In Prince William and elsewhere in the country, a math textbook series has fomented upheaval among some parents and teachers who say its methods are convoluted and fail to help children master basic math skills and facts. Educators who favor the series say it helps young students learn math in a deeper way as they prepare for the rigors of algebra.

The debate over "Investigations in Number, Data, and Space," a Pearson School series used in thousands of elementary classrooms, including some in Arlington, Fairfax, Loudoun and Howard counties, is one of the newer fronts in the math wars. Such battles over textbooks and teaching methods are fueled in part by the anxieties of parents who often feel powerless over their children's education, especially in subjects they know.

I found the parents' reactions interesting on a number of levels. As someone who grew up in the military, I moved frequently. An inevitable consequence of military life is that for children, their education becomes a patchwork of different pedagogical methods and curricula as they are bounced from state to state and school district to school district. Some are better, some worse. I faced the same problems when raising my own boys: overseeing their education (and this is something I view as the parent's, and not the teacher's responsibility) can be challenging at times.

But I can honestly say that although there were times when I thought my children's teachers and/or their teaching materials were unbearably wrongheaded, it never once occurred to me to undermine what they were told to do. The message they got from me at home was simple: this is your job as a student; put in whatever amount of time is required for you master the material. If you need help, it's available, but whether you do the work is not negotiable and the terms under which you do it are not either. Suck it up.

I would not want to be a teacher these days. Without having had time to get into this particular program in depth, the example provided by the Post is less than compelling. Unfortunately, their graphic does not display, but the problem on the front page when like this:

Traditional approach:

42
+34
76

The steps a child would take to solve this problem follow:

2+4=6

4+3=7

= 76

New approach:

42 + 34 =

2 + 4 = 6

40 + 30 = 70

70 + 6 = 76

Now you tell me which approach actually contributes more to a child's fundamental understanding of what he or she is doing during the process of addition? The parents' main complaint against this method seems to be that it is "too hard" and that students are "struggling" with it. Well guess what? When one has to actually think one's way through a problem as opposed to simply memorizing a rote algorithm without ever mastering the underlying concept, one often finds it a struggle at first.

One parent (a meteorologist with a degree in atmospheric sciences) has gone to the trouble to make a video explaining why alternative methods of teaching math are so wrong/bad. She succeeds in raising a valid concern that, if some of these methods are taught as she presents them (and we don't know that) they may be confusing. Personally I found one method very easy to understand and thought it, also, would enhance a student's understanding of place value.

This math professor presents the opposing viewpoint and asks what I believe parents ought really to be concerned about: "What is the real goal of mathematics education?"

Is it to pass a standardized test? To memorize rote algorithms (which can, after all, be easily taught at home)? Or is it a mix of concept and skill mastery?

I think he's right. I have mentioned this many times, but I tutored college algebra, stats and calculus for many years and found that in addition to lacking skills, the vast majority of students had little or no understanding of what they were doing or why they were doing it. They just wanted to be given a quick, easy, painless way to pass what they viewed as a meaningless exercise.

But that is not the point of education. The true goal of education is to teach us to reason. We do use math in every day life, and a huge part of the reason we don't retain the skills we learn in school is that we never understand how they "fit into" our daily lives in the same way verbal skills do. We lack the context that would allow us to link math to the rest of what we know, to make it useful and relevant. That 'context' is that math involves critical reasoning skills that every human being ought to develop more fully in order to understand things like politics, practical economic forces that affect our lives, or just every day physics. Mathematical illiteracy is responsible for all sorts of poor decision making, and if people understood that better they might be inclined to spend more time mastering these critical skills. Moreover, in an increasingly technical world, America is falling behind in math and science literacy to the point where we are being forced to import math talent from abroad..The world is becoming more rather than less complex, and math fluency is no longer optional for employees who want to be competitive in a rapidly changing global marketplace.

My youngest son and his wife attended St. John's College in Annapolis. St. John's is an unusual school in that it focuses exclusively on a Great Books curriculum. Consequently, he has never taken a modern collegiate-level Calculus class (or any other college level math or economics class, for that matter). Nonetheless, his undergraduate education prepared him to think, and he had no trouble being hired in a highly technical field where he works with PhD economists on mortgage risk algorithms.

The St. John's curriculum is non-traditional by any standard you care to name, and yet it produces students who easily move into diverse fields because they know how to think.

Interestingly, the protest web site against this method cites (as support) a rather lengthy study of the Singaporean mathematics program, which ranks #1 in the world in math education:

Singapore’s framework, shown in Exhibit B, lays out a balanced set of mathematical priorities centered on problem solving. It includes an emphasis on computational skills along with more conceptual and strategic thinking processes. The framework covers a relatively small number of topics in-depth and carefully sequenced grade-by-grade, following a spiral organization in which topics presented at one grade are covered in later grades, but only at a more advanced level. Students are expected to have mastered prior content, not repeat it.

By contrast, the frameworks of Florida, Maryland, New Jersey, and Ohio exceeded Singapore’s average numbers of topics per grade by 70 to 160 percent. If Singapore’s excellent test performance is evidence that its curriculum exposes students to about the right number of topics per grade, then these states’ test performance suggests they cover too many topics and should reduce breadth of coverage and deepen topic instruction.

I just find it interesting that so many parents these days want to go to war with their school systems. While I can sympathize, I think I might insist my child learn the mandated method, but also teach them to check their work by the traditional method. There is nothing that says a parent can't add to what their child learns at school (and I often did). But I don't see how it can be good for your child to let him see you undermining the school, even if you disagree, and even if he or she has to work a little harder.

Anyway, it's an interesting dilemma. What do you think?

Posted by Cassandra at February 20, 2008 06:37 AM

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Comments

Now comes the time when some smart ass blog devotee (me) points out a minor flaw in the Web Goddesses work:

"The steps a child would take to solve this problem follow:

2+4=6


4+7=7"



*** You're welcome. :-P

Posted by: Frodo at February 20, 2008 10:13 AM

Bwa ha ha ha ha!!!! :)

When I hit Post I was thinking, "Yanno... you really ought to look that over..."

But then the phone rang.

Thanks!

Posted by: Cassandra at February 20, 2008 10:17 AM

Cass,

Personally, I've never cared how someone got to the correct result on a math problem, as long as they could reliably repeat the steps (i.e. they aren't guessing or throwing numbers at a wall). But the problem with the "new math" as I've seen laid out in the meterologist's video that I can see is that it is NOT teaching children 'coping' methods to help them understand the math. It seems more focused on time consuming matricies that DO work, but make no logical sense. And the bit about division being completely dropped? That's asinine! If we were able to learn long division in school, why are today's children magically unable to?

But on a lighter note, here's another math related video I belive you will enjoy:

http://youtube.com/watch?v=rLprXHbn19I

Posted by: MikeD at February 20, 2008 10:21 AM

Uhhh smart ass here again ...

"Traditional approach:

42
+34
76

The steps a child would take to solve this problem follow:

2+4=6

4+7=11"

Shouldn't it be 4+3=7

Posted by: Frodo at February 20, 2008 10:25 AM

Yep.

Wasn't paying attention :p

This is what I hate about MT - the posting window is very small and I rarely notice it when I make a mistake. If I have time I paste things into Word so I can actually read them (something I find impossible to do in MT).

Posted by: Cassandra at February 20, 2008 10:29 AM

No, I don't care either, Mike.

When I tutored, I used to show people 3 or 4 ways to solve a problem b/c I usually found different people have different ways of stepping through a problem. So you pick the one that feels the most natural to them and they retain it better - plus I learned more when I was more flexible about solving problems instead of forcing everyone to solve problems the same way.

That's why I'm surprised parents would insist all kids HAVE to learn the way they did. That's dumb. Tell your kids to learn it the way the teacher is teaching (b/c they have to attend class and fit in, not force the class to accommodate their 'special needs') but also give them another way if they are struggling. That way, they learn that with enough effort, they can overcome a difficult challenge and they also learn there's more than one way to skin a cat.

Posted by: Cassandra at February 20, 2008 11:02 AM

You know what I find really funny about this?

Adding, subtracting, multiplying and dividing are all skills that can be taught fairly quickly. So this is a tempest in a teapot. Schools spend SO much time on this crap. They go OVER AND OVER AND OVER IT. But the basic skills themselves (the ones these parents want their kids to learn) are not difficult.

In fact, their argument is that they are simpler! So just sit down and show your child how to do it, if in fact it is far and away a simpler and superior method. Give him or her 1-3 problems a day to practice by that method a day.

That's hardly onerous. I did that with my boys when they had trouble making letters the right way b/c it was not the teacher's responsibility to ensure their fine motor skills were at the same level as their peers (My boys were both young for their grade level, but could both read and form all their letters well before kindergarten. They just couldn't write small letters with a pencil without making some of them backwards).

Personally I thought it was stupid for kids that young to spend so much time on penmanship. My boys read far above grade level and it was a massive waste of their (and my) time. But I didn't undermine the teacher's authority. I just told them that was the rule and they needed to work a little bit harder than everyone else to make their letters. It didn't kill them. They just went outside a bit later after school.

Posted by: Cassandra at February 20, 2008 11:11 AM

Answer: homeschool, or move

Blockheads. They are all blockheads.

"Strategies for solving problems."

Christ on a crutch, this is just plain stoopid.

Posted by: Don Brouhaha at February 20, 2008 11:41 AM

Mr. Brouhaha! Go to the principal's office. ROFLMAO.

I hated school, and if it were not for the very few talented and dedicated teachers I encountered, I would have quit. Most teachers are lazy self serving morons. They comprise the bottom third of college graduates. Classes are geared to the lowest common denominator - retards.

My first grade teacher refused to teach me to write left handed. I refused to write. A parent teacher conference was held in which the so-called teacher had her head ripped off by irate parents. I was reading the highschool literature when I was in the third grade. I annoyed my teacher who confiscated my books. I refused to do anything for the bitch. Another thermonuclear parent teacher conference was called.

My mother taught high school and was a graduate of Stanford and Cornell. Public education in this country is a disaster. I salute the few good teachers out there. Most are not competent to flip burgers at Mickey D's.

Posted by: Mark at February 20, 2008 12:41 PM

I hold a teaching credential (multi-subject k-12 in California). I was surprised to find that over 50% of the students in my credential class had 'liberal arts' majors... a major that required 1 class of college math at the algebra level, or alternately, by taking a learning-to-teach-math type course. For credentialing, you are required to take a math methods course, and, you must pass a multi-subject exam that includes math. Most of my teacher classmates had learned math by rote steps. They did not understand why those steps worked. When I teach math, I start from some basics, for example, you can only add and subtract like objects... not 1 ten plus some ones, have to convert that 1 ten into 10 ones to add to the ones... this simple rule reduces the learning needed to solve your 4 tens + 3 tens or fractions (4/10 +3/10). Once kids (and remedial teens and adults) get the idea that basic math tools can be re-used, they are more likely to think their ways through problems. If a teacher just teaches a procedure without why it works, there's a lot of memorization and a lot of unnecessary relearning, and, a general dislike of math quite often follows.

Posted by: Heather at February 20, 2008 12:42 PM

You just said a mouthful, Heather.

I tutored in California, and many of my students were going for the CA teaching credential :p They had a terrible time passing the CBEST, which is a scary, scary thing.

I sent some friends a very lengthy article on the "Singapore method" that was tried out in Montgomery Cty. It, also, raised a furor with parents and teachers. There was an unintentionally hilarious comment in the article from a veteran Math teacher who said (and I quote):

"Until I learned this method, I never understood the math I was teaching to my students"

[thud]

Nonetheless, the parents were up in arms about it and will undoubtedly scuttle the program.

Once kids (and remedial teens and adults) get the idea that basic math tools can be re-used, they are more likely to think their ways through problems.

Exactly. The brain is always scanning to figure out what to retain and what can safely be discarded.

I have a general theory about learning that jibes with your comment: it's that until we have a place to "file" information, it isn't retained. If we can relate it to something we already know, knowledge gets moved up on the importance scale because we think "Aha! I may need that!" But if we see no use in it, or it doesn't seem to relate to anything, why keep it around?

Math, to many students, seems like one of those things they won't need. If we were better at stressing the connections to other subjects and its value as a reasoning tool, I think students would be more likely to retain it. I know I was bored silly by math until I was an adult and began to see how it could help me become a better thinker.

Posted by: Cassandra at February 20, 2008 12:59 PM

I have three different approaches. They are necessary, but one thing I have noticed with my children is that manipulating the problem with
beads or counters helped them learn to increase and decrease via addition and subtraction. That is a concrete ability. To move to numbers with a place value is abstract and has to be practiced in conjuction with the concrete.

Some children don't grasp it or the logic behind
it until they go back to the very basics of counting with beans or M&Ms or whatever. I don't necessarily want to undermine the schools, but
I do think that if EIP is being offered, that the
nuts and bolts are being taught in those classes.

Posted by: Cricket at February 20, 2008 01:21 PM

I use Montessori Math, Saxon and a couple of upper level algebra courses. Jacob's Math is one of them. Homeschoolers LOVE Singapore.

I compared it with my beloved Saxon and decided
to carry on with Mr. S. It has worked for 15 years.

Posted by: Cricket at February 20, 2008 01:28 PM

I am a teacher, a tutor, a parent of a school-aged child in public school, and a homeschooling parent (I homeschool my 4 year old year round and my 6 year old in the summers and on breaks). I tutor math and I'm currently tutoring 2 college students in algebra.

I have many thoughts on all of this that are jumbled and I do not have time to sort them all out so you're going to get a ramble.

First, the relationship between parents and educators has become adversarial which has led to parents doing exactly what the parent in the article did - undermining the teacher. Think you can do it better than the teacher? Fine. Pull your kid from school and homeschool him/her. Otherwise, align yourself as the teacher's ally and help your kid learn the concept the teacher is teaching in ADDITION TO the way YOU learned it. There is nothing wrong with having an arsenal of methods for solving ANY KIND OF PROBLEM - math or otherwise.

Second, if the TEACHER is the problem that is a different story. That calls for a discussion with the administration but it sounds to me that the parent was taking issue with the method being taught not the method of teaching.

Third, I agree that our scope and sequence when it comes to curriculum - ANY curriculum - is to broad. The United States education system has become "quantity over quality" oriented and it will be our undoing if we are not careful. Like I tell my kids...you are never going to be good at EVERYTHING. You're welcome to try out everything in search of what brings you joy and then focus on that but please do not think that you will be good at everything. Better to find what it is that you ARE good at and devote yourself (not obsess, just focus upon) to that rather than dabbling in dozens of things and never being good at any of them. There was a strong movement back toward the "core" subjects in the 90s and I really think it would behoove us to take a second look at that idea.

I had one of my teens at church complain that she didn't understand why she had to learn all that was taught in school. Especially math. She had no desire to become an engineer so why bother? We had a nice hour-long discussion about how math factors in to just about every aspect of daily life. We also discussed why being educated and therefore able to hold intelligent conversations with others is a benefit of learning. Something I've been mulling over in my head for a while. I'll have to write my thoughts down once I get a moment.

Sorry to ramble. It's been that kind of morning.

Posted by: HomefrontSix at February 20, 2008 02:44 PM

Not rambling at all.

I think we've become very uncomfortable with failing (or even mediocrity) because it makes kids 'feel bad'. But unlike Lake Woebegone, not everyone can be above average at everything. If they could, it wouldn't mean anything.

I really suck at anything involving rotating objects in 3D in space. I am really, really bad at it. It hurt me, learning to sew b/c you have to be able to work around that a lot. I can't tell you how many sleeves I ripped out of armholes before I learned that I'm almost dyslexic about that stuff and I have to SLOOOOOOOOOW DOWN AND FOLLOW THE DIRECTIONS TO THE TEE. Also with math, as you noticed this morning, I'm quite good at math but my computation skills are lousy unless I focus on what I'm doing. I make mistakes all the time. So when I do math, I have to work against my natural inclinations and be absolutely ANAL about lining things up and showing all my steps.

As long as I do this, I can ace tests and I rarely got below a 97 on anything in school. But man... let me get overconfident (which is a perennial problem with me) and I will ballocks it up every time :p Self knowledge is key.

I loved engineering in HS, but I could never BE an engineer b/c I lack a critical aptitude, and you can have all the smarts in the world, but then you watch someone who does that sort of thing as naturally as breathing and you realize that you just aren't cut out for that. For someone like me who had never run across something they couldn't do, that was like a slap in the face.

But hey! Lighten up, Francis!

I enjoy watching people do things I can't. And where you aren't good at something, you either work harder to compensate (if it's really worth it to you), develop a coping mechanism, or avoid that activity altogether.

Posted by: Cassandra at February 20, 2008 03:21 PM

When I was teaching calc and diffeq's I often found that it wasn't so much about the student but the teacher. A good teacher will often need to cover the same material using 3 or 4 different methods. I always found that all the students could grasp one of the methods. I think this holds true in any level of mathematics instruction.

There are some rare exceptions obviously.

Posted by: Allen at February 20, 2008 04:09 PM

Even with the Investigations materials, kids aren't getting it. That is what is used in my school district and part of what I had to use last fall during student teaching (3rd grade). Yeah, the kids can draw the pictures (3 dogs, each having 4 legs, there are 12 legs in all), but they weren't making the connection to multiplication. Some things, like the times tables, need to be learned by rote.

I think part of the adversarial relationship between parents and teachers has a lot to do with education being a field dominated by those who lean left - children are being taught things (and I'm not talking math here) that do not match up with the values parents hold. When/if parents get involved in their child's education, so teachers think the parent is meddling where they don't belong. Some teachers kind of like having uninvolved parents.

I lean towards using those "tried and true" methods that worked, back before our testing, compared to the rest of the world, began to slip. If a child has trouble with those methods, then you can try some of these (convoluted) methods (like the "lattice method" of multiplication).

Posted by: Miss Ladybug at February 20, 2008 04:37 PM

Well, y'all are going to hate, hate, hate me for saying this but I was a pretty smart kid (at least according to the durned standardized tests.

In 3rd grade I took some dumb test and tested out of the normal public school system where we lived. So I got to go to a 'special' school. Yee ha.

But even kids who are smart, in 3rd and 4th grade, are often not ready for abstract concepts. I still remember gobbling up the French classes I took in 4th grade.

And I still remember waking up in a cold sweat over my math class. For probably 10 years after that, I had nightmares about waking up back at old CCES. In fact, I was still having them after I had my first child :p

It didn't kill me. But I often wonder why a 3rd grader needs multiplication? It seems to me that when a child is truly ready to learn something, he or she will learn it quickly and fairly painlessly. In Europe, they introduce a lot of these topics later than we do. And yet, kids learn them just fine. They also accept that not all kids *will* learn them to the same level of proficiency. Hence, A levels, O levels, and whatnot. And whatever happened to trade schools?

Go figure.

Posted by: Cassandra at February 20, 2008 04:47 PM

back before our testing, compared to the rest of the world, began to slip.

Did you watch those videos though, Miss Ladybug?

There was an interesting aside from that Math prof about the 1940s - a math teacher saying that 60% of the kids weren't learning the material THEN either.

And there was a major difference back then. Not everyone went to school, and not everyone went to school all year 'round. And we were a far more homogeneous society then.

There are a LOT of reasons why our test scores have slipped, not all having to do with curriculum and culture. I found that interesting (and surprising!)

Posted by: Cassandra at February 20, 2008 04:56 PM

Aw hell, I'm still trying to add up how many times I could have sex in 30 days if'n I got TLB to join that church!

It boggles the mind!

I still don't get why you want to add a step to normal math to get the same result? But then I actually like calculators. And course plotters. And GPS.

Just call the new math "Sex Math" and watch how fast kids pick it up. You want to get jiggy with math, appeal to their hormones and they will learn!

So I got to go to a 'special' school.

And I still remember waking up in a cold sweat over my math class.

And was that a short bus you rode to school on? Heh! Cold sweats over MATH? Hmmmmmmmmmm....!

Posted by: JHD at February 20, 2008 04:57 PM

Cass~

I had seen the one video (from the meteorologist) when Michelle Malkin linked to it some time in the last few months. Haven't taken the time to watch the other one (I should be sticking to shampooing the carpet, *not* reading and commenting on blogs...).

You do bring up a good point about academics getting pushed down to younger and younger grade levels. That is not good. I don't recall when I learned multiplication. All I remember is that I had to memorize the tables through 12 times 12. You are completely right about the average child not being developmental ready to do some of the things they are being asked to do in school.

School was always easy for me, until I got to the 9th grade and I was placed in Honors classes (physical science, algebra I, English). That was kind of a kick in the head because I'd never truly had to apply myself to get good grades until then. That was the first (and only) time I got a progress report (physical science). I'm the nerdy girl who took 5 years of math in 4 years of high school (taking Honors Algebra II and geometry my sophomore year).

Also, "tracking" students has become un-PC. In a general education elementary classroom, you will have the slow students, the at-grade level students and the gifted students. The general education teacher is expected to met the needs of all three groups. However, that gets progressively more difficult - the slow students will fall further and further behind because they are unable to master concepts needed to move on, while the gifted students get bored and (potentially) start misbehaving in class. Maybe that's not so much the case in secondary education, but I think that has a huge impact in the primary grades. And there really isn't a point to it: the kids know who the "smart kids" and the "dumb kids" are without being tracked.

Posted by: Miss Ladybug at February 20, 2008 05:13 PM

I KNEW that JHD could inject the right level of humor into this. Heh. :)

I'm sorry if my comment about "blockheads" offended anyone. I know quite a few scholl teachers, and most of them are nice people who try very hard to teach kids that refuse to learn, at some level.

Math came very easy to me, up to a certain level (Linear algebra and multi-variable calculus had me skunked when I was 19, but..well..), so it sometimes bothers me when people struggle with something that is so...elementary? I know that it is harder for kids to grasp some new concepts, but I guess that my main peeve is the general approach that some of the schools/teachers make.

I have two sons (8th grade, 5th grade), who are both bright, if sometimes lazy, boys. There mother (my wife) works endlessly with them to get their homework "right", and she constantly complains to me that she is doing the teachers' job, because the boys aren't "getting it" in school. I don't have objective evidence to back this up, but it is bothersome that normal, reasonably intelligent kids (other than mine, that is) are struggline because, maybe, some teachers are slacking off, and frankly, can't or won't teach very well. I can think of several of my older sons' teachers that are just exemplary; smart, energetic, organized, etc. But I don't live in Lake Wobegon, where all the children are "above average", so what happens to the "average" kids, whose parents aren't as nutty, er, dedicated as my wife?

And speaking of the "good old days", my Dad just about dropped out of High School back in 1940, for various personal reasons, and struggled hard to keep his grades up (with a full time job on the side) yet he was not a dummy or a slacker. The human condition hasn't changed that much. So it goes.

Posted by: Don Brouhaha at February 20, 2008 05:31 PM

Well, I know with my sons that one had little trouble with math and the other had to struggle with it. He scored pretty consistently at or below the 50th percentile unless he worked.

The thing is, he's not a dumb person. He is actually gifted when it comes to verbal aptitude - he's just lopsided. He scored 98th or 99th percentile in most of the verbal aptitudes. So I think that really hurt him when it came to math. He became unduly discouraged when that didn't come to him as easily as English.

I don't think I have a whole lot of what you'd call "math" aptitude.

I think I am able to reason my way through via a lot of coping mechanisms. I believe the reason I'm able to do well is that I am more able than a lot of people I know to see connections between things and discern patterns. But "math" aptitudes?

My brother has that, in spades. But then he's a mathmatician - he has a PhD and the whole 9 yards. He used to do puzzles as a child b/c he enjoyed them. I hated that sort of thing. That's why I don't think I have natural aptitude. When you have an ability, you're driven to use it. I don't have any desire to solve number puzzles. I will say that I did enjoy doing the math I had to learn in college as an adult though. Sick, huh???

But I think I really just enjoyed the mental challenge. Had it come easily I don't think I would have liked it all that much.

Posted by: Cassandra at February 20, 2008 05:47 PM

Wow, what a subject. I grew up a military brat. In 2nd grade, in a DoDD school, I was put into TAG (Talented and Gifted). From then on, it was Honors and AP level in all core courses until I graduated, from another DoDD school. Even going in and out of the civilian schools, I stayed in the gifted set. In fact, I saw some of the same kids state-side as I did overseas. I never gave it much thought. It was just my reality and I didn't think there was anything unusual about it. However, the math courses were never a strong suit for me. It was the only thing I struggled with, even though they were the higher level courses. I too was one of those nerds.

And then I had 2 daughters of my own. My oldest was born with serious medical issues, and I was told that at best, she would be mildly retarded. My first concern - how was I going to help her grasp concepts that I never had to learn, really? I never had to put much effort into school. My mom swears I came out knowing how to read. Turns out that my daughter has stomped all the dire prognises and is far from retarded. But she does have learning disablilities, though the schools never caught it. It was because we finally got tired of reteaching everything she was supposed to have learned in the classroom every night. By getting in the administrations face, so to speak, we eventually got the school to test her and put her into an IEP.

Thankfully my husband is a math genius, in that he can very quickly conceptualize the figures and break it down to a very easy method. In fact, I think he naturally does this "Investigations" sort of thinking. I can't. Plain and simple. In fact, after all that studying and struggling in school, I still need a calculator to do the simple math. I can do it, but I have to literally write it out on scrath paper. But throw all the harder stuff at me, and I'm golden. Bring on the polynomials...so long as I have a calculator to do the simple math within the equation.

If it weren't for my husband's hard work with my daughter, we probably would have completely lost her in 4th grade. She had slid so far back, even with all our help, that year she was reading at a 2nd grade level, barely, and math was at the 1st grade level. She's still on the IEP in 7th grade, but hardly needs help anymore. Its more for confidence building now.

I think the problem lies with the parents. I take full responsiblity for how far my daughter slid back. I should have been more pro-active in her schooling. But as a whole, we've shifted too much responsibility for our children's schooling and welfare to the school systems. But there is a difference between being pro-active and being confrontational for the sake of itself.

Posted by: tankerswife at February 20, 2008 06:30 PM

I really hated algebra in high school. And while that may have had as much to do with a teacher whose idea of *instruction* was to write the next days assignment on the board and then leave the room, the more relevant reason was that it felt like I was being programmed....."Just do it that way to get the answer you're supposed to get. Don't ask why." For the longest time, I thought that it was my fault that I didn't *get it*. Until my college roommate (Masters degrees in both Computer Science and Math) called me one day during her senior thesis year to tell me she could now tell me "Why". At that point I figured that if it takes a Master's degree to be able to explain the subject, then it wasn't me afterall. Because *channelling Stuart Smalley* "I'm good enough, I'm smart enough, and doggone it, people like me."

Well, excluding certain Blog Princesses and sundry trolls

Posted by: Sly2017 at February 20, 2008 06:33 PM

I think there is a time and a place for rote memorization. Memorizing alleviates the stress of having to remember what 7x9 is while trying to understand the concept of 7x9.

I learned how to spell the word "piece" before I learned that there are words in which "i" comes before "e", except after "c". Learning the rule after learning the word led to an "AHA!!" moment when I put the two together in my brain.

I'm one of those annoying people that has (as Cass puts it) 'math aptitude'. I can just see the numbers in my head. I do math problems for fun. I have the AP Calc review book on my nightstand. I'm weird. But in 8th grade when I was in Algebra I, I couldn't grasp it to SAVE. MY. LIFE. I worked and worked and worked. I had a tutor. I re-did my homework and all of the examples that my teacher gave over and over and just could not get it.

Then I took geometry. And loved it. So I figured that my brain just wasn't wired for Algebra. But then I took Algebra II in 10th grade and sailed through it. Brain development is a wonderful thing. My brain wasn't ready to grasp abstract concepts necessary for success in Algebra when I was 13. But, by the time I hit 15 and took Algebra II, my brain could handle the concepts.

I do agree that maybe we foist concepts on kids before they are ready. But I also agree that we no longer allow our children to feel inferior or even mediocre and that is sad. I think it is a good thing to realize that you are not the "shizzle" at everything. Keeps you humble.

Posted by: HomefrontSix at February 20, 2008 07:00 PM

"I'm good enough, I'm smart enough, and doggone it, people like me."

Uh.......... NEVER MIND! ;-)

Medical Boy is a whiz at math but he got royally screwed with Honors and AP classes. In GA they don't weight those classes vs regular curriculum for admission to state universities (like UGA, GA Tech, et al). So, he pulls a 3.92 in AP classes and can't get admitted to UGA for all the hundreds of 4.0 standard course kids. Talk about a wake up call. Plus our state universities were required by statute to admit x-number of minorities. A quota by any name other than quota. That has since been removed but it was in place when he graduated. 58% of the regular course freshmen lost their Hope scholarships and flunked out. High school grade inflation strikes again. Even with AP, Medical Boy had a hellova' freshman year as even he wasn't prepared for the college curriculum. Math and Science he breezed through but struggled with the others. He was actually taking some outside remedials to play catch up.

Luckily a fine private institution decided they'd rather have excellent students than quotas and average students. Funny how that works. Came through five years of school only owing about ten grand from a $35,5k/yr college due to grants and scholarships. Moral of the story? If you're going to excel in AP classes be prepared to chase private college education instead of state schools with their touchy feely politically correct admission procedures (unless you're top 1%).

Meanwhile, back at the ranch. Soccer Girl is attending a state school with only a handful of Honors classes in high school and doing just fine. She was an average high school student but has excelled in the college enviroment. Math was/is her downfall altogether which is probably why she's going to teach history in high school and coach high school soccer. Absolutely loves history and it has actually become a passion for her. Go figure! Perfect fit for her. She'll have her Masters before she even starts teaching. To each his own eh?

Posted by: JHD at February 20, 2008 07:32 PM

I was eventually placed in the "gifted students" program in my senior year in high school, where I was a f**k up. I had an awful time with algebra. I loathed geometry. When I went off to college something clicked. Algebra made sense. I still hated geometry with its stupid proofs and theorems.

As luck would have it, my freshman calculus professor was a hotshot from Princeton and Yale. He was a little Jewish guy who looked like an owl and was smart as hell. He would not use a text book. His lectures were art. I was never so engaged in a subject and did very well.

Years later I went to graduate school and then new how to "learn". It made a difference. Problem sets are the key to math and the sciences. Literacy is a whole different proposition, requiring some maturity. Language is an amazing thing. Ask the Blog Princess Who Never Sleeps.

Posted by: Mark at February 20, 2008 08:08 PM

I, too, am a product of DoDDS schools, but we only moved every 3 or 4 years, so I didn't have to go to all THAT many schools. K through 2 in San Antonio public schools in the mid-70s, 3-6 in a DoDDS school in Germany, 7-10 in El Paso public schools, then my last two years of high school in Germany. I started with the "talented and gifted" deal in 7th. Before that, I think schools (especially DoDDS schools) were still able to "track" students by which teacher they were assigned to. I took "honors" classes through 10th grade (and I recall being the only one in class one time that was able to solve a particular proof - wish I could remember what it was...). When we PCS'd back to Germany at the beginning of my junior year, there weren't "honors" classes. But, only the "honors"-type kids were the ones taking trig and pre-calc. We had the coolest teacher. He was also the football/soccer coach. He would introduce a new chapter with lecture, give us the assignments and when the test would be, then leave us alone unless we needed help, in which he'd go over things again.

Posted by: Miss Ladybug at February 20, 2008 09:57 PM

The goal should not be to teach students to add. It should be to teach them how to have this very argument. When they can tell you which method they think is the best approach, and why, you've succeeded at teaching them the math.

Posted by: Grim at February 20, 2008 11:45 PM

Cass,

As a bit of a school heretic: hated it! I have a couple of opinions on the topic you raised in this post.


How will I help my 4 year old daughter with math homework that gives points for following a method I am completely unfamiliar with even if neither of us derive the correct answer? I also viewed the screed against the new math teaching methods and dislike the divorce from traditional mathematics instruction. As I understand it, the new method does not even teach the algorithms that I learned.


Is this another boys/girls divide in instruction which disadvantages one group in order to make something clearer to another group? Left purely to me, all students would be taught mathematics exactly as it was taught in 1920. For some reason these students were able to actually create and break unique encryption systems, they conceived, designed and built computers for the first time ever. They programmed the damned things. They not only designed atomic weapons they went beyond that and built atomic power plants and hydrogen weapons. They designed, without any computers whatsoever some of the most advanced aeronautic craft ever fielded from the B-17 to the B1 bomber, not to mention the Saturn V rockets, V1, V2 etc.


These scholar/scientists "understood" math.


These days by every single account nobody in any school in America "understands" math. The dismal performance of students on the academic tests simply prove this every day and yet the schools of education continue to insist on finding "new and improved" methods of instruction. I think they do this because the schools of education graduate the dimmest 10th of all college graduates and less than 1% of these losers actually understands math and of them, less than 1 in a 100 actually is capable of teaching/instructing students in math.


"follow the teacher's guide young phys.ed teacher and you too can school the tykes in the appropriate algorithm and they too will approach your understanding of fundamental mathematical processes."

Drat, no html tags to paragraph. C'est domage.

Posted by: Curtis at February 20, 2008 11:46 PM

"For some reason these students were able to actually create and break unique encryption systems..."

It seems to me that it's not surprising that someone with a 1920s education in math could break an encryption system created by someone with at 1920s education in math. Their minds were in the same place.

This is one reason the Navajo system worked so well: it was just totally outside the enemy's experience. They didn't even know how to imagine the basic structure of the language, which they would have to know before they could begin breaking the code.

Posted by: Grim at February 21, 2008 12:18 AM

Grim~

I think you've hit the nail squarely on the head...

Curtis~

I am a recently certified teacher (M.Ed), but I don't have my own classroom yet. I think that, unlike many elementary education students, I've got a good understanding of math. I haven't had to use all that higher math (trig/calc) since I got out of high school (don't need that with an undergraduate accounting degree, either). Depending on the age you're teaching in elementary school, math can be as simple as learning your numbers and shapes, and being able to recognize patterns as well as being able to duplicate or create them. Teaching money is also considered a math skill, although I'm not sure what grade that starts in (at least 1st). But you are right that some teachers teaching math don't really understand what they are doing. But, you wouldn't really have a gym teacher teaching math. I make the assumption that most states require secondary education teachers to have majored in their subject area (e.g. - a math teacher would major in math AND education; ; my dad had to major/minor in History and German to get his certification in those subjects (he likely tested out of a lot of German, since he was a linguist for the Army). Elementary education is different. For my master's, I took a semester long class that was basically "how to teach elementary" whatever: math science, social studies, English. Content area mastery for teaching elementary is assumed. Then, you have to pass your certification test. For a secondary education teacher, you have the content area you want to teach (e.g. - math). For elementary education, your certification exam covers all the subjects you are expected to teach. Has a lot less depth. At the testing location where I took my (computer based) certification exams (both content area & the pedagogy & professional responsibilities exams), the lady who ran/monitored the center seemed to marvel at my raw scores: 90+%. That made me feel sad - it indicated to me that she doesn't see those kinds of scores much. The question is: how to we fix that problem. Math knowledge starts in elementary school. The math taught in elementary shouldn't be difficult for an adult, especially on that is college educated. But, to get more focus (in all subject areas) for elementary education majors would be difficult. When you are going to school to become a teacher, you have no idea what grade you will end up teaching once you graduate and get certified. My certification is early childhood through 4th grade. There is a huge difference between what I'd teach in pre-K/Kinder and what I would teach a 4th grader..

Posted by: Miss Ladybug at February 21, 2008 12:31 AM

> I think he's right. I have mentioned this many times, but I tutored college algebra, stats and calculus for many years and found that in addition to lacking skills, the vast majority of students had little or no understanding of what they were doing or why they were doing it.

The problem, Cass, is when **the teachers don't understand the reason for teaching it that way either**

-- which is usually the case, since this stuff is often decided from on-high by people who don't teach and don't understand the stuff either.

I recall when I was young (the 60s, yes) there was a lot of furor over "The New Math" -- which was not being taught at all well... it was the first effort to create "a new way" as opposed to the rote-forms which WORK at the least (do we REALLY, REALLY need "new" means which teach our students LESS than the current system? They can barely make change as it is, and our predecessors learned enough to go to the MOON with these "lame" techniques).

Now, I have a much greater math ability than most, to the point where I taught myself calculus using a textbook when I was fifteen. As such, I've gone a lot farther in math than most.

Now, the reality is, it is possible to "derive" numbers from what is called Set Theory. You can use the properties of sets, which are fairly obvious to all when demonstrated, to develop the idea of counting numbers. From those you can get to integers, from integers to fractions, and from there to much more advanced concepts.

**THIS IS WHAT THE 'new math' WAS***

The problem is, if the teacher does not understand the WHY of the method, they can't answer the child's questions, or much less frame counter-questions to help the child learn/figure things out for themselves.

The advantage of those rote methods are threefold:
a) They are readily learned and understood, and are time-tested for this quality.
b) They were, as noted above, clearly adequate to get men to the moon.
c) MOST people really, really don't NEED to understand numbers deeply. I personally think they should, but I have a pro-math bias, so I am careful not to overvalue my own skillset. Most jobs do NOT use calculus, even if the major in question uses it as a weed-out course -- Hell, architects don't even use Trig after they leave college, so all people really need to function in our current society is a good, functional knowledge of Algebra. More is GREAT, but it's NOT NEEDED, despite the commercial which suggests otherwise.

Too many people can't make change properly. This country does NOT need "more and better" techniques for educating. To do this properly requires not only testing the technique to show that it actually produces a better understanding than the "rote" methods (and no, I don't believe anything resembling functional tests of this sort of thing really, really get done, since it would take YEARS to do so, testing kids several years later to see the long-term effects), but it would almost always require a serious training effort on the part of the school admins to make sure that the teachers UNDERSTOOD why they were teaching it the way they were, as opposed to "the other way". Training is never a well-done thing in any environment, as most organizations fail to grasp that the up-front value isn't visible (though the back-end value is enormous) -- but it certainly has up-front costs.

Sorry, I'm a Luddite on this one. Use methods that WE KNOW WORK to teach math. We're getting into the third generation now who can't grasp basic math concepts. That has bad implications for both this nation and for the world as a whole. Democracy works when its populace is literate and capable. It's nothing but a bleating mob of sheep when neither is true.

I forget who it was that said:
"If this educational system had been imposed from outside the nation, it would constitute an act of war"

Posted by: obloodyhell at February 21, 2008 09:01 AM

> My first grade teacher refused to teach me to write left handed.

I've had similar idiots in school. I got an 'F' in fifth grade for reading... at the same time when I was reading '2001: A Space Odyssey'! They kept giving me this utterly boring crap to read that I had no interest in at all.

The point wasn't to learn to read, it was to learn to hate reading.

Seriously.

I've noticed this even through college -- most people get out of college and NEVER read anything voluntarily ever again -- or if they do, it's some random thing which has no learning value at all, like Barbara Cartland novels.

The point seems to be to make people get so sick of reading CRAP that they have no interest in reading that their brain associates reading with pain and discomfort.

Schools aren't about learning -- they're about indoctrination.

This is why homeschooling works so much better -- it's about learning and NOT about indoctrination.

Posted by: obloodyhell at February 21, 2008 09:13 AM

Have u try the
Math study online bookstore Cocomartini.com

http://www.cocomartini.com

I get all my textbooks for this semester from this bookstore. All are brand new textbooks and half price discount textbooks and cheap textbooks.

Good luck and wish some help.

hehe ^_^

Posted by: Jessica at February 21, 2008 11:51 AM

My quarrel with the public schools began 15 years ago and has been reinforced because of moves to states where there was intellectual dishonesty practiced in order to keep their accreditation.

There are other issues, but suffice it to say that
you find what works, and if you are ANY kind of a mentor/parent/teacher at all, you do your damnedest to make sure that your students learn and if that means giving them homework and holding them to a standard, then that is what you do. It is up to them to do it. I see it as a two way street. If the teacher is busting his or her gut to be there and prepare a lesson, it is rude to not pay attention. Teacher's pet crap be hanged.

But I also take issue with classroom overcrowding, because every child needs to learn according to ability. Our special guy has a self contained classroom...he also goes out to Resources and one other class. He is NOT looking forward to high school, and that is looming at the end of this summer.

Posted by: Cricket at February 21, 2008 05:07 PM

>Schools aren't about learning -- they're about >indoctrination.

Well, the worst of them are. I had two teachers who were saints in the first 12 years. The rest were varying degrees of moron. This was the public school system, first in Washington state and then in California. They were the only reason I made it through high school. One was my fourth grade teacher, the other my high school English teacher for the "gifted" program. She was a Stanford graduate, and believe me, NO ONE gave this lady any lip.

I had been placed in an English class taught by a Mexican woman who couldn't pass retard English and I was supposedly college bound. I told my counselor I would not take a class from this idiot and the argument escalated. My mom was a smart woman who also taught Latin and English at the school I attended. She raised hell about it. I took a 3 week vacation from school and refused to comply with any requirtements. Yep, full scale mutiny that almost got me expelled. This wasn't very bright, but none the less what I did to make a point.

One day a PE coach decided I was going to call him "sir". I told him I would die first, that I loved and respected my father, whom I did not address as sir, and that I didn't even like the the jerk. He could go piss up a rope. Off to the principal's office.

Anyway, back to the revered Monterey Morrisey, my senior English teacher. I would have walked over red hot coals for her. She is gone now, but was a tremendous personality and influence on me at a critical time in my life.

After my mutiny, my mother and Ms. Morrisey flat out refused to teach the then hip version of ebonics. They said it was racist crap and guaranteed second class citizenship to those it was inflicted upon. I was laughing myself silly after having been read the riot act for my misbehavior. You never saw an administrator back down so fast in your life.

Posted by: Mark at February 21, 2008 05:14 PM

Mark~

Special teachers can make all the difference. I still keep in touch with my sixth grade teacher, who has finally retired as of a couple of years ago. She taught in DoDDS schools for ages. I also keep in touch with two of my high school teachers (they're married): I was in his government class and did a class period as an aide, and I had her for accounting. They were also DoDDS teachers. I swear, most DoDDS schools were like going to a private school - small classes and (generally) excellent teachers (yeah, that math teacher/football & soccer coach was a DoDDS teacher, too). I pseudo-keep in touch with my high school German teacher (DoDDS), but he suffers from BDS, so it's pretty much the exchange of Christmas letters...

Posted by: Miss Ladybug at February 21, 2008 05:35 PM

If you look at the history of education there was a movement that aligns with the progressive movement in America, probably starting with Dewey that put more emphasis on socialization than on rigor. Michael Barone calls it softening. Your reference to the forties aligns with this softening and was promoted by the establishment.

After sputnik there was a temporary harding and an increase in rigor that benefited the next generation that ironically went on to revert back to the softening. Perhaps you have heard of the Rhodes scholar Clinton and his wife.

The math in question sounds interesting to me. I would teach it, after I taught the traditional method.

As a teacher I find myself teaching the same thing in a variety of ways until it clicks with as many as possible.

Posted by: Pile On at February 21, 2008 08:29 PM

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