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27 Sep 2005  19:59
tour de force
Engineering school is a rude awakening for most college freshmen. Many students are surprised to learn that their previous thirteen years of formal schooling have not adequately prepared them for the rigors of engineering school. Sadly, about 2/3rds of them, some very bright motivated students, won't make it through the program. This is what you learn by the end of freshman year: 1. You had been coddled the past thirteen years by your K12 teachers. You were mostly spoon fed the material, at a slow pace, and then tested on how well you could regurgitate the exact same material back to the teacher in the exam. Rarely, if ever, were you required to apply the knowledge you had learned to solving new problems you hadn’t seen before. As a result, you could, and probably did get by, without mastering the concepts as well as you should have. You are finding out the hard way that most of your knowledge is still at the inflexible stage. This would be most apparent in... 2. Algebra: A course you took four years ago and didn’t learn well enough is coming back to haunt you now in calculus. Calculus seems much more difficult than it did when you took it last year in high school. This is because the pace is twice as fast and the exams require more than a regurgitation of what was taught (or rather won't be, see below). You see, mathematics is brutally cumulative. Calculus is really 10% calculus and 90% algebra (which includes a healthy does of trigonometry and geometry); and, the calculus step isn’t all that difficult usually. Most of the difficulty lies in either setting up the calculus step or finishing the problem after the calculus step. Calculus isn't all that difficult provided you've mastered algebra. In high school, they allowed you over the algebra bridge without paying the full toll and you’re paying the price now, especially if you hobbled over on your graphing calculator. Anyway, you’ll need to know calculus and algebra cold if you expect to pass Physics I next semester. But this is going to be close to impossible because... 3. Your professors don’t teach and you can barely understand your TA’s poor English. This is more of an expectation problem; you’re still expecting to be coddled like you were in high school. Now you are expected to read the new material on your own and attempt to solve the problems before coming to class. This is a feature, not a bug. By teaching yourself, you will be forced to understand and master the material, assuming you are doing the homework problems beforehand. Which you haven’t been doing because there just isn’t enough hours in the day to teach yourself and then do every problem assigned in every class. So you dutifully copy down the answers that the TA gives you during the class review all the while thinking “hey, that wasn’t so hard, now that someone’s showed me.” But, “understanding when explained by others” is not the same thing as the “ability to explain to others” which will become brutally apparent... 4. When you fail your first exam. The first test you’ve ever failed in thirteen years. You crammed the whole night before, but the test was too hard and too long. Goodbye unearned selfesteem; hello magic number 7. Seven is the number of things you can hold in working memory at one time. Partially learned knowledge uses more of these seven slots and takes longer to process than fully mastered knowledge. Your brain is being tested to its capacity for the first time and it's not prepared. You’ll become casual acquaintances with magic number 7 this semester and good friends next semester in Physics I because... 5. All those damn physics equations. Your brain is full. It feels like every time you learn something new it’s pushing something else out – like your name and your address. Spring semester brings with it Chemistry II (which requires you to remember everything you learned in Chem I), Calculus II (also brutally cumulative with Calc I), Computer Programming (learning new languages isn’t easy, especially when that language is C++); English Composition (your only easy class, too bad you have to do a term paper that’s twice as long as anything you’ve ever written before); and lastly Physics I, which will be... 6. The course that you’ll blame when you transfer to business school. Physics I – the rock upon which many engineering education ships have foundered. Two reasons – word problems from hell and the magic number seven. Physics is your first real test in your education career. It tests how well you are learning not only physics (under a withering course load of other difficult courses), but also how well you previously learned algebra and calculus. It is the latter two that will be your demise because you need every brain cell you can muster to learn physics today. If you’re expending too many brain cycles recalling how to do the necessary calculus (most likely because you don’t sufficiently know the underlying algebra) sooner or later you’re going to meet the magic number seven. Meeting the magic number seven is like running out of active memory. You become overwhelmed and inefficient. Eventually, it all ends in tears (or an extra year of college after you’ve transferred to a nice soft major like human resources, communications, women studies, etc). So you lash out and look for someone to blame... 7. Like your college engineering department. Wrong. The train was slipping off the tracks well before they came into the picture, most likely sometime in elementary school. Don’t blame them because the train finally derailed at their station. Don’t be like the drunk who’s looking for his lost keys under the streetlights because that’s where the most light is. A career in engineering or in one of the hard sciences was effectively foreclosed to you by the 8th grade,. Most likely, you would have been none the wiser had you stayed in the soft fuzzy land of almost every other undergraduate field of study. Everyone would have been happier too because, well, you don’t know what you don’t know. Anyway, you can at least find solace in the words of Homer Simpson when he said to Lisa and Bart after they failed: “Kids, you tried your best and you failed miserably. The lesson is, never try.” But why blame yourself when you can blame the real culprit... 8. Your rotten K12 education. Oh sure, they meant well; but look what happened. You see, you’re not part of the lower half of the bell curve who probably shouldn’t be pursuing a career in engineering or the hard sciences anyway. Nor, are you part of the two standard deviations and above gang that have the ability to succeed and compensate for a rotten education. No, you’re part of the curve that needed a good education to succeed and you didn’t get it. And, it wasn’t a single chop that lopped your head off; rather it was death by a thousand tiny paper cuts. The accumulation of thirteen years of inefficiencies and unsound practices that prevented you from mastering and overlearning the material you needed to succeed in a rigorous college curriculum. Instead of teaching you content and facts and making you practice until automaticity, your wellmeaning teachers were feed a bunch of scientifically and cognitively unsound educational fads  constructivism, discovery learning, childcentered education, and social promotion to name a few. They all sounded so lovely in theory, yet in practice have consistently failed to adequately teach students as you have just found out. The hard way. This advice may have arrived too late to help you; but it is not too late for that kid who just started kindergarten who lives down the street. This article is really for his or her parents, but they probably need to hear your story first before they begin to take it seriously. After all, you believed everything your K12 educators told you and your parents, and look what happened.
 contributed by Kenneth DeRosa, October, 2005
updatethe magical number 7, plus or minus 2 Confessions of an engineering school washout more confessions of an engineering school washout the Terminator, or 'the magical number 7, plus or minus 2' On Having a Math Brain (by Carolyn) Wayne Wickelgren on mastery of math & on creativity & domain knowledge late bloomers in math & Wickelgren on children's desire to learn math math brain debunked (by Carolyn) math professors versus computer science professors Wayne Wickelgren on math talent grandmasters and the magical number 7 Wickelgren on introducing algebra Wayne Wickelgren on algebra in 7th & 8th grade Wickelgren on math talent & when to supplement late bloomers in math & Wickelgren on children's desire to learn math Wayne Wickelgren on mastery of math & on creativity & domain knowledge Wickelgren on why math is confusing
Back to main page. CommentsAfter entering a comment, users can login anonymously as KtmGuest (password: guest) when prompted.Please consider registering as a regular user. Look here for syntax help. Here's another one.  CatherineJohnson  27 Sep 2005
Wow. That's a keeper.  SusanS  27 Sep 2005
File under people unclear on the concept: Some time ago, during a corporate template committee meeting (this might actually be less exciting than you could imagine), someone brought up the 7 +/ 2 concept in a discussion when to break up numbered lists in technical documents. In the end, some people were pushing for all numbered lists to contain 7 +/ 2 steps. First, it's not apparent to me how bandwidth issues would apply to a numbered list of steps. At the most, you'd usually only have to remember the last step, this step, and the next step. Second, some procedures have only one or two discrete steps, so adding steps to meet the magic number is just silly. But even more important, if it did apply to such a highly structured set of tasks, surely the appropriate number would have been "not greater than 5". If most people can only keep 59 things in mind at once, then some part of "most people" can only keep 5 things in mind at once. Still, since the number was magic and all it must have some mystical application to all things, so I guess I was wrong.  DougSundseth  27 Sep 2005
Wow, that is sooooo true. I work in the office of an engineering dept. at a college, and my husband is a Master's student in engineering. We've had students who struggled through our engineering curriculum in 68 years, because they flunked Calc 1, then passed it, then flunked Calc 2, then flunked Physics 1, then finally passed both, etc. No more! We've instituted a rule that if a student earns 3 D's or F's in the 1st two years worth of engineering curriculum he/she must change majors. We hope that this will wake students up to the fact that for whatever reason, be it lack of motivation or lack of prerequisite knowledge, they are not ready to pursue engineering. We do let them reapply after spending 1 year away from our curriculum, but most of them have already found a major that fits them better by then.  AndyJoy  27 Sep 2005
Susan no kidding we should hand this out to parents of Kindergartners also to teachers of Kindergartners and to the NCTM, NSF, Prentice Hall, & Scott Foreman and everyone else under the sun
 CatherineJohnson  27 Sep 2005
it is definitely the magical number 7, plus or minus 2 ++++ so, uh, people were contemplating ADDING stuff to get UP to 7?  CatherineJohnson  27 Sep 2005
that would severely defeat the purpose of knowing about the magical number 7, plus or minus 2 in the first place  CatherineJohnson  27 Sep 2005
I realize it's time for me to go back and read The Magical Number 7 again. It was published in 1956, and it's a classic. Here's the conclusion:
Summary The Magical Number 7, Plus or Minus 2: Some Limits on Our Capacity for Processing Information by George A. Miller  CatherineJohnson  27 Sep 2005
I'm serious about handing this out to people, though. This is the single best WAKE UP AND SMELL THE COFFEE piece of writing I've ever seen. This thing is The Terminator of math ed writing. It just keeps coming.  CatherineJohnson  27 Sep 2005
I mean, what exactly is your constructivist comeback here?  CatherineJohnson  27 Sep 2005
There isn't one.  CatherineJohnson  27 Sep 2005
We should get Sigourney Weaver to do a staged reading The Mathematics Monologues  CatherineJohnson  27 Sep 2005
I wonder if AMERICAN EDUCATOR would publish it? Or EDUCATION NEXT?  CatherineJohnson  27 Sep 2005
Holy freakin' wow!  IndependentGeorge  27 Sep 2005
This is very familiar territory for me... I'm actually a biochemistry washout. I switched to economics during my third year, when I was taking Physics, 2ndyear Organic Chem, and Math for Physical Sciences, and had Physical Chemistry looming on the horizon. I think I could have handled any one of them (I got through OChem, calc, and stats just fine, but that was spread out over two years), but together... My choice was to either take six years to earn a degree in something I was struggling with, or get the heck out. I didn't so much hit the magic number 7 as I got splattered against it headfirst.  IndependentGeorge  27 Sep 2005
PLEASE don't tell me ECONOMICS is EASIER than BIOCHEMISTRY! I think of economics as The Hardest Subject On Earth  CatherineJohnson  27 Sep 2005
I didn't so much hit the magic number 7 as I got splattered against it headfirst. That's going in Wit and Wisdom of Kitchen Table Math  CatherineJohnson  27 Sep 2005
Catherine  econ got easy once I discover the Costanza Theorem: All of my instincts are wrong; therefore, I must do the opposite of what I think. Seriously, though, I was good at the chemistry. I got chemistry. It was the intersection of chemistry & physics that killed me. In undergrad econ, you rarely had to deal with more than 2variable calculus (and even then, it was all calculation; no theory at all). Physical chemistry involves calculus along n dimensions, and was fairly theoryheavy. I was good at Newtonian physics, struggled with electricity/magnetism, and gave up before I could fail thermodynamics/quantum mechanics. It was my third year, I figured if I was struggling that mightily with the physics and math at that level, I would be completely lost when it came time for PChem (taken during your senior year; including lab, the course met for 20 hours a week). I think I might have done well in any of those classes individually; but all at once was way too much to handle. As they say in the economics department, "sunk costs are sunk"; I changed majors before I added another $25,000 to my student loans.  IndependentGeorge  27 Sep 2005
I love it!!! I absolutely love that an engineer can write so elegantly and get his point across so well about an engineering education. I, unfortunately, cannot. But I will tell you that I majored in Chem E. I must have had an old fashioned math and science education from my public school because I found that the first year of eng school was just a repeat of what I had in high school. So I was able to get used to all things in college including the pace of college classes with material that was already familiar to me. It made life a whole lot easier.  AnneDwyer  28 Sep 2005
i'm still in shock  CatherineJohnson  28 Sep 2005
Catherine  econ got easy once I discover the Costanza Theorem: All of my instincts are wrong; therefore, I must do the opposite of what I think. Well that one's a big help, I agree!  CatherineJohnson  28 Sep 2005
and here i've been thinking the Summit of Hard Math Courses was econ  CatherineJohnson  28 Sep 2005
I know nothing  CatherineJohnson  28 Sep 2005
otoh, i'm glad to hear this, because my reallife goal for Christopher is that he should be able to handle the math involved in economics his dad is a historian, Christopher is a social studies freak, I'm a writer (and majored in psychcog & social psych, as it happensin undergrad) so the chances of his being drawn to academia are high. I've like him to be able to at least consider going into a part of academia that involves math, and has job prospects outside the university.
 CatherineJohnson  28 Sep 2005
Arnold Kling says academic economics has become insanely mathematicalis that right?  CatherineJohnson  28 Sep 2005
The other thing I've been thinking, and this is pure speculation, is that the field of history may experience another wave of math. Back in the....60s? 70s? historians were trying to use math & statistics in history, and it didn't work out, primarily because of inadequate historical sources. But the little I know about calculus at this point (mathematics of change??) tells me that someone's going to try to find a way to apply calculus to history that will be different from the statistical efforts made in the 70s. For instance, 'big history' is now a reality. Ed just ordered a copy of Maps of Time: An Introduction to Big History by David Christian. Big history is one strange concept, and the fact that it's come into existence tells me there will be more strangeness to come...  CatherineJohnson  28 Sep 2005
"You see, calculus is 10% calculus and 90% algebra (which includes a healthy does of trigonometry and geometry); and the calculus step isn’t all that difficult usually." That is my opinion too. I had algebra I in 8th grade and Calculus as a senior. It took me until my junior year in high school to feel like I had mastered algebra. Calculus had some new concepts and ideas, but it wasn't that difficult. For most students, it's all over before they even get to algebra. The problem is not college. The problem is not even high school. The problem is grades K8. It bothers me that people complain about high schools and colleges, but fail to trace the problems back to the source.
 SteveH  28 Sep 2005
"Arnold Kling says academic economics has become insanely mathematicalis that right??\" Yes, that is right. On the other hand, it may be a passing fad. But no, econ is far from being the pinnacle of hard math courses. That honor would probably have to go to algebraic geometry or group representation theory. And yes, it's a fantastic post.  BernieJohnston  28 Sep 2005
Bernie, I think algebraic geometry is tougher than group representation theory. But thanks anyway ;)  CarolynJohnston  28 Sep 2005
The problem is indeed K7 elementary math which fails to adequately prepare most students for algebra in 8th or 9th grade. In both the traditional (at least in the US) and the constructivist curricula, students are just not taught to think algebraically until day one in algebra class. At least in the traditional curriculum students there is a possibility that the students have mastered multiplication, division, and fractions which will free up some brain capacity for learning algebra. And, since many of the most important elementary math concepts are reviewed during algebra, at least for the kids who learn algebra, there is some compensation for the previous seven years. This doesn't help the group that won't adequately learn algebra, and, to boot, they won't relearn elementary math either. Turning to the constructivist curriculum, the mishmash of nonsense taught in K7 certainly doesn't teach elementray math basics to mastery (strike one) and doesn't teach algebraic concepts any better either (strike two) since students consistent fail to outperform the traditional students. Moreover, their nonmastery of the basics will hobble them in learning algebra. This is why I think the Singapore curriculum is so effective in raising performance. It teaches the basics to mastery and gradually introduces algebraic concepts, so the junp in difficulty in algebra class is not so abrupt. Plus, TIMMS is clarly showing that Singapore is far more effective at teaching math to the lower parts of the curve.
 KDeRosa  28 Sep 2005
"The problem is indeed K7 elementary math which fails to adequately prepare most students for algebra in 8th or 9th grade. In both the traditional (at least in the US) and the constructivist curricula, students are just not taught to think algebraically until day one in algebra class." Bingo. Again.  CarolynJohnston  28 Sep 2005
At least in the traditional curriculum students there is a possibility that the students have mastered multiplication, division, and fractions which will free up some brain capacity for learning algebra. This is absolutely true, IMO. I haven't been able to arrive at a stable opinion of my own K12 math education, but I did certainly acquire procedural fluency in the four operations applied to integers and to fractions. Just that alone has been a huge source of 'capacity' in everyday, real life.  CatherineJohnson  28 Sep 2005
TIMMS is clarly showing that Singapore is far more effective at teaching math to the lower parts of the curve. Absolutely.  CatherineJohnson  28 Sep 2005
What is the 'jump' to algebra? I'm assuming it's the jump from specific numbers & number expressions to variable expressions. But is that what you mean?  CatherineJohnson  28 Sep 2005
I skipped all that college stuff (it did go too fast in some subjects, too slow in others) by teaching myself engineering. I have worked for some large aerospace companies and hardware/software I have designed is protecting you in flight. In fact some math routines I designed were flying on the F16. May still be. BTW I went to one of the top science and math high schools in the country. Omaha Central. I might add that the US Navy knows how to teach. They cram about 2 to 3 years of engineering training into 6 months of theory and 6 months of practical application. Once you have your specialty down. Mine was electronics. However, I knew that so well that I was often teaching the course and helping the slower students pass. Being a radio amateur at age 13 helped a lot. In any case the Navy went faster but for me was easier. Why? The instructors knew their subjects backwards and forwards. If asked for an explanation they could give one. They worked hard to get inside the minds of the students to figure out what the student's problem was. They cared. Why? Because they were graded on how well they taught the material. They lost their jobs if they didn't do well. No tenure. M. Simon
 KtmGuest  28 Sep 2005
I got PChem in my first year of college. I found it rather easy. I hit the wall in multivariable differentials. (which I now get) Heat transfer and fluid flow (which I got in the Navy) some find very hard. I sat in the back of the class reading motorcycle magazines and occasionally correcting the UC Berkely Physics Professor's mistakes. Now there was a hoot. The prof rarely called on me. I made him look bad. Still, he was quite good. The #1 problem in our teacing corps is tenure. M. Simon  KtmGuest  28 Sep 2005
And yet. College was not for me. So what if it takes 6 or 7 years to learn engineering. Shouldn't desire and tenacity count? Such desire worked for me. But I had to do it outside of school. Being outside of school did help me. When microprocessors were new and there were not enough teachers to go around I taught myself. School can teach you how to learn with help. Learning on your own teaches you how to learn with no help. It ought to be valued more. In fact learning with no help is exactly what you want on the frontiers. M. Simon  KtmGuest  28 Sep 2005
M. Simon This is incredibly encouraging, because I've been thinking math is harder to selfteach. I do selfteaching all the time, on all kinds of different topics, but math has seemed much less approachable this way. You're making me think I'm wrong.
 CatherineJohnson  28 Sep 2005
Tenure is a huge problem. If you paid & promoted folks on how well they teach, you'd see good teaching.  CatherineJohnson  28 Sep 2005
In any case the Navy went faster but for me was easier. Why? The instructors knew their subjects backwards and forwards. If asked for an explanation they could give one. They worked hard to get inside the minds of the students to figure out what the student's problem was. They cared. Why? Because they were graded on how well they taught the material. They lost their jobs if they didn't do well. This backs up what I was saying about academic incentives in this post  some teachers are conscientious, but if good teaching isn't built right into academic incentives, then it's just a matter of luck whether you get it or not. Actually, it makes perfect sense that the DOD would have the best engineering training around. In fact, I believe Mr. Saxon was an electrical engineering teacher at the Air Force Academy in Colorado. Yes, he was. Here's his bio.  CarolynJohnston  28 Sep 2005
C++ is the most God forsaken complication piled on top of complication with notation from hell. I'd rather do bare metal programming i.e. assembly language (which most C folks do not get). A really elegant language which was object oriented before C++ came on the scene is FORTH. A pity it never caught on. Programming would be a lot simpler. Thus easier to do and easier to test and debug. And no time wasting stack frame context switches. BTW the stack frame is an abominatiion. And yes I have used them (out of necessity) in writing driver programs. And pray tell why is the ability to only pass one item out of a routine (without variables) a good idea? Data Stack, Return Stack. A very good idea. And have you ever tried to design a processor that uses C as its native language? It is an abomination. With FORTH such a processor is elegant and simple. Plus there are a lot fewer gates switching for each instructiion  lower power. Did I mention pipelines? Which are a kludge that wastes power and instruction cycles and gates (especially on context switches) to cover up the deficiencies of using C. And how about branch predictors? Which basically is another version of the Turing stopping problem. Which can only be done poorly if at all. The theory is "we will use a lousy language everyone knows and cover up its faults by throwing a lot of complicated hardware at it". FEH. C is exactly what you get when the software and hardware are not a unified discipline. And we do not teach them as a unified discilpline. Why? Because hardware is much harder to learn and we need a lot of coders fast because our core language is lousy. FEH. M. Simon  KtmGuest  28 Sep 2005
I believe Mr. Saxon was an electrical engineering teacher at the Air Force Academy in Colorado. I didn't know that!  CatherineJohnson  28 Sep 2005
I always heard that he'd had trouble learning math, and had sat down to write a textbook that would have taught him math the right way.
 CatherineJohnson  28 Sep 2005
Another myth dispelled.  CatherineJohnson  28 Sep 2005
How much of the stuff inside my head is just completely and totally 100% wrong?  CatherineJohnson  28 Sep 2005
AND WILL I FIND OUT BEFORE IT'S TOO LATE?  CatherineJohnson  28 Sep 2005
I am against C+++  CatherineJohnson  28 Sep 2005
I am for FORTH  CatherineJohnson  28 Sep 2005
I would like the world to be a more rational place  CatherineJohnson  28 Sep 2005
I always heard that he'd had trouble learning math, and had sat down to write a textbook that would have taught him math the right way. Another myth dispelled. Catherine  John Saxon may not have been a math whiz. He may have had a HELL of a lot of trouble learning math. That was the point I was trying to make with my Math Brain post.
 CarolynJohnston  28 Sep 2005
The answer to teaching physics is PSSC Physics. It teaches you how to think physics. In high school. The experiments are elegant, simple, cheap. It fell out of favor when some new fad came along. The Physical Science Study Comittee was the answer to weak science education in the post Sputnik "America is falling behind" scare. Very little math on the tests. A lot of exceedingly hard thought problems. It made you understand the relations in your bones. We know how to do it right. The question is why don't we? BTW my #2 son went to Auburn High in Rockford, Illinois and got an excellent science education. So good he was helping his friends. So even podunk towns can do it well with motivated teachers and students. Naturally they have a gifted program. Rigorous. Disciplined. Hard. Excellent preparation. In fact it was so good that he passed out of most of his first year courses at the University of Chicago. (BTW my school  1 year  as well) He is a language major (Russian) but could have done engineering or science had it been a major interest of his. Full scholarship too. Our very best do well in America. Why? Because teachers compete to teach the gifted. The fewer the talents of the students the fewer the talents of the teachers. Which is probably not bad. What hurts is that the drop off in teacher talent is quite steep below the top 10 or 20%. Tenure. and Fads. BTW a lot of it starts at home. There are things middle class parents do that those on the bottom do not do. Like talk to the kids from day zero. Homes filled with puzzle toys and books. Like teach the kids phonics at home so that whole language doesn't ruin them at school. M. Simon  KtmGuest  28 Sep 2005
M Simonwhat is PSSC Physics? Is it like SMSG math?  CatherineJohnson  28 Sep 2005
"C++ is the most God forsaken complication piled on top of complication with notation from hell." I started with Fortran (card decks) and graduated to C in about 1980. I like C, but I don't like C++, with all of the frameworks and classes upon classes. At one point I was going to write a large class that handled all sorts of vector and matrix operations. Then I realized that it added nothing to the simple (and much more transparent) function library approach. It might be cool to have notation that handles dot and cross products, but no one else would be able to figure it out. I do remember that even for C there were some who felt it was their duty to create impenetrable code. It showed that you were a good programmer that knew C. I don't get too excited about computer languages anymore. The all have their strengths and weaknesses. I have seen a lot, from Fortran, to Pascal, to APL, to Snowball, to PL/I, to C,C++, and Java. And, I have used all sorts of assembly languages. I just want things to stop changing. I was not happy when there was a push to Java and CSharp. And now they all assume that you "App" has to be internet friendly and load it up with all sorts of baggage. OK, OK. But I didn't start this.
 SteveH  28 Sep 2005
Wow, this really is a small internet. I'm actually a semiregular reader of M. Simon's blog, which covers energy policy and economics better than anything I've ever seen in the mainstream (as in, not trade journals) media. Welcome to our treehouse, Mr. Simon; I do hope you stay. Just out of curiosity, how did you find us? I started reading your blog because of your contributions over at Winds of Change; as far as I know, these two blog worlds have never crossed.  IndependentGeorge  28 Sep 2005
"C++ is the most God forsaken complication piled on top of complication with notation from hell." C++ is my native language, actually. Its design is not ideal  it's an objectoriented graft onto a procedural language. But it serves its purpose well enough.  CarolynJohnston  28 Sep 2005
Oh my goodness! I didn't even know about M. Simon's blog! Thanks!  CatherineJohnson  28 Sep 2005
"What is the 'jump' to algebra?" I think one difficult conceptual jump is the introduction of variables for the first time  variables that need to be isolated and manipulated in order to solve the problem. In elementary mathematics, the variable is there at least implicitly but it is already isolated on the other side of the equal sign. Another difficult conceptual jump is the use of multistep algorithms to solve almost every problem. The only place this is really needed in elementary math is the long division algorithm which we all know isn't always being taught effectively. Another is having to recognize and manipulate algebraic chunks as a single unit, especially when fractions are involved. How is a student who hasn't mastered the manipulation of fractions with constants going to be able to manipulate fractions with complex algebraic expressions in them? Now imagine the hapless student trying (slowly) to solve a problem having a coupel of complex algebraic expressions (some in fraction form) using only her partial and/or inflexible knowledge in the seven placeholders she has in memory.  KDeRosa  28 Sep 2005
On Carolyn's PSSC question. Yes, PSSC is the science analog of SMSG. I remember some high schools in Detroit where I grew up using the PSSC text. I don't know too much else about it, but have heard it was good elsewhere and now here. Regarding the "jump" to algebra. When I learned arithmetic (as it was then called), we had to solve problems to find what "n" was, which was rather simple algebra. I remember getting an intro to algebra in the last few weeks of 8th grade, and I can recall it making perfect sense (letters for numbers, expressing mathematical ideas in symbols like John is two times older than Bob, and we would write J = 2B). I also recall in 9th grade when I had the full fledged algebra class, that suddenly "arithmetic" seemed a whole lot easier and I wished they had taught us this stuff in the 6th grade. I think this is the natural progression to algebra. If you pave the road correctly, algebra will seem a natural extension of arithmetic. I've heard it called a generalization of arithmetic. But in today's hodge podge of socalled math classes, kids are lucky if they know their math facts let alone how to do the basic operations without a calculator. So algebra is indeed a jump, and oneunfortunatelythat many are sadly unprepared.  BarryGarelick  28 Sep 2005
SteveH sez I just want things to stop changing.
and i say bravo. why i am not a computerhead:
following up on my early plug for languagelog,  VlorbikDotCom  29 Sep 2005
" ... manipulate algebraic chunks ..." When I taught college algebra (!?!) I used to call them "chunks" too. I spent a lot of time showing the students how to move things around in rational expressions, like moving anything up or down in a fraction by just changing the sign of the exponent. First, however, I had to explain how everything is a fraction if you divide it by one, and everything has an exponent, even if it is just one. Algebra is a long slog, with many conceptual leaps. Even if you know how to add, subtract, multiply, and divide fractions with numbers, fractions that contain several variables, constants, exponents, and perhaps trig functions can seem like another world.
 SteveH  29 Sep 2005
Barry  if John is two times older than Bob, then J = B + 2B = 3B, not 2B. Pet peeve. "older than" = "as old as".  KtmGuest  29 Sep 2005
Argh, that was "not equal" but my "not" got eaten.  KtmGuest  29 Sep 2005
Steve First, however, I had to explain how everything is a fraction if you divide it by one, and everything has an exponent, even if it is just one. I think this is a bit of a 'foundational concept.' I'm finding myself, now, telling Christopher that  ( 3) can be thought of as 1 x  3, or as 1 x 1 x 3. The idea that everything is a fraction is extremely useful & important, I think....  CatherineJohnson  29 Sep 2005
Steve fractions that contain several variables, constants, exponents, and perhaps trig functions can seem like another world Let's put it this way: they definitely come as a surprise.  CatherineJohnson  29 Sep 2005
KDeRosa^{?}'s tour de force piece is one of the most extraordinary pieces of writing on the importance of math proficiency early on that I have read. Could I get permission from KDeRosa^{?} and KTM to reproduce it at my site with brief introduction and commentary?  CharlesH  09 Oct 2005
Reading this through again just now, I still laughed out loud when I got to the part about blaming Physics 1 for your transfer to business school. This essay is brutally cumulative.  CatherineJohnson  13 Oct 2005
thanks for the update; very well done.  VlorbikDotCom  13 Oct 2005
My favorite part is the drunk looking for his keys right under the light. That just says it all.  SusanS  13 Oct 2005
 CatherineJohnson  18 Jan 2006
One other thing that must be considered is the philosophy of Education of the placing doing the education.... Some colleges have a reputation that they want to protect and have students beating down their doors to get in. In these schools it's more common for the philosophy to be, to restrict their diploma to only the smallest most gifted students. In these schools the testing is more to differentiate the ability of different students than to test for their mastery of the material. How do you know when you are in one of these schools... when a passing grade is much lower than 100% ...ie if a 30% is passing.... Some colleges are more interesting in educating everyone. They focus on the material to be learned and they would consider a class a success if everyone got 100% on the tests, as they want everyone to know the material.
 KtmGuest  11 Jun 2006
 
