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arrghh
First of all: once again, I'm sorry to be MIA -- I'm looking forward to becoming a regular on my own blog some time again soon.
Second: help! help!
C's second calculus test came back today: a disappointment, and a Bad Sign. And I am fresh out of enthusiasm for dealing with another year of high school math. Meaning: I am fresh out of enthusiasm for dealing with high school math teaching and high school math grading and high school math hiring of high school math tutors to remediate high school math grading and high school non-learning of high school math and on and on and on and then further on and on some more.
I'm done.
Also: calculus tutors are few and far between. I found only one last year, and the lone session he had with C. didn't help. Other parents have told me they couldn't find calculus tutors, either, and for years I've been hearing things like: "My son did well in BC Calculus. We were lucky because his father can teach it." As I recall, the mom who told me her husband could re-teach BC Calculus at home also told me that her husband's first cousin was an economist who had won the Nobel Prize. I'm pretty sure I'm not making that up.
Nobody in this house can teach calculus. I haven't even finished taking algebra 2, and Ed has forgotten the calculus courses he took in high school and college and doesn't care to revisit them.
So here we are.
Also - and this is a repeat - last year's math class was a total, effing disaster. The teacher was and is seriously ill but is still teaching, and the kids were and are dropping like flies. A huge percentage of last year's AP Calculus AB students got 1s on the AP test. Ones. And when I say "huge percentage," I mean eighty-five or ninety percent: the guy broke the bell curve. This was the teacher C. had for pre-calc, so C. is bringing to this year's calculus course an epic level of non-preparedness.
The teacher C. has this year is supposed to be fantastic and in fact told us he was fantastic on Back to School Night (he actually said: "I am it," which was exhilarating at the time), but if the grades are not great then the learning is not great, either. Fantastic is as fantastic does.
Ed is thinking we should just transfer C. to AP Stat (or maybe it wouldn't even be AP Stat - maybe just "Stat Honors," a class in which, according to C., students recently took a test on bar charts after completing a bar chart project) and be done with it.
That's pretty much how I feel, too, but it leaves the problem of algebra 2 and calculus, neither of which C. will have learned in high school -- and neither of which I want him taking in college since he'll likely be attending a school with kids who are a lot better than he is in math. At this point it is crystal clear to me that there is no reason on Earth to take a math course in college, pay for it, get a bad grade in it, and not learn any math. And I'm thinking the same principle holds true for high school. Why spend a single second of your (child's) life in a non-required math course so he can not learn math?
Last data point: C. did fine on the first test in the class and thought he did well on this test, too. He did great on the diagnostic test going in, and is doing well in physics. His mistakes on this test appear to be mostly "careless errors" (I have a whole new take on the nature of careless error thanks to the SAT) and a failure to follow correct notation, etc. In short, he appears to understand the material, not that I would know.
Of course, if that's the case then he needs more practice - but how do we swing that? The teacher doesn't seem to use a textbook, and I'm not going to be able to scrounge useful practice sets this go-round as I did for the 3 years when C. was in middle school.
(Could I talk to the teacher? Why, yes indeed I could talk to the teacher. But seeing as how talking to a math teacher has yielded exactly zero results over lo these many years, talking to the teacher wasn't my first impulse. Writing a help desk post was my first impulse.)
So...any thoughts?
We had a great, great precalculus tutor last spring at the very end of the school year; if we'd hired him at the beginning of last year, C. might have learned pre-calculus. We could hire him again (I assume) and decree that this year C is actually going to learn pre-calculus, which means we could pay tuition for C. to study bar charts at his Jesuit high school and pay tutoring fees for him to study pre-calculus here at home --- who says Americans have to de-leverage?! If you've got kids in school and you want them to learn math, deleveraging is not for you!
Or....or what?
What else is out there?
He could enroll in a community college precalculus course -- when?
Now? While he's in high school? (While he's in high school commuting 15 miles there and back every day?)
Then take calculus over the summer?
Another question: are there solid precalculus and calculus courses online? I took all of the ALEKS geometry course and part of the ALEKS Algebra 1 course, and as much as I want to like ALEKS, as much as I do like the tone and feel of the site, I don't think ALEKS replaces a good teacher or a good textbook. But do others out there think that might be the way to go?
What about online schools and colleges? I know there are universities that offer online math courses that kids take when they've been expelled or can't physically attend their local schools for some reason. Is that a possibility? Any recommendations?
And while we're on the subject, can anyone out there explain to me how in this country does a smart student with no discernible learning, attentional, motivational, or emotional difficulties whose talents and interests lie in history/social science actually learn some damn math?
What does it take?
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104 comments:
I have no personal experience with him, but I have heard numerous raves about Courtney James' tutoring from fellow moms in our local homeschool support group. He tutors AP Calculus BC according to his website.
oh- interesting!
Thank you so much!
(I think you may have mentioned him before -- yes?)
Not sure I'll be particularly helpful, but...
1. How bad is it really? How much does this one test impact his class grade? I wouldn't think careless errors on a single test would be a reason to jump ship...
2. Isn't it C's responsibility to be talking to the teacher? Sure, you can do it, but he's going to need to be doing that when he is in college. Also, his current teachers might be more helpful to a student than a parent.
3. I don't know how it works, but my daughter's high school has math tutors that kids can go to for help. Is there anything like that available? (I'm guessing not.)Can you find the names of the math tutors at any nearby colleges and see if they would be interested? Also, with high school calc, help can sometimes be found from teens who have recently taken the course or have learned calculus elsewhere. Any really mathy kids in the area who might be able to help C? Of course, if his problem is careless errors, it might be difficult to figure out what kind of help he needs.
anyway...good luck...I suspect I'll be pulling out my hair about similar things in a few years.
Can you go to the local college's math department and ask if any good students would be willing to tutor?
My husband is an excellent calc tutor. Come see us...
If you scan the test and send me a copy, I can give my professional opinion on whether it's worth sticking with calculus or whether the errors show gaps too big to patch.
Also, there may be no reason for C. to ever take calculus during this phase of his life. Many colleges offer a wide-range of non-calculus math courses that count towards the requirements of non-technical majors.
For example, NYU's "Morse Academic Plan" lists the following four courses as the ones that fulfill the quantitative reasoning part of its requirements:
Math Patterns in Nature
Elementary Statistics
Probability, Stats, & Decision Making
Math and Computing
http://map.cas.nyu.edu/object/map.courses.quantitative.1112
I don't see calculus on that list. :)
Oh, wait, there's more.
You can get exempted from QR at NYU by having an SAT math score above 600 or by taking a course from the alternate list (which does include calculus).
http://map.cas.nyu.edu/page/exemptionsprofexams#quantitative
In my experience, this is not uncommon.
If it helps, I sat down and had a talk with the head of admissions at Stanford, and he repeated over and over that Stanford does whatever they can to avoid penalizing a kid for the shortcomings of his school, because kids can't choose their own schools. They want to see what the kid did "under the circumstances."
You've mentioned before that NYU is your first choice school, and there is no #2 (for very practical reasons.) If so, now might be a good time to have a talk with NYU admissions about your situation. After that talk, it might be much clearer what you should do.
If it turns out that calculus isn't going to be necessary, C. might be able to turn his attention to accomplishing something significant that is more in line with his own interests and of more interest to NYU.
But, if he needs to continue with calculus, then it may be time for C. to show them what he's capable of "under the circumstances." A kid who scores an 800 in reading ought to be able to learn from books. He may as well get used to it. Even in college, you can't count on having a teacher who really teaches. There's a reason the SAT tests reading comprehension, not listening comprehension.
I recommend that you keep your eye on the prize. You don't want to damage his opportunities at the last minute. Lots of students enter top colleges without having taken calculus, and doing really poorly in a class may not be interpreted as challenging oneself.
What does C. think?
"The teacher doesn't seem to use a textbook, ..."
No textbook for calculus? If he is "it", I would ask him what "it" can offer for help, since there is no textbook. I would first try to figure out whether the problem has to do with new or old material. I always say that algebra (I & II) are hard, not calculus. Then again, it could be that the teacher is not "it". How are the other kids doing in the class?
"His mistakes on this test appear to be mostly 'careless errors' "
Then I wouldn't necessarily throw in the towel yet, but just when you thought you could relax a little ....
Jean - where are you??!! (I'm in Westchester.)
Isn't it C's responsibility to be talking to the teacher?
He will, but we assume from experience that will go nowhere. He's done the talking-to-teachers thing; his friends have done the talking-to-teachers thing. Pointless. A FWOT, as CJ used to say.
If an experienced teacher can't figure out on his own that a classroom full of students getting 75s on math tests means a whole lot of students aren't mastering the material, one adolescent coming to his office for consultation isn't going to convince him.
In fact, I don't think students should be expected to resolve learning issues by "talking to the teacher," although I understand that I am virtually alone in this view.
I expect teachers to teach well enough that students don't have learning issues in the first place. That is my core expectation, I'm paying for it, and I think the money I am paying should buy me some level of guarantee that my kid will actually learn math in math class. I'm not paying them to hold math classes. I'm paying them to teach math.
And let me stress: C. is smart, hard-working, and diligent. He's paying attention in class; he's doing all the work. He's been excited about math for the first time ever this year - and now it's back to Careless Errors and Threatened Cs on the College Transcript. And every month we write the checks that buy us more of this mishegoss.
I don't value the 'service' I'm paying for, I resent paying for it, and I flatly reject the notion that it's up to C. to somehow persuade a middle-aged man who holds all the power -- while C. holds precisely none of the power -- to fix the situation.
I am SO fed up, especially after the Back to School "I am IT" performance.
As to that, Ed and I are belatedly realizing we were most likely the victims of another snow job like the one that started us on the path to parent radicalism back when C entered 6th grade: a charismatic performance by a charismatic teacher who was in fact promising us a year of pain in the form of big red Ds and Fs on papers.
The calculus teacher is fantastically charismatic; his Back to School performance needs to be YouTubed. Amazing!
But he wasn't telling us what we thought he was telling us.
He opens with a dramatic story about his first year teaching precalculus in the school, when he flunked a bunch of kids on their first test (RED FLAG) and the principal called him into his office to TALK.
From there he goes on to complain lustily that C's school puts everyone in his class: the smart kids, the dumb kids, and all the kids in between. On the blackboard he actually lists all the classes he teaches and the number of students in each class. It's HARD to teach so many kids at so many different levels, he tells us parents!! SO SO HARD!!
Then he tells the assembled parents that he's the best math teacher in the school. (He tells the kids he's the best **teacher** in the school.)
To prove the point, he tells a fabulously entertaining story about a student no one ever expected to take calculus, and this teacher not only got him through calculus, but when the kid got to college he found out his college calculus course was easier than his high school math course!
So the mom called up the teacher and said, "My son got an A in calculus in college!!!! Should he take calculus 2!!???!!!"
And the teacher said, "NOOOOOOOO!!!! HE CAN'T TAKE CALCULUS 2!!!! GET OFF THE SHIP!!!!"
This story elicited hoots of laughter, but now I realize: oops, another SIGN.
So now C. has a 75 on the SECOND test of the year, and neither of us expects to hear any mea culpas from The Best Teacher In The School.
We expect to hear Youa Culpas.
Or Yourstupidkidda Culpas.
SOP
btw, as to college students working as math tutors --- so far I haven't found that to be a particularly promising avenue.
Good teachers really do have "pedagogical content knowledge," just as Liping Ma discusses. C. has now had two fabulous math tutors, one at the end of precalculus last spring and one this summer for SAT math. Both of them not only knew the subject they were teaching inside out, they also knew exactly what kinds of mistakes and misconceptions kids have about the content, and they both had a strong sense of how much practice and what **kind** of practice kids need to learn the material.
btw, I have begun tutoring math myself and have now tutored 3 kids very successfully (2 of them classified SPED, I think). I'm a rookie, so I'm learning on the job, but what I find is that the time I spend "explaining" math is extremely limited.
I spend most of my time overseeing my version of "deliberate practice": writing problems on the fly, walking kids through the solution, then watching them do the problems on their own --- and constantly circling back later to see if they can still do it, etc.
Plus I'm constantly trying to build a 'seamless whole' or 'schema' inside the student's brain: this goes with this, and that is the next step, etc.
Last year I watched a high school math student tutor another student, and that's not what was going on. The h.s. student was just going through the material in the textbook and re-explaining it to the kid who was having trouble learning.
Teaching writing, too, I spend very limited time explaining grammar or telling kids how to write. VERY limited. I spend as much time as humanly possible having them practice the concepts I'm trying to teach.
Eventually, I aim to have my writing course be practically all reading, writing, and sentence combining (along with a core of sentence diagramming - which so far seems to be valuable).
I'm not there yet because such a course is going to be fantastically labor intensive and I'm still pulling together the materials which is also labor intensive.
I need to figure out a way to have writing students practice constantly that doesn't consume 24 hours of every day --- not sure how to go about it.
I've always regarded math teachers not using a textbook as a bad sign. Not using a particular textbook assigned by school district may be a good sign (school districts often pick the worst of the worst textbooks), but not using any book is bad.
There are many good calculus textbooks out there. Go to a college library and browse to find one that matches the kid's style.
There are good on-line math classes. I posted about Art of Problem Solving at http://gasstationwithoutpumps.wordpress.com/2011/04/19/good-online-math-classes/
But the AoPS classes are not for everyone—they aim for the students who are bored in the regular-pace math classes and who need a few challenging problems rather than tons of practice exercises. Their textbooks are also quite good for self-study for the same group of kids. The AoPS books and classes may not be a good fit for the problem you are facing.
Check to see whether the errors are really careless errors or whether they are random flailing. A student who has an inflated view of their skills may say "careless error" when they make any sort of mistake, even one that shows fundamental skills missing.
It is not unusual for a strict teacher to have half the class fail on the first real exam---that happened in the first honors calculus class I took in college. Everyone in the class was used to being a straight-A student, so it came as a shock to everyone. Most of them ended up working hard in the class and many ended up with the As they were used to. A few gave up, though they probably had as much math skill as the rest. Determination to succeed is as important as ability in such a situation.
I have no idea where Westchester is, so it must not be very near me. I live a couple hours north of Sacramento.
Lots of assorted thoughts.
first: the charismatic teacher snow job was something I saw at MIT an awful lot. my worst math courses-- my WORST--were taught by a charismatic teacher THAT I SOUGHT OUT OVER AND OVER AGAIN.
It wasn't until YEARS later that I understood that he'd taught me nothing, and that it wasn't actually my fault after all (There were classes where it was my fault. These were not those.) I figured it out years later when I had noncharismatic teachers who just taught me, pure and simple. I did the work, the made it clear and in easily digestible chunks, and I aced it-as did any other student who slowly and methodically did the reading and the homework.
But the charismatic teacher was what we all wanted, because it felt revelatory for a few seconds, before the fade came, and we were no better off than before. Teach C. to be skeptical of the snow job!
I agree most college students can't tutor. Deliberate practice is necessary. Doing the problems is necessary, but even there, there's something more: you need to develop your pedagogical content knowledge to where when you see an error, you don't just say "aha, that's an error; here's the right way." you must uncover the REASON they have that error--gsw/op was really nailing it with this comment: "Check to see whether the errors are really careless errors or whether they are random flailing. A student who has an inflated view of their skills may say "careless error" when they make any sort of mistake, even one that shows fundamental skills missing." as a tutor, you must delve until you find the source of the misconception and correct it at the source. Otherwise, you're constantly painting over a crack in the wall caused by a shifting foundation.
Specific thoughts for C.:
1. Schaum's outlines. They dont' teach the material to any depth, but they have a zillion worked out practice problems and a zillion more for you to do.
http://www.amazon.com/Schaums-Outline-Calculus-5th-ed/dp/0071508619/ref=sr_1_1?s=books&ie=UTF8&qid=1318699437&sr=1-1
2. Get a real calc text. I'd start with Thomas, though Thomas and Finney is fine too. With every edition, there's less content and more diversity pictures. Thomas and Finney was in 7th ed when I was taking calc 20+ years ago.
http://www.amazon.com/Calculus-Analytic-Geometry-3rd-Mathematics/dp/B0000CKUFL/ref=sr_1_11?s=books&ie=UTF8&qid=1318699378&sr=1-11
is the 3rd edition. 6 bucks.
last comment: 1) find out from high school what's the last date they'll let him drop out of this class.
2) talk to NYU admissions.
3) I'm firmly with you that it's insane to expect a student to fix a problem with a teacher at this stage of their life.
RH --- THANK YOU THANK YOU THANK YOU!!
I've just scanned the test - will email shortly.
Thank you!
That said, I'm pulling him from the course. Writing the post last night, reading through all of your comments, writing my long Comment about the situation ---- the situation has now been clarified in my mind.
He's out.
This blog has basically 'saved' me every step of the way ---
For years, ktm helped me teach C. the math he wasn't learning at school.
Later on - and today - the blog has helped me know which path to take.
So now my question has shifted to how he's going to learn precalculus and calculus (regardless of whether his college requires him to take calc).
What's the best path?
Ed really doesn't want to spend a fortune on a private tutor to teach him pre-calc ---- but what if another student took it with him??
Could we put together our own little course outside school?
I'm going to contact Courtney James; I'm also looking at the various community college courses.
(And what about The Teaching Company course?? It's not a course...but it might be an adequate base - ?)
A kid who scores an 800 in reading ought to be able to learn from books. He may as well get used to it. Even in college, you can't count on having a teacher who really teaches.
I'd almost say that especially in college you can't count on having a teacher who really teaches. (Have I mentioned I've HAD IT UP TO HERE? oh, right. I think I did.)
I've pondered that question: how much can you teach yourself from a book and at what age can you start doing that?
I'm self-taught in most things; teaching myself stuff I don't know anything about well enough so I can write about it is almost my job description.
But...that's my job. I've done it a long time; I have a particular set of 'thoughts' or 'heuristics' I use to teach myself that no kid is going to have. (Most adults wouldn't have them, either; why would they?)
Also, I don't think it's a great idea to teach yourself math. You really need a teacher ---- and there are precious few good math teachers out there.
This gets back to the "flipped classroom" issue: can you really learn well from a static entity like a book or a software program or a video on YouTube?
Yes, you can learn.
But can you learn well?
I don't think so. You need the interaction with a TEACHER: a person who is paying attention to YOU and to what you know or don't know.
And by the way, I think a live, human professor giving a lecture is superior to a videotaped lecture.
A live person giving a lecture is getting feedback all through his lecture from the live people sitting in front of him or her, and he's adjusting if he's any good.
At this point, C. probably does learn very well from books alone -- but that is not the case in math.
And with math you have the issue that there aren't a lot of math books out there written for self-teaching. I want to teach myself combinatorics, and so far the Art of Problem Solving book is the only text I've come up with and it's not satisfactory wit
(btw I remember someone -- was it lgm?? -- recommending the Arlington Algebra Project sheets on probability and counting, and those seem terrific. They don't have an answer key, unfortunately, but they're an excellent resource.)
I just picked C. up from 'service' (he's working with autistic kids---) -- seems like he should get credit for years of service around here----
Anyway, he said that the few kids who are sticking with the AP calculus teacher (the one who is sick) told C. that the course is fine as long as you teach yourself.
The teacher is worse this year (his illness is progressive). Now they are having trouble hearing him speak.
A lot of the kids in the class have dropped it & are now in C's "Honors Calculus" course. (That's why C. is in the course, in fact; he's in this course so as to avoid the other teacher's course.)
Jean - I'm moving to Sacramento!
No textbook for calculus? If he is "it", I would ask him what "it" can offer for help, since there is no textbook.
lollll ---- oh, man
Steve's been with ktm since the very beginning, just so you all know -- he can probably see me SITTING HERE DECIDING ***NOT*** TO FIGHT THIS LAST FIGHT 'CUZ AT SOME POINT YOU HAVE TO CALL IT A DAY
That's right: no textbook. So if he missed something in class, there's no way to pick it up, 'cuz there's no textbook.
Actually there **is** a textbook, but they don't use it.
There's just the notes he puts up in class, the HW (which he doesn't collect or read), and the tests. No quizzes, either.
--You need the interaction with a TEACHER: a person who is paying attention to YOU and to what you know or don't know.
YES YES YES YES YES. You do, until you are very expert. In grad school in math, students learn from books, but even then, they work together doing problems in books when they don't have a teacher--they from study groups for a reason, they give oral presentations on their work or someone else's work for a reason--other people ask them questions, throw out ideas, etc. so they cement what they know.
It's a skill developed as an undergrad math major but overwhelmingly most high school kids can't do it, and it is not the time to get thrown into the deep end of that pool.
gasstation - thank you - I will read the post!
Unfortunately, I'm pretty sure the AofPS courses aren't what C. needs at this point ---- I wish they were.
But I'll read & see.
The fact is: he needs precalculus.
He learned nothing last year.
I had a scheme to have him re-take precalc this summer but we spent all our time on SAT math ---- which wasn't altogether a bad thing because he has a **much** sturdier sense of arithmetic, basic algebra, and early geometry than he did before. Much better.
Our SAT math work was all remedial: it was all about finding and filling the gazillion gaps in his math knowledge.
SAT math, by the way, seems to me to work quite well as an at-home diagnostic.
I was constantly finding holes in my own knowledge.
kcab - I just read my rant-y comment of earlier on -- I HOPE I don't sound like I'm 'yelling' at you!
(I probably do - and I'm sorry!)
I'm yelling at the school.
We went round and round about the math course last year, and this guy was supposed to be the solution.
That's what we were led to believe.
Allison - that is fascinating.
(Can I put the Comment about charismatic teachers up front? Or would that be too personal?)
I **know** you're right -- and I've known it for years. But charisma is charisma; it works.
Ed said this morning that there was a voice inside his head saying "this isn't right" but he ignored it --- and the exact same thing was true for me, too. There was a voice inside my head going "Uh-oh."
And we mutually ignored our voices saying the exact same thing -- a math folie a deux!
What the guy actually said was -- I've just about got the whole quote -- "You [parents] must be sitting there thinking to yourselves, 'This guy thinks he's IT. Well let me tell you, I AM It. I am IT."
In print that sounds obnoxious, but in person it was a flat-out promise to teach our struggling kids math. That was the message.
Correction: That was the 'text.'
The subtext was something else altogether.
...when I had noncharismatic teachers who just taught me, pure and simple. I did the work, the made it clear and in easily digestible chunks, and I aced it-as did any other student who slowly and methodically did the reading and the homework.
Right.
Right.
And I **know** this. I **know** that charisma is a danger sign.
This guy's performance was absolutely amazing. Amazing! Tour de force.
Tour de force is bad.
eachers who just taught me, pure and simple. I did the work, the made it clear and in easily digestible chunks, and I aced it-as did any other student who slowly and methodically did the reading and the homework
RIGHT!!!
Just teach the material in clear and easily digestible chunks ---- and C. will learn it.
That's all we need.
Will he be a mathematician?
No.
Will he be a physicist?
No.
But then again, they aren't mathematicians and physicists, either.
you must uncover the REASON they have that error--gsw/op was really nailing it with this comment: "Check to see whether the errors are really careless errors or whether they are random flailing.
right ---
I see one arithmetic error on the test; I also see an error that I don't know how to categorize
It wouldn't be random flailing, in my view: he had the right answer but then didn't write the answer down as a coordinate pair ----
assuming the issue there is what I'm guessing the issue is (two roots of the equation? I haven't looked closely) I would interpret his error as being more in the nature of his knowledge being too procedural still ----
he also failed to distribute a minus sign
that's been an issue forever
back when he was in 6th or 7th grade he'd say, "I just forgot the minus sign!!!!"
and I'd say the difference between plus 100 degrees and minus 100 degree is the difference between life and death
this is a household routine
so again, in this test, he forgot to distribute a minus sign
on the other hand, that really can be a careless error
Several times, working SAT problems, I've missed minus signs ---- (or failed to count correctly how many positives and negatives I have) ----
so....failure to distribute the negative can be in the 'careless error' category
RH will tell me
Schaum's outlines
Great idea!
I have several; I'll get the one for precalculus.
That's where we have to start.
Also - what do you recommend for a precalculus text?
(I'm ordering the calc text you recommended.)
Catherine,
My son's tutor is in Manhattan tutoring calc and pre-calc to fellow students. That's probably too far, but she is there. I had her tutor my son all summer since his pre calc and trig grades went way south by the end of the year. I just had her pound in what she thought he needed for calc. He's doing okay after a rough start.
Going to his teacher is the best thing, even if he's there every week.
SusanS
I also bought George F. Simmons Precalculus Mathematics in a Nutshell for her to use if she needed to. i got that recommendation from someone here. I'm not sure if she used it, though, because she was a copious note taker and had all of her notes to look back on.
She did discover that Purplemath had pre calc stuff on it, but I haven't gone over there to look.
Susan
I liked the AoPS Precalc book, but it may not be the right one for C.
Note that for any textbook, course, or teacher recommendation, it depends at least partly on the fit between the student and the resource. There are many, many precalc books that cover roughly the same material. But the order of presentation, the assumptions about prior knowledge, the style of presentation, and the number and difficulty of the exercises all differ. Finding the right match can be tough.
Foerster's Precalc with trig
http://www.amazon.com/Precalculus-Trigonometry-Connections-Paul-Foerster/dp/1559533919/ref=sr_1_4?s=books&ie=UTF8&qid=1318715627&sr=1-4
may be a good classic choice. We've not used it, but my son used his
Algebra and Trig book http://www.amazon.com/Algebra-Trigonometry-Functions-Applications-Prentice/dp/0131657100/ref=sr_1_2?s=books&ie=UTF8&qid=1318715627&sr=1-2 a couple of years ago and found it quite straightforward. The style is not as fluffy as many of the more modern texts.
I am (at least) one who recommended the Simmons text Precalc in a nutshell at some point. Catherine, you've probably already got it. But Schaum's outlines for precalc are great because they have SO MANY PROBLEMS. They aren't great for teaching from scratch, but they are great for practice.
Oh, feel free to pull that comment about charismatic teachers up front. It's not too personal. Come to think of it, I fell for the charismatic grad advisor too, even though he never had time for any students whatsoever.
I feel for your frustration, Catherine. My most academic daughter had a College Algebra/Trig (this would be called pre-Calc in your area, I think)
teacher who was AWOL in many ways, and angry towards the kids to boot. We arranged for tutoring, but it didn't help much. On the other hand, she was a very bright but not "mathy" kid, and had no plans to major in math/physics (she was a Zoology major). Her bad grades in math in HS, and her very mediocre SAT score, did her no real harm. If she ever wants to go to grad school in Zoology she will have to re-enter the math world, but she will have a reason, and her department will help her out, is my guess.
Oh, no fear, I thought you were yelling at the school more than me. I'm appalled that a private school is so unresponsive to student needs.
I want to say though, that I see the ability to approach an instructor and request guidance/assistance as a learned skill, one that is crucial in college. More globally, students need the ability to realize that they need help and to search out places to get that help. So, my thinking was that getting help might be something he should practice.
As far as learning precalc, would it help if he was working through a book with another student? I imagine it will be hard for him to stay motivated to learn math on his own, but it sounds like there are other kids in the same predicament. One reason that I liked having my DD review algebra by taking an AOPS course was that she was motivated by the on-line class time with other students. AOPS might not be right for him, but having planned math time and someone he needs to keep up with might be good aspects of that model to borrow.
...or not, kids are different & I don't know what motivates C...
--So, my thinking was that getting help might be something he should practice.
I agree. Students need to practice this, just as they need to learn what they need help with.
They should start, though, by practicing on someone who will give them positive feedback--someone who actually helps them, rather than someone who discourages them from asking anymore.
Catherine,
First of all, the textbook issue: these are the textbooks that most colleges in our area use: Calculus by Stewart, James and Calculus, 9th Edition Larson/Edwards. I taught out of the Larson book this summer.
As for what you should do, I don't know. But my impression of calc classes at universities (college) and community college is that it is the same course but much smaller classes at the cc.
MIT has a single variable calc class available for free on their open courseware website. I have watched many of the videos and I like the way concepts are explained. It's not a live professor or a tutor, but you know the information he is teaching is very good.
As for the test he failed, was it a calc test or a precalc test. In other words, was the teacher testing them on the information they should know before coming into the class or was it the first test on limits?
My son's tutor is in Manhattan tutoring calc and pre-calc to fellow students.
You're kidding!
She's here?!
(Is she going to school here?)
I'll call -- gotta get her name...
I love Precalculus in a Nutshell. I think Allison mentioned it -- I had already found it on Amazon, so I was glad to hear she likes it.
Oh, no fear, I thought you were yelling at the school more than me. I'm appalled that a private school is so unresponsive to student needs.
Oh, good!
I want to say though, that I see the ability to approach an instructor and request guidance/assistance as a learned skill, one that is crucial in college.
That's obviously the case, but I resent it like heck. Colleges are charging many, many thousands of dollars; they hold our kids' futures hostage; and they take even less responsibility for outcomes than K-12 does.
It is quite difficult for a person who doesn't know a subject to analyze his own learning or lack of learning -- and although you can practice the social skill of approaching a teacher during office hours, I'm not sure many students can practice an abstract skill of knowing-what-they-know and knowing-what-questions-to-ask to any great degree.
A student can know when he's completely at sea, but if he's completely at sea, he's not going to solve that via a conference with the teacher.
In other words, was the teacher testing them on the information they should know before coming into the class or was it the first test on limits?
It was all precalculus (and he got a C -- but he got a B+ on the first test & thought he did well on this one, which is a bad sign .... given the fact that he learned virtually nothing last year, we see nothing but trouble ahead.)
The other issue - C. explained this to Ed in the car - is that kids are dropping out of AP calculus and coming to this class. These are some of the best math students in the school; they're fleeing AP Calculus to this class, and there seems to be essentially a bell curve grading and testing approach. The teacher hasn't said so, but that's the way it seems to be.
C. has had several teachers who have explicitly said they don't grade on a curve; teachers have said, "I want you all to do well; I want you all to get As."
If this teacher is grading on a curve, C. is going to be in the middle.
That doesn't work for college transcripts -- and I can't at the moment tell whether it works in terms of what he's actually learning or not learning.
Anne- thank you!
I'll have to look to see who the author of the class textbook is (they do have a textbook; it's just that the teacher doesn't use it).
Thanks for the tip about the MIT course --- !
I am really disturbed by many things you are saying. Back in the dino days when I took AP calculus (and other college track math), it was expected that there would be a bell curve and that more C's would be given out than A's. And 75 was a common grade on an exam. Now you seem to be implying that everyone should be getting A's. Is that what you are saying or am I misreading? Because if that is true, no wonder my college students seem so entitled.
Secondly, you seem to subscribe to a magical theory of teaching - that a "great" teacher is going to stand in front of this happy audience and in an hour a day, "fill them up with knowledge". Somehow this great teacher is going to be able to look at this sea of faces and magically know exactly the misconceptions of each and everyone of them and in that hour, be able to meet the needs of each student. Sorry, but it doesn't work this way. In fact, people who do research in college level STEM education are focusing just on figuring out how to assess students misconceptions. It isn't easy, and doesn't happen because of some kind of ESP. That is where techniques such as clickers, pre-assessments, and Think-Pair_Share come in. But these are all methods that take time and are hard to fit into that sole hour where you are supposed to be lecturing.
Lastly, if your son is really and truely making careless mistakes, instead of actual mathematical mistakes, then you need to address the situation in a completely different way. My son also makes careless mistakes in math. So we work on the carelessness, not the math. It is really a different skill. If your son is careless, it will be a problem in many math and science classes in the future, so best to address it now.
Catherine,
Yes, she's in school there for the year. Email me if you're interested. I'll also talk to her mother.
She's pretty busy, but she's your classic overachiever. She had to pound into my son that he was going to be working his butt off more than he ever has if he wanted to make A's or B's.
SusanS
"These are some of the best math students in the school; they're fleeing AP Calculus to this class, and there seems to be essentially a bell curve grading and testing approach. The teacher hasn't said so, but that's the way it seems to be."
It's the AP calculus death march, but it's not just the top kids who are dropping away. It just took them until 12th grade to do it. I see it in my son's high school. In a school of 1600+, there is only one AP calc class each year. Math is not that difficult.
As I mentioned once long ago, this isn't a mathematical base camp where students can regroup for the college attack on a STEM career. They are not at a base camp, but at the top of their own math mountain. Part of it could be a grade problem based on rising bell curve expectations on smarter kids, and part of it could be math "gaposis" finally catching up with them.
There is also the issue of what one can expect from a school in terms of teaching. There can be individual teacher problems and there can be systemic problems. Also, individual teacher problems can highlight systemic problems because they create gaps that never get fixed. It's a great school cop-out to claim that teachers can't know and fix all of the misconceptions and issues that walk into a class when they allow those problems in the first place. This starts in the early grades. They trust the spiral.
In the case of the AP calculus high school math track, the kids are much more homogeneous. In our high school, you can't proceed at the honors or AP level unless you have something like a grade of 80 or 85. This should make life easier for students and teachers. Teachers should know all of the problems that students can have. It's too easy to pin the blame on students. If your top students are having problems, you should at least take a look in the mirror. If you assume that struggle is a necessary part of learning, then you may not be able to see when bad teaching is causing a problem.
Bonnie, about the grading curve . . .
I think what Catherine is saying is that the bell curve is being upset in her son's class because the AP Calc kids (the top of the curve kids) are fleeing the AP class and landing in her son's non-AP class. I'm sure Catherine will correct and/or explain when she has a chance.
Bonnie- no time to respond just now - but I'd like to remind you that I am myself a college teacher. I am also a tutor; and, stretching back in time, I won the teaching award at the University of Iowa as a graduate student.
I chose to teach the most remedial class this year, and, yes, my goal would be for every one of the students in my class to earn an A.
Absolutely.
I'll also say, again, that this teacher routinely tells students in his class that all of the other math teachers are bad -- except for the teacher he trained, whom he calls his "grasshopper."
I am strongly opposed to grading on a curve.
I believe - and this is still, today, a radical belief - that all schools should be run on the principles of the Morningside Academy in Seattle, which promises two years of progress in your child's weakest area or tuition refunded.
Alternatively, schools should function the way tutors and private instructors and coaches function: if the tutor doesn't get results, he or she is replaced.
We understand this principle when it comes to athletics and music training, but not when it comes to academics.
Somehow this great teacher is going to be able to look at this sea of faces and magically know exactly the misconceptions of each and everyone of them and in that hour, be able to meet the needs of each student.
It's funny you say that -- because that's pretty much what the guy does!
He cold calls (I do, too); he reads the kids' faces and calls on the kid who looks like he doesn't understand the problem.
That method has worked quite well for C. in terms of motivating him to do ALL of his HW the instant he gets home.
I don't handle things that way, however. I use cold calling to keep everyone on his toes as much as possible.
>>>Somehow this great teacher is going to be able to look at this sea of faces and magically know exactly the misconceptions of each and everyone of them and in that hour, be able to meet the needs of each student.
It's not rocket science. I can figure out in 1 minute what the misconception is and find out where in the notes the topic shoud have been addressed but wasn't...and I was in high school in the 80s. These days, I pull out the relevant section in Dolciani or Foerster and hand it to the kid. Lightbulb on, problem fixed. Beats afterschool tutoring or giving up one's lunch.
My kids are taking the same class this year (Alg II/Trig). Order of magnitude difference in teaching...I have one kid copy the other's notes because a logical presentation in concept notes and example problems beats random monkey see/monkey worked examples any day. Add Dolciani on top, and we get the abstract plus graphical explanation too.
I haven't had a chance to read all the comments yet, but I had a thought about the problem of the charismatic teacher.
Years ago, I read some relationship advice in a woman's magazine, of all things, that I thought had a very good point. The advice was: "When you're with a guy, don't ask yourself how you feel about him -- ask how you feel about yourself when you're with him." In other words, don't choose the guy who awes you with what a brainy, funny, terrific guy he is -- choose the guy who makes you feel brainy, funny and terrific.
In the school setting, the advice would be "don't choose the teacher who impresses you with his brilliance, choose the teacher who actually helps you learn."
If every kid in an AP calc class got an honest 5, then yes, they should all get As. There is no reason they should be penalized at all for someone else's success. Standards-based grading works. Straight scale does too. And in college, straight scale grading in large courses yields a bell curve naturally, because that is, essentially, what the law of large numbers says will happen.
At the college level, an experienced teacher with a bit of empathy who has taught a subject a few times before should know every single misconception their students will have, and work hard to avoid them in the first place. They'll know because the same misconceptions will occur class after class, year after year, student after student. The best teachers write their courses to avoid them when possible and address them head on otherwise . The next best do what they can to ameliorate them.
If you don't know your material, or don't have any insight, then yes, it can be difficult to understand what the kids are missing. That should not be license to blame the student.
Lgm, btw, *which* Dolciani do you use? What year? It matters because you cannot believe how bastardized that work has become in various and sundry publications and editions.
Just as school administrators label parents helicopter parents to malign honest reasonable attempts to get their kids help, teachers label students entitled to malign students putting responsibility on the teacher.
Yes, some kids feel entitled. I know of kids who get to their first college course and feel betrayed that there are no 'study guides' like there were in high school. These study guides were these packets of info that basically did all the distillation of knowledge for the kid. Of course the kid feels betrayed. But a professor who blames the student has missed the point: how in the WORLD would a hs student learn to study when their teachers all give them these study guides, rather than teach them how to learn?
This is all a piece of the "learning vs teaching" false dichotomy. Those who believe it was always the student's responsibility to learn have given themselves an out where they don't admit they have to teach.
Sure, the students need to learn to learn. From whom should they learn that?
I just got back from a conference of computer science educators. The topic of typical student misconceptions was a huge topic there. We had many discussions about this, amongst faculty at schools ranging from large research intensive public universities to regional state u's to elite private liberal arts colleges to community colleges. We found we were all saying the same things. Yes, we know the catalog of typical misconceptions. There are even research papers out there which analyze these (physics has an especially rich body of research on student misconceptions). That part is not hard. What is hard is finding ways to overcome the misconceptions. In our discussions, we found we all had the same experience - we could structure lectures, and homeworks, and in-class assignments around the common misconceptions. We could work individually with students (the ones who had learned to come to office hours to ask for help - an important skill that SHOULD be learned in high school), explaining the concept until we were blue in the face. And yet, all of these strategies seem to have no impact.Students will still have those same misconceptions.
Someplace I remember seeing a study (I wish I could remember the reference) that found that students who had seen a physics demo designed to correct a misconception were able to successfully answer questions right after the demo, showing they had supposedly corrected their misconception - but a week later, their answers showed the misconceptions all over again. The problem is, it takes far more than a demo or an elegant explanation to eliminate incorrect ideas that are part of a student's core view of how things should work. The student, not the teacher, needs to grapple with the concept, over and over.
An example (and this one came up at the conference repeatedly) - students in introductory CS do NOT understand variables. They don't get that variables are simply storage locations with a name, and that assignment is an active operation that entails computing the right hand side expression and then *placing* the result into the left hand side variable. So to counteract this, we all do some variant of the following -we endlessly diagram boxes on the board, placing values into them as we trace through the program. We tell the students that they must never call the '=' operator "equals". We make the students diagram changes to the boxes themselves, as they trace through the program. We do it over and over, consistently. And yet, all of us joked, we have had the experience of students insisting that
33 + 5 = y;
is a valid statement. The students don't get it. They think that the box diagrams are some peculiar form of torture that has nothing to do with getting a program running. They haven't done the hard work of *connecting* the diagrams to the programs, or thinking through the reasons we are so insistent on using the term "assignment".
This is one small example. We deal with piles of these misconceptions all the time. Mark Guzdial had a particularly chilling paper recently that detailed how little students understood about algorithms and programming even after 2 semesters (and his study was at an elite school with good students). I am convinced that even though we know the misconceptions that students will have and even though we have designed our teaching to deal with those errors, students will not eliminate their misconceptions until they have spent a good bit of time thinking hard and struggling with these concepts. We can design experiences that guide them in the process, but without their mental energy, the students are not going to *get* it.
So while I agree that there are bad teachers who make the process harder than it should be, I don't believe there are any magical teachers out there who can just do something that is so special during classtime that students will learn hard concepts without struggle, and without thinking and working with the topic outside of class, on their own. At least not in computer science.
So Allison, you are saying that in college, on top of all of the other massive amounts of material we need to teach, we also have to teach the students how to learn without study guides? Are we trying to turn college into a 10 year program or what? As it is, it is almost impossible to teach enough computer science to our students to satisfy the employers in 4 years. Why can't the high schools take on that task? Better yet, the middle schools? I need to get my students through data structures and analysis of algorithms and concurrency and large system architecture, in addition to being able to write about technical material coherently, read requirements, communicate effectively, and hopefully know a smattering of topics besides computer science. How can we do that if we have to spend a year or so teaching students how to learn things?
Allison,
I have an early 90s copy of Dolc. Alg I. Agree it has been watered down, but there is enough left to be helpful. The Alg II text I have is early 60s and appears to be the same edition as the one I used in high school...it was good prep for college for me as I learned to unpack a text and follow an abstract explanation. I have yet to see my sons come home from public school with notes containing the word 'theorem' or an abstract or graphical explanation of any part of topic in Alg I or II, with the exception of graphing equalities and inequalities. Apparently core basic curriculums are verbal explanations with the minimum amount of material covered.
lgm,
Would you mind posting ISBN numbers?
You'd cry if you saw whact I recently saw--a middle school/pre algebra text using the title "Mathematics, structure and method" that has terrible terrible content. Dolciani is one of several authors, and I have no idea what that work it once corresponded to, but I found it because someone to whom I'd told "find Dolciani" found this abomination on Amazon and didn't know it was lousy.
If every kid in an AP calc class got an honest 5, then yes, they should all get As.
oh my gosh!
you said it!
thank you!
I've been off-and-on wrestling with what my answer is to Bonnie's question (which I think is one way of asking the core question about what school) --- and that's the answer.
If every student in a class can get an honest 5 on the AP test --- that is FANTASTIC. That's what I want schools to shoot for; I'm shooting for my own variant of it with my composition kids.
btw - and this is something I've thought about quite a bit (interested to hear what all of you think) -- I think it would probably be better, on balance, to separate the grading and teaching functions.
The goals of teaching and ranking or sorting aren't really compatible (and of course when the same teacher grades/ranks and teaches there are issues of grade inflation for some teachers & grade deflation for others ---- )
I heartily endorse exit exams like the AP tests and the Regents exams here in NY (setting aside the issue of whether the Regents exams are still good, of course).
A friend of mine who grew up here in New York told me that in her high school - and I think this was common - your final grade was either the grade the teacher had given you over the course of the year OR your grade on the Regents, depending upon which one was higher.
I think that's a fantastic system for every reason in the book.
An exit exam/final grade system like that one allows teachers to use 'summative grades' to motivate kids while avoiding the issues of grading on a curve, favoritism, etc.
We could work individually with students (the ones who had learned to come to office hours to ask for help - an important skill that SHOULD be learned in high school), explaining the concept until we were blue in the face.
I haven't read your comment closely (I will!) - but wanted to pick up on this.
Assuming I haven't missed something critical, you're telling us that students with misconceptions seek out their professors for help -- and the help doesn't help.
That is my point; that is what I have seen over and over and over again. Extra help doesn't help.
I think for most of us it makes intuitive sense that "Seeking Extra Help" (it's always capitalized here in my extremely well-funded district, where the ability to Seek Extra Help is prized above all skills) is a critically important skill students should learn as early as possible ---- but is our intuitive sense actually supported by reality?
In my experience, the answer is no.
Extra help doesn't help; thus the ability to Seek Extra Help isn't a particularly useful skill (not for clearing up misconceptions, at any rate. Establishing your identity as a student who seeks extra help may be important for other reasons; my Scarsdale friend told me that there was an unwritten rule there that any student who attended Extra Help sessions automatically received a higher grade, regardless of whether he learned the missing material.)
btw, I came to this over the course of years of believing in Extra Help and tutoring myself. But time and again we had so many dreary experiences with Extra Help, which never, ever, ever Helped, and our friends had so many dreary experiences with Extra Help, that I began to see things differently.
At some point, I began to respond quite negatively to the very mention of Extra Help. I remember so vividly attending the parent orientation night for our high school here in town: the principal AND the guidance counselor must have spent a half hour going on and on and on about all the massive, countless, endless hours and hours and hours of Extra Help and Peer Tutoring our kids could receive starting on Day One at the high school, when they would apparently already be flailing in math and everything else under the sun.
If a school's pitch to parents is: We have tons of Extra Help, that is a very bad sign.
It sounds like the school is saying: Your child will have lots of personal attention with his teacher, one on one.
But what is really being said is: your child will have trouble learning what the teacher is teaching.
Another post I've been meaning to get around to: Extra Help at college.
I had dinner the other night with a friend I'd been out of touch with. Her son has "slow processing" -- and school has been a struggle pretty much from third grade on.
At the same time, he's very bright. (I'd like to know more about processing speed ---- I worked with another friend's son this summer who has slow processing. He failed his Algebra Regents, so I worked with him and in just a few days' time he went from a 57 on Regents to a 79, and if we'd had a few more days he would easily have passed with an 85 or higher. Here's my point: this boy is a slow processor but a fast learner. He was the same way as a kid; I know because I worked with him on Saxon Math Fast Facts pages.)
Anyway, back on topic.
My (first) friend's son has slow processing and has been accepted by University of Vermont, which apparently has a widely respected "Access" department. Access means the people who run the learning centers.
So that sounds good on the face of it ---- but the creation of large, booming "Learning Centers" is predicated on admitting students you know will struggle and flail or fail in the classroom. That is the **plan** more or less.
Flail or fail in the classroom; then somehow the Learning Center is going to make it all better.
I've never seen it work that way in K-12, and I don't think it's going to work that way in college, either (although I gather it's different with writing. Ed says the learning center at NYU is enormously helpful to students writing papers ...)
Here's an example of what I mean.
My friend's son is interested in psychology, so she brought that up to the Access person.
The Access person said that one of the main things she does is keep students **out** of courses she knows they're not going to be able to handle -- and the entry-level psychology course is one of them.
So here is my friend's son, accepted by U Vermont and interested in psychology -- and he's being told he shouldn't take Psych 101 because kids with processing issues do badly in the course.
The whole thing makes no sense.
If the traditional classroom model isn't working for (some) students, a non-traditional Learning Center add-on doesn't fix it -- and isn't something parents & students should be paying for in any event.
No one buys a car that's a known lemon on grounds that there's a really great repair shop close by.
There's a history teacher at C's school who has fantastic AP scores - unbelievable. Ed can always quote them off the top of his head....
I think he's got something like 50% of his students at least getting 5s. (I'll ask Ed when I see him again.)
His grading sounds pretty harsh (though C. did well). C. has an underachieving friend who got something like a C or a D in the class and scored a 5 on the AP exam.
That fact tells you everything you need to know about this teacher: he can take a kid who's having some trouble getting motivated, staying on track --- all of those things --- and THAT kid gets a 5.
He's amazing.
Ed just came in --- 55% of that teacher's AP World students are getting 5s on the exam.
And this guy has a HUGE teaching load. Much larger than public school teachers.
If your top students are having problems, you should at least take a look in the mirror.
THANK YOU!
boy, no kidding
Another issue where seeking extra help is concerned: I am an adjunct. I don't have an office.
How do students Seek Extra Help from teachers who aren't on campus any time other than class time?
I give out my email address & phone number - but emailing a teacher asking for the assignments you missed isn't the same thing as Seeking Extra Help.
How many college teachers are adjuncts these days?
It's the majority of the faculty, right?
If so, then logically the skill students really need to acquire is the skill of learning inside the classroom.
In a school of 1600+, there is only one AP calc class each year. Math is not that difficult.
wow
Interestingly, my own district seems to have a rising population of kids in AP calculus --- which is pretty amazing.
I don't know whether to credit the school or the parents and the tutors.
Another factoid, though: Irvington traditionally had a terrific math program all the way through. That all fell apart with the adoption of Trailblazers and the subsequent retirement of the math chair who had trained all the teachers to give "shuffled" problem sets for all HW.
I remember seeing a study (I wish I could remember the reference) that found that students who had seen a physics demo designed to correct a misconception were able to successfully answer questions right after the demo, showing they had supposedly corrected their misconception - but a week later, their answers showed the misconceptions all over again.
Oh, absolutely.
repeat, repeat, repeat.
I was thinking about that today: how many ideas and facts in academic subjects can you learn in one exposure?
I'll bet it's very few.
I have the Foerster book!
ok, funny story
The Learning Center at the college I teach in is VERY active & present in the students' lives (& I think it's pretty good, too: an impression based in the work they did with a student of mine last year).
This year, a very nice guy from the Learning Center has been coming in to my class to recruit kids to attend Learning Center workshops for new freshmen --- and the workshops are on things like "Brush up your grammar" or some such.
So there are my kids, enrolled in my class, which is the most remedial class offered in English, the first class in a year-long sequence of two classes, and they're in my class because they **don't** write grammatically (among other things) ----- and the Learning Center is offering a two-hour workshop whose purpose is to ---- what, exactly?
Fix their grammar in two hours?
Tell them about the need to write proper sentences now that they're in college?
Well, if you can fix their grammar in two hours, then they don't need to take a year-long sequence of composition courses whose purpose is to fix their grammar, now, do they?
OK, ok, I know the Learning Center people aren't expecting to 'fix' anyone's grammar in two hours --- but what **are** they expecting?
My class runs from 8:30am 'til 10:55am, so if any of my students attended the workshop, which was being held that afternoon, as I recall, they would have spent 4 and a half hours in one day attempting to improve their grammar.
That's just way too much grammar.
I don't believe there are any magical teachers out there who can just do something that is so special during class time that students will learn hard concepts without struggle, and without thinking and working with the topic outside of class, on their own.
I don't think anyone has advanced the notion of "magical teachers" who somehow implant knowledge in students' heads sans deliberate practice.
A core theme of ktm has been the lack of deliberate practice provided to students by their schools -- that and the lack of formative assessment, which is an intrinsic part of a deliberate practice regimen in athletics and music training and should be in academics as well.
As far as I can tell, "explaining" is a fairly small part of good teaching, at least in terms of time devoted to explaining vs overseeing various forms of practice. I spend as little time explaining grammar, writing, and reading as possible; I spend as much time as possible having students practice these things -- and I'm trying to figure out how to spend more time on practice in a way that works for my students and leaves me time to do all the other things I'm supposed to be doing.
I also desperately need practice **activities** that work ---
Blogger must have eaten a comment of mine earlier, oh well. One point of it was that there is active discussion on a variety of university campuses regarding grade inflation/deflation. Engineering, and often science, courses are much less grade inflated than most others, causing a lot of angst and claims of grade deflation (which I think is probably false). Anyway... standards based grading seems like a good idea, provided the standards don't then become debased.
btw - and this is something I've thought about quite a bit (interested to hear what all of you think) -- I think it would probably be better, on balance, to separate the grading and teaching functions.
DH has been saying this forever, or at least the last 5 years. He teaches design courses, which entails a lot of coaching students and teams. I'm not sure how grading would be separated in his case, but I'm sure he has ideas. I can see the point, that a teacher should be aligned on the same side as the student, rather than sitting outside of the relationship as would be needed to grade objectively.
On intractable misconceptions: for the past 10 years, I have been trying to get students (grad students and seniors) to correctly implement a dynamic programming algorithm that I give as a homework assignment (the Smith-Waterman affine-gap cost alignment algorithm, not that it matters to my point).
I have tried many different approaches, including explicitly telling them the most common bugs and how to avoid them, walking them through a correct example (with or without an incorrect one), giving them general principles, …
I have never had a year in which no one made the mistake I warn against most strongly. In a good year only about 25% of the class makes that particular mistake. In years when I tried less successful methods (or had students who were harder to teach), as many as 50% made the same mistake.
A different teacher is teaching the class for the first time this year (and amazed at how much work it is to teach). I am interested to find out whether he has any better success on this problem.
If a school's pitch to parents is: We have tons of Extra Help, that is a very bad sign.
Uh oh
OK, so when you teach your college course (and I don't know what subject you teach), how do you divide up your 3 hours per week in terms of "explaining" vs "deliberative practice". And what is "deliberative practice" in your field? Do you believe that students should work on their own outside of class? Or do you believe that everything that is worth knowing should happen should be mastered during classtime?
One of my core beliefs is that time is the currency of teaching - time spent on the task, that is, time spent grappling with the hard concepts, reading the material, trying things out, trying to solve problems, etc. The time can be in the classroom, or it can be outside of the classroom, but it is necessary. As students are less and less willing to spend time outside of class working on class material, we are now adding time in various ways to our courses. In computer science, we have a huge amount of material that must be mastered by graduation. Plus, we need to teach a new way of thinking (new to most students, that is), which is algorithmic or computational thinking. So time is already a huge problem. To deal with the problems that students have with learning this material, many schools are adding time to the classroom experience in one way or another. Many schools are increasing the time spent in introductory CS courses from 3 hours/week to 4 and even 5 hours/week. Other schools, like ours, are stretching out the introductory sequence, traditionally 2 courses, to 3 and even 4 courses. Of course this creates upwards pressure - do we eliminate upper level course so they graduate on time? Do we make the program a de facto 5 year program? I don't know. All I know is that, based on many years of teaching CS, is that focused time seems to be the most important factor.
DH has been saying this forever, or at least the last 5 years. He teaches design courses, which entails a lot of coaching students and teams. I'm not sure how grading would be separated in his case, but I'm sure he has ideas. I can see the point, that a teacher should be aligned on the same side as the student, rather than sitting outside of the relationship as would be needed to grade objectively.
Right!
I really want to be on my students' side (not that a 'tough grader' ISN'T --- but you probably know what I mean).
These kids can't do college-level writing, and they have taken out loans to REPEAT what should be a high school level course in college.
I WANT them all to succeed -- and I want to be allying with them in that effort.
The fact that my class has an exit exam makes that possible. You should see their faces every time I bring up the exit exam - which I bring up every single class. They GET ALERT.
Psychologically & emotionally & motivationally it works out SOOOOO well.
(And, of course, since I do grade their performance in the course I do have the use of summative grades as a motivator --- )
I do think Extra Help (aka office hours) can help, but only if the student is willing to participate actively. Too often I see students who come in mainly wanting me to repeat what I said in lecture because they weren't paying any attention. That isn't helpful. Or the student is so upset and panicked that he or she has thinking blinders on, and can't approach the material with the focus and flexibility needed to eliminate those pesky misconceptions. Or (and this is probably 75% of the students who visit) they want the program debugged, quickly, so they don't have to think about it any more. Those modes of Extra Help are not really helpful, agreed.
When you get a student in who is trying to get a difficult concept, though, and who is willing to talk through it, and maybe draw some diagrams, and answer questions as we go, then yes, that can actually help the student.
I have never had a year in which no one made the mistake I warn against most strongly. In a good year only about 25% of the class makes that particular mistake.
Fascinating!
I wish I understood your field --- wish I could work over in my mind how a person might go about increasing that number ---- ????? (Not saying it's possible -- just saying I'd like to puzzle it through.)
I've been thinking you need to show the mistake --- show the wrong way as well as the right way --- but you've just said you do that, right?
btw, in teaching composition, it's just absolutely predictable that students are going to do the opposite of what you tell them --- there's no way to stand up in front of a class and say that the supporting ideas have to be ideas not a list of examples and have that translate to practice.
I don't expect it, too, and I haven't seen it happen ----- EXCEPT that there will be a couple of kids who are 'ready' to 'grok' this----
If a school's pitch to parents is: We have tons of Extra Help, that is a very bad sign.
Uh oh
lollll --- I take it your high school is big on Extra Help?
I think the idea of separate mastery testing is one that is coming, but it poses difficulties in fields like mine. I would imagine it is a problem for design fields too. Given that a successful computer science grad is a person who can DO particular things rather than who knows certain things, how do we test? Employers are already grappling with this - since employers don't trust that our students have the skills they need, most of them test candidates. But they way they test is interesting. They usually have the candidates DO things - solve this puzzle on the board, come up with an algorithm for this problem, create a tricky SQL query. Usually, it is oral, sometimes on the phone, and you are expected to talk your way through your solution. This process makes sense because mastery in computer science is really about a certain kind of problem solving skills. But how are we going to do that with, say, 400 students in CS2? But if we go the easy way, and assess with traditional exams, we will end up teaching the wrong things to our students.
Many schools are increasing the time spent in introductory CS courses from 3 hours/week to 4 and even 5 hours/week. Other schools, like ours, are stretching out the introductory sequence, traditionally 2 courses, to 3 and even 4 courses.
I teach writing -- and writing, while in theory much simpler than a subject like computer science, is fantastically difficult to do (and difficult to learn to do, I think).
For me, the more class time, the better. I'm now trying to give my students as much out-of-class VERY SIMPLE HW as possible. By simple, I mean the Prentice-Hall grammar sheets I linked to; some Whimbey sentence-combining exercises - which I discovered last year my students can't do on their own; and for the first time some 'copywork'.
At the end of last year, I talked to another teacher who told me about a student who had flunked the course 3 times in a row. This is a remedial course that doesn't count towards the student's English requirements.
He said his students told him, "We're not doing enough writing" -- and I'm trying to take that to heart.
That teacher now has his students write one 5-paragraph essay in class every single week.
I'm not there yet (still trying to figure out how to fit in grammar & reading - AND how to fit in grading one paper a week and all the other things ---) but I know he's right.
I need to be giving my students as many short EFFECTIVE reading-writing-and-grammar exercises as I possibly can.
Another issue: they have some reading difficulties, which means we need to spend class time reading the fables & folk tales out loud.
I also need to think how to make use of the Learning Center. I had a student last year who took every paper he had to write to the Learning Center; that gave him an extra level of one-on-one teaching.
This year, though, I'm having them write everything in-class ----
Wait!
I could have them write their paper in-class and then take it to the learning center----
They're doing a paper in class tomorrow; I think I'll experiment with that.
Just tell all of them to go to the Learning Center with their paper and ask the person there for help with revisions.
"I've been thinking you need to show the mistake --- show the wrong way as well as the right way --- but you've just said you do that, right?"
Yes! Yes! That is the problem. We can show them the mistake over and over, explain why it is a mistake until we are blue in the face, and some percentage of them will still make the mistake. Sometimes I wonder if they are listening at all, but they claim they are. They just "don't get it".
Another example - sequential flow of control. A program that is written as
step1;
step2;
will execute in that order - step1 will be done first, then step2. Sounds simple, huh? You would be AMAZED at how many students don't get that. Yes, they can parrot the information back, and if I explained the idea to them, and then ask them on a quiz if the computer will do step1 first, they will get it right. But, when faced with an actual program that has an error because the statements are in the wrong order. a certain number of them will not be able to figure it out. Even when I sit with the student and point it out, they will still not get it. The student will insist that, since there is a statement to print a result SOMEWHERE in the program, it should print the right thing. Even though the statement that computes the result occurs AFTER the statement that prints the result (which causes the error), the student will insist that the order of the statements is not a problem. That is because, deep down, the student is still clinging to the magical belief that the computer just "knows" the intent of the statements. Even though he or she can parrot back the factoid that the computer executes statements in order, the implications of that have not sunk in. And I can explain it over and over, I can trace it on the board, and still some number of the students won't get it.
I think the idea of separate mastery testing is one that is coming, but it poses difficulties in fields like mine.
RIGHT!
That is my ENTIRE issue -- and pretty much my motive for writing this blog for lo these many years.
In our own case, the mastery issue is so glaringly obvious: we have an intelligent child without learning or attentional or motivational issues who has taken one math course after another WITHOUT MASTERING THE MATERIAL -- AND THIS IS UNIVERSAL.
It doesn't work!
There's a book called "Permission to Forget" that I haven't gotten to yet but that says all these things much better than I ever well. The author, who was a teacher & then a superintendent (and now a consultant) says that schools give students "permission to forget" whatever they've learned that year.
Now, I would NOT put it that way.
It's not the kids who have "permission" to forget --- they're kids. They have terrific memories.
It's the schools that have permission to let the kids forget.
Schools need to adopt precision teaching. Period.
Adopt curricula and teaching methods that produce fluency in whatever subject you're teaching.
And, btw, this is a school-level issue.
An individual teacher has very limited ability to adopt precision teaching. You need the time, you need the celeration charts, you need the curricula, etc.
Isn't the Learning Center just the same thing as Extra Help?
BTW, the Learning Center is useless to us because they don't have anyone who can do computer science. They try to hire student tutors, but those students can make far more money doing technical work and are not interested.
Bonnie - I'm going to see if I can think that through (the comment you've just written). Not that it will help, but it's a fascinating puzzle.
If there's a consistent mistake students make over and over again --- is there any way to short circuit it: to reduce the amount of time 'til they stop making it --- ?
That's really a fundamental question for all learning.
I confront it all the time trying to teach myself math.
I spent quite a lot of time just not being able to grasp the difference between a combination and a permutation -- EVEN THOUGH THE DIFFERENCE SEEMED OBVIOUS!! -- and then one day I 'got it.'
(I'm still a novice at doing problems, which I find very confusing. I missed an answer on an old SAT because I couldn't tell from the grammar whether order mattered or not, for instance. But the **core** issue of the difference between a combination and a permutation is now clear in my mind.)
Isn't the Learning Center just the same thing as Extra Help?
In the case of writing, no.
Can't remember if I've ever gotten a post up about this.
People always say "writing is editing," and it's true.
Writing is editing.
However, novice writers can't edit themselves -- most professional writers can't edit themselves well. Kellogg's research on the careers of professional writers (I think it's Kellogg...) shows that professional writers take TWO DECADES to learn to edit their own writing.
(That's why the writers' workshop approach is sooooo wrong: the premise is that students will write a bad first draft and then edit it into a better second draft --- when in fact self-editing when you're a beginner is much, much harder than simply writing a decent first draft.)
In the real world, the functions of writing and editing are separate and distinct: that's why editing is a profession unto itself.
When a student takes a paper to the Learning Center, he is essentially getting an editor.
My sense is that when a student watches you edit his paper - or when he edits it with you - he probably does start to get a feel for self-editing....but I'm guessing that.
In any event, he is often able to at least SEE firsthand that editing makes his work much better ---
--I think it would probably be better, on balance, to separate the grading and teaching functions.
I've thought this in the past. In a sense, I've thought the corruption of grading when done by a teacher is too likely. I've mentioned the idea of separating the grading from the teaching to some friends educated in India. Basically, that's the way it works there in their university system (both getting in and getting out, if I understand correctly.)
They've cautioned against it. One, the stakes end up very high for the test. Two, the corruption endemic in a system with the stakes so high is a problem. Three, "teaching to the test" is all that happens then, and there is no room for interesting subjects, approaches, or innovations in curriculum or pedagogy.
On the whole, the downstream effects of this are to limit innovation and effort both by the teacher and the student, to limit risk taking, and to limit pushing anyone. The cultural effect is to kill innovation in every sense. My Indian colleagues overwhelmingly preferred the US system.
"I spent quite a lot of time just not being able to grasp the difference between a combination and a permutation -- EVEN THOUGH THE DIFFERENCE SEEMED OBVIOUS!! -- and then one day I 'got it.'"
Yes, you put the time into grappling with the concept. That is the point I am trying to make. I don't think there is a short circuit for this process. It has to happen INSIDE the student's head. Teaching practices that claim to short circuit this process, in my opinion, too often provide the appearance of learning the concept without the actual deep learning that is necessary to be able to use that concept to solve problems.
Yes, you put the time into grappling with the concept. That is the point I am trying to make. I don't think there is a short circuit for this process. It has to happen INSIDE the student's head.
oh, yes; I am a big-time grappler!
However, I know from the experience of the precision teaching people that learning can take more time, or it can take less time.
There's no question that's so.
BUT -- at the neurological level learning is all about myelin --- and it takes time for myelin to develop
They've cautioned against it. One, the stakes end up very high for the test. Two, the corruption endemic in a system with the stakes so high is a problem. Three, "teaching to the test" is all that happens then, and there is no room for interesting subjects, approaches, or innovations in curriculum or pedagogy.
Makes sense.
But then -- the (old) NY system is probably a good compromise, right?
In that system, a student's final grade was EITHER the grade the teacher gave him or her in the class OR the grade on the Regents exam, whichever was higher.
But here's another observation.
I don't see, with AP courses, teachers turning their classrooms into pure test prep exercises --- and in AP courses someone else always grades the exam.
(I think it **can** happen that an AP class is a test prep factory, but I haven't seen it - and I've seen a lot of problems in K-12 education at this point!)
What is the difference?
'so when you teach your college course (and I don't know what subject you teach), how do you divide up your 3 hours per week in terms of "explaining" vs "deliberative practice"'
In my classes, almost all the deliberative practice happens outside the 3.5 hours a week of class time. My students generally put in 10 hours a week outside of class. That is about the only way to do it for some of subjects I have taught (computer programming, technical writing), as the skill that needs to be developed takes more time than a 70-minute class has.
I try to spend half of my class time answering questions and clearing up misconceptions, and half the time laying the ground work for the next exercise.
Incidentally, teaching writing and teaching programming are not as different as they seem. The same sorts of errors occur in both. There are surface mechanical errors (semicolons, in both) that obscure deeper problems, like an inability to order thoughts sequentially, or an inability to break thoughts down into component parts.
The 5-paragraph essay is like the freshman programming assignments—it is good for testing mechanics and trivial ideas, but tells us almost nothing about the student's ability to do real work.
I've had students come out of 3 or 4 programming classes still unable to write a small program, because everything had always been scaffolded for them and they had no idea how to break a problem down into smaller subproblems.
I've had students come out of 3 or 4 writing classes unable to write a proposal or a design report, because they were unable to divide the bigger project into coherent sections and unable to divide the sections into separate paragraphs. All the writing they'd done before seems to have been stream-of-consciousness, with no overall structure.
The inability to structure their thoughts is a major problem for students in both writing and programming and is a bigger barrier to progress than mechanics (though even that lower barrier seems unsurmountable for some students).
Some AP classes do devolve into teaching to the test. The AP Bio classes started failing in that way, with students cramming in huge undigested masses of factoids. The College Board is revamping the AP Bio test to be less factoid-dependent. We'll have to see if this helps.
The AP calculus and physics classes have not devolved in the same way, because the tests are well aligned to the curriculum—they test what the students are supposed to have learned. Teaching students to be able to do what they are supposed to prepares them very well for the tests.
Incidentally, teaching writing and teaching programming are not as different as they seem. The same sorts of errors occur in both. There are surface mechanical errors (semicolons, in both) that obscure deeper problems, like an inability to order thoughts sequentially, or an inability to break thoughts down into component parts.
very interesting!
Disagree about the nature of the 5-paragraph essay, however
It's much more difficult to write a good 5-paragraph essay than it is to write a good 5-page paper.
I've had students come out of 3 or 4 writing classes unable to write a proposal or a design report, because they were unable to divide the bigger project into coherent sections and unable to divide the sections into separate paragraphs.
right - analytical thought of any kind is a huge, huge challenge
I'm not sure analysis can be taught -- and while it's obvious that background knowledge is essential to analytical thought, I'm not sure that analytical thought naturally emerges from background knowledge...
>>Lgm, btw, *which* Dolciani do you use? What year? It matters because you cannot believe how bastardized that work has become in various and sundry publications and editions.
I am using the first ones I could find as I was in a rush at the time.
Alg 1 is copyright 1997,1994,1992,1990 by Houghton Mifflin ISBN 0-395-77116-1 and the title is "Algebra Structure and Method Book 1".
Alg 2/Trig is copyright 1970,1965,1963 by Houghton Mifflin. The title is "Book 2 Modern Algebra and Trigonometry Structure and Method" and it says it is a revised edition in smaller print under the title.
From what others have told me, the older editions don't have ISBN numbers and are superior.
Compare to this:
Amsco Alg2/Trig Test Prep
which is what my one son is getting - your basic 'how to' that any NHS student could deliver.
Hi gasstation! I completely agree about the similarity between teaching writing and teaching programming.In fact, I have noticed many times that my best students in programming heavy courses tend to be people with very strong verbal skills. This is often obscured by the fact that English may not be the first language, but digging in, I usually find someone who has strong verbal skills in some languages. Not all verbal people, though, are good at programming of course. Something else is needed - the ability to see patterns easily, and to create abstractions. Some students who are strong at math are good in that area, but to my surprise, I have often found that our top math students are not good in computer science.
I also always assign some unscaffolded programming assignments because I think all the scaffolding gets in the way of really learning how to program. That doesn't mean I just let them loose, of course. But they need to write the entire program themselves, to really appreciate the process. I always tell my students that computer science is a contact sport.
The difficulty that I have is that my students will *not* spend 10 hours outside of class on assignments. If I can get to spend 2 or 3 hours outside of class, maybe every other week, I am lucky. They get trained in K12 to expect that all learning should take place inside a classroom, and nothing seems to convince them otherwise. That is why we now take 3 semesters to cover the material that was covered in 2 semesters back when I was an undergrad.
Catherine said "I'm not sure analysis can be taught -- and while it's obvious that background knowledge is essential to analytical thought, I'm not sure that analytical thought naturally emerges from background knowledge..."
analysis CAN be taught. That's what CS folks teach, some other engineering disciplines teach, physics programs teach, math programs teach.
You're right, analytic thought doesn't emerge from background knowledge.
Now, how is it taught? It can't be taught in a vacuum. It is better taught in a given subject discipline, and then after it's been applied to that subject, a more general analysis skill can be derived (this is why Industrial Engineering and Operations Research are really programs that only make sense at a graduate level, AFTER an engineer has seen a process in a work setting, or after hey've grappled over and over again with the same kinds of problems in a variety of disciplines.)
Many grad school programs essentially teach this analysis skill by discovery learning/constructivism. This is the irony of it all--in the end, most sci and eng grad programs are deeply constructivist. They don't actually know how to teach it, so they ask student to mimic what their professors and mentors do until they've intuited it. Other specific courses in grad programs do try to explicitly teach it, but mostly, it comes from being asked over and over "how to you know what you know? Do you know an equivalent or similar problem? What conditions must be satisfied for X to work? How would you know if those are satisfied?" etc. until the students see for themselves how to analyze.
I used to teach a course on systems analysis for programming using a book by James Martin that included a gazillion different methods. The Holy Grail seems to be some sort of process that can automate analysis, design, code, and test. This can only be achieved in a general sense, but that doesn't stop some from selling specific solutions to the whole problem. Unfortunately, things like the Unified Modeling Language (UML) end up being used for documentation, not analysis. I'm working on a project right now where we are going backwards from code (using Enterprise Architect) to generate the pretty charts and pictures. The joke about UML is that only 20% is really important, but nobody will say which 20%. Everybody has their own variation, like design for test and test for design, or whatever.
I remember (back in the '70s) being infatuated with Warnier-Orr Diagrams. I quickly realized that automated systems analysis techniques work best for projects that have been done before - where there are no surprises. For many projects, you don't know what you have to do until you do it. That's why I'm a big fan of prototyping. Digging into details forces you to not fudge in terms of analysis. Too many top-down analysis procedures allow you to gloss over details and risk factors.
So, can analysis skills be taught? Techniques and organization can be taught, and processes can be followed, but what happens for projects that have major new parts? That's where the content knowledge, skills, and experience come in. You can't follow a procedure that eliminates the need for those things, and if you have those things, your don't need the procedure so much.
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