3rd grade math - am I crazy or are they?

OpiefromMayberry · February 13, 2007, 7:12pm

neb,

“But over the years, your spouse has probably tended to tell you more of the “crazy” parents stories…as her sounding board, she’s not apt to tell you about the wonderful student/parent combos, and as mentioned by other posters,”

No we actually talk about all of them good and bad. She goes out of her way to buy gifts for room moms who help out through the year. We are very thankful for the extra hands and help. We also keep track of students when ever possile. She remembers alot of kids, (she has a great memmory, at least she never forgets any thing I did wrong;) )and kids remember her. She had a note under her door this fall before school from a 27 year old who was finishing grad school and was showing his wife around his ol elementary. Saw my wife’s name and stopped and wrote a very nice note about how he still remembered her and who he was becoming. Really nice tears. So we do know about the goods along with the bads. Just very few talk about the goods on this site, yet each family has had a teacher or two whom have had a great impact on their child’s learning process/

“I think that you do tend to go a bit overboard on defend-the-teacher-everytime.”

Not everytime.99.9% of the time…maybe What I am trying to do is attempt to point out other possibilities to a situation. It doesn’t mean I’m right, it means I’ve pointed out another possibility.

Until more details are presented, we don’t know what is reasonalbe or not. Mid’s example when explained as 30 minutes of sitting doing nothing IS a completely unreasonalbe thing for a teacher to do. However I wouldn’t feel the same way if it was only 3 minutes. details change the senario.

“No, the written instructions did not require the art (it was listed as a “fun idea” in the sections that listed “books & movies you also might enjoy on this topic”) Yes, he did a careful, neat job of it (albeit in pencil instead of colored markers.) And no, his parents did not usually allow him to follow only the instructions he wanted to follow. (Quite the opposite-Dad was retired marine drill sergeant…I’m sure you get the picture. First word out of their kids’ mouths was SirYesSir and Yes Mam!)”

Yes, but you could understand why I would ask? no? yes? details change the possibilities.

" And, in the later meeting with the principal, she admitted she’d judged his artwork to be “failing” quality, but the theme was A quality so she just “averaged” the two to give him a C.She also admitted that she did not take points away on papers lacking artwork. Fact was, she didn’t want to teach in the first place, she wanted to be an artist but knew that’d be hard to pay the bills. So she went for the art education degree…but instead of getting the full-time art teacher job, she got the long-term sub in a regular classroom job instead. She was way too far from what she really wanted to do, and her job performance showed it. That, I think, was the real life lesson there: if you’re not happy with what you’re doing, it’s difficult to do a good job of it."

No arguement here as you explained pretty clearly.

I’m not trying to be overly personal in my questioning statements. You can see that details clear the fog of a situation up. I think you can also see that in general terms, the questions I pose are reasonable until greater detail is given.

snoopyiscool · February 13, 2007, 7:13pm

Ahh, third grade. I remember problems quite like the OP’s example. I too despised explaining math problems, because I never saw the point of explaining why 3000 is bigger than 300 [it just is]. At least that’s what The Man told me.

theghostofsnappy · February 13, 2007, 8:16pm

oh, who are the “math folks” you are supporting?

You may re-read the thread if you wish.

*I think everyone posting on this thread values learning to write elegant proofs. But, the type of rhetoric put forth by the OP’s teacher is ridiculous beyond belief - similar to “showing” your work - even when you that you didn’t do any. Perhaps if she had assigned problems of a more appropriate difficulty level - which actually required him to go through a series of steps - he could have explained such. *

Well, if you aren’t doing work - there’s a problem. But the issue is, even when you aren’t doing work, you are. Every thought process in problem solving should have a non-unique set of steps, from reading to QED. If you can’t explain what you’re doing, then you don’t know what you’re doing. Plain and simple. Again, I’ll reiterate my point that it doesn’t matter what you know of think you know, but what you can show.

Don’t tell me that as someone with a “degree in mathematics” your professor required you to write long-winded explanations of that which was “intuitively obvious to the most causal observer”.

See above. Intuition doesn’t buy much, and can often be wrong. That is why we have proofs.

I was taught to write proofs in a clear manner that outlined the logical steps taken to reach the necessary conclusion. In addition, I was docked points for improper word usage (for example: using “such that” where I should have written “where”). Anal? Yes, but I as a PhD student in a top (5th in my field) economics program, I have been commented on my proofs.

jbusc · February 13, 2007, 9:09pm

Ahh, but as a famous mathematician once said, “if I had more time, this would be shorter.” As I’m sure you know, in a proof, it’s very important to be as concise as possible while still retaining the rigor. In that sense, teaching unbounded verbosity is almost as bad as leaving out intuitive steps.

Again, ridiculous. One time, a professor told me a story: an advanced PhD student in engineering came to him, top grades, but had trouble writing the dissertation - and he asked the professor, why do I have so much trouble coming up with original research? And the professor answers, well, when you were in about 5th grade, probably on history or some other non-technical subject, you wrote an answer that was correct, but it was not what the teacher was expecting, and so you got no credit, and you couldn’t figure out why. And the student answers, how did you know that about me!?!?!

Teaching like that stifles creativity and independent, original thinking, things which are crucial not only for PhD research but many other careers and parts of life as well. Assuming the essay was well written and had proper spelling+grammar, that person should have received an A+ for creativeness.

marite · February 13, 2007, 9:39pm

I agree that verbosity is bad, that concision is a characteristic of good writing in general and of elegant proof-writing more particularly. I do think that the math problem described by the OP was not sufficiently challenging and that may explain why her son wrote what he did–an incomplete explanation. But the opposite of incomplete explanation is not a verbose one. It is a complete and concise one. It can be done.

reflectivemom · February 13, 2007, 11:35pm

But Marite,

The example offered by the “rubric” was verbose and the antithesis of “good writing”.

reflectivemom · February 13, 2007, 11:39pm

theghostofsnappy stated, “You may re-read the thread if you wish.” When asked “oh, who are the “math folks” you are supporting?”

It is obvious that you know not that of which you speak. The true “math folks” on this list were not sharing your position on this topic.

But, had I known your field was “economics”, I would have better understood your position.

marite · February 13, 2007, 11:54pm

reflectivemom:

It was. But the fact remains that “I looked at the 100s and 1000s” is not a complete explanation. So you looked…and what did you find? and what did you conclude?

When he was preparing to take the AP-Calc exam in 8th grade, my S received the help of a retired Calc teacher. The main thing they worked on was the Free Response Question section which requires that students show their work. Points are given for a wrong answer but correct steps; points are deducted for incomplete explanation even if correct answer. It was not easy. My S had gotten into the habit of not showing all the steps (“it’s so obvious”). It’s a habit that’s been difficult to shake off. Hence my wish that we had insisted earlier on his providing full explanations instead of just providing the correct answer.
In college, my S is grading other students’ math problems. Points are to be deducted for incomplete explanations.

karthikkito · February 14, 2007, 12:53am

You could possibly use this incident to illustrate the connection between multiplication and division…

a/b > 1 .: a>b, etc.

Princedog · February 14, 2007, 1:14am

The IB math exams are all free response and this is also the case. They used to award some points to a correct answer with no work, but as of last year or so, the mark schemes say to award no points for a correct answer with no work. This is probably not because they actually care whether you do things in your head or not but because of their sensitivity to the advantage of calculators (particularly since IB math exams aren’t all calculus). As of next year (2008 exams) there is going to be no calculator use on the SL/HL Methods exams, at least on the first paper which is where it’s most useful. They’ve caught on to the fact that people can use their calculators without really understanding a process which is something I don’t really think the American exams recognize. For better or for worse (I don’t really know or care all that much) having an advanced calculator is a big advantage on the SAT math tests (for everyone below those with extremely advanced mathematical intelligence anyway).

Even on the current exam they will have questions that ask for exact answers so you have to add by hand or something because doing it in the calculator won’t give the full decimals. We’ve done a binomial expansion one like that from a past exam although I don’t remember the whole thing, just that the right answer had like ten decimal places and you won’t get it correctly using a TI-83. I guess the problem is not all countries participating in the exams have access to work with these advanced calculators before or even during the exam so they are trying to make it fair. The SAT allows TI-83s but at the same time says “oh it can all be done by hand.” Well yeah if you want a worse score than everyone else. That hurts the people who can’t buy a $100 calculator.

Somewhere along the lines of this topic, we watched a documentary in TOK called “The Proof” about a mathematician named Andrew Wiles who went into isolation practically for years in order to prove Fermat’s Last Theorem. It was interesting (we ran out of time so I haven’t seen it all). It was produced by NOVA. I have no idea where you would get this but this man became interested in the proof as a child so maybe a kid who is really good at math could relate or learn something from it.

theghostofsnappy · February 14, 2007, 1:26am

*The true “math folks” on this list were not sharing your position on this topic. *

The true math folks? Excuse me? I had profs encourage me to apply to top PhD programs in mathematics. I chose my field, and I’m happy with it. May I ask, pray tell, what is your background? And to that end, how contemporary?

But, had I known your field was “economics”, I would have better understood your position

See above. You don’t know what you’re talking about.

theghostofsnappy · February 14, 2007, 1:41am

Ahh, but as a famous mathematician once said, “if I had more time, this would be shorter.” As I’m sure you know, in a proof, it’s very important to be as concise as possible while still retaining the rigor. In that sense, teaching unbounded verbosity is almost as bad as leaving out intuitive steps.

Oh, but of course. Time is the key factor there, and in being pressed for such, on-the-fly constructed proofs are often a mess. They still must be logical. Published proofs are hardly as elegant in their original form, and post-pub, are subject to much review and refinement. Its almost as if there’s a convergence in elegance…hmm, I smell a publication. ;)

binx · February 14, 2007, 8:02am

In Germany, my d’s math exams were usually 3 or 4 questions, each one long and elaborate. Partial answers were the norm – D came out of exams saying, “Well, I got part of it, so I know I didn’t get a 6.” (A 1 is everything right; a 6 is everything wrong.) The emphasis was on the process, rather than the result. It was a really different way of teaching/testing, and was hard for her to come back to the “absolute” mentality. Sometimes her math tests (like the SAT) here are multiple choice. Another disadvantage she had here was having to learn to use a calculator. They just don’t in Germany. Her struggles with Calc BC in the beginning of the year had to do with the fact that (besides knowing only German terminology) the rest of the class had been using graphing calculators for 3 years.

She’s bright and capable in math, but not a natural. It’s been a challenge. (She had a horrible 5th grade teacher - long story - who convinced her she was bad at math. That didn’t help. My H was really disappointed to see her turn against math; she was his highest hope for another engineer in the family. She is the kind of kid who has, for the fun of it, memorized the first 155 digits of Pi. She wears t-shirts that say things like, “There are 11 kinds of people; those who understand binary and those who don’t.” She has decided she wants to major in “something that doesn’t have absolute right or wrong answers.”)

Referencing a post above regarding requiring work to be shown – I think this is not only due to calculators, but also due to cheating. It’s easier to copy someone’s answer than to copy someone’s process.

reflectivemom · February 14, 2007, 8:32am

Marite stated:

"When he was preparing to take the AP-Calc exam in 8th grade, my S received the help of a retired Calc teacher. The main thing they worked on was the Free Response Question section which requires that students show their work. Points are given for a wrong answer but correct steps; points are deducted for incomplete explanation even if correct answer. It was not easy. My S had gotten into the habit of not showing all the steps (“it’s so obvious”). It’s a habit that’s been difficult to shake off. Hence my wish that we had insisted earlier on his providing full explanations instead of just providing the correct answer.
In college, my S is grading other students’ math problems. Points are to be deducted for incomplete explanations.

But, Marite, your son’s needs are not all students’ needs. My son also grew up never “showing his work”. However, when he took The AP Calc BC exam in 9th grade, he had no problem with the free response sections. He didn’t need tutoring or practice to learn these skills. He was able to clearly show his work without all the silly “writing across the curriculum” types of exercises of the OP and in fact always got “full credit” for these problems.

While, your son may have benefited from such practice, my son had no need of such.

One of the reasons I contribute to these types of threads, when I rarely post on others, is that too many people believe “the way they learn is the way all should learn”. Skills that help those with language/linguistic gifts may not be necessary and may actually harm the developing thinking style of those with more a visual/spatial or intuitive problem solving approach.

reflectivemom · February 14, 2007, 8:47am

theghostofsnappy stated, "the true math folks? Excuse me?I had profs encourage me to apply to top PhD programs in mathematics. I chose my field, and I’m happy with it. "

Good, I’m always glad to see poeple who have a passion for their field of study.

Your happiness with your field of study is not the issue. It’s about a way of solving math problems. You previously stated that you aligned yourself with the “math folks” on the list -in support of the OP’s teacher. I asked for clarification as to who these “math folks” were - you told me to “reread the thread”. I did - those posts that I identified as sharing your view were not posted by those who would be generally considered “math folks”. If you care to explain who you were “calling” math folks, I’d be glad to reconsider my response in light of additional information.

marite · February 14, 2007, 8:54am

reflectivemom:

I think you misunderstood my point. My son needed to be reminded to show his work because no one had asked him to do so before–including ourselves. He got the right answers; that was enough to persuade us that he knew the concepts. But that turned out not to be enough. Not for AP Calc, not for college math.

And my point is that unless one starts early, one gets into habits that are hard to break out of.

By the way, writing across the curriculum is catching on in colleges as profs are alarmed at how badly students write. I recently heard Physics profs say that they will insist on more writing in their courses. And that was well after my S took a college physics course and got his first problem set back with the comment that “even in Physics, we use English, you know.” Obviously, a string of equations held together with “since” and “therefore” was not enough.

I’ll grant you that the illustrative answer given by the teacher was verbose. But it remains true that the student’s answer was incomplete. An equivalent answer would not have gained credit on the FRQ. And I suggest that it is not a bad idea to cultivate good habits.

By the way, the reason my son needed help preparing for the AP-Calc was that neither of us ever saw an AP Calc exam before, being immigrants; and my S was learning AP-Calc on his own out of a book while still in 7th and 8th grades, rather than in an AP-Calc class.

tokenadult · February 14, 2007, 10:03am

That is a lot of what drives curriculum reform at the K-12. It can no longer be assumed that the holder of a high school diploma is a competent writer, as would have been assumed a couple generations ago.

It’s a true statement: the rubric was verbose, but complete, while the student answer (as described in this thread) was terse, but incomplete. The golden mean is perhaps fewer words, but fully enough words to describe all the key steps. And proofs for beginning learners will tend to be more verbose, because not every step will be “obvious” to such an audience.

Does anyone have any links to Web pages about how to write proofs? I collect those for a FAQ I maintain.

reflectivemom · February 14, 2007, 10:06am

Marite,

I didn’t misunderstand your point at all.

I think, perhaps, we have the same “end goal in mind” but disagree regarding the means necessary to achieve it.

I believe there is a huge variation in the abilities, personalities, etc. of students - no one methodology works for all. If you believe your son benefits from this type of writing exercise/practice, I’m glad you were able to find tutors to provide it. My son didn’t need it and I’m glad he was able to escape from such. He was also fortunate enough to be allowed to independently study all his math - beginning in 2nd grade, thus he was never at “the mercy” of such techniques.

marite · February 14, 2007, 10:12am

Sorry, reflectivemom, It’s not learning style I’m discussing. It’s what’s required.

My S is grading problem sets of prospective math majors who are taking Honors Calc classes. This means that not only have they passed AP-Calc BC with flying colors, but they may have also taken college math classes before coming here. And their answers still get docked for incompleteness.

Tokenadult has it just right.

marite · February 14, 2007, 10:16am

Tokenadult:

For AP-Calc, the CB’s AP-Central has a website that shows how to score the FRQ. It isn’t proof as would be understood in college math, however. Most college math departments have proof-writing classes. At Harvard it’s Math 101. There must be a corresponding class at MIT whose Opencourseware would make materials accessible.

3rd grade math - am I crazy or are they?

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