On a non-political note. Many of you know I’ve been tutoring physics (which is fun.) I find lots of parents ask me if I know of any chemistry or math tutors. I decided early on to stick to one area because it’s more efficient to have a bunch of high school physics students rather than a kid in algebra, another in trig, another in geometry, another in physics and so on. So my answer is I don’t do chemistry, math or any of those things. (I’ve answered easy math questions in a pinch. Calculus– no problem. But don’t ask me to do synthetic division!)
That said, I’d like to have a personal list of tutors so I could give contact names to parents who would then be responsible for doing things like calling references and so on. (I’ve actually started a list putting something on a neighborhood forum.)
If anyone is or knows of a good Chemistry or Math tutor in the DuPage Co. Illinois area, I’d love to meet them. Heck, I get full enough I might need to know some Physics tutors to give out as names. FWIW…. any science or programming tutors. I’ve had parents ask me for tutors in C programming.
(Those wondering: Why not advise parents or students to contact any of the zillions of tutoring services? Those services tend to charge parents two to three times what the tutor is paid. Also, their tutors tend to be private contractors. So if a consumer can generally get exactly the same tutor if they know how to find them. And, there’s lots of room for price savings between the amount asked by the service and paid to the tutor. So, I know I’d like to be able to give out a list of name to parents (or even get together and meet people for drinks or coffee sometime.)
Anyway, open thread. But keep the DNC/GOP/TRUMP/HRC stuff on the other threads!
Lucia,
I don’t know anyone in your area, but I do have one suggestion pertaining to math. Look for Chinese students or post-docs with science or engineering backgrounds on top of looking for anyone with a pure math background. The Chinese are 3 years of ahead of American students in math. My daughter has a Chinese tutor (who is working on a PH.D in in civil engineering) to keep her Chinese intact, and my son wanted some help with Algebra 2. I asked the tutor whether she could help my 15-year-old son with math, and she said yes. She has been handling it with no problem. I also have another Chinese tutor to help me learn Chinese (the tutor is studying ultra-sound)– she said she could handle the math no problem. You may want to poke around Chinese student forums and post what you are looking for. (To find forums, I would google Chinese Student Associations for the various Chicago colleges and start from there.)
Off topic somewhat, but I can’t help mentioning it today. My son, who is very ambitious and self-motivated, shocked me today. He unhooked the monitors to his gaming computer and just shut it down — said he was wasting too much time. Honestly, I feel a little bad for him — he needs to be a kid. However, I realize there are much worse scenarios out there.
JD
Got thinking that maybe Dupage is a bit far from the Chicago universities. I would add that my son gets tutored by Skype with one of his tutors, and that works very well. Additionally, in thinking it over, virtually all PhD students or post-docs of any backgrounds would probably be looking for extra money. No reason to limit the search to Chinese, although many of them are looking for extra ways to make some money.
JD
Yeah, the distance and commute time makes the cost/benefit for tutors doing chicago/naperville unfavorable. It’s one thing to drive that distance for a 6-hour, 8 hour day. But it tends to be a problem for a 1.5 hour tutoring session.
Skype works for some students, not others. I find Skype is ok for older students but less so for the ‘totally lost’ or the younger. Some online platforms exist that help do equations, sketches. But still…
I yesterdays session with a college age student the two of us where thrilled because… (this is not made up) there was a wheel chair in the room. We were doing circular motion, and could discuss rotation and translation, and there was a prop just sitting there for us.
In the meat-world one can do things like tie a cat toy to a string and whirl it around and so on. So in person has advantages. (Not sure in Chemistry, but in physics it does help to drop things, whirl things and so on.)
Lucia, I see where you are coming from. All I would say is that grad students or post docs, if you could find them in your locality would be very useful.
JD
Yes. If NorthCentral or Benedictine had good math/science graduate programs, I’d try to put a flyer there and find some. Alas… not really. (Their undergrads are probably ok!)
Lucia,
I am much too busy with other work, but my wife (PhD chemistry, Lehigh) regularly tutors in chemistry. We are in Florida, but she quite often tutors via Skype. Sharing files and a video link seems almost as good as face to face. If anyone is interested in Skype tutoring, let me know.
While Skype has the right cost, videoconferencing tools like WebEX and Go to Meeting have a number of advantages including the ability to record the conference.
Eli,
There are programs available to record Skye calls/conferences. I have never had good experiences with Go To Meeting. Perhaps it has gotten better.
I used to use gotomeeting. Google hangouts is easier, what my group uses now. (Lots of geographically scattered developers)
SteveF,
Actually, I’ll put suggest your wife next time someone ask for chemistry. I take a small number of students- but Chemistry I get asked for Chemistry consistently. I figure it’s up to parents to decide whether online is worth a shot. (In fact, One of the Moms is of a current student asked about Chemistry a month agoe- so I’ll check and pass that contact on. It’s just that recently I realized I get asked so often I need a list!)
WRT to skype: seems to me it depends on age. The technology is mostly fine, but (at last for me) being able to see the student, body language etc. can make a difference with young students. One of the highschools around here does physics freshman year in high school. I also have college age students. A high school freshman who is frustrated whose communication skills aren’t great and who feels totally …. online can be riskier than in person especially if the tutoring need is identified in late October.
A college student who gets a tutor early, online will generally work as well as in real life. College students tend to sort of know what they don’t know better than high school freshman whose ability to assess what they don’t know often amounts to just saying “I’m totally lost. I don’t understand anything.” But college students at least can often tell you the book chapter, title, what the topic is named and so on. (Yeah… not much. But compared to the utterly lost level a 15 year old can present, it’s infinitely more.)
AP Physics final test prep: Online works just fine The tests are well defined. You can tell them “don’t waste time on X, it’s not on the test; do spend time on ‘Y'” You can point the to the right time of exercises and so on. Plus for these students its mostly just final questions to ‘perfect’ to be able to do things at a decent pace, and with reasonable confidence.
WRT to recording: Most high school students won’t benefit much from recording. Mostly they aren’t going to watch them. So no matter how good the video is, with high school students, the utility is fairly limited. (Not totally limited – but fairly.) Its in the nature of the beast– and by beat I mean “15-17 yo kid”. (Hypothetically, the videos could be useful– but they need to be very focused on what the kids needs to do “this week”; it can’t just be generally useful and so on.)
I would just add that Skype tutoring for my 15-year-old son (who is motivated and a good student) in English has worked very well. Have had zero problems and save a little money that would otherwise be spent on travel expenses. I think Skype would work for good students trying to get better but not for totally confused students.
If someone is interested in obtaining a Chinese tutor by Skype or Wechat, here are a couple of links where someone can place a post looking for tutors. http://www.nwucssa.org/miscellaneous/jobs
and http://uiuccssa.nodebb.com/category/5/%E4%BA%A4%E6%98%93%E5%8C%BA-marketplace
JD
JD Ohio,
The links are great!
Lucia,
I’m tempted to say I might be interested in tutoring C at some point in the future, but. I’ve got some big buts to sort through:
.
1. I’m not all that well educated. I’ve got a bachelor of science in computer science from 25 years ago. I like to believe I’m expert in C, certainly have used it an awful lot over the years, but. ~shrug~ I’m certainly not a professor of computer science.
2. I’m not local.
3. I’m too busy.
.
#3 might change. The company I’m working for is a startup, if they fold, I might suddenly find a lot of time on my hands. I’ll let you know if #3 changes at some point. It’d be up to you if you want to recommend somebody without better academic credentials. [Edit: C really is a pretty simple language anyway.]
Lucia: Wording of potential ad for tutors:
….
Looking for math tutor for 15-year-old boy. He is a “B” student taking Algebra 2 at this time. Is having a particularly difficult time with xxxx. Will pay xxxx per hour [$20 is my price — expect Chicago rates to be higher] If you know the math, there is no need for math degree. For instance, physicians and engineers who know the math would be welcome in addition to Math students. Call Susie at xxxxx or email at xxxxx.”
JD
PS Many Chinese physicians in the US cannot get residencies and are pursuing other fields such as finance or computer programming. They are happy to do this work. In fact, one of my tutors is a Chinese doctor pursuing a different field.
Hi JD,
If I might ask, why are you learning Chinese? If you are, how is it going? Written too? Do you have other languages?
Mark,
There are two things with tutoring:
1) Knowing the subject matter at a higher level than is taught so you can be very comfortable answering.
2) Specifically knowing what is taught at the entry level.
Sometimes, you really forget what is harped on and what you have to explain clearly. By the time an engineer has a Ph.D. they almost never get asked something like “Which of the following are Newton’s 3rd law pairs?” (It’s a very easy question…. but no one spends any time thinking about that anymore and sometimes the reaction can be “huh”? The difficulty is that if a kid highers a college kid they might actually give the wrong answer, which is worse than, “huh, let me remember what ‘Newton’s 3rd law pair means.’)
So generally speaking, you want to find a syllabus at a community college, scan it, scan through some assignments and see what is asked. This probably won’t take a lot of time, but there’s a chance there are a few things where you’ll say… oh. yeah. (They are in the ‘everyone knows, but don’t remember that sort of question.)
JD Ohio,
On rates:
1) The national’services’ you find online (Chegg, Varsity Tutors, ClubZ and so on) charge $50-$80 for online and/or having someone come to your home. (Some services are more cagey about what they charge, some less.)
2) They pay tutors who are subcontractors between $15-$30. (Varies from service to service. But basically, you can count on the notion the tutor gets paid no more than half but probably more than a third the customer pays.)
3) All these tutors are subcontractors. That means if a parent finds them independent of the middle man, the parent can negotiate a price. If that tutor is working with a service that pays them $15 for online, they will certainly take $20 if you find them independently. (Then, eventually, when they have word of mouth — some of which may be from you–, they will raise their price. 😉 )
Meanwhile, lost of tutors advertizing on places like Wyzant, craiglist, thumbtack charge $20-$80. And depending they can get it. (Craigslist takes no cut, Wyzant takes a percentage that declines if the tutor stays with Wyzant and so on.)
There are some “free boards” that exist– but those boards often don’t have anything to prevent the tutors from spamming with fake recommendations. ( And honestly, a consumer with their brain engaged can tell most recommendations are fake. It just doesn’t make sense that a 21 year old tutor who retained customers will have over 200 enthusiastic reviews all posted withing the past… oh… 6 months. If you retain a customer for a semester or two, they will at most post 1 review. )
But basically, my list is so parents can find the tutors and cut out the middle man. Parents want to find the tutors and the tutors want to be found. Right now, the “middle men” are very expensive.
So there is a huge spread. A person can probably easily find an online tutor for $20/hr — and they can be good, bad or indifferent. Likely the same happens at $80/hr.
I’ve settled at $40/hr because I think $80 is outrageous. Now that I have word of mouth at $40, I have zero trouble getting all the students I want, I have two parents of kids I tutored last year tell me the younger kids are entering physics next year and alerting me they want me for next fall. (You might ask: “Why not raise prices? Because I don’t want to. Also, I take no more than 5-6 students a semester. I’m working on developing helpful ‘online testbank’ like things. My students are sort of guinea pigs )
But anyway, with respect to prices:
My guess is prices aren’t much higher in Ohio than in Chicago– because while demand might be higher in Chicago, the supply is too. I would also guess the closer you are to a large university, the greater the supply and the lower the prices. The further…. the lower the local supply. The prices might not rise much, but the big problem is finding someone at all. But that means: online.
JD
Yep. I’m guessing there would be lots of students/people in the US, UK and so on in similar situations.
Also: if someone wants online, it’s hypothetically advantageouss to look in other countries. I had a listing on a Canadian site. A mom in Chennai, whose kid was studying for the AP Physics C contacted me. He was in the “polishing” stage. He got a 5; honestly, he might have gotten that with no tutoring. But maybe not– he did have some questions and we resolved them.
A local mom laughed that I had a kid in India– since so many of the tutors in the US are from India. But I pointed out that the hours worked great. He was out of school during our normal working hours. Similar things could happen for kids in the UK or Australia. And likewise tutors in India have good time matches with American students provided American parents are willing to hire them.
.
Thanks Lucia. I’ll remember it if my schedule opens up.
Lucia,
“Now that I have word of mouth at $40, I have zero trouble getting all the students I want…”
.
May I suggest that alone indicates you are worth more? I don’t know your market area, but most tutors with an advanced degree in a suitable subject area charge somewhat more. Several tutoring companies charge $70-$80 per hour and subcontracted tutors net $50 or so. As an independent, you can charge closer to the $70 figure, especially if you are local and work face to face. Heck, a couple of years back an MD with a somewhat less-that-brilliant child thought nothing of paying $80 per hour to my wife for tutoring in general chemistry at the student’s home…. 6 miles away. We are talking ‘anything, really anything, to help my dumb kid get into the school I want’.
SteveF,
I know I can get more. And yes many parents aren’t price sensitive at all. Lucky for me I don’t get really dumb students. (But even parents of smart students aren’t very price sensitive.)
I just have this feeling that $80 is… well… gouging. Also, at $40, I’m willing to fire students who won’t work! I’m sure Donna has seen families that will pay $80 with the notion that if you just “explain” the homework, the kid will somehow learn. Then the kid doesn’t do any homework on their own, then they don’t do so great. I hate that situation. I’m realistic about how much extra work kids will do– but I want kids who will work.
Tutoring companies do vary in what they charge/pay. I may end up charging $50– but I feel better if I charge $50 and the parents pay $50 than if I get $50 and the parents pay $80.
For what it’s worth, chemistry and physics seem to be areas where demand is strong with supply weak.
Lucia,
“For what it’s worth, chemistry and physics seem to be areas where demand is strong with supply weak.”
.
Hard sciences are, well, ‘hard’. Nature of the beast. Donna will take students for $50 per hour, especially if via Skype. I will let her know that $75 may be gouging. 😉
.
Yes, there are some students who just don’t want to work at all (very wealthy kids often fall in this group) but I think it is more often they are averse to thinking… a characteristic they share with less wealthy kids. The reaction I often have listening to Skype sessions is ‘deer in the headlights’.
Oh… you don’t have to go by me. I hate marketing… My “marketing” is a sign in the neighbors yards, entries in 3 online boards (need to find more) and an occasional craigslist add when I’m not full. (No add at craiglist right now.)
Certainly, I see math tutors asking $80.
Oddly, I see tutors advertising who claim they can tutor anything and everything and charging a lot. I always think…. really? I mean, you can tutor math, and physics and biology and chemistry and environmental science and take students from 6th grade-college, but it’s much less effort to tutor only physics, than to try to remember those pesky math things no one does later on. (Who does synthetic division after you’ve learned to find zeros using calculus?! Who the heck remembers the pesky notation in geometry— unless, of course you teach geometry. )
I always wonder if those people get students or if the reason they claim to be able to do a good job at everything is they really can’t keep students and they figure they’ll attract more students (who they will eventually lose) by saying they are available for freakin’ everything.
Oh. I like in person tutoring, but I won’t drive very far. I’ve decided: No cook county. Even parts of DuPage are too far. So that makes a difference to what I charge.
Another possibility: ring up your nearest university chemistry department and see if any of the graduate students tutor on an individual basis, and if so if they’ll share their list.
(I don’t live in your area, but back in the 20th century, grad students often did this on an individual basis…and since they get teaching duties anyway as part of their studies, sometimes they’ve got relevant experience.)
Back in the early 70’s as an undergrad (albeit one with multiple grad level courses) I tutored both ‘disadvantaged’ kids for my college and a few outside students who were preparing for the MCAT test. I received the royal sum of $7.00 per hour (about $40 in today’s dollars). That was the best pay grade I had ever had.
SteveF,
Some of the job postings still announce tutoring jobs for $8/hour. It’s usually community colleges. Possibly it’s teens tutoring younger kids. Highschools organize ‘peer tutoring’ which is basically having good high school kids tutor younger kids. That’s generally free.
So prices are all over the map.
And then there is “test prep” for ACT and SAT. Test prep is the bread and butter of the services that bundle tutoring. I’m sure it helps some— so all kids should do some. I’m also sure that beyond the obvious things like taking a few practice tests and getting pacing under your belt, it needs to be done effectively.
My guess is Princeton and Kaplan are the place to go if you are going to pay for that. Their ‘test prep’ tutors specialize with that, do it for years and train. Those services also do their best to figure out how to know precisely what the questions are and carefully determine whether certain bits of advise are even useful. The advise to skip hard questions can work to an extent– and it can certainly be good on college tests. But on ACT/SAT it might be is perilous. It’s probably good for students who find one-three questions “hard” -you certainly shouldnot spend the rest of the hour trying to solve it. But there is a down side to “skip the hard ones”. The ACT/SAT the tests are heavily timed– you get maybe 45 s to 2 minutes per question. If the kid is likely in the lower range, they’ve already wasted 20-40 seconds reading the question to decided before they can decide it’s “hard”. If they find more than 1 in 5 “hard”, they aren’t going to finish they ones they think are “easy” ones and come back for another cycle.
(My strategy for ‘hard’ questions was see if I could do process of elimination, cross out the ones I’d eliminated on the question form, and then come back to fill the bubble. But I knew I would get through all the questions and come back. I always knew kids who did not finish. That strategy didn’t work for them. My guess is they should guess from among the narrower choices and fill in the bubble right away.)
But oh my, test prep tutoring sure would be boring. . .
Lucia,
“My guess is they should guess from among the narrower choices and fill in the bubble right away.”
.
That is what I would advise. My memory is there usually are one or two answers which are pretty obviously wrong and two or three which are plausible (you have to actually do the calculations correctly to rationally choose between them). So if you are not confident you can actually do the calculation correctly, a guess between 2 or 3 plausible answers is not a bad strategy. Of course, some are so lost that they can’t eliminate even nutty answers, so for them no strategy is going to be helpful except ‘don’t waste time on things you don’t understand at all.’
Lucia,
One of the interesting things I learned by tutoring (repeated in later life when ‘tutoring’ consulting clients) was that tutoring forces you to make your subject knowledge more clear and organized…. to change from ‘just knowing’ how to do something to a more complete logical structure that adds ‘exactly why I know that’.
Oddly, tutoring also helps with test taking strategies. To have useful questions for one of my students I did find a test bank (from a book that’s different from the one her teacher uses.) We were going through multiple choice. There was a question that asked for center of mass. I looked at the answers laughed and said, you wan bet the answer is “d”– before doing ANY calculations.
How did I pick “d”.
There was a set of pairs of answer:
a wrong_x1, wrong_y1
b right_x, wrong_y2
c wrong_x2, right y
d right_x, right y.
e right y, right_x.
So, the “right y” appeared in two answers for ‘y’. the “right x” appeared in two for ‘x’, Nothing else appeared in two answers! (The totally correct answer being transposed was gravy.)
Of course, I just went by the “matchiness” of it.
So we did the problem. Was the answer d? Yes.
The student was amazed. I said that happened pretty often. . . (Not if I write a test on moodle because I know that it’s a stupid ‘trick’.
Actually, it’s better to just ask for each individually.
Lucia,
I’m curious to know your opinion about the on-line Khan Academy programs.
I’ve recommended it to others without having first hand knowledge of it.
Adrian
Lots of people tell me precisely what you tell me: They recommend Khan Academy even though they have no first hand knowledge of it.
I don’t have much of an opinion on Khan academy. None of my students ever use it. I’m guessing that at the high school level it’s probably a good resource for a motivated student who for some reason wants to self-teach themselves something at their own pace during the summer or in parallel to the class.
I have seen some of their videos. Generally speaking, if I hunt for a video on a physics topic, the Khan ones are not the worst, but not the best. When I’m looking for a good video that explains something clearly I have never picked the Khan academy one. Better ones always exist.
Presumably, someone could assemble a good introductory curriculum based on Khan academy, and perhaps someone has. But I have no idea how anyone goes about using Kahn Academy efficiently. For me, trying to figure out how to organize it so a student can benefit from it in a time efficient manner would use up lots of my time.
Perhaps someone needs to have some sort of online thing that explains how to use or find Khan Academy efficiently. Until they do, my knowledge of their system is going to remain where it is: at a level where my opinion of their system is uninformed.
Adrian,
I should add something else: many who tell me they recommend Khan and admit no first hand knowledge also clearly don’t even have second hand knowledge. I’m not even sure they have third hand knowledge. Generally speaking, they have heard of Khan Academy generally from someone else who also doesn’t have first hand knowledge and likely doesn’t have second hand knoweledge.
In fact, I don’t know anyone student who used khan academy. And the most I am aware of is some physics teachers sometimes link to some of their videos– as a resource for students who missed a class.
As I said: it might be terrific. Or not.
Adrian:
To give you an example. Here is a video on “the elevator” problem.
https://www.khanacademy.org/science/physics/forces-newtons-laws/normal-contact-force/v/normal-force-in-an-elevator?ref=physics_staff_picks
Is it good? Bad? Indifferent? And when deciding who is it good for?
Is the parallel structure of discussing 4 questions in parallel good for kids who are trying to concentrate? Is mentioning “j” direction good? (It’s almost never used in algebra based physics courses; it is used in calculus based physics courses.) Could it have been better to indicate direction with arrows (up, down?) Is the digression about ‘g’ being constant– but that it might vary good– in context? Or not? Is it good or bad that he never writes down Fnet=ma? That’s just in words?
All of these are real questions.
My sense when watch these is that many of these choices are sub optimal at any level. (If the kid is doing conceptual physics, there should be no “j” notation. If they are in Calculus based physics, he should show his coordinate system so we get repetation on “what j is”).
My sense is it’s generally better to do one application as a whole– with the free body diagram, the equations and so on. And then move to the next. I think that four problems in parallel tends to be difficult for students to follow. Of course I could be wrong; maybe students find that terrific.
The other difficulty is that (a) videos are slow — and ponderously slow if you know most the stuff. (b) students can’t stop to ask questions, which is a big problem if they are confused.
That said: I can’t say the videos are bad, but generally, if I know a student, (or even a level a class is aimed at) I can find a video better suited to a student at a particular level.
I find the AP exams tend to have multiple choice where the other choices are what happens if you make a specific error in solving.
On the other hand, there was once a (non-AP) test for a high level competition,
lim x->0 sin(3x)/x
Choices: 1,2,3,4
Lucia, I have some questions concerning your tutoring experiences. I find your discussions on that topic of interest to me as they relate somewhat to my past experiences.
As a graduate student in chemistry I had a job grading papers for a young professor who was teaching a general chemistry course that was not taken by chemistry majors. The professor had a rather unique approach to grading these papers and for testing. It was all based on the idea of attaining a pure grading on the curve. The tests required answers to chemistry problems that had to be accompanied by a detailed explanation of how the answer was derived. In this way a student giving a correct answer could be downgraded by giving something less than a perfect explanation as determined by the grader – and in this case yours truly. The professor instructed me that no one gets a 100% as that ruins the curve.
To make a short story even longer: I was provided a good look into the range of comprehension of these students that were not chemistry majors – even though this approach required a great deal more effort on the part of the grader. I was surprised by the high level of comprehension and understanding of chemistry by some of these students.
The above was a long winded lead into to my questions. Are the students you tutor physics majors or intent on being physic majors or students who require physics for some other major? I would think, and perhaps incorrectly, that a physics major would not require a tutor for physics. If you tutor both types do you find differences in their reception to your tutoring and would your tutoring approach differ?
What part does patience play in your tutoring? I can teach those with whom I have no close family connections by always being aware of the fact that impatience is a major weakness of mine and would get in the way of teaching or tutoring if not consciously controlled. When I have to instruct my wife on just about any subject that has any complexity I will defer to others to do the task. She knows my weakness and thus sometimes when she does not get what I am telling her she claims it is because of me and particularly if I raise my voice level any bit above normal. She does not have that ready excuse with others and I think that might help – or alternatively in might be that I am a poor instructor. What helps in my instructing or tutoring is that the person learning is very motivated to learn and shares my deep interest in the subject matter. Enthusiasm is a great counter to my impatience.
As a graduate student the research lab was in the same area as my research professor’s office and I could hear students in his office asking for help with their chemistry and most times hearing my professor tell them in loud voice that they needed to study more before coming to him with their problems. He was a good teacher with me so I could relate to his reactions to some of these students and particularly those that visited him merely to make brownie points. That my professor was human in these matters was revealed one day when a drop dead beautiful female student of his walked into to office to ask for help with some chemistry problems. For his crew of research students in his lab he was heard instructing her for what was a relatively lengthy time – given his penchant for sending students like her quickly on their way. When his crew and the professor went for coffee we had several comments on our observations of this student meeting anomaly and whether it was a one-time thing or he was changing his approach.
Lucia,
I, too, am interested in the questions kenneth asks. I had been thinking of how you tutor. Do you let the student tell you what he/she finds troubling? Do you ask questions to appraise their comprehension? Do you follow along on the syllabus they are tracking?
I was never tutored, nor did I tutor, although maybe music lessons might be similar. I did teach CAD on a one-to-one basis to over 200 people over the years, but that was with them driving the machine and me sitting behind them leading them through what they needed to teach themselves the rest of it. 20 hours was usually enough.
????
jferguson
Ouch! I honestly think it is bad practice for someone to intend it to be impossible to get a 100%. If the reason for this desire was to create a “perfect curve”, that’s … horrible.
I think its better for someone to have an idea what they want students to learn, and write challenging tests that can at least hypothetically result in 100% if a student has mastered all the intended content. Often even student with very good mastery will get things wrong for a variety of reasons. These can range from forgetting to divide by two, not quite understanding a question and so on. Given this, curves do tend to just happen over time.
It’s a blend. I’ve had students intending to be engineers, architects, doctors, and some who are taking the more challenging classes to make their resumes more attractive to get into college generally.
Don’t know. The fact is: I am patient. This is a long standing personality trait. It can have upsides and downsides.
Enthusiasm for learning helps. No amount of patience can overcome utter lack of trying on the part of the student. If a student won’t read, do their any homework on their own, watch videos or anything they need something other than a physics tutor. Homework help might keep that sort of kid from getting an F but they usually won’t get to “B” or better. (Or they might, but only because of memorization skills and tests that reward non-thinking.)
When I was on the faculty at Iowa State, if a kid had no specific question, but just said something like “I don’t get problem 2”, I would hand them the marker and tell them to show me how they started the problem saying I would help them with their issue when we identified it. (Once a 2nd student was in the room with a kid who clearly thought you just tried to get the prof to do your homework, and the 2nd student just started laughing when I did this. The look on the first students’ face…. It was especially funny because the first student had insisted we do his questions first– which was fair enough, he’d gotten to office hours at quarter to 1 and waited in the hall, but this was a kid whose strategy was to try to get a TA or prof to ‘explain’ every problem. The second student was one whose strategy was to show up only after he was stuck. )
Some of these students don’t really get that it’s possible to get negative brownie points.
Kenneth
Ideally, all of the above.
But bear in mind: The students who don’t try their own homework don’t have questions. The ones who do have specific questions benefit greatly from getting those answered.
With respect to the syllabus: I try as hard as I can to locate their syllabus so I can have suitable questions to provide before they cover the material. But this can be harder than you might think. (Seriously. Sometimes you would need to request under FOIA.)
“Appraising comprehension”: not formally because
(a) students have tests and quizzes with great regularity at school (sadly, they often don’t have their tests or quizzes returned to them. If they did, I could look them over and identify precisely what they did wrong. But. No. )
(b) the changeover in topics means that there isn’t time for them to have material presented at school, try to “get it”, have their tutor “appraise it” and then– if they have mastered do extra stuff before their test or quiz. In fact, they will pretty much have a test or quizz just about the time the tutor could “appraise”. They they move from “kinematics” to “newton’s laws” and so on. (The stuff does build, but still..) And finally
(c) you usually see a student 90 minutes a week. A test or quiz on last weeks material… well they probably just had a test or quiz on that. And beyond that, you can’t have 30 out of 90 minutes of tutoring time be “the quiz”.
When I can get a jump on the syllabus, I can bring appropriate materials to study just before they start a topic or at least near the beginning of the cycle. The teacher assignments follow and “supplement”. One student last year has a teacher who posted assignments on the web. So I could bring similar complementary assignments we could walk through– I could appraise what she didn’t know while she showed me how she did them– and then she did the assignments he assigned.
Students will generally do their class assignments because they want the points. But if you help them with theirs and they give them extra…. not so much.
Oddly, there are teachers whose style thwarts tutors getting the syllabus and helps the students who just want a tutor to “help with homework”. Quite a few teachers don’t give out syllabus’s, don’t use a book, don’t post solutions, don’t have lists of objectives and so on. Oddly, from what I can tell, many of these think the force the kids to do their own homework by giving out nearly no advance info. If the kids have a tutor, the reverse tends to be true.
But if the teachers are transparent, I can “appraise” and “give extra stuff”, and explain the things they are having trouble with right now. That’s the ideal.
MikeN
Often. Most are very good. They are much less ‘gameable’ than lots of other tests.
But my impression is generally the AP would not give you a pair of center of masses to find precisely because mixing up the cm along the ‘x’ and that along the ‘y’ is a common error. People who make the easy to guess ones know that– but the have the layout I showed above. And guessing the right one when it’s a pair because just too easy!
That said: even the AP has it’s ‘guessable’ moments. Not infrequently, you can eliminate 3/5 answers to some “content” questions when the answer is a formula by merely checking dimensions. Are you looking for the period of something…. it better have dimensions time, not 1/time or mass/time or time squared and so on. Are you looking for speed at the bottom of the hill? That better have dimensions l/t, not something else.
Sometimes this doesn’t work– but it works often enough that if you can’t think of the derivation quickly, you need to switch to “check the dimensions”. (Mind you, dimensional analysis is a topic on the AP physics syllabus, so arguably, you are getting points for knowing something. Still, I don’t think it’s what the question means to test.)
FWIW, I have a client from India who has expressed his frustration that he can’t manage to convince his kids to use process of elimination on multiple choice. The dad had to take lots of multiple choice entrance exams and he knows it’s worth a chunk of points at the high end. But his kids reaction to eliminating and guessing really is “blank stare”.
Lucia,
Thank you for answering my question about the Khan Academy. I watched the TED presentation and worked through a range of his videos. I also read some reports of his idea that the kids do their actual learning at home and then do their “homework” in class where the teacher can monitor those who are having difficulties and who need help. Apparently it is actually being tried in several schools but I haven’t followed up to see how well it worked.
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It seems to me that in class the teacher is always too fast or too slow for any individual. There are advantages in being able to wind back the video to repeat a part you didn’t get. If you are fast, it would allow you to learn a lot more beyond the class syllabus.
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From experience I know how dangerous it is to draw conclusions without sufficient data. That is why I asked for your opinion. I don’t know who would use the example you gave as I have been away from school for so long, and personally I still think in lb rather than metric. It didn’t seem it would be hard to follow to me.
Who hoo! One of my students did her extra problems!!! (I can check on moodle. That’s the sort of student I like!)
Adrian
Of course. But that’s separate from the question of what level is that video aimed for.
The questions I asked aren’t merely the issue of whether it was “too fast” or “too slow”, but for example:
1) Irrespective of “speed” if it’s high school only AP Physics calculus C students will use “i,j,k” for vectors. No one else uses that at all.
2) What is the person trying to achieve with that video. If it is AP Physics C, “elevators” problems ought to be used to help them to learn to adapt solutions to solving other more complicated probems. That presentation didn’t seem to do that. It doesn’t for example, ever write down F=ma, so that the student can start seeing the formalisms they will apply to later more complicated problems.
So:in some sense, the video is not “too fast” (in fact, it’s pretty slow for anyone.) But the person who made it didn’t have an audience in mind.
It’s the latter problem that results in my nearly always finding a better video for any level of student who might want a video.
This is called “flipped classroom”. I have no idea how well it works.
The general idea that kids learn at home and do “homework” in class could, in principle, work just as easily with books, hand outs etc.
The advantage of books is there tends to have been some consistent editing from beginning to end, and parents, tutors or other helpers can flip quickly through to identify what material is covered. Also: the author and editor generally know the level they are intending to write their book for. Is this geared for 6th grade? 8th? Sophomores? First year college? Calculus based? Trig based?
Presumably there is an advantage to videos– there are times when I like them. (I generally like short videos). But I generally find videos actual teachers made for their actual students in real course are better than Kahn academy videos. That said: this is filtered by youtube’s popularity filter. I’m sure some really bad ones exist and get no views.
jferguson,
One of the differences with music lessons and classroom tutoring is that voice, flute etc. teachers are generally not trying to dovetail with what the band, choir or other are trying to do. Also, nearly all students of voice/flute etc teachers will practice in between. Otherwise they would just quit voice/flute/clarinet/trombone and so on.
Lucia,
I visited my daughter’s school when they were introducing Chicago new maths. The presentation was for parents. It seems the first lesson for 6th graders was to learn integers!
I was learning simple calculus at that age. You can guess how I felt. They are abandoning it only this year after it was shown to be a disaster.
Lucia,
I agree in general about music lessons. On the other hand during my years of contending with the french horn, I often got help from my teacher, who was independent of the school system, with parts I confronted either in the school orchestra, or in the pit bands I played in. Who would think that broadway shows sometimes had french horn parts, but they did. These were amateur productions btw.
I hadn’t read your reply when I wrote the above. There are some truly excellent long videos too. DVDs put out by the Learning Company of the best teachers/lecturers in the subject -such as history. A nice complement to books that take up less room than the 2ft of Durant’s History of Civilization, of which we have 10 of the 11 vols.
Adrain,
I certainly did not learn simple calculus in 6th grade. I took college calculus in senior year in high school. I had algebra in 8th grade, then geometry, algebra II, precal/euclidiangeometer/trig, then calc.
And honestly, up until now, I haven heard anyone tell me they took simple calculus in 6th grade.
Lucia,
I was fortunate enough to go to a good private school in England. Most kids here don’t learn calculus at all, but to be fair most of the other subjects, including music, were taught well I thought.
“Adrain” is part of the plumbing.
Lucia, I think you answered my questions but got J Ferguson and me mixed up in replying. I do not know about Ferguson but I am sensitive at my age of all older men sounding/looking alike even though I suspect I have some years on JF.
Note: I do not do emoticons.
Ok Kenneth, you have some years on me?? I’m 74. I would add that at this august age, the only thing I seem to be better at is fooling myself.
Well. Since it’s come up.
I 😮
LOVE :>
emoticons! 🙂
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But I’m sorry to hear some don’t. 🙁
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Willard once told me they were unbecoming (at least the smileys), so I’ve sort of been stuck using them ever since. The things I do for people…
Lucia,
I missed responding to one of your earlier comments. The big advantage of kids working on computers is that Khan has it set up (with flipped classrooms) so the teacher can see what they’ve actually looked at and where they are having problems.
Of course if the kid isn’t interested nothing works.
j ferguson (Comment #153286)
I am older than you but I will not say by how much.
I remember the story of two sisters who never wanted to admit their age. They knew that the Hill sisters who lived in the same town either looked younger than they did or were younger and on being (rudely) asked their ages they would reply that they were as old as the Hills.
Warning: Old person jokes may not be appropriate (or funny) for all posters here.
Which reminds me after my evening martini, of course, that I was at a school reunion recently where the guy who was usually the MC could not do the job due to failing health and the gal who is the usual organizer take on the mission and from the podium ask the attendees to relate school stories from the past. It was without success until one lady who said she usually was hesitant to speak at such gatherings started relating school stories and then family stories and then how the youth of today are not up to our standards from back in the day and then … At my table I told the group that we needed to applaud when she paused the least bit and when we did she paused for a moment longer and then went on again. After her next pause the gathering arose in standing ovation and the MC quickly thanked her for her comments.
Now I have to make the connection to this thread or be considered what I mention above. I’ll ask Lucia if she has had any experience tutoring older people outside her family and how that task would differ from that used for young people.
Kenneth,
Not tutoring older people. But I’ve had the experience of “helping” my mother “learn” how to do stuff on her PC. Jim and his brother did their best to teach their elderly parents to do things like…. use a personal computer at all, pay their dvd and so on. My mom is better tat learning how to do stuff on her PC (probably because she did use computers for school stuff as far back as the 80s.) Jim’s parents definitely became hopeless at learning new technology.
The problems for the L’s were a combination of reduced learning ability, littel cross over from other familiar tasks and — sometimes — vision and coordination. Remotes are not designed for people who have trouble seeing, identifying and pressing the right small button. And if you don’t get the positive feedback of the tv or dvd doing what you intended, you learn even more slowly.
Adrian
That’s the theory about why it’s supposed to work. YMMV.
Lucia, I actually found that I was a lot more patient with my parents and my wife’s parents in dealing with instructing them than I ever was with my kids and I think because I realized the limitations that as you mentioned can come with age. I am also quite patient with my grandkids and am not sure why – probably because they are my grandkids. My sons say it because I am losing testosterone.
Ken,
I think parents have trouble teaching kids school type skillz. There may be something biological involved. Seriously.
Or the kids not learning may make the parents anxious, and that makes the parents turn into poor teachers. My mom was a school teacher– even evidently a pretty good one. None of us wanted her to “help” us. EVER.
Parents teaching kids and spouses/partners teaching each other are complicated by strong pre-existing emotional relationships which preempt the normal student/teacher relationship…. to the point that the teaching process can be non-functional, and negative in net value.
🙂 Yeah I suspect my step kids would rather go to the dentist than have me help with their homework.
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My older boy is driving me nuts with his performance in math right now (7’th grade, just basically arithmetic at the moment). I sit with him as he does his homework, making sure he’s got everything down. He seems OK. Come test day, BOOM! It’s like it all leaks out of his head, or he panics or something. Or I guess it’s possible that somehow the homework problems aren’t representative of the test problems. Haven’t gotten to the bottom of it yet.
mark bofill (Comment #153303)
As a past failed (non) instructor of my kids you should take this advice with a grain of salt, but do you think that by sitting with your son doing his homework you are not putting (undue) pressure on him to do well on tests and that might be affecting his test performance.
I do have to admire you for your efforts with your son. My kids would never allow me to get involved with their school work and wanted to be very independent. They also did not apply themselves to their abilities in high school and through part of college – as far as grades were concerned. My daughter and oldest son are very intelligent. My oldest son’s mother-in-law thinks he is a genius. My daughter has major problems getting along with people. My youngest son has specialized knowledge in the areas that interest him which is almost encyclopedic. It took me a while to reconcile that my kids were going to do things their way and that at some point I had little control of that. That does not mean that parents should give up trying. Heck, my wife still gives our grown kids advice. All involved, except my wife, do not take it very seriously.
Kenneth,
Thanks. I actually do try to let my kids alone to manage their own studies, except when their tests results start dropping. My boy failed his last math test with a 48/100.
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He’s got some issues; he’s ADHD and on medication for it. Not a dumb kid by any stretch; rather good at sponging up information and retaining it. Certainly not photographic memory, but pretty good. Better than I am at history as a matter of fact.
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I don’t know. :/
[Edit: but I welcome comments and suggestions!]
mark bofill
Not simple calculus like Adrian had in 6th grade? 🙂
Does the teacher return tests? So many don’t these days. But really, it would be so much easier for parents to diagnose what the problem is if the parents could have the tests. All the possibilities could be considered:
Is there a disconnect between tests and homework? Teachers will rarely admit there is, but it does sometimes happen. There is no way to detect the problem except seeing the tests and comparing to the homework– and it takes time. So having tests and homework flashed before you isn’t going to let you tell. If there is a mis-match, you can then either talk to the teacher or– and this may be the more successful approach– teach the kid the sort of skills that match what the teacher tends to test.
The other possibility if you are there when the kid does their own homework:
1) Make sure the kid reads his problem and starts on his own. Some kids don’t read the problems if you are there. They need to be the one to start.
2) Only help if they are stuck. (In this regard, cooking dinner or folding laundry while the kid works is a useful over lap.)
Thanks Lucia,
Now that you mention it… Yeah. That could be it right there.
Earlier on, me and my wife were baffled by the fact that he’d score perfectly on his homework and do poorly on tests. It’s online homework. It turned out his homework modules are structured such that there is essentially no penalty for guessing and guessing wrong. So the habit he got into was to take a couple of wild guesses for starters. Of course, come test time there is no second chance to guess.
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This may have led me to over involve myself with the process. Perhaps I need to monitor to make sure he’s not doing this without taking the lead / getting him started solving the problem.
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Thanks Lucia.
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[Edit: Sadly, no. I don’t get tests back, I never see them at all.]
Lucia,
How many hours should it take to learn simple arithmetic like adding,subtracting and dividing? Serious question.
I didn’t start going to school until I was eight as a result of WW 2. I never felt the lack of the various grades kids go through these days before that age.
I knew that I was behind and so paid attention in class. By the time I realized you didn’t have to work I was ahead of the crowd.
It seems to me that the present system wastes much time and is almost designed to teach kids how to goof off. I suppose it also depends on IQ but look back and consider how long it should have taken to learn what your learned.
Maybe I should clarify. It’s not a fixed number of problems. The modules throw problems at the kids and the kids keep going until they get the score they want, some sort of rolling average thing.
Adrain
I don’t know how many hours on those. But we finished adding, subtracting, multiplying and dividing by 4th grade. But there are many topics between “long division” and “simple calculus”. For example generally kids cover at least this sort of stuff:
Pre-algebra.
Introductory algebra/ advanced algebra / linear algebra
Geometry.
Trigonometry.
Some statistics.
Euclidian geometry.
Set theory.
It may well be that the present system wastes time. I’m sure IQ makes a difference. But perhaps you could clarify what you mean by “simple calculus”.
Yah. When I say ‘arithmetic’ I don’t mean my kid doesn’t know how to multiply or divide. Ratios, converting ratios to fractions to decimals, applying ratio’s in solving word problems; that’s the stuff he’s on right now. Maybe I shouldn’t have called that ‘arithmetic’, although I thought that was was it was. I tend to lump all simple math without variables into the ‘arithmetic’ bucket in my mind.
Mark Bofill,
Technology can be used for good…. or ill. Sadly, I’d say a lot of it is not well thought out.It’s evolving, but it’s often difficult for anyone to anticipate what can go wrong with a brand-spanking new thing. Especially when they are enthusiastic about this kewl modern thing.
Obviously, even if you don’t want a penalty for a wrong answer, someone needs to notice the fact that that strategy is going on. It’s quite likely the system is structured so the teacher can easily be blithely unaware of what’s happening precisely because the system is supposed to reduce the amount of mindless grading. But while doing so, it’s severed a connection that also forced the teacher to observe certain things (even without recognizing they observed these things that way.)
Mark
That sounds like “pre-algebra”. Often called “7th grade math”.
Kid’s learn stuff like associative, commutative, distributive laws. How to read word problems and set them into math. Usually they cover some geometric formulas (areas of simple shapes, circumferences). Pythagorean theorem.
The classes tend to not be called anything other than “math” until you hit “algebra” which then has a name. Kids start to deal with fiddling with symbolic representations (x, y) rather than just numbers.
For what it’s worth Mark, I think many algebra II topics and trigonometry are harder than differential or integral calculus– especially if calculus is taught in a very “applied plug and chug” sort of way. As in “memorize rules for differentiating polynomials and sin/cos”. The only remotely difficult thing in calculus I and II was was that some differentiation and integration requires knowing trig. 🙂
So perhaps some systems pull the “trig/algebraII/etc” stuff out of calculus and teach it before kids get the other more mentally challenging stuff.
But otherwise, the arithmetic to algebra hurdle is a rather large one. The one to calculus…. not so much.
You could teach calculus even earlier than sixth grade if you wanted to, particularly doing basic derivatives and integrals. Actually understanding it is a different issue.
I’ve got hopes for the boy. I’d formed the impression that he’ll do alright once he reaches algebra, although I honestly don’t remember what I based that on and don’t want to make something up now. 🙂
He’s good at ‘plug and chug’. I can almost ‘program’ the kid procedurally to solve a problem. It’s comprehending what he’s really doing and how to apply it to other problems, the conceptual part that he’s weak at. That’s probably the hard part for most kids, I’d guess.
Aw well. I’ll get him through to some reasonable level of competence by whatever device.
[Edit: MikeN, exactly.]
MIkeN,
Yes. If calculus was just “taking derivatives of polynomials, sin and cos”, it could be taught in 5th grad. It’s easier than algebra and word problems related rates and so on. It’s very “memorizeable” which kids tend to be naturally good at– as opposed to “thinking”.
That said: knowing how to differentiate and integrate simple functions is not more useful than algebra, geometry or trig. So it’s not clear why someone would want to teach calculus in that order.
I remember having stuff like simple “series” in gradeschool– mostly idetnfying patterns. Not sure what the point of that was– but whatever… it’s harder than learning d(x^n)/dy = nx(n-1) dx/dy.
Mark Bofill — 7th grader.
…..
For what it is worth — my experience with my now 15-year-old boy and 11-year-old girl. When necessary, I can be quite strict, however, I always try to find ways to have my children, of their own volition, want to do what I want them to do. If they are motivated to learn, many things fall in place.
…..
So, I have had an elaborate system of bonuses for grades and test scores that worked particularly well for my children, but especially my son. When I first implemented it in the 5th grade, he went from the top 23% in Ohio to the top 5% with virtually no effort on my part. He got $5 for every A, an additional $5 for “A”s representing scores of 95 or above and double if he got all “A”s. Also, I gave him $100 if he scored in the top 5% in different subjects on state tests and $50 if he scored in the top 10%. This helps a good deal with my daughter but not as much.
…..
Another example with respect to motivating my daughter. She spent 6 boring weeks in China with her aunt and uncle this summer. (In the past, she really enjoyed it). I would skype her every day and she would legitimately complain of being very bored. In the past, she had always said she wanted an Iphone and I said that they were too expensive. I do want her to go to China every summer so that she doesn’t forget her perfect Chinese. I put 2 and 2 together and told her I felt bad for her and that if she wanted an Iphone I would pay $300 towards it and that she could have it because she was having such a difficult time in China, and notwithstanding that it was good for her to visit her family in China.
When she came back, she got the Iphone and was deliriously happy–thanking me again and again. My hope is that when I set up a visit next summer, she will remember why she got the Iphone. [and I will also plan to give her something really nice, assuming that I can’t find enjoyable things for her to do.]
….
In terms of your son, I would consider some kind of positive incentive. If he really wants an Xbox, or really likes money, I would use whatever he wants as an incentive. I would tell him that I am trying to help you and to help you I want to give you an incentive. I would make clear that if he tries and has difficulties that is no problem. (Also, if he tried and couldn’t do it, at the end of the process, I would [without telling him beforehand] give him a lesser reward simply as recognition of his effort)
….
My experience has been that if you give children positive incentives without pressurizing them, they figure out how to achieve the goal for themselves better than you, the parent, could figure out. Just ideas from me that you can evaluate with respect to your circumstances. Good luck.
JD
Lucia,
“But otherwise, the arithmetic to algebra hurdle is a rather large one. The one to calculus…. not so much.”
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Not my personal experience at all. I thought just about every math subject was simple until first semester calculus. I think the problem was that the course was taught by the purest of pure mathematicians. He thought that once a ‘theorm’ had been presented and a ‘proof’ given of some calculus concept, the application of that concept to solve problems should be ‘obvious by inspection’. He NEVER showed any ‘applied plug and chug’ methods. After the midterm test (and the first C- I had ever gotten in a math course!) in desperation I talked with the RA in my dorm (senior in mechanical engineering). Turned out there were a dozen kids on my dorm floor with the same issues (and the same professor). So he called a group tutoring session in his room (where he had a small blackboard) and in a couple of hours he laid out the ‘plug and chug’ methods, and connected them to the ‘proofs’ the professor was so enamored with. One tutoring session and I was fine… never had another problem with math.
JD,
Thank you. In fact this has been my strategy (positive incentives) in the past, and it’s worked pretty well with the kid in question. Unfortunately the wife and I don’t see eye to eye on it. I’m not sure I can do justice to explaining her argument (I don’t remember it well, maybe because I disagree with it. Maybe I ought to try to understand it better. :/) So it’s been difficult to maintain a consistent motivation policy.
Maybe I’ll resurrect the discussion with her though.
Lucia,
“perhaps you could clarify what you mean by “simple calculusâ€.”
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As I recall, we were taught differentiation as a way to figure out rate of change. It is not difficult and a useful concept to have in one’s head early on.
It’s too far back to be sure but I think we were doing algebra and Euclidian geometry.
If you recall, I was complaining about the school teaching pre-arithmetic at this level and wondering what they had been doing in the prior years.
Adrian: “complaining about the school teaching pre-arithmetic at this level”
I don’t think integers are pre-arithmetic. Isn’t the point of teaching about integers part of the process of differentiating between types of numbers (integer, rational, irrational)? In my recollection, that is not needed for arithmetic but is part of building up to algebra. But that was a long time ago.
I took calculus senior year hs. teacher was head of math department and we had her for both trig and spherical trig.
The first class, she gave a problem which involved a barrel into which two different fluids were flowing at specified rates and a drain from which the perfect mixture was flowing – perfect because there was an Evinrude outboard doing the mixing – she was from Wisconsin. I think the question was what would be the proportions in the barrel after 10 minutes.
Of course no-one was able to crack it. After about 30 minutes she asked if we thought this was the sort of problem we might come up against in later life – assuming a technical life. Most of us agreed that something like this could lie over our horizons and we were off and running.
JD,
Interesting comment. To start with I’ve always been poor at languages, even English in the early days. So learning to be fluent in another language that way (particularly Chinese!) is a great advantage.
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What I have found is that it is easy to learn anything that I’m interested in but difficult if I’m not. I’ve never figured out what makes one interested, or how to become interested, in a particular subject. I suppose a bribe would have helped 😉
it could be that the barrel was half full of one fluid and only one other was incoming. I really can’t remember it other than it wouldn’t succumb to algebra.
Adrian,
Lots of American kids have rate of change and related rate problems early on– about the time they are doing what they call “word problems”. I know I did and I know kids I tutor had those long before they hit physics. It’s obvious they know this because some problems we’ll do and one might say “Oh. I can do that using related rates”. Obviously, they need to know rates for chemistry, which most take as sophomores. (They also need to know logs and exponentials by then. That’s not “addition, subtraction, division or multiplication.”)
Generally, America kids don’t differentiate to get the rates– until calculus– but I agree it would be easy to do so. They might get the rate from the slope of a curve– but differentiating using actual algebra rules, generally not.
That said: I think the hard part isn’t learning d(x^2)/dx = 2x which kids can memorize just as easily as A=Ï€r2. It’s understanding “slope” = “rate” and understanding what to do with rates etc.
On complaining about them discussing “integers” the first day in 6th grade, you should bear in mind that might not have been the first lesson on “types of number”. I don’t know what did happen in your visit to the school. But as you’ve said little, it might have been refresher because they were moving on rational/irrational numbers, imaginary numbers, taking square roots and the like. It generally useful to discuss things that are not irrational numbers when you start to approach that topics involving irrational numbers. The issue of rational vs irrational, Ï€, numbers like e &sqrt; 2 and logarithms.
For what it’s worth, “integers” is on the Kahn academy curriculum for 6th grade. So perhaps that’s what your kids teachers were using. 🙂
https://www.khanacademy.org/math/cc-sixth-grade-math
SteveF
Yep. You see, the problem wasn’t that calculus was hard. It’s that lots of college professors didn’t want to teach the “how to” (which they then proceeded to test!)
I found trig harder because of all the proof of trig identities. The reason for doing those escaped me…. until calc where you needed to do them for some of the integrations.
I found synthetic division tedious. Not hard so much… but … oy. (I don’t remember it either!)
Mark, now that you mentioned it my youngest son had ADHD and also did poorly on tests in grade and high school. He has been able to compensate for this later life and in those areas where he has interests he has way above normal comprehension and recall. His abstract reasoning is probably still not one of his stronger skills.
I should also note that I have a grandson who is severely autistic and with whom we had almost given up on his progressing. He was in fact regressing. A few years ago he started to progress and in fact at times has progressed at a rate were we did not always appreciate what he could comprehend and do. He continues to have all the quirkiness and behaviors of his autism but he can follow rather complex instructions and communicates using an ipad. He also has very good spatial memory and recognition – probably better than I and definitely better than his grandmother. He and his mother lived with us for several years and he lived nearly a year and one half with his grandmother and me after his mother become physically incapacitated and could no longer care for him. In that time period I think I learned more about what motivates kids like him and how to best instruct them. I learned that you have to have patience and plenty of it and that was learning experience for me. I also learned that he could play people like a fiddle to get what he wanted.
While we attempt to communicate his capabilities to others involved in his life they are often surprised at some point with what he can do. We found a very good residence for him and a good school. He loves school and does very well given his autism. I have been very impressed with the teachers and staff he has had in his previous school and his current one. Most of the teachers and staff are quite young and energetic and appear enthusiastic about their work. What most impressed me is how well they handle autistic kids and without overreacting even during a kid’s meltdown and how fast the kid comes out of his meltdown. My wife and try to learn from their techniques and while we are better at it than before we have not reached their level by a long shot.
Lucia,
It was called something like “Connected Math Program” and was being introduced as the new teaching syllabus at that time. Reviewing my notes this was for 7th grade. It was roundly criticized by non academics like engineers and some academics and wasn’t abandoned as a total failure until after my daughter had left the school system – knowing very little math.
The lady whose job it was to evaluates the program for the school couldn’t answer my questions and her only argument in favor of it was that it was recommended by the “experts” from the Dept of Education. Apparently that was all she required.
Hey, I’m perfectly willing to believe it was bad. Just not merely because they discussed “integers”.
The US system seems to constantly introduce “innovations” that end up being catastrophes. All are always recommended by some sort of “expert” or other.
If I were a parent, I would be leery of any “new” programs– unless they were being introduced because kids had been failing in the old one.
Replacements for “previously new introduced to great fanfare” is generally an improvement.
But “new, new! Great fanfare new!” Often dangerous. You don’t want to be the first set of kids doing that. The chances of failure are high.
Kenneth,
I’ve speculated since I’ve known my step son that with at least some ADHD kids, it’s not that they can’t pay attention to anything. It’s that they can’t control what they pay attention to the same way most of us can. As a result, perhaps some develop surprising expertise.
Thanks for sharing about the autistic grandson. I don’t know much about that, although my wife (speech therapist) used to work with some (one? some? I don’t recall have to ask her) autistic kids years back.
🙂 I’m always pleased to be surprised at what people who are thought of as severely disabled can actually do, given the right environment and help developing.
.
Thank you.
My best friend in college and I had a friend who had to take remedial math in order to get into the required freshman math class. My best friend and I were both chemistry majors and the friend with the math problem was majoring, as I recall, in some social study. After he had problems even in remedial math we took him on as a project. He did not seem to have a very good concept of abstract reasoning and appeared to want to learn strictly by memorizing. We worked with him without success until one day (and do not ask me why because I do not know what went click in his brain) he had an epiphany and understood how to reason his way through math problems. He passed the remedial course and aced the general math course.
Lucia,
It wasn’t just our school, but most of the schools in PA at least. I don’t know about the other States. As it was only abandoned this year there are a whole slew of students going through college that are woefully behind in math. No wonder we do so badly in statistical comparisons with other countries.
My daughter was not interested in going into science or engineering or I would have had to find another school. She’s just become a registered nurse and is continuing college to get her BSN and possibly masters. She could make a living as a dancer and performs professionally.
“a problem which involved a barrel into which two different fluids were flowing at specified rates and a drain from which the perfect mixture was flowing – perfect because there was an Evinrude outboard doing the mixing – she was from Wisconsin. I think the question was what would be the proportions in the barrel after 10 minutes.”
A bit like a hat lost over a boat problem?
Barrel not filling up.
So flow in equals flow out.
Perfect mixture out so volume in equals volume out.
Proportions must equal ratio of volumes going in over time.
Why would 10 minutes matter?
What did I miss?
It seems like academic teaching ‘innovations’ in the US are never tested in the field before being implemented en masse. People who may have some clue about teaching but no clue about how what’s being taught applies to the real world can come up with odd ideas.
The subject of calculators (and slide rules) came up the other day and one person remembered being told that they needed to learn how to do calculations in their head because they wouldn’t always have access to a calculator. Now it’s exactly the opposite.
Angech,
I’m having a hard time remembering the details, but problem starts with barrel containing some specified amount of one fluid, the drain and the filler flows were not the same, and i think with the rates involved the barrel was unlikely to fill in less than 1/2 hour – in any case that wasn’t the issue.
Angech,
These are pretty common concentration/mixing problems in calc and also chem. There is the fluid of some kind going in (or perhaps two), and the fluid already in the tank, and some of the combined mixture is going out.
angech,
In Chemical Engineering it’s called a continuous flow stirred reactor. You can solve those problems by brute force numerically and get a reasonable answer if your time steps are short enough. But usually the differential equations have analytic solutions.
DeWitt Payne (Comment #153339)
Sort of, but not always. Several recent ‘innovations’ have been successfully implemented in other countries, in some states, or even in pilot programs, so it is not true that they haven’t been tested in the field. However, it’s clear that the problems of adoption across all schools, by all teachers, with the ensuing startup training requirements and discontinuity in the curriculum, are not trivial.
DeWitt,
The calculator things is funny. I memorized all sorts of borderline useless crud because useful calculators only because available just after a graduated high school. This sometimes is somewhat useful tutoring– after all, knowing sin(30)=1/2 is useful when presented a student physics problem that has a 30 degree angle and you can tell at least part of the solution is bang on correct without pulling out the calculator.
Students blink when you use the 3,4,5 triangle stuff really fast too. But really, that’s no longer actually important. (In real life things are conveniently 30 degrees or 3,4,5 anyway.)
oliver, john, angech– yes. that’s a very common problem, both in calculus and later in things like early chemical engineering. Similar problems are important in other engineering– but it won’t necessarily be mixing fluids. It might be finding temperature. Same math.
lucia,
I don’t know about the rest of the posters here, but I still have to force myself to do math in my brain on a daily basis to keep the gears oiled. Based on my (limited) example, I don’t think it’s realistic for most people to remain proficient based on only some years of drilling in elementary school.
For me, the convenience of not needing a calculator to understand basic relationships and also catch major errors(and figure my tip at a restaurant!) is worth the mental exercise. (Besides which, people actually go out of their way to find mental exercises, e.g., crossword puzzles and sudoku!)
As for 30° triangles: they aren’t ALL 30° but they often are! (And many cases are close enough that it’s still a useful rule.) 30, 45, 60, and small angle approximations can get you pretty far in practical settings! 😉
oliver,
I would never use a calculator to figure a tip!! It’s not even a matter of forcing. Among other things, I don’t carry a calculator around– and it’s a simple calculation.
Definitely: I do approximations w/o a calculator. And I round at the end anyway. I’m not leaving a tip that’s something like $3.41– it would be rounded to 3.50. Heck, possibly $4. Depends on context. This isn’t something where precision is required.
But High School teachers… (and even undergraduate problems) the teachers generally want 2 sig figs (or so– depends on subject). So if the angle is 35 degrees or 25 degrees, they really do need to hit the calculator buttons. This is true even if later on people value getting the order or magnitude quickly and leaving precision until later.
(Actually: I could go on about some HS teachers. I know one who uses Hewitt’s Conceptual physics, has all the students use g=10 m/s2 and then docks them if the don’t report the “right ” number of sign figs in a result– with “right” sometimes being something like 3 sig figs if everything else has sufficient units to justify that. My thought is…. what the F***? If your rounding g to 10, don’t harp on sig figs. I’ve never spoken to this woman– but I’ve seen the points docked; the poor student is trying to “get” the entire idea. The best I can say is “Your teacher is pretending 10 is an ‘exact value’, so– even though it’s not– go alont with that. The response is– of course– but it’s not really… right. Answer: no. Of course not. But if you want the points from teacher x pretend it’s exact and don’t argue. You ain’t gonna win. Rest assured that with teachers like this, you don’t want to round — unless it’s multiple choice, in which case.. other story.)
olver
By the way, I think this is spot on. I think quite often, the “system” doesn’t quite understand the problems of discontinuity in curriculum, teaching methods and so on.
When I was in 5th grade, my 5th grade teacher was a 1st year teacher. The poor guy….. He was very enthusiastic. He decided we were all going to do “self paced”. This was all the rage. And if you hear the promotional discussions, it sounds great in principle.
But what really happens:
1) A teacher teaching his first class ever has about 25 kids in a room.
2) NONE of the kids have ever participated in a class where the learning was “self paced”. Naturally, some consider “do no math” an option and do that. When they did, they often considered designing nifty new paper airplanes a useful activity; applied spit-ball spitting was also a popular activity.
3) This guy found himself as 1 teacher for 25 kids– each going at different rates. Within a week, every kid is on a slightly different topic (except for those doing nothing at all. ) So on any given day, the teacher had to have on hand a bunch of different materials answering different questions.
4) The idea of “self paced” had been ‘tested’. But where? At some university lab school where each teacher has a number of student teachers in the room. The “official” position on the presence of student teachers was that this created more work for the teacher because they are spending time “training” the student teachers. But in a students go along “self paced”, I’m pretty sure having 5 adults per 25 students available to answer questions (and discipline kids shooting spit-balls) is better than 1 adult/ 25 students. And that’s true even if the student teachers are “trainees”. But the promotional materials all described this as so easy to do it could be done even with the ‘burden’ of student teachers to train. So– clearly– the thought went– this would work even better when that burdne was lightened and the teacher could devote themselves to the 20-30 students in the class without the diversion of the “burden” of the 5 student teachers. Well… hah!
5) No other teacher in the entire school did “self paced”. None had ever done it. So the first time teacher had no one to get any practical advise from.
Even if the ‘self-pacing’ could have been made to work eventually, this situation had all the elements of “catastrophe” written on it. Many spit-balls were spat. Kids abilities to create paper airplanes soared. Little math was learned.
The guy quit teaching and took a job at International Harvester (I think) the next year.
Lots of school systems fell for “self paced” during the late 60s early 70s. Entirely schools transitions in a snap. Entire building were built. Those building new schools also often had “open floor plans” to encourage “interaction”. You’ll find all sorts of late 60-s early 70s schools that were retro-fit to add walls which– as many know — damp something called “noise” which often arises when you have 200-400 people (especially kids) all “interacting” at any given time.
Butterfield– the junior high on the west side of Libertyville was “self paced” the first year it opened. That changed within a year or two. You can read here:
https://en.wikipedia.org/wiki/Libertyville_District_70
I’m pretty sure the walls went up within 2-3 years. The first year with no walls it was a 5th-8th grade school. We at Highland counted ourselves lucky to be at the “old school” where the (old) sewing machines worked, spit balls were not spat constantly and so on.
Lucia, question for you. There is a teacher who uses shortcuts like g=10, and takes the students out camping. She has them pitch tents that are square pyramids of height 1.5 m. While doing so, the camp was attacked by a bear. Can you tell me the color of the bear?
What do people think of Common Core? I am reflexively against it, but haven’t really followed it.
It took me forever to comprehend that integration is a summation.
MikeN,
Brown, black, or white, depending where the camp is.
In late ’60s, a new middle school in Barrington, IL was all the rage in the architectural magazines. It was open planned, carpeted, with a vast space with some steps. In one of the photos, there were a few groups of students each group clustered around a teacher. It never occurred to me that the crosstalk would have made this scheme unworkable, but then I didn’t visit the place – I wasn’t involved in school design.
That this scheme was acoustically impractical was probably discovered on opening day.
None of that sort of discovery ever made it into the architecture magazines.
I imagine similar things happen in lots of fields. I believe it happens in software development. Right now I’m working alongside a different team who likes to stay on the ‘bleeding edge’. Continuous integration and [fully] automated testing, the whole nine yards. Heh – those guys spend 4 hours catering to the needs, shortcomings, and defects of their ‘latest and greatest’ tools for ever hour they spend actually working on the product. I’m not exaggerating that at all, we measured it.
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I prefer stuff that’s had the kinks worked out. I like to stay a year behind the cutting/bleeding edge; let all the adventurous youngsters step on all the landmines for me.
MikeN,
I don’t know what “common core” even means. I’ve looked at documents discussing it. I’m often mystified– but my generally feeling is it’s just too “high level”. But that might be because I have to plow through so much crud before I can get to the part that’s remotely useful to me as a tutor. So I give up and decide there are other ways to learn what I need to know.
Obviously, as a tutor, I’m a supplement. I’m always going to be trying to help students with details so they “get” what their teacher is expecting them to get whether or not I think that’s a great pedagogical method, whether or not I think the “common core” or “NGSS” or any other “thing” is good, bad or indifferent. I can’t override the teachers choices about what specifics this kids is going to have– or even — whether the kids is going to be forced to demonstrate mastery of a particular method the teacher thinks is somehow “helpful”. I think (though I’m not sure) those details are not discussed in the “common core” which leaves lots of choices to teachers. (As it should.)
That said there is something additional in science– and I do find it more useful than reading “Common Core” documents. These are the NGSS (Next Generation Science Standard) which do (at least now) seem to achieve a level of detail that permits people who have not mastered “education-eze” to feel like they can extract some clue as to what is expected of students.
Here’s one for “energy”: at the highschool level note especially the red clarifications which I’m pretty sure were added since the last time I saw these. (Which was at least 6 months ago.)
http://www.nextgenscience.org/topic-arrangement/hsenergy
Before the red was added, I honestly couldn’t tell if they were saying the kids should build their own CFD models (which would be ridiculously hard) or whether the kids would be doing what the clarification says– which is in the vicinity of sane. Provided I am understanding it, kids learning to do traditional “roller coaster” problems were they find the maximum height a roller coaster car can safely reach given it’s initial velocity at the bottom of the hill are ok on the bits that involve “kinetic energy” and “gravitational energy”.
Here’s force interactions:
http://www.nextgenscience.org/topic-arrangement/hsforces-and-interactions
This is actually lower level than nearly any physics student I see. I have not yet seen any who don’t do 2-D motion of some sort. But at least the clarification permits me to know what the first bit actually means.
Last summer I took a “modeling workshop” for teachers. Many were sort of nervous about NGSS– which they know they and their kids will be measured against. I suspect back then, the red “clarifications” weren’t in there. And let me tell you, I’d be nervous being assessed against the unclarified NGSS because I couldn’t tell what the kids were really supposed to know, think, do etc.
mark bofill,
Yeah. One time Jim made the mistake of upgrading his operating system as soon as it was possible to do so. Mac tend to have most upgrade be smooth, but there is always something you, personally, don’t forsee and it’s nice to let other people on your team discover things like, “your favorite bit of software hasn’t been upgraded to work with the new OS yet. But it will be… just wait a few weeks….” (Never mind the stuff that will never work with the new OS. It’s nice to know in advance so you and hunt for replacement tools before your upgrade.)
j ferguson (Comment #153362)
My kids attended a new high school in Wheaton IL that used the open class room concept. It lasted until the school was turned into a middle school which was the year my youngest was a senior. (The school has since gone back to being a high school but without the open room concept). There were many complaints about it and when my wife and went for our first teacher parent meeting I recall asking how this concept was supposed to work and on getting rather vague answers from the young teachers we asked I remember commenting to my wife that teachers may have become less articulate over time. Thinking back on the situation I think those teachers were not so sure what the concept was or how it was supposed to work – or so turned off by it that they did not want to talk about it.
Mark B,
when colleagues fall in love with the tools and forget the objective, it’s hard to imagine that productivity loss isn’t conspicuous.
When I started in architecture there was a little of this, guys produced beautiful working drawings, but the message the builders needed might have been adequate had 2/3 of the time been spent. this sort of thing was incremental so i couldn’t decide the drawing was ‘done’ and take it away from the culprit. Producing pretty drawings was the motivation and I had to accept the cost in time as cost of doing business.
When CAD came it could be worse. Managing something going on in a machine is a lot harder. I couldn’t walk through the office after everyone else had gone home and look at what was on the boards. Although drawings sometimes did not scale to the required dimensions such that what might look ok wasn’t and CAD at least offered the possibility that if dimensions were ‘snapped’ to the elements, they wouldn’t lie, it was possible to complete work much faster if you didn’t ‘snap’ and of course then, the plots lied.
big problem was with people falling in love with the process and constructing elaborate ‘virtual’ models of the project which would be the basis for views which would comprise the construction documents which were the only thing anyone really wanted – and the only thing we were paid for.
these virtual models could become almost complete and include all sorts of things which would never show on the construction drawings. amazingly, the file-size in bytes was the best way to detect this.
I suppose there is a universal truth in here, but my conclusion after escaping this business was that people weren’t likely to be productive if they weren’t smart enough, and if they were, they’d get bored with it and start making mistakes, after maybe 18 months.
Mark, do your guys have a deadline for shippable product?
Kenneth,
It’s a sudden death type situation. We’ve got sales and marketing guys out trying to get people on-board with our system, and we’ve got a system in a somewhat dubious state of readiness, which we’re trying to improve. 🙂 Pretty much par for the course in my experience, although this is sad to admit. At most (not all, but a majority) of the shops I’ve worked in, usually the process of building the boat isn’t really complete until well after the maiden voyage.
[Edit: I guess which just illustrates my point. The product my group is developing is going to be ‘bleeding edge’ for awhile. It’s just how it works out.]
Kenneth,
I’ve been in the Wheaton building of which you speak; that’s where the modeling instruction workshop I attended was held. I commented on the “no windows” thing– the teacher explained it had been one of those open classroom buildings that had had the walls added later. No windows was also a “thing” at the time. The idea was students would focus better on the class if there were no windows.
On the “explanation”– I heard some of them at the time.
Evidently, among other things kids were supposed “seamlessly” flow from one group to another. So a 5th grader might “seamlessly flow” over to the 6th grade class and vice versa depending on the day, level, interest. So the lack of walls was supposed to result in not marking the students as being limited to a particular grade.
And teachers could “seamlessly” flow to the students who needed them. Sorry, but this doesn’t work if you have 1 teacher to 25 students. There is enough need for that teacher with their 25 students that they can’t be monitoring whether there is a more urgent ‘need’ by one of the 400-600 other kids in the room who might need that teachers specific attention.
And do you really think all these kids who’d never been in this situation would “seamlessly flow” to the class that was teaching precisely what they needed that day? (No.) How could the kid even tell? (They can’t.)
Kids in the 6th-8th grade were going to “seamlessly flow” over to sit next to a kid the liked. (Sometimes that other kids might want the other kid to come over so they could improve their spit-ball techniques, gossip or whatever. Sometimes the target kid didn’t even want the other kid to come over. Other options were possible. )
This idea was very expensive. It didn’t work. Mercifully, it was so obviously bad — and possible created even agony for teachers than students — so it went away pretty quickly.
I’m sorry, I should have addressed ‘J’, not ‘Kenneth’.
j ferguson,
Or they just can’t focus on what the downstream customer cares about and believe that they as “the expert” in what the are doing know better.
My sister is a law librarian She reports that she’s going to some law librarian gatherings (probably professional development) and some of the librarians go on and on about how they like to “go the extra mile” when doing a search which meant after all the cases were found, compiled and so on, they sent the papers out to someone to uni-bind it. This was a process that was available in house by for the librarian in question and took days (2-4), but these particular thought it looked so much more professional and so was a better product.
My sister met scads of these people.
My sisters view was that many of the attorney’s she did searches for were pressed for time. Often — for whatever reason— case deadlines, discussions and so on were approaching. No (or practically no) attorney would pick the unibind with a two-day delay over the immediate delivery of a velobound object or even hole-punch, put it in your notebook. The attorneys often told her they needed stuff done yesterday, and she interpreted that to mean sending out to unibind was not what they wanted.
But it gets worse because it turned out these librarians who were into “unibind” were grumpy that the attorney’s didn’t express appreciation for the loveliness and beauty and thank them profusely for going the extra mile. . . Still… they unibound.
Sis figured putting in her two cents was not worth it and bit their lips.
I’m not sure what the social dynamic at these law firms was. In principle, the attorneys are sort of “boss” and the law librarian not so much. But it could very well be as you describe with your drawing department.
Hi Lucia,
I’m pretty sure the Barrington building was windowless.I wonder what i would have done had I not been able to look out the window in primary school.
Lucia, those open classrooms, according to my sons, were a boon for their more recalcitrant buddies and their extracurricular activities. I knew some of these buddies and hear these tales to this day at gatherings. Some of these buddies have had very successful businesses and business careers – and in spite of and not because of open classrooms.
j ferguson,
The main potentially correct positive of no windows was (at the time before low e glass and triple glazing etc.) reduced heating/cooling.
Kenneth,
Well… some of the those recalcitrant student learned social and sometimes even “bizniz” skillz…..
lucia,
If you still have one lying around, pull out a slide rule and show it to one of your math students and see if they can figure out how it works. Were the bamboo slide rules considered higher quality than the aluminum ones? I can’t remember now.
DeWitt,
Any I had were left at my parents when I graduated high school. I’m sure my mom will not have saved that. There are certain things she saves and others …. not. Which she thinks worth keeping are a bit mysterious. But a slide rule she will almost certainly not have saved.
I seem to remember the existence of plastic seeming sliderules too. For high school, the cheaper ones were fine.
Hah: sliderules:
We have the K&E log-log duplex decitrigs of both Dad’s (both EE’s) plus mine, plus a Picket & Eckel aluminum round ‘slide’ rules which has a spiral log scale which i think is 10 feet long. For any pilots here, it looks a little like a prayer wheel. My brother-in-law still has his Post.
I had a Picket & Eckel aluminum rule in HS. Dad gave me the K&E so I could have a ‘real’ slide rule. The P&E was pretty much same as the decitrigs- but had rollers on it and it could bind if not lubricated. I always wondered if picket & eckel was made up to sound German and the manufacturer was really named Prima & Smith; Luis and Keely don’t you know.
the K&E’s warped and could get sticky – we used talcum powder on them. I think the Post bamboo ones were probably the best – bamboo neither warped nor bound – But and it’s a big but, there was a pecking order to these things and in the early ’60s despite the binding, the K&E’s were considered the class act – shows how nuts some of us were.
the MIT tech museum had a room full of slide rules when we visited a couple of years ago. I would never have thought that remembering how to drive them would impress anyone, but it did. one of the kids, looked at me, guessed that i was familiar with them and (gasp) might have used them in anger. So I conducted a short seminar on how they worked and the even greater value of being adept at guessing what the result ought to be so you could get the order of magnitude right.
I don’t know if any other engine school ever did this but in late ’30s University of Minnesota ran it’s EE’s through a semester of how to estimate (fake, guess, ??) what the answer to a problem might be so you could either decide the thing wasn’t worth pursuing or have a grip on what the order of magnitude of the solution should be.
Dad told me that this was the single most useful skill he ever developed. He could sit in a design meeting and suggest that a particular course wasn’t likely to lead to anything useful because the numbers would work out to something like ### and that wasn’t going to get job done.
K&E = Keufel & Esser. Their sticks were mahogany. Honduran, too.
Lucia,
I tell myself the older generation always thinks the upcoming one has gone to pot, but I keep reading articles like this. “Dumb American Youth”
https://www.lewrockwell.com/2016/10/walter-e-williams/public-schools-produce-dumb-kids/
If Prof William’s figures are anywhere near correct the situation serious and getting worse. Where do you stand on this?
Just saw a trailer for a National Geographic Channel series, “Years of Living Dangerously,” about climate change. It had, well, a certain air to it. Just checked online, and it turns out that Joe Romm is their chief scientific advisor. Hmmm…
Adrian:
The figures are probably correct. But I’m not sure what that signifies.
https://www.lewrockwell.com/2016/10/walter-e-williams/public-schools-produce-dumb-kids/
As usual with people slamming the young, they hold up their own generation as somehow more accomplished. But when reading the following, bear in mind: people give themselves credit for mastering things they may not have mastered:
I’m sure he filled in the maps. We filled in similar maps in the 60s. And I would suspect that many of the kids who remember filling in the maps forget they didn’t consistently get 100%, they certainly didn’t know what the average in the class was, and even those who did pretty well may have forgotten where Ohio is when presented with some sort of survey 20 years later.
What does the verb “interpret” mean in this context? (Real question.)
Have you read a food label lately? I have. These days labels have ridiculous amounts of information printed on them. I find it difficult to believe lots of college grads cant real a label and determine that the box contains a “pizza” as opposed to “macaroni and cheese. On the other hand, I can perfectly well believe they might not be able to “interpret” the “significance” of the presence of “citric acid”.
Besides that, perhaps the reason the number who can “interpret” the label has fallen because many people have learned that much of the information is of no value to them. I’ve got a can of tomato sauce here. It contains no fat. Did I learn very much by reading that lable? No. Tomatoe sauce rarely contains any fat because tomatoes don’t contain fat. And really, there is very little reason to be so concerned about fat that I learn that from a label. I know olive oil is pretty much all fat without the label. Tomatoes, not so much.
Sure. I don’t think this means much. I bet more people knew who Joltin’ Joe DiMaggio was than who the Speaker of the House was at the time Joe was playing. (Who were the various speakers of houses back then? I don’t know. But we all do remember Joe. And this does not constitute a “problem”.)
The author lamenting the incompetence of the students fails to tell us if these “everyday tasks” are “flushing the toilet” or “heating a pop-tart”, or “changing the washer on a faucet”. Owing to that elderly authors lack of competence in conveying this important information, I have no idea whether I should be even remotely concerned the kids can’t complete “everyday tasks”. Nor whether I think their competence is less than some previous generation’s.
It’s all well and good to pat yourself on the back for having been able to do something that is not totally useless. I’m sure we could find that today’s kids don’t know how to use a slide rule. And yet tons of people used to be able to do so. Oh. The. Horror!
I do agree there is a problem with believing everyone should go to college. The problem isn’t merely “standards”. The problem is that we actually need plumbers, machinists, electricians, hair dressers and a variety workers with different types and levels of skills. And some kids would be happier and more prosperous being a plumber than doing some “college” stuff. But that silly authors has to make it seem like the problem is kids are “stooooopid”, when the problem is even if they aren’t stupid, we still need plumbers.
Lucia,
I suspect you are basically right. Thank you. I searched for the paper by the American Institutes for Research and failed to find it, but did find another reference that mentioned “Balancing a checkbook, comprehending newspaper articles, and calculating the cost of gas”
Also: These tasks range from straightforward to complex, and fall into three categories: reading comprehension, critical thinking and analysis, and practical mathematics.” as some examples.
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As for the food labels I suspect it is a matter of disinterest. In my case I can’t read most of them any more because the font is so tiny.
I thought the statement “Reported by Just Facts, in 2009, the Pentagon estimated that 65 percent of 17- to 24-year-olds in the U.S. were unqualified for military service” bad news though.
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The ACT college readiness results seem in line with IQ and as you say it is crazy to think every kid should go to college and not just because we need plumbers. I gather one is again allowed to talk about that after being forbidden for many years.
I recently watched Rushton speaking about IQ here. https://www.youtube.com/watch?v=yZ65PSrSgAo but it is probably too long for your taste. I was surprised by India because of the bright ones I had met here, but I suppose it is not easy to immigrate without relatives to help.
j ferguson,
My Grandfather, MIT class of 1927, spent time when I was young teaching me and my cousins concepts of approximation and estimation. He said he had been taught this as a student at MIT. He taught us “rules of thumb”, like acre-feet of water, basics of timber cruising, the value of critical thinking, etc. I can’t say that all of his lessons were appreciated at the time, but over the years I have come to see their value.
Adrian,
I’m not that discouraged by “65 percent of 17- to 24-year-olds in the U.S. were unqualified for military service”. We have an all volunteer army and part of the “qualifications” is to have a reason to take only the cream of the volunteers. Enough people volunteer, so those making qualifications may be placing them high precisely to have a way of not taking the ‘lower’ placing ones.
Hi Hunter,
‘basics of timber cruising’ ??
j ferguson:
Re timber cruising: read this to get far more than basics.
From a quick glance, there are some interesting statistical methods in there, e.g. see p. 126 et seq.
Thanks much HaroldW,
I used to know a fellow who did this in the pulpwood industry in Georgia. i hand’t realized the work was so subtle, but of course it would have to be to be manageable.
hunter,
I wonder how much progress has been inhibited by a ‘need’ to have an exact number and the time it takes to get one. I cannot remember any credence given to approximating an answer in primary or high school, although we did get a slight hint in physics which i think was taught based on a PSAC (??) package which included a lot of neat do-it yourself experiments including making a micro-balance with a common pin, a soda straw, two razor blades, a match box and some tape. I think the course materials and the idea originated at MIT.
j ferguson,
At the early levels in physics there is tension between ‘understanding concepts’– which don’t require numbers at all, being able to check whether the concepts can be applied to get an answer, figuring out how to be able to have teachers detect both full proficiency and errors and a bunch of other things. Some of the “need” to have “exact numbers” is that it’s easier for teachers to grade 30 sets of tests/papers etc if they can scan and quickly check as correct numbers that are “the same” as each other. It discourages approximation which is a very good skill (especially in physics) but it just makes grading easier. Explaining grades is easier too.
Tutoring, it is certainly possible to see what strategies different teachers, book etc. use. (Some teachers books do better; some worse. Some…. well.. nutty! Others, great.)
I remember in early physics, having to do problems on accuracy vs precision.
Mike N,
Yes, but I don’t think the issue hunger and j ferguson are discussing is having students learn about accuracy and precision. There are some separate pedagogical issue that have to do with students
* learning and understanding physical concepts,
* learning some general aspects about how to assemble the concepts to do problems and so on and
* how to get order of magnitude estimates of answers.
vs. worrying about getting a correct answer to ‘n’ significant digits (and worry about what the number of significant digits are and so on.)
Students do need to understand ‘significant figures’, “precision’, “accuracy” and so on. But early on, they also need to know what the principles are, and how to apply them when there is a bit of complexity. And sometimes having them worry about whether then answer has one, two, three or five significant figures and/or worry about them reporting it correctly to said number of significant figures can get in the way of the student first understanding how to do the problem at all. The student spends so much time worry about whether the answer should be reported as 2.123 N vs 2.12 N they get overloaded and the concept of Impact = change in momentum just flies right out….
To do order of magnitude estimates requires a firm understanding of how to do the problem at all.
J ferguson was commenting that he doesn’t recall any high school teachers giving credence to the notion that ‘order or magnitude’ calculation were useful– even though at later stages this may be one of the most important skills for a practicing engineer, researcher, designer — and yes, manager. (Of course precision matters too… but first get the order of magnitude!!)
I’d say J ferguson was right that h.s. teachers do not give credence to the notion that order or magnitude estimate are of the greatest importance– and instead at least seem to care much more about precision. But I can see both good and bad reasons many teachers don’t or wouldn’t do accept answers like “well… its about 2 N” from students. (That said: some might accept it.)
But I’m pretty sure high school teachers ‘not spending much time on order or magnitude estimates” has very little to do with anyone trying to actually teach the “accuracy/precision” issue. It has to do with lots of other things that range from “how kids actually learn and internalize stuff” to “what sorts of things are practical impossibilities if you need to grade 30*5 sets of homework several times a week.”
Luica,
Being able to make order of magnitude estimates is for sure closely tied to a solid conceptual understanding of the subject area. I can’t remember a single case where a high school teacher talked about making good order of magnitude estimates, and few cases where they talked explicitly about the important concepts of a subject area.
SteveF,
The teachers definitely think they talk explicitly about important concepts. Whether it comes across that way to students is another issue.
But wrt to assignments I see I definitely do not see much attempt to have students do order of magnitude estimate. Part of that might be that teachers may be covering order of magnitude of simple things (like: about how long is a football field? How tall is a building) way at the beginning. But kids don’t rush for tutors yet at that point.
Some physics books do that sort of thing at the beginning of the book. ( For all I know the chapters tend to be skipped. Or not. Dunno.)
Say Lucia,
Thank you for this bit of advice:
and
Made a difference this go round. 90% on his latest math test!
(Yup, it’s definitely pre-algebra. Factoring expressions with variables right now.)
Anecdotal update:
Yet another pre-alegbra test for the boy tomorrow. On reviewing with him tonight, I discover that he’s got a decent grasp of the ‘algebra’ part of it (doing the same thing to both sides, figuring out what he needs to do to simplify the expression and ‘isolate’ the variable). His problem is the fundamentals. For example, he’s got only the haziest idea of how to solve -15 + 5, or that it’s really the same as 5 + -15 or 5 – 15. Or how to handle -15 – -20. Or what the resulting sign is when a positive is multiplied by a negative, or a negative by a negative.
I think this is interesting because I remember a professor diagnosing the same type of problem for my class in one of my calc classes (calc 4 I think, whatever the heck that was). I distinctly remember her giving a calculus test on the first day of class. The next day, she announced without preamble, “Your calculus is fine. Your algebra sucks!”
Anyway. Looks like I’ll be hammering down the gaps in the basics for awhile…
mark,
Yeah… I see similar things. Often its more “lack of confidence”.
The other things I see– and I blame the format of many of the ‘worksheets’ is an extreme unwillingness to write all the steps down.
Mind you, I think kids have always wanted to just focus on putting down the final answer and as little as possible. (I’m suspect I did; I suspect my classmates did.) But the reason I’m blaming worksheets is when the teachers give these out, they (often) have the absolute minimum amount of space available to squeeze in a solution.
To explain further: Yesterday one of my students was doing one of those classic relative velocity problems. “The boat moves across the river…..” (Some were the boat moves (a)perpendicular to the water; some (b) move perpendicular to the shore, some parallel upstream, some downstream and so on.)
The student has trouble translating the word problem into the relative motion problem. She’s got the 1-d down–so she actually gets the physics. But the problem seems to be translating the words in the 2-d problems into which thing the problem is saying– so she can sort out (a) from (b). So ideally the student should:
1) Make a sketch (river banks, arrow for boat velocity relative to water, arrow for boat velocity relative to bank, arrow for water velocity whatever the problem tells you needs to be translated into a vector). If the “word problem” is more dense than usual (and the ones taken from Holt are), put stars, dots or squares to indicate any known or requested locations. (The one yesterday named cities Cozumel and something else.)
2) Then, sort out the arrows into the appropriate triangle for adding vectors.
3) Now do the trig/math etc.
The space between problem statements on the work sheet is maybe “worksheet”1″ and 1.5” which is just enough to give the false impression that that enough room to work the solution. But not for a learner to fit in the set up sketc under (1). the teachers solutions show (2) and (3) with a very small not entirely explicitly labeled triangle for (2).
Anyone who knows how to do the problem will recognize what the triangle is supposed to mean because at this point they can do (1) in their heads. But (1) is a really important part for a learner!
So the students impression is “this problem involves a triangle. But I don’t understand how to make the triangle.” And in fact, that’s entirely right. She doesn’t know how to go from the work problem to “the triangle”.
Obviously, one could suggest she do all her work on paper and then rewrite the last steps to turn in for credit. But (a) students don’t like to do that (b) they never have and (c) the structure of the worksheet implies it’s not desired by the teacher.
Oh… well… But really. I greatly prefer if the teacher gets problems out of a book and collects homework that as worked on sheets of paper. (Mind you, were I teaching 20 students, I would dread collecting or looking at those sheets. So I get why they don’t want to do that. But… really…)
Lucia,
The problem with word problems is the extra step of required conceptual understanding. A^2 + B^2 = C^2 for a right triangle is easy to memorize and do by rote. Much harder is to see how motion in two dimensions can be broken down into orthogonal vectors, so the right triangle equation can be used. Unless someone walks the student(s) through the conceptual steps, while using the standard formulas, they usually remain lost. I hear the conceptual confusion all the time when my wife tutors via Skype; that’s chemistry, not physics, but the same issues with inability to grasp the concepts.
My younger one gets stuck with an extreme form of this. He gets a worksheet on Monday with all problem for the week, in columns for each day. The space provided is just barely sufficient to write the answer legibly. Forget about doing the work on the worksheet, absolutely no way.
.
I sometimes wonder if these teaching methods don’t lose sight of how kids are eventually going to use math in their lives. Maybe there are cases I’m not thinking of where a quick answer is more important than anything else. Certainly my field isn’t one where I regularly have a lot of complicated math to deal with, but when it comes up, being sure I’m right and that I didn’t make a mistake is definitely a lot more important than getting an answer quickly. Being able to show my boss or coworkers what the heck I did (so they can convince themselves too) is important. If it takes an hour, so be it. Doesn’t come up much, but there have been a few cases over the years anyway.
.
But of course I ‘get’ that school time is limited and valuable and there aren’t hours to devote to single problems. Still, I remind my kids constantly that in real life, making sure you’re right or making sure you’ve written stuff down so you can figure out what you did wrong is almost always more important than getting to the answer a couple of minutes quicker than you could have by figuring it out in your head.
.
Rambling on a bit : I thought about diagrams for the pre-algebra kid. Went back to the number line to see if that would help him grasp what was going on with some of the basic stuff. It helped some, but I quit when I hit trying to graphically explain -n – -m and realized all I was doing was confusing the heck out of the kid. :/
.
Anyways. Thanks Lucia.
SteveF
Exactly right. The hard part is what I called “part A”. That’s where the concept is.
One of the problems is the space on the work sheet makes it virtually impossible for the student to work through that bit. The posted solution makes it look like the bits that “matter” are parts “b” and “c”– which is just math. (I’ve seen some of the ‘posted solutions’ from a particular students worksheet, because older years stuff is still on the web. There is nothing there to help them with the “set up” stuff!)
Anyway, I tried to concoct some exercises for the student so she can focus on “part A”. But really, the worksheets with teensie beensie tend to encourage kids to skip over that part entirely. Of course a student whose “got it” can squeeze the answer in there. But the arrangement really tends to communicate that the problems starts with “first miracle occurs resulting in the appearance of a triangle’. Next: Do the trig problem.
Few of the students have trouble with the trig!
Mark
I’m not even so worried about ‘real world’. I’d like it if the worksheets were organized to let them do the things that will help them pass their later tests!
You mentioned some reasons for writing stuff down– showing coworkers, finding your mistakes later and so on. But there are actually additional reasons to write stuff down. One of them is that it helps the student remember things like formulas and also helps turn the homework into a study guide if the need to look at it when studying for a comprehensive final.
Actually writing something like
∆x = vot + 1/2 a t2
and then knocking out terms and substituting numbers helps them remember. And while doing questions fast is not an important lifetime skill, doing them fast on the test is. Oddly, while it seems faster to just write numbers down, I think it’s actually not– not even on a test. Writing the formula from memoryand drawing arrows through terms that equal zero and then writing a second line with the numerical values substituted in is faster than hunting for on an equation sheet, substituting values in your head, then writing just the numbers. But the fact that there is just enough room to write the minimum possible on their worksheets— often not even enough to write the formula with symbols tends to train them to write as little as possible. This is not useful.
Lucky for many of us older people photo-copies were expensive way back when. We had to do stuff on our own paper. While I think the inclination to write as little as possible is always there, at least the worksheet didn’t force people to retain that terrible habit.
(I know some people will say once you know the stuff, you don’t need to write as much. That’s obviously true. But you certainly need to write stuff when you don’t know it yet!)
Thanks Lucia. My kids don’t (yet) have a lot of stuff like that to write out, but they will soon enough. I’ll remember that. 🙂