Winter prep time

Unbalanced Reaction posted an interesting thought about when to refocus on work over the holidays -- on the 28th of December. I left a quick, off-the-cuff, answer that I work on Wednesday (which happened to be the 22nd and 29th this year), but that was before I settled down to work today and started noticing the time stamps on various files that needed attention.

You guessed it: Lots of them were dated around the 28th, regardless of the day of the week over the past five years or so! Fascinating.

There were quite a few others dated around the 20th (circa the Winter Solstice as I mentioned in my comment). Those were usually the syllabus, which I got done quite a bit earlier this semester that in the past. In fact, I noticed that I was about a week early on quite a few things this year, things that would normally get done after Christmas around the 28th.

I never noticed that work pattern until you brought it up, UR. Great insight. We both work in that natural gap between Christmas and New Years (what feels like a Wednesday), although I clearly also like to work about 5 days before Christmas.

So, no, Unbalanced Reaction, I'm not generally the model of efficiency, but this year has been an unusually good one for keeping focus on priorities by doing them as soon as I could rather than when they absolutely had to get done. I don't know if I was more stunned that I thought of working on the massive revision of my teaching plan while proctoring, or that I actually did it.

Well, I worked on work things, at least. Christmas lights didn't get put up nearly as soon as they should have.

And blogging. You should see the queue of semi-written articles. I think they will all get finished up tomorrow, but at least this one is going out only a day late.

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Productivity

My blog friend Dean Dad has a couple of bees under his bonnet that rival those of much older, semi-senile faculty. One of them is his obsession with the Credit Hour, even when (at other times) he worries about articulation and the transfer of course "credit" from one institution to another. He reminds me of one college that got rid of grades to foster creative risk taking, only to discover that no one wanted to hire their students because it took too much effort to evaluate the individual portfolios. That college no longer exists.

His latest version of the argument, in a blog last month, is to blame it for a lack of productivity in academia:

Third, we've defined what we do in a way that defeats productivity improvements. We measure learning in units of time. Until we stop doing that, no amount of efficiency-tinkering will make enough of a difference. A three-credit class required forty-five hours of seat time thirty years ago; it still does.

Actually, it doesn't. We only require 42 or 43 hours of seat time (plus final exams) at our college. They have to learn the same physics content in 28 weeks of class time that they once had 30 weeks to learn. You see, we measure learning in units of chapters in physics books, and engineering schools expect the same prerequisite knowledge they always did. AFAICT, everyone deals with this by cutting back somewhat on topics that students never learned anyway, but that does not help the overall learning cycle for the core material in the course.

Side comment: Somehow the same has not happened in math. Calculus takes longer now than it did when I first encountered teaching it, although that change might be making up for the lost weeks I mentioned above.

Besides, this is all a red herring. Productivity is not what one student learns, it is the cost of producing that learning. Productivity is about the difference between one professor running a tutorial for a single student and having an 80 student lecture/discussion class. And there, I know my productivity has increased significantly in just the past decade because my annual enrollment has grown by more than 50%. That means a lot more money is paying for my time, which is all that matters for the college's bottom line.

Side comment: An assistant chairman in my distant past also argued that failing students was a way to increase productivity in the department. It enabled them to squeeze twice as much money for the same amount of learning. This doesn't always work, of course, because repeats can displace other students who might be more likely to learn the material and pass the class.

And my productivity has increased because, in the days of smaller enrollment, I was also teaching labs. That is three hours of my time that only generates one credits worth of income from a small number of students rather than three credits worth for twice as many students -- a factor of SIX in income for my time! Using an adjunct instead of a tenured professor has lowered our cost there while freeing me to generate more income for the college.

One complaint I don't understand is

Fourth, unlike almost every other sector except health care, we have to invest in technology even when it doesn’t improve our own productivity.

No, you don't. That is a cop out. Managers like yourself did not have to replace blackboards in every classroom with SmartBoards and projectors without doing any study to see if they improved learning. (By the way, that is not a one-time capital expense. Projector bulbs are expensive and projectors wear out. There is also more security required because of a significant theft problem.) Indeed, they didn't even do a study to see if increased use of Powerpoint might reduce learning!

He also blames tenure, although he is actually blaming a seniority-based pay system rather than tenure. You can have tenure without automatic pay increases and you might need step pay increases without tenure, to keep your best people. Besides, as I alluded to above, one way every college has increased productivity is the use of contingent faculty, particularly at universities where the benefits are the greatest. I say this because the fraction of classes taught by adjuncts at my college has been stable for a long time at about 50%. (I am counting classes rather than people for a good reason: we have a significant number of adjuncts who only want to teach one or two classes.) I think this is possible because the salary disparity is not as great as at universities.

And productivity gets harder to define when you shift from a Community College environment (where he and I work on the teaching side) to a Research University environment (where I used to work on the research side). Is a professor's time better spent in the classroom generating credit hours or in the lab generating grants with overhead and jobs for students that help support enrollment? I think we all know that the answer to the last question is "yes" at an R1 institution, where it even includes the creation of non-teaching faculty positions that exist solely to bring in additional contract dollars.

And that last detail is why I think, in another article from last month, Dean Dad completely misses the point made by Historiann. Historiann is at a Wannabe Major University, just the sort of place where managers do profit (pay increases and job jumps up the ladder) by shifting resources to areas where they are more likely to get more research grants that generate more "overhead" (indirect cost recovery) and more administrative positions. There isn't much (make that ANY) value to the university if Historiann publishes another book. There is a lot of value in the 40% that gets siphoned off of a grant, and even more if the professor's salary and benefits and all other expenses (office, light, heat, staff support) can get charged to the grant while an adjunct with no benefits and few of those expenses teaches hir class that semester.

I have little doubt that what I just wrote is "far removed from any reality I [Dean Dad] can recognize", but it is a reality I am very familiar with.

But I would not put all of the blame on the managers who made it happen. Many faculty are complicit in the expansion of the university research enterprise because their lives are devoted to research and graduate and post-doctoral education. It is an unfortunate reality that history cannot compete with biochemistry at this game, and tight budgets will push money to where it creates the most return for the people managing the university.

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Students helping students

Dot Physics offers an excellent suggestion for communicating good study habits to new students: have this year's students tell next year's students what they need to do. Better yet, he posted what his student's wrote.

I know it is a good idea because I have been doing something similar for several years. It started with an end-of-semester question about prerequisites. (If you follow my blog, you know that I have identified the failure of students to comprehend the meaning of "prerequisite" as a long-standing problem for advanced classes like calculus and physics.) That info got shared with the math faculty who taught those classes, and I think I have seen an impact on what students learned and brought with them to physics (and calculus).

Later, based on discussions with a colleague at another school, I tried something similar to what Rhett Allain is trying: collect advice from current students (mine is entirely anonymous) and distribute it via Blackboard to the incoming class. (That mechanism is still a weakness because our students don't get access to their Blackboard shell until the first day of classes. They really need this kind of info before then.) They seem to appreciate it, but I'm less certain how much it helps.

Measuring changes in the success rate of any class is tricky. There are lots of variables. (To name just one that could be measured, I started getting a significant number of kids with AP calculus experience after the depression of 2008 hit.) The biggest is that they are busy (work or play or both) and sometimes just lazy and unprofessional, still looking for the easiest way to pass. Thus, even though my students, like Rhett's, offer the excellent advice to read the textbook before class and start their homework early, they just won't do it no matter who tells them about it. But they will form study groups, and that sort of collaborative learning has grown significantly in the last few years.

Has anyone else tried this? Any suggestions on how to get them to read?

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Dot Physics gets Power wrong

Rhett Allain has a great blog at Wired.com, but I will not create yet another account just to comment there so my comments will be here instead.

Usually he is on the money, but in this case his bad experiences with ESPN Sport "Science" gets in the way of his analysis of a video about the power of NASCAR cars. For convenience or future reference, I'll embed the video here



and then get to the analysis.

Rhett first objects to the statement that the weightlifter being shown "exerts about 1 hp per rep". Yes, they meant "during", but what is wrong with that? The numbers are right if you take the 275 pound lift as being 2 feet (61 cm) rather than 50 cm (about 20 inches) in 1 second. The weightlifter is producing pulsed power during the lift, which is about half of that 1 second rep, but hardly resting during the other half.

Check out this video of a power lifter doing 26 reps on the NFL 225 pound lift, or this one where the guy does 72 reps at 225 pounds. The first one takes around one second per repetition, locking the arms out each time. The second one is a much shorter, but faster, lift that might make for an interesting video analysis to see what his power output is.

Estimating the average power is trickier, because you really can't use the work done ON the weights as your metric. If you did, the average power would be zero because there is negative work done on the weights as you lower them! !! However, if you shift your focus to the work done by (within) the muscle, it might be more than 1 hp for the entire time the weight is moving. Controlling a weight as it comes down is not quite as hard as lifting it, but it isn't being done for free!

What I like best about this example is that "power lifting" is one of the few cases where a physics term is used correctly in sports. Power lifting, where the emphasis is on multiple reps, is entirely about the rate of doing work in a way that reflects what is done in competitive athletics rather than just lifting the most weight. That is why the NFL tests on the number of reps of 225 pounds. (The NFL record is supposedly 43.) Yes, that is power. And I think it is more obviously power than the similar output required to climb a mountain on a bicycle even though that is probably the most extreme case of continuous power output by humans.

Rhett next complains about a statement that he actually misinterprets. The statement in the video (around 0:50) is that horsepower of a car engine is "calculated by measuring torque". This is 100% correct. Rhett says "First, horsepower is not measured by calculating torque (at least not in physics)." Right but not relevant, because they don't calculate torque. They measure torque and rpm and calculate power by multiplying the two together. Rhett says "I guess the only problem here is using “fast” to describe the relationship between torque and power." except that is not what they are doing. They are using fast to describe the angular velocity, just as you might use "fast" to describe the linear velocity if you said that power was about how fast you can apply a force (Power = force * velocity). This is 100% good physics. Rhett, you messed up this time.

For the record, in physics and engineering and the real world of dynamometers, you determine horsepower by measuring a torque curve (torque in foot-pounds as a function of angular velocity in rpm) with a load cell (which measures force) on the end of a lever that is connected to the load on the engine. Modern ones do the multiplication and plot both power and torque versus rpm, but the actual measurement is torque (or, if you like nits, force that gets autoscaled into torque on the graphical output).

I'll go along with the final nitpick about lifting the space shuttle. Yes, they should have included "in one second" at the end of that last sentence. 850 hp is, indeed, like bench pressing the space shuttle in one second. Time is important. But no one would confuse using a jack (in his video example) with "benching". Everyone knows that you bench press a weight in less than a second unless you are totally whipped, so the same would apply to benching the space shuttle.

My negative nit pick: The video correctly describes the historical origin of horsepower as a marketing term, but the draft horses shown in the video (e.g. at about 0:30) produce more than 1 hp. James Watt used the small horses used in mines as his reference point for selling his steam engines.

My other negative nit pick is that engine size is not nearly as important as the rate of fuel consumption. After all, a top fuel dragster only needs about 550 cu.in. (compared to 358 cu.in in NASCAR) to make over 8000 hp (rather than 850 hp). It is all about the fuel and the rate you can burn it -- and how long the engine lasts! You have to put power in to get power out. Like the co-host commented during his 259 mph test drive of the Bugatti Veyron Super Sport on "Top Gear", before the pro took it to 267, you can actually see the gas gauge moving when you are burning 1.7 gallons per minute pushing out about 1200 hp. Wide Open Throttle is like that. (I'll have to save for another day the effort to figure out the Reynolds number comparison between air and treacle they used. I like it, but I'm not buying it.)

But I also have a positive nit pick. I loved their description of the added power from opening up the exhaust, although they oversimplified it a lot. Part of it is to "tune" the exhaust so it resonates at a frequency that matches the rate at which you want to pull exhaust out of the cylinder. Back pressure from the exhaust makes the engine less efficient. Getting a rarefaction as the exhaust valve opens is ideal.

However, the distinctive engine sound they played comes more from the Doppler effect than the resonating pipes. You need to stand next to one to appreciate that.

PS - The best thing about the Top Gear Bugatti video is you can actually see the exponential approach to terminal velocity as the spinning of the digital speedo slows down.

PPS - This was started ages ago, but only finished up and posted at the end of December. I'll try to monitor comments to be sure they don't sit too long in the moderation queue.

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News Flash!

Rand Paul promises to carry the message to Washington that Kentucky is not happy that big government turned an incipient depression into a recession; they want a full fledged great depression along with reduced military spending, cuts to Medicare, and tax cuts for New York billionaires.

OK, those aren't his exact words, but it is what his words meant. He never would have gotten elected if he had said what would result from cutting government in the middle of a depression.

Earlier today, Rick Santelli (a former hedge fund manager now reporting for CNBC, who practically created the Tea Party with a live rant from the floor of the Chicago Board of Trade) argued that the Fed action in September 2008 along with Bush's TARP bailout of major banks (October 2008) and Obama's stimulus plan (February 2009) is responsible for the depression that started in the summer of 2008 ... and then moments later hoped that the Fed would ignore his economic ideas and come through with more quantitative easing, arguing that the markets he follows would collapse if we don't get more stimulus because the Republicans in Congress sure won't provide it!

I can see why he got out business and became a reporter.

I have to wonder what Santelli would say on Wednesday if the Fed were to announce that there won't be a second phase of quantitative easing (QE2 in current parlance) in response to public demand for less government intrusion in the markets. I'll bet he would panic as the bond market collapsed.

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Assessment

Not sure if I have much to say about this particular story, but it definitely deserves mention here because of my "promise" to engage in questions about the A word in response to an excellent article by Dr. Crazy last month.

An article today in IHE asks the musical question Why are we assessing? (I know why we are -- our accreditor insists on it -- but that only begs the question.)

Sorry, nothing to see here for the moment. Well, not nothing. This particular observation

We now have a number of intriguing published instruments although, for many, evidence of their quality and value remains a work in progress.

from the article definitely deserves flagging. Are they really saying there is no "there" there? That no one knows if there is any value in the institutional effort we have started? Sure sounds like it.

Fortunately, we have a functioning system at our college so faculty have been given the lead to design assessments that make sense in each general area (composition, math, science, history, etc) and for different courses within that area. Agreeing on what is Really Important has been an interesting exercise, as has been the process of comparing how each of us might assess a particular item in our own courses. We don't often talk about tests, and different ways of testing or grading, so that has led to an interesting conversation that will continue for years.

I think what we are doing will have value to each of us, even if it proves worthless on a cross-institutional level to the ed bureaucrats.

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Future engineers at Auburn!

One way to tell a university has an engineering program:

A fan is seen holding up a sign that says kg m/s² to celebrate a touchdown by their freshman QB, Newton!

That kid's physics prof needs to count that as a "win" for applying physics knowledge in a new situation.

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More on class prep

One of the "career advice" articles in IHE contains an outline of what is termed the Sunday Meeting.

This is first rate, although I don't find it all that revolutionary. I've always done that.

Indeed, I've done some of it over the summer so my entire semester is planned out on a calendar that combines all of the major tasks for every class I teach or have important managerial responsibilities to carry out.

Now it is time to get back to my regularly scheduled Tuesday Grading.

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Preparing for class

There is a nice question/poll today from Unbalanced Reaction concerning prep time for class. I'm in the 1 to 15 minute category, but that is for classes that I have taught (many times) before and represents an average that often includes zero if "prep" means actually writing out detailed notes for what will happen in class.

And that isn't because I use my old notes in class, even though I have them with me.

I sensed this incipient digression as I wrote my comment at UR's place, so I will digress here instead. Most of my prep time is spent on the broad outline of what I will do, what might be considered a lesson plan if actually contained any detail beyond Problem x or Example of topic y.

Prep is usually more about clearing my mind to see if there is something new I should try. Lately that means what I write below, but also an approach that puts EVERY key formula for a new subject up on the screen, rather than having them show up here and there as we deal with new parts of a single topic. Then I only use those few things in everything else I do.

I used to have problems worked out so I could "work" them without having to pause to do calculations, but I have decided that is a bad model for the students even if I pause to use an air calculator before writing the answer down. It turns out that, despite being a digital non-native (wrote my first computer program my senior year in HS and didn't own a calculator until I started grad school), I am a lot faster than most of them are at slamming the keys.

So I might project a problem, either prepared or out of the book, but then all of it gets done for real in class. I've observed people who have the answers on plastic or ppt, and the kids (who I am also observing) just don't get the details. Sometimes they can't see the details, other times they just follow the terse bits on a ppt printout outline -- but never put together a coherent solution. Of course, some don't ever take good notes or recognize my board work as how I actually do the problem myself, but that is a different problem that requires constant teaching effort.

The only time I make sure I have the worked version handy is when I put up a problem for them to do. Then I want to be able to flash memorize the key results so I can provide right/wrong advice as I move around the room.

The important thing is that I have fixed in my head the need to be very procedural in everything I do in class. I don't need notes for that. In fact, my notes are not as good as what I put on the board.

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Three Un-related Topics

All below the jump ... thoughts about perceived quality of faculty at a CC, the Gates Foundation and education, and keeping happy as a professor -- all triggered by recent items in IHE.


Faculty quality at the CC Level

Hat tip to an IHE Quick Take, pointing to this article in the Detroit News. Michigan is apparently facing the question of whether community colleges should be allowed to offer 4-year degrees in selected fields. They probably got the idea from other states where CCs now offer BS degrees in nursing or education.

Michael Boulus, executive director of the Presidents Council of State Universities of Michigan, said:

"Community colleges do not have the base of professional educators needed to provide accredited bachelor's degrees."

to which I say "BS". Reminds me of nearby Wannabe Flagship, where they try to claim that our organic chem class (30 students) is worse than theirs (300 students) when our professor used to teach ... THEIR class as an adjunct!

I'll use nursing as an example, since it is an area where there remains some prejudice against licensed RNs who earned an AS rather than a BS degree. (Yes, I know that you cannot move up into surgery or anesthesiology without the BSN degree, but I am talking about entry level positions.) It is convenient because I can look at the requirements for the degree at Wannabe Flagship and see clearly that (a) they do require important non-nursing courses that are not in our AS program, and (b) our CC teaches every one of those non-nursing courses at a level that they accept for transfer students, and (c) that many of their classes are taught by adjuncts and typical adjuncts and full-time faculty have an MSN as their top degree. There are some doctorates (including an EdD or two), but those are only needed for the MS and Doctoral programs, not the undergrad BSN degree program, which explains why there are so few of them.

Our faculty are just as educated, experienced, and licensed as theirs are and could teach the same upper-division classes that theirs teach. Our program is accredited for the RN license by the same national organization that theirs is, and ours has the same high pass rate that theirs does ... and higher than some other programs in the state. Yes, we do need to hire more faculty, but that is just for our growing AS degree program. You see, Wannabe Flagship has very limited admissions and does not offer any program that can be taken by non-traditional students, so we turn away many qualified students. And there is no shortage of demand, even in today's economy.

The propagandist for the state universities in Michigan is either a liar or ignorant.


Education Research

A Friday Viewpoint at IHE posed a challenge to the Gates Foundation to fund more research, but I have in mind some nonsense embedded in the article.

The author says:

There were some 65,000 doctorates in education granted over the last 10 years for which we have data (1999-2008). During the same period, there were about 21,000 doctorates awarded in chemistry. Which do you think has had the greatest consequences, knowledge-wise?

I know that comparing education and chemistry in this way is unreasonable; for one thing, many of the education degrees were awarded to practitioners, rather than to researchers.

BZZZZT, but thank you for playing. Those persons with a chemistry PhD are all, every last one of them, practitioners. And that identifies the main problem with education degree programs. Few of them have faculty whose research is based on actually doing (say, teaching elementary school) what they teach. In contrast, that chemistry PhD actually does chemistry, including the ones who are teaching chemistry at a university. In my opinion, that is why education research has not made as much of a dent in our national K-12 problem as, say, chemistry research has improved batteries and many other important products.

I might add more (like references to what others said about Gates and accountability for outcomes from those projects), but time to move on.


Enjoying the job

Also from Friday, we have this ad dressed up as Career Advice from IHE. There are some good things in there worth thinking about, but I'll start by observing that if you get migraines as a stress reaction to the research demands of your 1-1 teaching job at an R1, you really should think about moving to a teaching intensive college or do what the author did: Join a leadership program to learn how to manage research (rather than do research) and start the move up into Provost world.

The real lesson in there, which does not require buying the book, is that you need to identify your "soulful values" and set your goals around them. Since regular goal setting is part of what every professor at my college does each year (as a way to encourage us to stay "fresh"), that is a useful way to think about how to choose among many things that one can do to improve teaching.

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English?

Ah, two nations separated by a common language.

I see every indication that the following part of a story is written in English, but I have only the vaguest idea[*] what they are talking about. See for yourself:

Spinner Graeme Swann found massive turn to take 2-14 as Pakistan struggled.

England also had batting problems, but Eoin Morgan and Michael Yardy put on 67 from 43 balls in a five-wicket win.

They came together after Luke Wright had been bowled on the sweep for a duck, leaving England in a precarious position at 62-5 after 10 overs in Cardiff.

Many players on both sides had made batting look difficult on a slow wicket, with the ball stopping in the pitch.

I wonder if the British feel the same way when they read the description of someone "throwing a pitch" in baseball!

But one thing I like about British sportswriters is that they don't mind being rude when describing someone who "produced a series of desperate swishes at fresh air". We could use a bit of that when a millionaire strikes out.

[*]
I know a bit more than I let on. I've actually played a bizarre version of street cricket (using trash cans for wickets) with some Aussie-Americans, but it would take a lot of gin for me to sit and watch a match on TV. But I am only guessing at what "2-14" means, and I have no clue at all what a "duck" might be.

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Mentoring

Today I am blogging to myself. You see, I know I wrote several brilliant ?? comments giving advice to new faculty and my thoughts on mentoring new faculty, and ... well ... now I am a mentor to a new faculty member. So what was it I said?

Took more time to find these than I thought it would.

Mentoring New Faculty (April 2008)
Concerning my thoughts about our college's mentoring program.

Advice for a New Professor (March 2009)
Includes links to two other articles and a few thoughts of my own.

New Adjunct (July 2007)
Although directed at a question from a first-time teacher, some of this is probably relevant in many situations.

I'm sure there are others (like in my "jobs" area or dialogs on other blogs), but I don't have time to track those down right now. Will update later when I think of one.

Dean Dad on becoming an Administrator
On one level, completely irrelevant. On another, totally relevant. Anyone in a new job has to learn, and listening is how you learn. For that matter, even people who have been on the job for years still have things to learn. Listening is how learning happens.

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It's a miracle!

The VERY long-awaited assessment of research doctoral programs by the National Research Council is, so they say, going to be released on September 28.

I think that makes this update of the 1982 and 1995 reports about two years late.

Why? Could the fact that they will release a revised version of the Methodology guide, updating the 2009 update of the 2003 report that proposed a methodology for this new set of rankings have anything to do with it?

It sure sounds like they kept tweaking the methodology until they got what they wanted. Will there be a hue and cry? We will see. The biggest problem is that the data it uses are so old that they will probably have to start the next study before ink is dry on this one.

However ...

I can't wait to see if that means "traditional" top schools remain above one physics program that I thought should have been marked with a bullet (record rating lingo) based on some of the raw data from 1995. Those data suggested that one program in particular had higher cites and other objective measures of research quality than the schools between it and #1.

For the record, that program was #10 UC Santa Barbara. Their Pubs per faculty number was second only to #1 Harvard, and their cites per faculty (178) exceeded Harvard (170) as well as #2 Princeton (110) and #3 MIT (121). Notice that gap? I sure did.

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It's Showtime, Folks!

Syllabus ready? check

On-line homework ready? check

First day activities prepared? check

Lab instructors prepared? looks like it


Campus parking lots empty? not for long!


I love visiting campus on the weekend before classes start. There are always a few freshmen wandering around looking for their classes, probably under the mistaken impression that they will be able to drive up and park right in front of the buildings. Ha! Not unless they get there before 7:30 AM.

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Offices

Inspired by a dream Profgrrrrl had about being forced to swap offices, I remembered that I was talking to my old major professor this past week and he came up with an hysterical, slightly fictional, story:

All of the faculty in a certain new building spend all of their time walking around looking for a better office or any lab space that they might be able to steal. No one dares leave a lab too clean out of fear it might look vacant and get taken from them.

He added that the only thing that distracted these faculty from looking for more lab space was their attempts to get someone else to teach their class next semester so they could do more research.

Their challenge? No one wants to take over their class unless they get a nicer office or some of that precious lab space in trade. Catch 22! As a result, they wander the halls forever like Marley's Ghost, dragging a chain of publications behind them and moaning about offices and teaching loads to anyone who will listen.

When they need a rest, they go to the Dean's office and moan there.

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Thesis Repulsion Potential

Jorge Cham is brilliant.

Follow the link above to his latest cartoon at PHD Comics. Click to the previous comic to see the setup.

For those of you who don't know this, which might be everyone reading this blog, the potential shown in that cartoon is typical of the attractive force that holds protons and neutrons in the atomic nucleus. The nuclear force is short range and weakly attractive, but there is a very large repulsion at short distances that arises, essentially, from the Pauli exclusion principle acting between the quarks that make up the proton and neutron.

That repulsion sets the size of neutron stars.

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Data Storage Media

An important reminder from Unbalanced Reaction about data backup brought the following question to mind:

How many different types of storage media do you have at home? (I don't care if you have the hardware to read them or not.)

Although I suspect I am missing something, here is my list of the 9 (possibly 11) different types of media that are in my house:

• Internal magnetic disk and external half-terabyte drive (I think it is also magnetic)
  
  
• Flash drives
  
  
• CD ROM
  
  
• DVD
  
  
• Zip disks! (that part of Zoolander is so out of date now)
  
  
• 3.5" floppies
  
  
• [uncertain] 5" floppies (I might have tossed those)
  
  
• [uncertain] 8" floppies (ditto, written under CP/M)
  
  
• Magnetic cassette tapes for an auto-loader backup system
  
  
• 9 track tapes (plural)
  
  
• punched cards
  

Time to do some more summer house cleaning ....

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Mathematics (and Physics) and Calculators

This is the third of three articles concerning calculators and mathematics triggered by a blogspot and IHE blog article by Dean Dad, a community college dean who appears to be writing from another part of the country yet has the same problems we have at our CC. The original article concerned calculator use in Developmental math classes that typically cover fractions and 7th grade algebra, but the comments spanned a range from that topic through mathematics and its applications beyond calculus. My first article merely laid out a common set of definitions, but does include a few assertions about various types of calculators and levels of mathematics that might deserve comment. The second article tried to focus on Developmental math but also included some comments about Algebra. In between these, I posted a shorter article that included a more polemical set of comments about the "modern" Z80-based Graphing calculators. Comments on the second article made me realize I also owe the community a long-deferred article about the math preparation of elementary ed teachers.

My second article limited itself to classes that are remedial in the sense that their goal is to get students to finally learn skills that were supposed to be taught in elementary and middle school as well as the first year or so of high school. College Algebra occupies a fuzzy territory because it is sometimes learned in high school (where it would be Algebra II) but is considered a college-level math class that is sometimes a general education requirement. I included it in my previous article because it is not the only gen-ed math option at our CC and serves many masters. In this article, I will take up the issue of most interest to me: whether students are prepared to use calculators and algebra to do physics, calculus, and (perhaps) engineering problems.

My expectations

As noted earlier, I allow my students to use a Scientific calculator and I expect them to have a decent one and be fairly fluent in its use. I do not allow them to use a Graphing calculator or one that is capable of doing computer algebra. The former is excluded because I do not have time to police all of them for cheat sheets, the latter is excluded because I want a level playing field. They can use MathCAD or Maple or Mathematica when they get into upper division classes where everyone will be using equivalent tools on any given assignment. I expect them to do algebra with pencil and paper in a freshman physics class.

The calculus teachers here have a similar expectation. Many (but not all) give exams where no calculators are allowed on part of the test, but a Graphing calculator (mainly for the numerical integration feature that is on some Scientific calculators as well) is allowed on others. Sometimes they even use a computer algebra program on an exam, but that is rare.

One thing I mentioned in a comment on Dean Dad's blog was the importance of defining outcomes. I forgot to mention that outcomes are best defined so the match the desired inputs for a subsequent class. It is for that reason that our calculus faculty require that students actually know certain derivatives cold, like times tables, and why they were stunned into disbelief when a student transferred here from a school where they used an Algebraic calculator that can do all of the basic derivatives and integrals symbolically. That outcome (being able to take a derivative with a calculator) is mismatched to the requirements of physics and engineering. (True, an engineer taking the "fundamentals" exam has a reference book handy that contains the basic derivatives, but the few minutes you are given to answer each question does not give you enough time to look up every basic result.)

Physics

In general terms, my views on calculators are similar to what Chad Orzel wrote in response to Dean Dad's blog. Real math (meaning math major math classes) have no need at all for calculators unless the topic is numerical analysis, and then you are better off with a programmable computer. Ditto for upper division physics majors classes, although they can have a computational component as well (that is, arithmetic rather than the symbolic mathematics of algebra or calculus). My impression from former students is that engineering expects correct computation as well as algebra, so exams require computation as well as the proper setup of the problem.

I should add that the exam security issues inherent in larger classes, where students are unavoidably sitting within copying range, also requires numerical variations between problems. (Exam fairness has, so far, kept me from putting totally different problems on versions used in the same class.) Most on-line homework systems also do this, although some have symbolic variations as well as numerical ones. This leads to an emphasis on problems with numerical values.

Further, because my students tell me what they do in their first engineering classes, I know computation is only part of it. Setting up the problem algebraically and simplifying before computing is ALSO part of it. For this reason, I require them to state the problem symbolically before plugging in the numbers. However, primarily because of their comfort level, I do not take off if they do the algebra with numbers present rather than keep the symbols until the end. (Having numbers and unknowns makes it easier for most of them to keep track of what is unknown and needs to be isolated or eliminated.) I'll let someone else break them of that habit later on, but I will encourage them to work on it in my class. That said, I do sometimes give exam problems where a symbol like L has to be in the final answer. See below.

Computing

What has surprised me is the degree to which students either cannot compute efficiently or use their calculators inappropriately when solving a problem.

The first problem has only become evident to me recently. I don't think it is a new development; I just happened to see a particularly egregious case last year where the student would evaluate something like A*B*C/D by doing A*B, write down the answer, enter the answer*C, write down that answer, then enter that answer/D. Painful. And slow. And prone to error. I should have suspected this sort of problem because the other version, entering ((A*B)*C)/(D), is a bit of craziness not uncommon in Algebra classes. They don't know order of operations and, even if they do, some have used bad calculators that violate those rules and been burned.

This is, however, a real handicap. They need to use one calculator type and use it enough to understand what it does under different circumstances, but might never have been taught that it is OK (and even necessary) to hit lots of buttons and see what they do under different circumstances. I'm going to mention that this year, going beyond such simple things as whether your calculator does -3^2 correctly or whether it knows automatically that the arcsin of 2 (or the ln of -1) is imaginary.

The second problem is doing algebra with long messy numbers in the equations. This came up in an earlier blog post about algebra, with some nice observations in the comments. This summer I've been thinking about where this comes from, and I am convinced it is because they never use realistic numbers in Algebra classes. Their equations all have numerical coefficients that are small whole numbers, not the 10 digit value for the y component of the velocity, v*sin(theta). There is no penalty for using 3 as a coefficient. There is a penalty for using 34.5619288 as a coefficient. They also seem to have not been exposed much to subscripts, so they are initially quite uncomfortable using Vx as a symbolic replacement for that nasty number.

My preferred solution would be to have pre-calc and trig classes use symbols with subscripts so they get comfortable with that math skill, just as I would like them to work with functions like g(y) or x(t) or even x(y). As we talk more about outcomes at my college, I have to see where those skills fit into the goals of our math curriculum. It might be that these are one-and-done skills (like some skills in physics) because instructors at one level don't know how important it is when you do kinematics in physics or power series in calculus and how much students struggle with those concepts. However, I also know that this is overly optimistic. Instead, I am thinking about ways to work those in from the beginning in my class, perhaps by starting with y(t) motion rather than x(t) motion and using v_y and a_y even when they aren't really required at that point.

Finally, there is the way I model doing problems in class. Comment number 4 on Chad's article mentioned math exams where you could only use a calculator on part two, something some of our math teachers do, but then came up with a nice insight:

it also could be used to introduce the concept of only taking out your calculator when you reach the stage where you've gotten the problem to its simplest state, and need only put in the numbers.

I've seen students do exactly that while taking an exam, just as I do, but I've never thought about really making a SHOW of pulling out the calculator at that point of the problem. I need to model that step as clearly and explicitly as I model algebraic steps when solving a problem. I also need to find or invent more problems where a symbol is in the final answer, like it would be if you were writing a program where a few values are fed in by the user but others are fixed by material properties or whatever.

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65 years since Hiroshima

One of these years I need to plan that vacation trip that includes a stop at Pearl Harbor before heading on to Japan in early August. I need to see where my car was built and visit ground zero of the first A-bomb used in combat as well as the place where it all started for the US in the Pacific. And Kyoto.

One of the odd things about these anniversaries is that, for my students, much more time has elapsed since Vietnam ended than had elapsed between the end of WW II and when I was finishing high school.

Another odd thing is that the film of the bomb going off was either taken or witnessed by someone I once knew, but he never talked about the experience. (In contrast, other people I know who worked on the Manhattan project or other war-related enterprises - such as code breaking - have shared that history and their views of the project.)

One particular irony is that there was an editorial about radiation exposure limits just a few days ago. (Hat tip to Chad at Uncertain Principles.) The dose limits were adjusted based on what was learned from single (acute) dose exposures at Hiroshima, but the editorial argues that we need to look more closely at the evidence from low level (chronic) exposures documented in the 60+ years since those first studies.

PS - I tweaked the posting time to match when (by Japan time) the bomb was dropped.

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Does your campus web site suck too?

I howled when I saw this on xkcd, which I read regularly:


Nailed it!

I visit college web sites while advising future transfer students, and it is rare to find one that makes it easy to find what a student needs, even if they have a "prospective student" link on the front page. And our college web site is as bad as most. So it pleased me a lot to see IHE pick this up in a story Wednesday.

I really like the comment objecting to the "three clicks" problem for key information, and REALLY like the person who is taking this cartoon to every meeting of a CC website revision committee meeting.

But the funniest part was the observation about pictures of "pretty girls studying under trees" on the home page.

Does your college have a photo roll including ethnically diverse but atypically good looking students studying under trees? Ours does. Using computers? (Yep) Interacting in a small group with a distinguished looking professor? (Yep) A link that takes you directly to the academic calendar or the college's majors with a clear list of requirements? (Sort of)

UPDATE:
IHE has a followup story about efforts at web redesign that starts with the student. Interesting followup. I know our college web site has been redesigned to use pull-down menus that have a laundry list of possible links, but we simply do not have a "prospective student" category nor any sense that most of the links off the front are not used.

However, I also have to wonder if "prospective" is too fancy a word for many of our incoming students, the ones that place into developmental reading classes.

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Trucks and Trailers and Vans - Oh My!

The first official sign of Fall!

Today appears to be the first Student Moving Weekend.

The first hint was the sudden appearance of U-Haul trucks over the last few days, some of which might have been people clearing out at the end of July, but students were clearly moving into rental houses around the area today.

Traffic accidents and under age parties won't be far behind.

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Calculators and Basic Math

This is the second of three articles concerning calculators and mathematics triggered by a blog article by Dean Dad, a community college dean who appears to be writing from another part of the country yet has the same problems we have at our CC. I have already commented on the blogspot version of this blog (more than once), which has collected a huge number of comments, but there are also a large number of comments on the IHE version of the same posting. I'll write as if you have at least read Dean Dad's article. The discussion has been quite wide ranging, often not bothering to make a distinction between the various levels of "calculator" available to students or the many levels of math classes they might be used in. (Definitions are given here to provide a common reference.)

In this article, I will take up the specific issue raised in Dean Dad's blog and the one I know the least about as an instructor - calculators and developmental mathematics - but also look at college algebra. I'm mainly interested in putting some of my thoughts on paper and seeing feedback I get from others about their opinions of the problem.

I'll start with a particularly telling comment from Dean Dad:

...part of me wonders if we’re sacrificing too much on the altar of pencil and paper. It’s great to be able to do addition in your head and long division on paper -- yes, I know, I’m old -- but is it worth flunking out huge cohorts of students because their high schools let them use calculators and we don’t?

This isn't about LETTING them use calculators. Part of it is about spending time teaching them how to use a specific brand of calculator rather than how to do algebra. However, as I wrote in my first comment on DD's blog (9:11 AM time stamp about halfway into the 50 or so comments that are there now), I think this is mostly correlation without causation. The real problem lies elsewhere.

I think the problem starts in K-5 and gets compounded by pushing kids along into the next class and lying about the content level of that class. That is, I don't believe for a minute that a student I advised had passed a REAL pre-calc class in HS just a week before I talked to her. DD writes about similar cases:

...students who have passed algebra and even pre-calc in high school frequently crash and burn when they hit our developmental math, because the high schools let them use calculators and we don’t.

I don't buy it, and here is why: Our placement test will put them into Intermediate even if they can't do arithmetic, provided their algebra score is high enough. And you can't work with logarithms and exponentials or trig identities (a given if it is really pre-calc) if you can't solve a simple linear equation written symbolically like I asked the student to do.

You might forget 6 months of math in a week, the newest stuff, but not 3 years of it. And if you do forget that much that fast, you should have failed that pre-calc class. You can't get to much new material if you spend most of the year re-teaching three years of previously-taught material de novo.

K-5 Curriculum:

I don't want to belabor this, but one reason they can't do arithmetic might be that they never learned it. I'm convinced this is the biggest problem we face because it also lies behind the existence of pre-calc classes that are really teaching basic algebra. I'm sure part of it is that teachers who never understood math and hate it with a passion are teaching it by-the-book following a curriculum none of you could possibly imagine anyone would use.

My analogy is to the "look say" approach to reading, where guessing replaced phonetic decoding of words and Johnny (not to mention a cousin with a high IQ who is now an senior engineer at the VP level) couldn't read. Using guessing to construct your own mathematics might work with someone like me (I feel eternal guilt for, AFAICT, being an unwitting subject in a math ed research project that was run before the days of IRB and informed consent where they deduced that this curriculum worked really well), but it is unlikely to work with someone who was not going to get a PhD in physics. Really good algorithms were developed 12 centuries ago and survived for a reason. As is illustrated here, for the Everyday Math curriculum, the most efficient methods are not taught first or (in some cases) are not taught at all in some schools. The starting point for Dean Dad might be to get out into the feeder systems for his CC and find what they are doing in fourth and fifth grade.

If I know anything about learning, it is that students always favor the first method they get taught. (That is one reason you have to really emphasize when conservation of energy or momentum should be used instead of Newton's Laws: they learned F=ma first so it is the first thing they want to try. I'm the same way.) That means it is a really bad idea to start with an inefficient method, but which some people find useful when doing 'mental math', and teach the more efficient one last.

Now think about how to teach synthetic division or multiplication of polynomials to someone who only knows partial quotients division or the lattice method for multiplication. Not pretty. Then consider that they might never have even heard about "invert and multiply". Not pretty at all.

Outcomes:

The answer to Dean Dad's fundamental question, whether students should be allowed to use calculators in an Arithmetic class, starts at the beginning - the first step of course design. What are the desired outcomes for this math course? If the outcome is to be able to do a certain amount of arithmetic with pencil and paper (not in their heads), then the only use of a calculator is to check your own work as you make up your own problem and solve it. Ditto if the purpose is to simplify fractions involving simple whole numbers as preparation for a similar skill with symbols. You need to change the outcomes before changing what you do in the class.

Personally, I'd be happy if they taught them how to do arithmetic on their Basic calculator. Seriously! My biggest complaint when teaching physics isn't that they can't do arithmetic (they can't), it is that they can't calculate worth a damn. Digital natives my ass. I was 22 when I got my first calculator and I am faster than most of them are, and I'm slower than I used to be. (Sure, I've been using one longer than they have been alive, but that only proves they haven't used the thing enough to be competent with it.) I mean, I've watched a student work out a product by multiplying two numbers, writing it down times all of the others, entering it again !!! and multiplying it by the next, etc etc.

I know they use their calculators a lot in our Algebra (meaning College Algebra) classes, but it must all be with simple whole numbers like we used back when there were no calculators. That is the only possible explanation for their struggles with 3 and 4 digit decimal or scientific notation numbers or their mysterious belief in rounding intermediate answers.

Algebra:

There really shouldn't be many numbers in an algebra class, IMHO. Somehow the appearance of Graphing calculators changed the curriculum to emphasize numbers and, curiously, de-emphasize graphing. Since you can't actually read a graph on a TI display screen, let alone interpolate on it using a ruler, they don't appear to know how to make or read an actual graph rather than a cartoon of a graph. This is a nightmare in the physics lab, but also in the classroom when data are supplied in a graphical representation.

I don't believe anyone has tried teaching algebra with a Scientific calculator and graph paper in decades. I doubt if anyone other than the textbook and calculator companies have studied it, and studies like that are notorious for the difficulty in controlling the student mix or the instructor effect. However, stories about students who finally got algebra in a class where only symbols were used - no calculators needed - are common enough to make one wonder how it would work. The studies (see some comments toward the end) seem to lack a smoking gun in favor of the primitive Graphing calculators used today.

There is another side effect. Since they don't know how to use their calculators, particularly concerning order of operations, they use parentheses like they were the only operator known to man. ((3)(2))/((5)). One result is they don't see the key role of the parenthesis to denote "function of". I've seen calculus students who think x(t) means x*t, although this could be partly due to the fact that x is never a function in calculator-based Algebra. I have to wonder out loud if this would improve if they all used HP calculators instead of TI calculators. Also see my next comment below.

Commenting on the comments:

Some Anonymous, writing at 5:56 PM, about 3/4 of the way into the comments, writes:

A kid that is getting good marks in algebra screws up their physics equations. i check with their math teacher, and they don't make those mistakes in math class. So I test them myself, and they can manage algebra just fine when x, y, and z are variables and a, b, c, and d are constants. Anything else and they're lost.

This could be a result of using graphing calculators. The TI-83 will only plot Y(X) unless it is in one of the other modes (where it is similarly limited). Parametric mode, the only place where you can do X(T), does not appear to be used at all until they get to Calc III. This really bugs a chemistry colleague, because they are always plotting the log of this versus the sqrt of that, neither of which is X or Y. Similarly, we start out in physics by plotting x on the Y axis and t on the X axis and it blows their minds. I'm tempted to start by doing only y(t) problems at the start of fall, then moving to x(t).

Mthgeek, aka timfc, writing at 7:45AM of the second day of comments, listed several references. The first of these was

The Arithmetic Gap
Educational Leadership, v61 n5 p55 Feb 2004
Summary: The students using calculators in school classrooms result in lower math scores than students who never use them.

I'd like to know what grade level this was, but it sounds like K-8 from the title. As for the second one that was listed, I don't ever pay attention to something like a meta analysis of 42 other papers that span middle school through calculus. Apples, oranges, confounding variables, design differences, and systematic errors make a tasty goulash but don't help with teaching Basic algebra. One other reference, discussing "computer assisted instruction" would appear to be irrelevant to this discussion. You can use computers as an instructional aid (instant HW feedback, for example) without using a graphing calculator - or any calculator at all.

However, the last reference from Mthgeek is rather interesting. It is a link to an article (Refocusing Introductory College Mathematics Courses) that has a link to a new textbook (Contemporary College Algebra: Data, Functions, Modeling) that implements some of the ideas from the study. That is, the study and the textbook are closely coupled, but I recognize some things in that report that are reflected in what we do in our Intermediate class with a different book. (I'll have to ask around, but we might have made this choice because Intermediate is a pseudo-terminal course for many majors in our curriculum. The situation discussed in the article does not apply as much to our college Algebra course, because it normally leads to business calculus or trig. The statement in that report that biological sciences don't go beyond Algebra is patently false in our curriculum. They have to take Calculus even if they don't ever use it.) That said, I strongly criticize the textbook author for conflating a graph on a Graphing calculator with a graph produced on a computer. There is no comparison in detail or quality.

Some Anonymous, writing at 11:21AM on the first day, said (in part):

1) middle school math is more focused on algebra as early as 7th grade. So students don't have enough mastery of fractions, percents etc
...
3) More students attending college- so the lack of good high school prep is more evident.
4) Content of dev math courses in college are aimed at preparing students for a precalc/calculus track. But those going into sociology or psychology ...

Developmental math at my CC is about preparing students for 9th grade math, not pre-calc. The Intermediate course barely prepares them for real Algebra, and certainly not for the calculus track. (Our failure rate is spectacular at every one of those steps.) Besides. students going into Psychology need a real, college-level statistics class that has college Algebra as a pre-req. Criminal Justice, on the other hand, has no real math requirements and our statistics show that the combination of our Developmental and Intermediate classes does a GREAT job of preparing them to pass the basic financial math class that constitutes their "college level" math requirement while teaching them about compound interest.

The fact that they have not learned arithmetic or fractions by the time they get to 7th grade (which is when we started Basic algebra when I was growing up) is the real problem. Three years should be enough if the curriculum and teachers were any good, but if they aren't or the kids don't learn it in 3 years, our schools track those kids away from Basic algebra for another year, or more. But this does help strengthen my point that the problem is really in the K-5 classroom.

I don't buy the "more students" argument because the fraction going to college has not changed that much in the last few decades.

Finally ...

If you have read this far, thank you. I want to close by saying that the problem really is deeply rooted in our educational system and very frustrating for all involved. The high failure rate in Developmental classes is a major problem that no one is ignoring at our CC.

However, many students fail because they never attend class, or don't attend frequently enough to engage with the instructor. With any instructor, no matter how talented ze might be. I've written about that in an old bit of wishful thinking about new student orientation. Coming straight out of HS, they believe they were taught pre-calculus or Algebra II, so they just don't believe they need to go to class and actually learn math. Older students, out of school for years or decades, know they don't remember anything from school so they take it seriously and often do quite well. An age-based breakdown of performance in Developmental classes might be worth looking at, Dean Dad.

Or Dean Dad might only need to walk by a classroom or three on a regular basis and take a sort of visual attendance. Is the room still full after 4 weeks? Maybe that, rather than calculators, is the real problem.

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Interlude - Calculator history

This cartoon from last week really captured my view of "modern" calculators.


Click on the image to see the entire cartoon from XKCD, including the highly relevant punch line.

I was originally going to riff off of this cartoon to discuss "modern technology" in the classroom, but then Dean Dad's article came along. Just for perspective, the current model (TI-83 Plus) shows up priced between $89.99 (on sale at Staples for the new school year) and just under $100 (at Walmart and Amazon). For comparison, the CPI says $110 in 1996 will buy about $150 of normal goods today, but computer prices have been going down even as performance increases. For many decades.

Further, the cartoon is not exaggerating the connection to 1996. Today's TI-83 Plus is still running on a 6 MHz Zilog Z80 microprocessor, an 8-bit cpu that dates to the mid 1970s (as an upgrade to the legendary Intel 8080 chip). The Z80 was used in such memorable machines as the Kaypro II (running CP/M), the TRS-80, and the Sinclair and Timex notebook-sized computers. [The Kaypro, like the Osborne, was a "luggable" computer that would have to be sent in checked baggage today. I still remember using both of those.]

Not exactly MODERN technology, particularly when you consider the limitations of the 96x64 screen compared to, say, a (much smaller) iPhone. This has practical effects in that the calculator has great trouble graphing certain kinds of functions and the interface for "tracing" to a zero is really crude. More importantly, for whatever reason, I see no improvement in algebra skills associated with the month or more of time spent specifically on using this technology. Students do not use the graphs to check their answers, but that is a topic for my other postings on this topic.

Other observations:

The Plus indicates it has 512 kB of flash memory rather than 32 kB of RAM on the original model. The Silver Edition has a 15 MHz cpu and even more memory, but the added speed is one reason why you can clear its memory so much faster than on the Plus. AFAIK, the main difference is that you can clear uploaded programs on the 83 Plus but cannot clear the equivalent programs that are installed OEM on the Silver Edition. The main advantage for students is that you can connect any of these to a computer and download modestly sophisticated applications into Flash memory that are run with the Apps key.

Naive instructors believe that students have to laboriously type in crude crib sheets listing, say, trig identities or chemistry and physics formulas as fake programs. Many do this, but TI provides sophisticated, indexed crib cards - and similar tools are also available from others on the internets. Anyone who "limits" students to a note card of notes but allows a TI-83 without clearing it is laughably naive. Might as well let them bring in a notebook.

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Calculators - Background Info

This is the first of three articles concerning calculators and mathematics triggered by a blogspot and IHE blog article by Dean Dad, a community college dean who appears to be writing from another part of the country yet has the same problems we have at our CC. The original article concerned calculator use in "developmental" math classes that typically cover fractions and 7th grade algebra. I have already commented on the blogspot version of this blog (more than once) and the two together have generated more than 80 comments. I added some more in my second article of this series.

I won't actually comment on this topic here. My purpose is solely to set the terms of the debate, as it were, because the wide-ranging discussions of this topic by Dean Dad and others are seldom clear about which of the four or more levels of "calculator" available to students are being discussed and/or which of the three or more levels of math classes (plus physics and chemistry) provides the context for the discussion.

The divisions I make are somewhat arbitrary and perhaps idiosyncratic, so I want to spell them out somewhere without cluttering up a discussion of the teaching and learning issues as I see them. That way I can link here for future discussions of this topic and not have to repeat myself.

Although I think three levels of "calculator" suffice for most classroom use, and hence for later discussion, I think I need to list at least five to make the definitions as sharp as possible.

• Basic - Here I have in mind a wide range of very cheap calculators that can do arithmetic, including parentheses and scientific notation, but cannot deal with trig functions.
  
  
• SCIENTIFIC - These calculators can evaluate all of the basic functions (trig, hyperbolic, log, exponential, power) but cannot store text or programs. Some can work with complex numbers and/or hexadecimal numbers. At the high end, some can numerically evaluate definite integrals or derivatives or solve simple equations, but they cannot show any intermediate algebraic steps or work purely with symbols.
  
  
• GRAPHING - Here I have in mind several calculators that are similar in capability to the TI-83Plus. They can do all of the calculations of a top end "Scientific" calculator, but can also make graphs and store programs (including large amounts of text that can serve as a sophisticated crib sheet). They can store text, but cannot work with symbols. Functions are limited to y(x) except in the rarely-used parametric or polar modes.
  
  
• ALGEBRAIC - These calculators can solve equations written symbolically and can, in some cases, even show step-by-step the algebra or calculus used in the solution. They are typically somewhat limited in how much calculus they can do symbolically, but they make it unnecessary to learn any of the derivatives typically encountered in calculus.
  
  
• Computer Algebra - Here I have in mind small computers that can run computer algebra programs like Maple, Mathematica, MathCAD, etc. Now you might say "a laptop is not a calculator", but there is actually a rather modest size difference between a notebook-sized laptop and the top end TI "calculator" that comes with a full keyboard and a wide screen. Besides, these are widely used in classes at the Junior level and above so they help frame the discussion.

The three in the middle, in all caps, are the ones I will refer to most often within the context of lower division classes taught at a community college.

For the record, I allow Scientific calculators in my introductory physics classes but do not allow formula sheets or cell phones or Graphing calculators to be used on exams. I encourage students to get one of the high-end Scientific calculators that can be used throughout their engineering career, including on licensing exams, so they become fluent in its use.

The four levels of mathematics classes are defined as follows:

• Developmental - The content here ranges from arithmetic and fractions (what I characterize as 4th and 5th grade math) to basic algebra (the first class where "x" is used, taught in 7th grade when I was in school). These do not carry college credit. A well-calibrated placement test determines where a student starts, and some have an exit exam to verify competency at a certain level.
  
  
• Intermediate - The content here is algebra through what I knew as the 9th grade level (the quadratic formula, for example, but no logarithms). This might earn college credit at a community college, but not at a university. It is not considered to be at the college level. A well-calibrated placement test is used to place students in or through this level of math.
  
  
• College Algebra and Trig - I group all of the pre-calculus "college level" courses here but exclude other "college level" classes that exist mainly to ensure that liberal arts majors can graduate even if they can't do college algebra. (Those other classes usually cover enough about exponential behavior to understand compound interest on credit cards and enough probability so you should know better than to play the lottery, both very valuable life skills!) At our college, College Algebra serves many masters so skills not needed for the pre-business curriculum are put in an "advanced" college algebra class (pre-calc) and a trig class. (I know that some colleges, like my high school and undergrad university, combine these into a single course but I will use our curriculum as my reference point.) A different, also well calibrated, test is used to place students above this level although most students take the class.
  
  
• Calculus - Although my students will usually take everything through differential equations and linear algebra, I'm mainly thinking about first semester calculus because that is where the bulk of students fail.

The distinction between Developmental and Intermediate might seem unnecessary to some readers, because both levels are usually non-credit classes at a university. Indeed, some universities define college algebra as a remedial course. I make the distinction because our math department teaches classes at the Intermediate level and above, while the Developmental classes are taught by a separate department that specializes in teaching those skills. I know that smaller colleges do not make this distinction, but we are not a small college. (We have more t-t faculty in our Developmental math department than a private school like Union College has in its regular Math department.)

If I just say "Algebra", I mean College Algebra. I will say "Basic Algebra" or "Arithmetic" when I am talking about Developmental skills classes.

For the record, our Developmental classes use a Basic calculator for some things but some exams must be taken without any calculator. (The placement test and exit exam do not allow use of a calculator.) I believe they allow the use of any calculator up through a Graphing calculator when they allow a Basic one, but that might depend on the instructor. Our Intermediate classes all use calculators. Our Algebra classes require a specific Graphing calculator that is also required for statistics. Our calculus classes are a bit less picky about which Graphing calculator students can use, but ban Algebraic calculators and computers except in some special situations.

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A big day in history

Today, June 16, is:

• the 65th anniversary of the first test of an "atomic" bomb outside Alamogordo, NM;
  
  
• the 41st anniversary of the launch of Apollo 11, the first mission to land men on an extraterrestrial body, the Moon.

It is also the 37th anniversary of Butterfield's testimony that President Nixon had been taping conversations inside the oval office, tapes that eventually showed he was guilty of obstruction of justice and other major felonies, but I want to talk about technology today.

So, in the context of "if we can put men on the Moon, why can't we stop the leak at the bottom of the Gulf of Mexico", what is the relative difficulty of these three tasks?

Based solely on the time required to complete the project, the Moon mission was by far the most difficult and complex. The project started more than eight years earlier, before we had even put a man in orbit. Although the Saturn I was already on the drawing boards as an orbital launch vehicle, the Saturn V project started in early 1962. After about 4 years of research and development, there were two unmanned test flights (both showing problems that had to be fixed) before the first manned test flights. Even though we rather boldly used the first manned test flight to orbit the Moon, almost two years elapsed between the first unmanned test and the Moon landing mission. Given that this was a very high priority project that went as fast as possible (too fast, at times, resulting in three astronaut deaths) with essentially unlimited resources in the early years, it is almost nonsensical to compare design and construction of the "capping stack" to a Moon mission.

Next would be the development of the plutonium bomb first tested on this date in 1945. Plutonium was first isolated in 1941, so it only took four years to determine that one isotope, Pu-239, could be used as a nuclear explosive (it was already known that U-235 could be used that way) and figure out how to produce kg quantities of it and turn it into a weapon. Like the Moon mission, this was a "money is no object" project on the same scale as radar and a pressurized bomber that could fly at high altitude and carry a payload big enough to drop an atomic bomb. So, on the basis of time alone, this was easily half as difficult as going to the moon even if you include the U-235 weapon and the need for both radar and that bomber if the project was going to succeed.

Of the two bomb projects going on at the same time, the Pu-239 weapon was by far more complicated technically. The only challenge with U-235 was producing the purified isotope. (That remains the reason it poses the greatest threat for the spread of nuclear weapons, but that is a topic for another day. Our confidence in the U-235 weapon was so high that it was never tested before being used on Hiroshima.) With Pu-239, you had to produce the isotope essentially one atom at a time in a reactor and then separate it chemically from a huge quantity of preposterously radioactive material. Even then, you have to figure out how to assemble it into a weapon that will explode. That was enough of a challenge that it required a test before being used in combat a few weeks later. Again, based on time alone, four years does not compare to a few months of work to develop the capping stack (and the tools to cut off the pipe and install it) as well as the temporary fixes that were used until it was ready.

It is a good thing that fixing the mistakes made by BP was not nearly as complicated as rocket science or weapons. Those took years, this took months.

As I said yesterday, I don't think most people realize how long it takes to design and build something, even something as "simple" as a highway. You don't notice it until construction begins, but the work was going on for years before that.

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Failure of the New Media

When looking for the official BP info about the status of the well in the gulf, I found the following comment on the Huffington Post's Social News prominently in the news stack on Google:

FREEDOM BELL

“Me either. When did Wells of BP issue email and comments during the past attempts. When did Obama ever go on TV during a past attempt?”

(This was a comment on a Huffington Post article reporting the great news that the well had been "shut in".)

Since Wells of BP issues a comment twice a day, and this one came during his regularly scheduled briefing, the answer is he always does this. How do I know? The link I was looking for when I Googled "BP" was their Gulf of Mexico response page. The schedule and transcripts of those briefings is the top link on that page, and shows a 2:30 CDT (3:30 EDT) briefing, the second of the day.

And anyone with a modicum of knowledge of politics knows that the President will hold a press conference or give a speech whenever he feels like it, usually several times a day.

Conclusion: This contributor to the New Media has no critical thinking skills and/or no ability to use the web to answer this question, or only has an interest in using rhetorical questions to malign the motives of the engineers trying to solve this problem and the politicians making sure they do what the law requires them (not the government) to do.

Much the same can be said of the following comment

Equinator

85 days, 16 hours. Why was this not done the first day? All that planning to watch out for the walruses must not have helped much.

Correct, but even if the planning had said they would try this, they would still have had to build the device after being sure it was engineered to work in this specific situation. I don't know what they teach the great unwashed masses in school, but nothing of any complexity can be done in a day. (It takes years to take a new car model from design to showroom floor. I saw a version of the Ford Fusion in 1999.)

The reality is that this is a magnificent accomplishment. No other failure of this type (there have been others) was stopped prior to the drilling of a relief well, let alone one at this depth.

Now, even if the casing below lacks integrity and they have to keep the valve open (which is what they have expected all along), they can connect this to surface ships and keep any more oil from going into the Gulf. Lets hope the pressure and seismic tests show no oil leaking down in the drill hole itself. That would be even better news.

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OMG - It's July!

I had planned to post this a week ago (obviously), so by now Dr. Crazy has beaten me to the punch. Yes, it is that time of year, the time when you realize that next month is August! The month when classes begin. Lest we forget, the month when meetings begin! The month when there will be a number of things on the table (figuratively and literally) that you know you could have done, oh, in July. Or June.

As an inveterate procrastinator, I have used false deadlines for ages. In this case, I am now pretending we are approaching mid August rather than mid July. Those things that need to be printed for the first few labs, the ones that don't even need to have a date changed? They are going to get done this month. After all, my classes are all full (and one is overflowing) so I know what the number count is likely to be and any leftovers can be used next semester.

Syllabus for fall? Almost done, apart from one tweak and final check of the calendar and exam schedule. Syllabus for the spring? Next on my list. (Winter break is always too short.) Busy work I know I will need to do during the semester? I actually got the template updated so I only have to work on the worst part of it during the next month along with one task I have simply avoided doing for, oh, about two years.

And I plan to clean my office. Next week.

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Celebrate Independence!

I think it was sometime in grad school, as I got to know more foreigners, that how odd it is that we celebrate "July 4th" as if a date could be the name of a holiday. (Do you have July 4th in your country? Of course, but it isn't a holiday.) Similarly, it is always celebrated as the "birth of the United States" even though it was almost 13 years later, in March 1789, that the United States government as we know it came into existence. But we don't celebrate a "constitution day" holiday like some countries do, nor do we celebrate the ultimate event that truly sealed our existence as a nation (victory in the War of 1812), although we could have celebrated two others of almost equal importance yesterday (victory at Gettysburg in 1863) or today (victory at Vicksburg, also in 1863).

So "Independence Day", or "July 4th", does multiple duty as holidays go. Including, of course, the opportunity to set off illegal fireworks while watching state-sanctioned fireworks, watching NASCAR fireworks (last night's wrecks were spectacular) and the start of the Tour de France (also featuring spectacular wrecks this morning) in HD, and dining on the least healthy food this country has to offer.

I didn't appreciate the length of the Revolutionary War or the huge gap between it and the formation of our nation until I took a middle school government class. I had a crazy radical teacher who thought we should know the real truths of the history that was behind the sound-bite myths of political speech. So I know that the Revolution War began in 1775, before we declared our independence. I remember that blew the minds of some of my classmates, but it made sense that they might have wanted to win a few skirmishes before putting it all on the line.

Ditto for the wonderful detail that George Washington wasn't the first President of the United States. There were something like a dozen of them (aha, Wiki has both the full list starting in 1774 and the ten who headed the government), each serving as the "President" of the single house of the US Congress that (weakly) governed the confederation that was the United States for 8 years, starting in March 1781 even before the Yorktown victory, negotiated the treaty of Paris in 1783 that actually granted us our independence from Britain, and developed a Constitution that would dissolve that government in favor of a stronger one.

One wonders if the United States would have been reconquered by Great Britain in 1812 if not for that stronger federal government. Ditto for surviving the unpleasantness that came along 50 years later. Would there be Spanish speaking nations of Texas and California to our west and Florida to our south if we had stuck with a Confederation that ended up a part of the UK (like Canada) or split in half across the Mason-Dixon line?

PS -
Our menu includes chili dogs, watermelon, and beer from Vermont. While you digest that, check out the great pair of videos that Unbalanced Reaction put up today. And Dr. Crazy got to watch fireworks from the porch of her new house!

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Leaky Student Memories

Dean Dad picked up on my article of a few days ago and wrote a great followup to my followup that linked it with an e-mail request for help and an anecdote of his own. If you didn't see it, go read it now (as well as the IHE version) along with the comments. There are good ones on both sites, several of which deserve additional remarks.

Since I already posted some comments as CCPhysicist on the original DD blog, I figured I should shift over here before getting carried away in his comments section.

First, I'll include the same back link to my early writings on the "concept of prerequisites". Those came in my first wave of academic postings three years ago when I started the blog. I find that early article interesting to read because some of my views have evolved since then as I have studied it further (sadly, I think some of that is unbloggable). I should also link to the article where my readers and I came up with the idea of using basics rather than prerequisites when talking to students. However, the one area that gets more and more of my attention is the role of K-12 testing, as mentioned in the comments on DD's blog. Those, first mentioned here, have strengthened every time I talk to students about their pre-college experiences and compare the current generation of students to ones who didn't grow up in that testing culture.

But enough of that. Let's get to the new stuff.

1.

Dean Dad told this story:

I recall a student I tried to advise at Proprietary U. He was several semesters into his program, and he was choosing classes for the following semester. I mentioned that course x was next in the sequence, and required for his program; he objected that it covered a software package he didn’t know. I responded that the software package was covered in the class he was currently finishing. His response, which haunts me to this day: “but that was over a month ago!” His tone suggested that I was being completely outlandish; he was just mannerly enough not to end with “duh!”

I found this fascinating because the student was still in the class that taught the prerequisite material! Presumably he still had a final exam to take, but maybe that is presuming too much about how they do things at Proprietary U. More likely it was a module on one programming tool that was tested with projects and the like before moving on to the next tool.

But I take some exception to DD's conclusion:

Some of that is just a cost of doing business. Memory can play weird tricks. .... But it’s also true that thoughtful course sequencing -- which presupposes both thoughtful curricular design and steady academic advisement -- can provide reinforcement of key skills.

precisely because the student was still in the class teaching that new skill. You see, not only didn't the student know the new programming language or tool, the student didn't know it was going to be used in the next class in what I assume (from the story) was a clearly defined sequence for a "workforce" type program like ones that my CC has. I see this as an oversight by the instructor, although it could very well be the fault of the university if the instructor was a part-time adjunct who was not even aware of the curriculum. (Why else would Prof DD be advising a computer science student, given what DD says about his academic background, rather than the instructor.)

What would I recommend in this case to a colleague? First, that the subject of this programming language should be introduced by identifying when (meaning both the future classes and semesters, but also the career types) it would be used. I recommend something similar to my calculus colleagues when they introduce limits to students who "just" want to learn derivatives, and do something similar at certain key points in my physics course. Second, maybe the exam on that language should include questions about where it will be used. Hey, that is an idea for my physics class! Third, don't just say it the first day. Say it at least every week, much as I use the "this week in lab" or "next week in lab" observation to link what we are doing (or did several weeks ago) to our lab class.

2.

Several comments made explicit reference to the known fact that it is always easier to relearn something than learn it the first time. I know this quite well, but that is not the problem I am talking about here. (Hey, I too forgot lots of things along the way, so I frequently use the prompting/review example technique Cherish wrote about in the comments. Ditto for what Ivory and Lisa wrote, as well as HS lab partner of Dean Dad. I'll come back to a few of those later, since I think they are worth emphasizing just for my own future reference.) The problem I am talking about is when students have allegedly learned something several times and still don't have a grasp of it. My favorite example (listed in one of my previous articles linked up above) is the logarithm. Widely used as an essential computation tool in pre-calculator days, it remains an essential tool because exponential behavior (and, hence, exponential functions) are so common in nature. But students don't seem to really get it until the fourth time around.

We first teach it in college algebra, and I have seen the test questions used as well typical final exam questions so I know the skill level in that class. We teach it again in a pre-calculus class, where (based on the principle described above) they should just pick it back up and move on to new applications. Yet I have seen students struggling well past the end of an exam period on a pre-calculus exam that mostly contained questions just like the college algebra class. That part of the class was effectively starting from scratch. However, the ones who survive that class and log integrals in calculus seem to have learned it when I give a pop quiz on them before starting RC circuits. The fraction that survive that sequence, however, is not large. I don't think it is an exaggeration to say that the lack of even partial retention plays a key role in our retention problems in math.

3.

Gordon McAlister mentions Problem Based Learning in a comment on the IHE version of DD's blog. Although I have an aversion to Three Letter Acronym solutions to all that ails us, I tend to note that all of physics and math is problem based. The trick is what problems you choose, and what problems you put on tests. My speculation that the student in DD's anecdote was in a class built around modules comes from my experience teaching physics. IME, the worst retention results from a class where the material is tightly compartmentalized. You know, where a student taking Test 4 asks "is this like what we did on Test 2?" Every test should be part "Final Exam" in the sense of sampling key older ideas. Some of the best math profs (in the sense that I love having their students in my physics class) do this on a regular basis, and I do it also.

4.

Ivory posted a link to this critique of the mini-PhD approach to the construction of a syllabus. Yes, this is part of the problem, and it is fascinating to see a familiar problem from physics addressed in the context of a history course. It is long, but all of it (along with the comments) is worth reading. Now we don't have the political baggage they do when deciding whether the Doppler Effect is worth our time (or an exam question) compared to some other worthy subject, but it is the same problem. Clutter obscures the essential.

For me, this is a work in progress, but I will state my criteria: will someone else expect them to know this topic, or is it one where they will be expected to look up the equation that applies to a particular problem and plug in the values? Is it a skill or is it a factoid? Will their BASIC skills get better if I go a bit deeper and challenge them in a familiar area or if I take up this new topic at a very shallow level? I think the answer is that we have to deal with the reduction from 15 weeks of classes (plus exams) to 14 weeks by dropping some things that used to be thought essential. However, I am always quite up front in telling my students that I am not skipping it because no one needs to know it.

5.

Ivory also pointed to an abstract that describes one of those Increasingly Common Five Letter Acronyms (that also needs a few lower case letters) for a teaching technique. It looks to me like this was used in a course that was originally modular (if this is Tuesday, it must be Botulism). This is something that is a lot easier to do in a course like physics, and is almost identical to what a math colleague does on his calculus exams. What I find interesting is the idea of making it explicit to the students that you are doing this: that is, that you value retention of a specific subset of the earlier material. Not by talking about it, but by testing on it.

Definitely something to think about in a survey course where this is rarely done.

But you know something? The humanities courses where I really retained the material (and that make visiting museums a joy) were ones where there was a unifying theme in the interpretation of disparate items. That made you look for patterns as new things showed up, and LOOKING is the first step to real learning. You don't learn if it just washes over you like a rogue wave.

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