# Gas station without pumps

## 2010 July 31

### High school stem cell curriculum

Filed under: Uncategorized — gasstationwithoutpumps @ 12:21
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The California Institute for Regenerative Medicine (CIRM) had a press release last February about their new high-school curriculum about stem cells, which just made it to the San Francisco Chronicle today.  The curriculum consists of 4 modules, each 4–7 days long, which would take up a substantial chunk of a biology class:

1. Embryonic stem cells, in-vitro fertilization, and pre-implantation genetic diagnosis
2. Adult stem cells, homeostasis, and regenerative medicine
3. The microenvironment, its role in cell fate decisions, and cancer
4. The immune system and the hematopoietic stem cell lineage tree

The first two units are supposedly suitable for regular biology classes, while the last two are more suited for advanced (AP or IB) biology classes.

I’ve not reviewed the material (stem cells not being one of my areas of expertise), but the group at UC Berkeley who put it together should know their material.

## 2010 July 30

### Should I be a teacher/professor/researcher?

Filed under: Uncategorized — gasstationwithoutpumps @ 10:29
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Paul Bogush asked what to tell students who ask “Should I become a teacher?” I tried putting a long comment on his blog, but edublogs rejected my attempt to type the antispam word and threw away my draft, so I’ll try again here, where I can save drafts and not have to deal with the limitations of the comment field.

As a professor who teaches mainly graduate and senior-level courses to bioinformatics and bioengineering majors, I do not get many students asking me if they should be K–12 school teachers.  Students considering that career rarely take the intensive courses needed for an engineering degree, and college seniors in engineering rarely consider getting certified as teachers.  Perhaps having a higher percentage of engineering majors going into K–12 teaching would be valuable, both for the teaching profession and for the future supply of engineers, but it doesn’t often come up as question from students.

What I do get asked about is whether (and where) students should go to grad school, whether they should stop at an M.S. or go for a Ph.D., whether they should look for a job in industry, in a national lab, as faculty at a research university, or as faculty at a teaching college.  The question is often motivated by the same underlying question as the one Bogush asked about: “Knowing what you know now, would you choose this career?”

If asked directly about my choices, I can easily say that I do not regret my choices and that I am in about as good a position for me as I can imagine.  Being a professor at a university that values both research and teaching is a good fit for me.

When I’m asked about what a student should do, I’m much less definite.  I generally answer with questions:

• Do you enjoy writing papers? How many have you written?
• How many classes have you taught?
• Do you enjoy standing in front of a group of people explaining difficult concepts?
• How good are you at organizing thoughts clearly and presenting them?
• What new ideas do you have?  Are they practical, money-making ideas or more fundamental research?
• What sort of hours do you see yourself working?
• Who is doing the sort of research that interests you?  Where are they?

I generally modify the questions a bit based on my knowledge of the strengths or weaknesses of the student (if I know them well enough), but I rarely give specific advice.  Occasionally I get questions from a student who has enormous talent but is uncertain of it, and I push them to be a bit more ambitious.  A little more often I get questions from students who are barely passing their classes, but think that they are brilliant—I gently dissuade them from going into Ph.D. programs, steering them a little towards productive work within their capabilities. Most often, I am dealing with students who could do any of the things they are considering, if they want to enough.  I try to provide them with some information about the consequences of some of their possibilities, but mostly I give them questions to ask themselves, so they can find the path that is most comfortable for them.

## 2010 July 29

### Solving an infinite radical chain

Filed under: Uncategorized — gasstationwithoutpumps @ 20:23
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Pat’s Blog had a post about infinite radicals, which looked at $3=\sqrt{x+\sqrt{x + \sqrt{x +\cdots}}}$.  The problem is just as easy to solve for $x$ if you replace the 3 with $y$.

$y =\sqrt{x+\sqrt{x + \sqrt{x +\cdots}}}$

$y^2 = x + \sqrt{x+\sqrt{x + \sqrt{x +\cdots}}}$

$y^2 = x + y$

$x = y^2 - y$

Note that this technique is almost identical to how one solves an infinite geometric series, so would make a good challenge problem right after introducing geometric series.  This could be appropriate for a math team recreational puzzle.

One can obviously generalize to $n^{th}$ roots:

$y =\sqrt[n]{x+\sqrt[n]{x + \sqrt[n]{x +\cdots}}}$

$x = y^n - y$

And of course one would have to discuss when the formal manipulation makes sense.  For example, $y=1$ leads to the “solution” $x=0$, which is clearly wrong.  It might be worth some calculator time for the kids to play with different values of $x$ to see when the infinite radical makes sense. The value of $y$ for $x=1$ should be a familiar number.

One could also solve the quadratic to see what values $y$ takes on for different values of $x$, and look for a relationship between the parts of the quadratic formula and the solutions to the infinite radical chain.

### AP creates penalties for not guessing

Filed under: Uncategorized — gasstationwithoutpumps @ 08:57
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The College Board is changing its scoring method for 5-way multiple-choice questions on the AP exams from $\left\{ {1 \mbox{ , if correct}} \atop {-0.25 \mbox{ , if wrong}}\right.$ to $\left\{ {1 \mbox{ , if correct}} \atop {0 \mbox{ , if wrong}}\right.$. The new system is easier to explain to people, but introduces a bias in the scoring.

Previously a student who knew nothing could either leave the question blank (score 0) or guess (0.2 change of getting a 1, 0.8 chance of getting -0.25, for an expected value of 0 and standard deviation of 0.5).  Students who knew anything at all were better off guessing.  Now all students are much better off guessing, even if they know less than nothing (that is, even if their chance of guessing the right answer is less than the uniform 0.2, they are still better off guessing).

Essentially, all students are now forced to guess, as the system has switched from one in which guessing was neutral to one in which guessing gets a bonus.  Put another way, AP has introduced a penalty for leaving questions blank.  This change is likely to have a gender-biased effect, as girls were more likely to leave questions blank when they didn’t know the answer, and boys more likely to guess wildly.

Since no one uses the raw scores, the shift in raw scores is completely irrelevant.  Forced guessing will increase the variance on the exam scores slightly, and cautious students will be penalized substantially until they learn to guess even when they know that they have no idea.  I can’t see any advantage to this change.

I think that the problem that the College Board is trying to address is one of terminology.  For years, people have incorrectly called the neutralization of guessing a “guessing penalty”, when there was no penalty for guessing (expected value same as leaving question blank).  So now we’ll have a guessing bonus instead.

Note: I’ve also heard that the AP test is going from 5-answer multiple choice to 4-answer multiple choice, supposedly to make the test easier.  Why is that a desirable result?

I’m only aware of 2 tests that have a real guessing penalty, the AMC-10 and AMC-12.  On those tests, the scoring is $\left\{\begin{array}{ll}6&\mbox{, if right}\\1.5&\mbox{, if blank}\\ 0&\mbox{, if wrong}\end{array}\right.$ for an expected value of 1.2 if guessing randomly, and 1.5 if left blank. Reducing the choices from 5 to 4 would give a neutral value to guessing (that is, if they can increase the probability of getting the right answer from 0.2 to 0.25, it is worthwhile to guess). On the AMC-10 and AMC-12, test takers do have to think about whether they really know anything about the answer before guessing. Personally, I would have preferred to see $\left\{\begin{array}{ll}3&\mbox{, if right}\\ 0&\mbox{, if blank}\\ -1&\mbox{, if wrong}\end{array}\right.$ which would have an expected value for guessing of $-0.2$ and 0 for leaving questions blank, but I guess that the test designers wanted to have only non-negative scores.

## 2010 July 28

Filed under: Uncategorized — gasstationwithoutpumps @ 13:54
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The site www.gradeinflation.com has some fascinating statistics on grade inflation at US universities, spanning several decades.  One plot starts around 1920, showing GPAs of around 2.3 (C+), gradual growth in the 30s and 40s to 2.5, which held fairly steady through the 50s.  In the 60s there was explosive grade inflation, bringing public-college GPAs to around 2.8 and private-college GPAs to around 3.1.  Grades held fairly steady through the 70s and 80s, then started creeping up again.  By the 2006–07 school year, private-college GPAs averaged 3.30 (B+) and public-college GPAs 3.01 (B).  The variance is now quite high, with some schools having a GPA over 3.5 (A-)  and others having a GPA of 2.7 (B-).  It seems that there really are schools using the “A is average, B is bad, C is catastrophic” grading rubric.

As I have long believed, there is a major difference between humanities and sciences grading standards.  What I didn’t realize is that the gap is growing.  In the 40s, the average GPA in the humanities was about 0.17 points higher than in the sciences.  In the 00s it was around 0.3 points.  In some schools, the difference was more than 0.5 points.  I think that there is a gap between engineering and science also (with engineering faculty being stricter graders than science faculty), but I have no data to back up this belief.

The site also gives a rule of thumb for guessing the GPA of a college:

$\mbox{GPA} = 2.8 + \mbox{Rejection Percentage}/200 + \left\{ {0.2 \mbox{, if private}} \atop {0 \mbox{, if public}}\right.$

The site examines several conjectures about why there has been so much grade inflation. It manages to reject some of the hypotheses as inconsistent with the data, but does not claim to have a convincing explanation of the phenomenon.

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