High Level Thinking and Lasting Impressions

Yesterday in my Curriculum and Instruction class we discussed the level of thinking required by various tasks.  The four levels of thinking as categorized in the text we are using are:

• memorization
• procedure without connections
• procedure with connections
• math

By "math" the author means solving problems for which there is no given procedure and can be approached in multiple ways.

My question is whether there is a strong correlation between the level of learning and the impact on our long term goals for our students.  I am also curious about the long term goals of the students themselves.  So today I wrote down three items on the board and asked my students which was most important to them:

• Preparing for future math and science classes.
• Developing problem solving skills that will be useful in other areas of life.
• Gaining insight that will help them understand deep and fascinating concepts of math and science.

In my Geometry class, the overwhelming favorite was the second option.  In my Algebra II class, the first one was the clear winner.  I chose these three goals to represent three different conceptions of the usefulness of a math education.  The first represents the idea that math is primarily a way to prove to society that you are intelligent.  If you learn math, you can get good grades now and in future math classes, and the higher classes are important because if you get good grades you will have a good chance of getting into the college of your choice.

The second option represents the idea that mathematical knowledge can transfer to other disciplines.  Most people don't become mathematicians (or scientists or engineers), but perhaps knowing some math may help them in some other endeavor.

The third option represents knowing math for its own sake, because it is interesting and beautiful and sheds light on the nature of the world we live in.  Not many students chose this option in either class.

My guess is that most math teachers would select the second option as the most important for a students in a high school math class.  However, many of us probably teach as if the first objective is primary.  This is because the curriculum is designed that way.  We (as in, the state) have selected a bunch of objectives that we think students need to master to be "college ready", that is, to prepare for the next level of math and science classes.  In order to make sure our students are prepared for these classes we rush through a textbook that organizes and isolates each concept in a very clean and logical manner.

I suppose one way of putting this is that our curriculum seems to push in the direction of presenting a lot of "memorization" and "procedure without connection" tasks in order to cover everything we need to cover to be prepared for college.  Of course, the idea that we need to have a whole catalogue of neatly separated mathematical procedures at hand in order to succeed in college may be erroneous.  It might even be better if students forgot everything they learn in math except for some broad problem solving strategies.

In any case, the aesthetic value of pure math seems to be pretty far down the list for both students and curriculum makers.

Research Lesson

Teaching is a pretty remarkable profession.  Every day there is so much to think about and so many decisions to make that it is almost overwhelming.  One of the questions that I had coming into the school year was how to give my students a sense of the "big picture." That is, how to make them feel like they are learning something important rather than just going through the motions and trying to solve a few repetitive puzzles.

As part of a class on Curriculum and Instruction I will be doing a "research lesson" that involves creating a lesson and gathering data about how effective it is.  At the beginning of the process we are asked to "map out a unit that brings to life long-term goals for student development, and that will move students from their current understanding/knowledge to the place we’d like them to be."

Long term student development?  Last year as I was teaching geometry I started to ge the sense at times that everything I was teaching was just going to be dumped immediately after the test.  I felt as if I was having zero impact on long term student development.  But what kind of impact is feasible?

When asked about their ultimate goals, many math teachers indicate that they want their students to become problem solvers.  The core curriculum mandated by the state has much more specific objectives.  An actual lesson plan is based on objectives that are even more specific than the state standards.  To what extent does meeting the specific objectives of a lesson help us meet curricular, and long term goals?  Does solving math problems really help students become good problem solvers, or does it exercise a more limited portion of the brain?

I am not sure a research lesson can address this issue, but there may be things we can observe during a class that will help determine what the long term impact is likely to be.

My Take on Ron Paul

There has been a lot of media attention lately about how the media ignore Ron Paul.  My view on this is that they are both right:  the ones who ignore him, and the ones who complain about people ignoring him.  The media is right to ignore the fact that he basically did just as well as Michelle B. in the Iowa poll because RP has a history of doing really well in obscure polls.  But the complainers are right to point out that if we are going to give a lot of credit to MB for winning, we ought to mention the RP did just as well as she did.

In any case, I don't think RP has any chance of winning the nomination.  I just don't.  But what about his views on the issues? As a libertarian, shouldn't I support him anyway if he shares my view on politics?  Well, lets take a look at his views (paraphrased from the issues section of his website):

Abortion:  RP is pro-life.  I think women should have the right to choose and pro-lifers should have the right to prevent their tax dollars from subsidizing them.

National Defense:  RP is a former AF officer that thinks we should end nation building exercises and refuse to get ourselves into wars without a clear national security objective.  Me too.

Guns: RP thinks the right to bear arms is essential to maintaining our freedom.  I don't think it is essential to our freedom these days, but I generally support the right to bear arms anyway because I am not sure whether there is any real harm in it and I think the default position should be less regulation of individual rights.  I think some particularly dangerous weapons should be banned, but my idea of what is particularly dangerous doesn't always match the battle lines drawn by the warring sides on this issue.

Education:  RP emphasizes the importance of home schooling.  I think a significant number of home schoolers are nutters, and there are much more important reform issues.  However, I support the right to home school and I support vouchers or tax credits for people who want out of the public system.  As a public school teacher, I also think we ought to support a public system that provides a great education for free to those who can't afford to pay.

Faith: Ron Paul states that he "accepted Jesus Christ as [his] personal Savior, and [he] endeavor[s] every day to follow Him in all [he does] and in every position [he] advocate[s]."  I don't like it when people bring religion into politics.

Health Care: RP wants to repeal Obamacare and focus more on health savings accounts.  I think this is a good idea, although I think Obamacare could be revised in a way that would make it acceptable.

Monetary Policy: RP is really worried about inflation, and wants to end the Fed.  I think macroeconomics is an arcane and confusing subject and neither I nor RP know enough about it to make strong claims.  But RP makes really strong claims.  I am not worried about inflation, and I don't think we need to end the Fed.  I do think that we should consider some creative alternatives to current monetary policy, however, such as the job guarantee plan I wrote about a few days ago.

Immigration: RP thinks that it is critical to "protect our borders" from incursion by low skilled workers.  I think we should open our borders to low skilled workers who are willing to work at the market wage (which may be below minimum wage).  RP is against amnesty.  I hate it when people use the word amnesty in the immigration context as if it were a bad thing.

Fiscal (Budget) Policy:  RP wants a balanced budget amendment, and he wants to end income tax, capital gains, and death taxes.  I think it is okay to run surpluses in good times and deficits in bad times as long as you have a sustainable plan (we don't).  I think we should end the corporate income tax, but keep regular income taxes and estate taxes.  We need a balanced tax system, and I think it is better to tax the dead than the living.

Energy:  RP wants to reduce restrictions on drilling, end the gasoline tax, and terminate the EPA.  I don't want to terminate the EPA, I think we can reduce drilling restrictions somewhat, but I don't want to end the gasoline tax because I think cars create externalities.

So there you have it.  Out of the 10 issues listed I am pretty much in line with RP on 2 of them (national defense and health care), I am ok with his position on 2 more (guns and education), and I am annoyed with his take on 6 issues.  Basically, I see RP as a small government populist.  I like small government too, but I don't think he understands the economy.  So, in the end I like having him around to mix things up but I don't think he is a viable candidate and I wouldn't be too overjoyed if he were.

Japanese Teaching Practice

Today I read an article about teaching practice in Japan.  It was a research article that followed a number of student teachers and their mentors and recorded their discussions.  The most common item of discussion among them was student engagement.  During one discussion, a mentor interrupted the student teacher to ask:

"Are there any places where the students use their heads?"

The response was pretty candid: "There is no such place, nothing at all."

I think this is an important question to be asking, but it comes with risks.  Anytime you want to challenge your students you run the risk of losing those students who don't want to be challenged. I have been thinking a lot about how to engage my students while at the same time keeping them accountable.  The method I am going to try will focus on notebooks.  If I want to have a challenging class discussion, I am going to ask a question and tell the students to respond in their notebooks.  Then I will go around and make sure everyone is at least giving it a shot before I open it up to the class.

Of course, this only shifts the problem from participation in discussion to participation in note taking.  But I think the latter is a more manageable problem. From day one I am going to emphasize that the primary expectation I have of them is to bring their notebook everyday and write down their thoughts when asked.  I will be frank that one of the main purposes of this will be so that I can observe their individual participation.

The second most important topic of discussion among Japanese mentors and student teachers was goal setting. Every lesson included a number of goals chosen from four categories: student interest, student thinking, understanding, and procedures.  Each lesson included at least one understanding objective and one procedural (or skill) objective.  I am not exactly sure what distinction they make between understanding and thinking, but I like the simplicity of the categories and the commitment to using them every lesson. I am making a pretty serious effort to break down each of my lessons into different objectives and it isn't always trivial.

Job Guarantee

Macroeconomics is mind boggling.  Sometimes it seems as if we could create a Utopian society of full employment and perpetual growth if we could only figure out the basic principles.  But we can't.  No one really knows for sure whether interest rates are too high or too low, whether the federal reserve should even target interest rates, whether we should base monetary policy on present factors or market expectations, and a whole list of other mysterious questions.  I don't even know if I have the questions right.

But I do know one thing.  The field is fascinating.  This evening I had the pleasure of reading about one class of proposals to shore up the nation's macroeconomic health: a public job guarantee.  The basic idea is that if the government guarantees everyone a job people can go work for the state during a recession and aggregate demand (the amount of stuff people buy) won't fall too far.  This will reduce the need for businesses to suddenly downsize, which will soften the impact of the downturn considerably.

Government jobs were a big part of FDR's plan to get the nation out of the depression, and India is currently trying to implement a job guarantee for its rural poor. But program's like India's have a serious problem.  The workers are employed in mostly meaningless projects.  They basically go around digging ditches that are never used. In general I think one of the main reasons we ought to have a small government is that no bureaucracy is capable of making very efficient decisions about where to employ labor. A public job guarantee would make the problem worse.  We could approach Soviet (or Indian) levels of inefficiency. Instead of rejecting the idea of a job guarantee for this reason, however, I decided to come up with a plan that I think would have the least negative impact on labor productivity.  Here it is:

The foundation of the plan is that the government would eliminate the minimum wage while at the same time creating something like a temp agency that offers anyone who wants the promise of a job at the present minimum wage.  However, instead of actually putting people to work, the government would hire them out to the highest bidder, even if the bid is below the promised wage.  The government would simply make up the difference.

The amount paid to the government would be set by the market demand for labor.  If it got really bad I could hire someone to carry my bags around full time for $10/month and the government would supply the extra $1200.  Thus, the government wouldn't really be giving everyone a job.  The market would provide the jobs and set the price for the labor.  The government would simply subsidize the process until there is no unemployment.

The program could become pretty expensive during a recession, but interestingly enough it would probably be less expensive than the present stimulus program. About 1 million people work for minimum wage, close to 3 million work for less than minimum wage, and right now there are about 14 million unemployed.  If the market rate for labor fell to zero, and the government supplied 20 million people with a $20,000/yr wage subsidy, the total cost would be $400 billion per year.  But this is a worst case scenario since the market price for labor would never actually reach zero.  (We would all get personal cooks and butlers before that).  The total amount of additional stimulus spending for the current recession has been about $1 trillion.  (Not including bailouts).

One problem with this plan is that workers may not have very much incentive to do good work if they are guaranteed a minimum wage job.  A solution to this would be to allow employers to offer performance incentives up to some maximum amount.  If there were no maximum, we might find ourselves in a situation where people making six figure salaries are getting a wage subsidy and the program could get really expensive.  Right now the federal minimum wage is $7.25.  Allowing employers to offer an additional $2.75/hr might be enough to incentivize good work.

This incentive would be added to the total after the government subsidy.  Since it would cost the employers money, it might reduce the market price for labor purchased from the government temp agency (or private agencies enrolled in the program).  You might end up with a situation where companies only pay the government $2.00/hr and offer up to $2.75/hr to their best employees.  The workers themselves would receive between $7.25 and $10/hr. People who want to make more than $10/hr would have to enter the unsubsidized labor market.

The program may make it harder for illegal aliens to find work, since they would have to compete against subsidized citizens.  But it might be the case that some employers would rather hire the illegals even if they have to pay more to get them.

So there it is, a plan to save the economy.  I don't claim to be an expert, and I don't know all of the unintended consequences such a plan would entail.  But it is interesting to think about.

Reverse Trolley Problem

The Trolley problem is a hypothetical that goes something like this:

Suppose a trolley (or train) is coming toward you and ten people are tied to the tracks.  You can flip a switch to divert the train, but if you do, you will kill another innocent person who is trapped on the alternate route.  What should you do?

Utilitarians usually argue that it is better to flip the switch because the death of ten people is worse than the death of one person.  Others object that if you flip the switch you are taking a deliberate action that will result in someone's death.  You are not responsible for the predicament the ten find themselves in, but if you flip the switch you become responsible for the death of the one, and thus it is morally wrong.

The trolley problem is often used to illustrate the action/inaction distinction in moral theory, but I think it has a more general application.  It is an instance where our "moral defaults" conflict with utilitarian considerations. The classic trolley problem is when our moral defaults suggest that some kind of action is worse than inaction.  But the reverse can be true.  Consider the war on drugs.

It is pretty clear that the war on drugs has some pretty serious negative consequences.  It creates a black market dominated by violent gangs, it costs a lot of money, it results in the incarceration of huge numbers of people, and it might even result in more drug use than less restrictive forms of regulation.  But most Americans still believe that we should continue the war because drugs are harmful.  If something is wrong it needs to be illegal and if something is against the law we need to enforce it.

The result of this reasoning is that we should continue the war on drugs even if utilitarian considerations suggest that doing so fails a cost benefit analysis.  It is a reverse trolley problem.  Drug use is like a train with one person on the tracks (the user).  Fighting a war on drugs is like flipping a switch so that the train kills ten people instead.  But we have to do it, right?  We can't just let that train kill someone!

Tax Credits vs. Vouchers

The CATO Institute argues that education tax credits are superior to education vouchers.  What is the difference?  A tax credit is when you reduce someone's taxes after they pay tuition, whereas a voucher is when you reimburse someone directly.  Seem like a meaningless distinction?  At first I thought so, too.

Thought they argue that they like tax credits better because they let people keep their own money rather than giving them other people's money, I suspect that the real reason is that education tax credits are easier to uphold in court (because courts buy the flimsy argument made by CATO).  That is, CATO continues to argue that way because the courts buy it and the courts buy it because...CATO keeps arguing it?

I don't know for sure, it is all too confusing for me to think about.  But, there is an important practical distinction between tax credits and vouchers.  Tax credits are only useful to those who pay taxes.  In our country, that is mostly rich people.  Vouchers can be given to very poor people (and sometimes vouchers are designed so they can only be used by poor people).  So tax credits are for the rich and vouchers are for the poor.  A cynic might think that is the real reason CATO likes tax credits.

The cynic would probably be wrong.  But you would be right if you guessed that is why I like tax credits.  Yep, you heard me right.  I like tax credits because they will be used mostly by rich people.  Why would I say such a terrible thing?  Because I believe that tax credits just might be a way to move rich people out of the public education system and induce them to pay more of their own tuition.  I think one reason education spending is low in this country is that rich (and middle class) people have the idea that the government should subsidize their education along with that of poor people.  But we aren't willing (especially in Utah) to raise taxes high enough to pay for a decent system that serves everyone.

One solution to this problem is to give rich people a modest tax credit and push them out of the public system.  Some argue that this might make them less likely to support public education, but they aren't doing much of that anyway.  I think people are willing to pay taxes up to a certain point, even if those taxes are clearly being used to subsidize someone else.  If those taxes have to pay for the education of too many children, no one is adequately served.  Sure, in the system I propose we might have some people getting a better education than others.  But everyone would be better off than they are now.