Florida Governor Ron DeSantis and Math Education

Florida’s Department of Education recently rejected 54 math textbooks for classes K-12. This blog post is not about the reasons given for the rejections of these books but a comment on a tweet about this from Florida Governor Ron DeSantis.

The governor’s tweet said: “Math is about getting the right answer, not about feelings or ideologies. In Florida, we will be educating our children, not indoctrinating them.”

The teaching of math is not only about getting the right answer but in learning to think mathematically. In other words, to arrive at the right answer one often first has to frame a problem in way that can be solved by using math. Specific problems and their solutions may have an emotional component.

An example of how to use math to get insight on a particular issue, in this case not ideological nor emotional, is the question of whether a rectangular television screen or a square television screen has the greatest viewing area for a given diagonal length.

The correct answer is a square, but how does one determine that? While it is fairly easy using calculus to determine that the largest area of a rectangle with a given perimeter is a square, it is more difficult to prove that a square also provides a larger area than that of any other rectangle with the same diagonal. You have to be able to think like a mathematician to prove this. Not all math is learning rote skills to get the correct answer, as DeSantis implies. (Since I don’t have the proof, I am going to resort to that statement in math textbooks which annoys math students no end: the proof is left as an exercise for the reader.)

As a final comment, in the example I gave, some may see a public policy issue. As the aspect of television screens changed to become more rectangular, television manufacturers characterized their models by diagonal size, not area. This may have misled some into thinking that a television set with an equal diagonal to their old square one had the same viewing area. This is not an issue I think is worth fretting much about, but only a way of saying that using math to get insight into real issues can have implications.

A Brief Comment on the Economy – Krugman and Summers

Paul Krugman said yesterday (April 10, 2022) on his twitter feed that he is worried about inflation due to wage pressures, even though inflation may decline somewhat in the near future because of the “bullwhip effect,” which can cause some freight and wholesale prices to decrease in the short-term. 

Krugman is now beginning to agree with Larry Summers and has quit what had been called “team transitory.” Both now agree that the Fed needs to increase interest rates; Summers has called for, among other things, an increase in immigration to alleviate wage pressures.        

However, there may be some differences in view. Summers has criticized the Fed for keeping monetary policy loose for too long and the Administration and Congress for too much spending to counteract the effects of the pandemic. Krugman has not as of now been critical of these government actions and has praised the good job growth in the economy which he says the media has underplayed. The data, though, compel him to recognize the inflation risk. 

Both Krugman and Summers are old enough to remember the stagflation of the 1970s and what Paul Volcker felt compelled to put the economy through to end a dangerous inflation cycle. Out of control inflation can be deeply corrosive to both the economy and the political system. Krugman and Summers do not want to relive any part of that again. For now, they are both correct; the Fed has to keep inflation in check even if that means some economic pain in the next couple of years. 

What is missing, though, is an explicit long-range model of the economy. Do they both really believe that the labor must be constantly subdued to keep inflation in check? Both are Democrats and should have some progressive ideas of how to deal with income inequality and not just at the margin (taxing a few billionaires more is probably justified but does not address the problem of growing income inequality). As far as their politics are concerned, I mention in passing that Krugman is the more progressive of the two, but Summers has been more active politically. 

Krugman is currently the more modest in his predictions, given that he felt compelled to leave team transitory. Also, to those who know him or follow him, it is no surprise that Summers is less than modest when giving his opinions, but he is almost always worth listening too, even if one does not fully agree. 

No one fully understands the economy, not even these two, and unpredictable events (there are those among us who thought Putin was bluffing to destabilize the west and get some concessions) can have an enormous effect. For example, Europe, too, is struggling with inflation under very different institutional setups than the U.S., different government policies, and dependence on Russian fossil fuels. Europe’s struggles undoubtedly will affect the U.S. both politically and economically.

Comment on the FDA and the CDC and Second Covid Boosters

Public health officials and agencies need to cultivate and maintain credibility in order to be fully effective. Unfortunately, there have been some missteps at the federal level. For example, remember the initial recommendation not to wear masks, which was subsequently changed. Also, recall the advice that the J&J vaccine was about as good as the mRNA vaccines, though anyone paying attention knew that this was likely not the case. Now the way the federal government has handled the approval of a second Covid vaccine booster makes one wonder what is going on in the federal health agencies.

On March 29, 2022, the FDA authorized the use of a second booster shot for individuals over 50. The CDC on the same day issued a media release, entitled “CDC Recommends Additional Boosters for Certain Individuals.”

The FDA took this action without consulting its Advisory Committee on Vaccines and Related Biological Products, even though the committee’s next meeting is on April 6. Why did the FDA not wait a few days and ask the committee for its advice on second boosters before taking regulatory action? Regardless of what the FDA officially says, my guess is that FDA officials thought they might get advice that was contrary to what they wanted to do. It is not clear that would have been the outcome, though, a prominent member of the committee, Dr. Paul Offit, has expressed skepticism of the need for second boosters for everyone over 50.

With regard to the CDC’s media release, its headline is misleading. The text of the statement does not recommend additional boosters. Rather, it says: “Following FDA’s regulatory action today, CDC is updating its recommendations to allow certain immunocompromised individuals and people over the age of 50 who received an initial booster dose at least 4 months ago to be eligible for another mRNA booster to increase their protection against severe disease from COVID-19. Separately and in addition, based on newly published data, adults who received a primary vaccine and booster dose of Johnson & Johnson’s Janssen COVID-19 vaccine at least 4 months ago may now receive a second booster dose using an mRNA COVID-19 vaccine.”

This wording is strange. It recommends that a broader group be "allowed" to get a second booster, though the CDC does not have the authority to do this. It reads as a recommendation to the FDA to do what it had already done a few hours previously.

The wording looks like a hasty bureaucratic compromise among government officials who probably are not in total agreement. There is disagreement in the medical community about this. The government's handling of this issue does not inspire confidence and is a further example of less than good public relations by public health authorities.

I do not know whether second boosters are necessary or a good idea for everyone over 50. I would like to see whether any consensus is achieved among the experts.

I also note that the attempt to manipulate press accounts on this subject have not been fully successful because of dissenting voices among experts. For example, here is an excerpt from a recent New York Times article, “Should you get another Covid booster”:

Many scientists are dubious about today’s decision.

The F.D.A.’s authorization allows anyone over 50 to receive a second booster. But experts pointed out that the limited research so far supports a fourth shot only for those older than 65 or who have underlying conditions that put them at high risk.

The most compelling data comes from an Israeli study that found that adults older than 60 who got a fourth dose were 78 percent less likely to die of Covid than those who got only three shots. The study was posted online last week and has not yet been reviewed for publication in a scientific journal.

“The Israeli study, in terms of mortality rate, is decisive,” said Dr. Robert Wachter, chair of the Department of Medicine at the University of California, San Francisco.

But that study, while it offers the only evidence, is deeply flawed. The participants all volunteered to get a fourth shot — and are likely to be people who are naturally careful about their health, said Dr. Paul Offit, director of the Vaccine Education Center at Children’s Hospital of Philadelphia and an adviser to the F.D.A.

It will be interesting to see what happens at the FDA advisory committee meeting on April 6.