Tuesday, December 29, 2015

Peer Review in Science and the Science Classroom

I think that peer review has a place in the teaching of scientific thinking. Science hangs its credibility on peer review. A scientist performs an experiment or a statistical test, draws a conclusion, writes it up as a journal article, and submits it for publication. An editor who is assigned the paper looks over it, identifies a short list of other scientists whose skills overlap with those relevant to the paper, and sends personal invitations to them to review it. Invitees then accept or decline, and those who accept volunteer their time to read the paper and consider its arguments. After usually a few weeks, the reviewers then provide summaries to the editor and the authors, including lists of their concerns or other feedback. Reviewers typically recommend that the editor accept or reject the paper. Reviewers who recommend accepting papers typically do so after first recommending revisions. Reviewers typically do not reveal their identities to authors, although occasionally they sign their reviews. In light of the reviews, and sometimes his or her own evaluation of the manuscript, the editor then makes a decision. In the event that the paper is not rejected outright, the authors typically then have the opportunity to respond to the reviewers’ concerns, with revisions or with further evidence substantiating their claims. The result often includes formal written discussion between the author and the reviewers through the editor. 

Just like authors, reviewers are human and subject to folly. Sometimes their recommendations are uninformed or wrong. Sometimes papers that perhaps should have been accepted get rejected, as well as the other way around. The peer review process is full of flaws from the initial conception of an idea through the time of acceptance or rejection, yet peer review has supported growth of the scientific enterprise and improved its capacity to build our understanding of nature.

My own experience with peer review has been interesting. As a mid career scientist, I am approaching having 50 peer reviewed papers in print. I have also served three years as an editor for a major journal in atmospheric sciences. I have personally reviewed hundreds of articles submitted by other scientists, and I received a formal editors’ award for those efforts. I have seen the process from all sides. In spite of all of its flaws, I love it!  

Peer review prevented publication of one paper I submitted as a graduate student. My conclusion turned out to be wrong, and I did not resubmit. A handful of other papers I wrote were also initially rejected, but after some additional analysis and revision of my conclusions, they were ultimately published after resubmission. I expect that others of my own papers should have been rejected, but were not. Sometimes reviewers are simply wrong. Their wrong conclusions can lead to poorly motivated recommendations of both rejection and acceptance. Yet, I have found that even when reviewers turned out to be completely wrong, my papers ultimately improved for having undergone the process. Critical reviews are essential to good science. A critical review based on good arguments is a good review. I think of a “bad” review as based on an incorrect conclusion about what results actually showed. Bad reviews sometimes lead to improper rejection of ideas. Yet, even after a bad review, I think the process as a whole still works (though not efficiently). I find that I can reflect on a bad review and revise my arguments to reduce potential that future readers come to similarly poor conclusions.

In recent years, as a professor, I have assigned research project reports to my students. I ask them in their projects to relate their own thesis research topics to those of the course. The weight placed on me to review tens of student papers at a time became too great to handle. I had to find another way to provide students with the feedback they needed. After I started serving as a journal editor overseeing the peer review process for scientists, I decided to treat the student papers as journal submissions. I receive the papers as an editor, then I invite other students in the class who wrote on related topics, to provide a formal peer review to the authors, including a recommendation to me, the editor, to reach a decision about “publication” of the paper. Regardless of my decision, the author then responds to the reviews, revises the manuscript, and sends the final product to me for a grade. The peer review process always improves the papers, improves student-learning outcomes, and reduces my workload.

I think that there is place for peer review in k-12 science and math education. In fact, I don’t think complete science education is even possible without it. Several attributes of good science education are well known. Learning to do science requires learning facts. It benefits from learned skills in technical mathematics and computer programming. It benefits from technical writing practice. But it also requires learning how to give, receive, and respond to criticism, whether the criticism is right or wrong. Effective direct criticism is essential to effective science. Science education should provide students with experience giving and receiving peer review, and responding constructively to reviews without taking them personally. Yet, peer review is almost entirely absent from the science classroom. Implementing peer review in the classroom is not without complication, but I think it is worth the effort required. In the real world, personal insults occasionally get exchanged in peer review, though they are out of place in the process. Receiving direct criticism as if it were a personal insult is also out of place in peer review. Yet, the process of making and receiving criticism could dramatically improve many aspects of the learning process. It can also lead to healthy conversation among students.

Peer review in the classroom could be blind or direct. Opportunity for direct criticism is optimum when students demonstrate techniques to each other, similar to what scientists do when they meet together for conferences. The feedback students give to each other, under loose supervision from teachers or mentors, can produce positive learning outcomes. In these settings, teachers should not usually simply jump in to correct errors made, but should help catalyze the process, letting interaction between students lead to correction. Opportunities for blind peer review could include things like inviting students to review each other’s homework. Possibilities are endless. Controlling bullying would be an important part of the process of instituting peer review in the classroom, but preventing or damping criticism should not be. Helping students to learn to not take it personally is part of the process. Peer review is full of flaws, but full of promise, and if it works for science, it should work for science education.

Saturday, December 26, 2015

How Scientists Categorize El Niño, and Lessons in Teaching and Learning Science

As most of you are aware, the tropical Pacific Ocean is presently in a state of extreme El Niño conditions comparable to the past big events of 1982-1983 and 1997-1998. This El Niño event has interacted with other phenomena to generate the recent heavy precipitation at the west coast of the United States as well as the recent extreme warmth here in the Northeast. Today, I provide you with some comparison of this event to past events, including some discussion of how a subset of climate scientists categorize El Niño events. Then, I use the example of discussion among scientists about how we describe El Niño to yield insights to improve science education.

I provided some explanation about the mechanics of El Niño in an earlier blog:

We measure the strength of an El Niño event by the difference in the surface temperature of the ocean from its normal or average condition at the same time of the year. The figure below shows this difference over the recent week: Warm colors indicate regions that are warmer than their average condition.

The most important region for identifying El Niño is along the equator from 180° longitude east to the west coast of South America. The present temperatures are higher than ever observed this time of year across some of the western part of this region, while near the west coast of South America, waters are warm, but not as warm as in 1997.

Scientists have devised several ways to track and categorize El Niño events. When we try to simplify complicated phenomena to better understand or explain them, we sometimes go too far, and our oversimplifications sometimes lead to misleading conclusions about how natural systems actually behave. Scientists craft questions in light of evidence and their own assumptions, and like anyone else, they are susceptible to folly. Luckily, over time, the scientific process tends to correct our false conclusions.

El Niño might seem easy to define, but every event has its warm water distributed differently. Scientists at JAMSTEC, the Japan Agency for Marine-Earth Science and Technology, along with other climate specialists around the world, describe El Niño events as if they all fit nicely into two types: the canonical, or east Pacific form, and the central Pacific form, often called “Modoki”, which means, “of the other sort”.


Images courtesy of JAMSTEC.

The figure on the left shows an average east Pacific event and the figure on the right shows an average central Pacific event. Events that are more like the east Pacific form tend to be associated with above average rainfall in California and abnormal warmth in eastern Canada and the northeastern United States. Events more like the central Pacific type often have brutally cold periods in winter in the Northeast and below normal precipitation in California. Given these different relationships with weather extremes, it is clearly useful to consider the behaviors of events that behave like the two categories. However, a scientist could incorrectly assume that all events fit cleanly into one type or the other, and then attempt to sort them all that way.

People like the convenience of being able to sort things into simple boxes. Describing El Niño events as one type or the other has become something of a fad in the community of scientists who specialize in climate variability. Yet, a more careful look at the scientific literature suggests that those scientists who like to sort them this way often disagree on the categories into which some past events should be placed. To further complicate matters, my own research has shown that individual events can evolve from one type into the other and even back again over the course of their lifetimes.


One way we track the progress of El Niño events is through instruments placed on buoys anchored in the tropical Pacific Ocean. Measurements from these buoys show the recent state:

The top panel shows the measured sea surface temperatures, and the bottom shows the difference from normal.

The 1997-1998 event looked like the image below at the same time of year:

Note the much higher temperatures observed in 1997 on the east side of the map, but also note the higher temperatures in 2015 in the middle of the map.

December 2009, for comparison, is frequently labeled as a Modoki event:

Conditions in the central Pacific region during 2009 were similar to those presently observed there, but the east Pacific is much warmer this year than in 2009. After comparison with 1997, I have heard a small subset of scientists label the present event as a Modoki El Niño. I find that argument preposterous. The present east Pacific sea surface temperatures seem to fit nicely in between the events of 1997 and 2009. These events illustrate clearly that El Niño occurs across a wide range of possible states. Trying to hammer each event into oversimplified categories is clearly misleading. El Niño is not simply an either/or phenomenon.

I think the example of scientists arguing about how to describe El Niño events provides a good model for teaching science. Textbooks and science classes all too frequently yield the impression that science constitutes a set of clearly defined theories that cleanly address a specific set questions. Real world science is not usually so easy. Developing a theory tends to be a long, arduous process. To begin with, the best questions to ask are not always obvious. Textbooks typically challenge students with pre written questions and with data, but they tend to spend too little time helping them to learn to ask questions themselves. Textbooks also seldom help students learn how to struggle through the process of seeking answers to their own questions in light of evidence. This process is difficult for scientists as well. Many questions scientists raise also turn out to be poorly posed when new evidence is considered, and these questions should be discarded or reposed. Identifying the type of El Niño represented in a given event is one such question. When the whole range of possible configurations of warm water is considered, a much better question is, how does the pattern of warm water in one event compare with the patterns of all past events? This more general question better allows the reality of El Niño diversity to shine through.

The quest for better science education cries out that each student of science be considered as an individual who can both pose questions and propose and test solutions. Experiencing the process of science requires allowing students, when presented with information, to learn to sift through it, crafting questions and testing their answers to those questions against the evidence. The best place for a wise teacher or mentor is to provide the environment, then to review the student’s methods and progress, providing feedback to the student. In other words, I think that the best way for students to learn science is to actually do science, like real scientists do, but at their own academic levels. That does not necessarily imply that students should constantly be performing expensive experiments. Mountains of information are already available, and students need to learn to engage that information to ask questions, to design pathways to answers, and to test those answers.

Monday, December 21, 2015

The Art of the Mistake in Math and Science Teaching

In retrospect, I think my first undergraduate class taught as a university professor was awful. I constructed detailed notes, which I carefully reconstructed on the whiteboard and in PowerPoint slides, which the students then dutifully transferred to their notebooks. I think they were zombies with pencils. Only the strongest students would ask questions in class, and their questions tended to reflect shallow understandings.The results of their first exam created a stunning revelation to me. The students seemed to have memorized each point I made, but they could not answer more complicated questions that required them to think independently.

I knew at the time that I had to engage the students and pass responsibility for learning on to them, but in practice I did not know how to do it. My first attempt at teaching was poor use of the traditional lecture. Don't get me wrong--some faculty are effective lecturers, and students seem to like the approach. Yet, numerous education studies have concluded that the lecture is among the least effective approaches for deep learning. The lecture is the easiest way to transfer large amounts of information into student's notebooks without engaging their brains! Sometimes this efficiency of direct transfer is needed in order to move forward to more interesting things, but when it dominates a course, it usually results in shallow learning.

Needless to say, I have revised my teaching approach. I still lecture occasionally, but I do it differently. When I simply want students to view lectures to gain first exposure to ideas, I sometimes refer them to YouTube and other courses already available online for free. Why should I teach such concepts myself when others have already done the work? Passing the burden for mundane things onto others frees up my time to focus on helping students to practice deeper applications of concepts in ways that help them better connect what they learn to the real world.

When I do lecture, I leave my notes aside, and I allow myself to make mistakes. I tell the students up front that they should not completely trust me, and that they should try to anticipate (and suggest) next steps. I know my technique is working when students comment to correct my mistakes. If I did make a mistake, I am thrilled when they report it and offer a fix. After they get acquainted with this teaching approach, when students misunderstand a concept, they often think I made a mistake, and they ask questions, so then I know they don't get it.  Many students who speak up in my classroom would never ask questions in more traditional lecture style classes, and their instructors would see little evidence of their lack of understanding until exam time. On some occasions, I work through complicated derivations in class, with an error woven into the mix. When I get to the end, if they have not discovered the error, I ask them whether the solution makes sense. If they cannot identify the error immediately, I assign them to find it, as homework.

My undergraduate course is computer programming and statistics in environmental sciences. I require the students to take a free online course in the computer language we use, then I give them datasets, which we analyze together. They use their own computers and devices in class, allowing them to play with the concepts later on their own time. I think this type of play is essential to build their creativity and their understandings of complicated concepts. In-class exercises are open ended, and we discuss and apply new techniques as they become applicable to questions that arise from looking at the data.

A large part of the course is a class project, in which the students find data online relevant to topics of interest to them. They figure out how to load the datasets themselves, and they apply analysis techniques in order to better understand the natural systems represented in the datasets.

Bottom line, I think, is that deep learning that preserves creativity requires students to actively engage with course content, with freedom to make mistakes and to experiment with their own ideas along the way. When faculty let go of a detailed script, faculty and students can engage with content, leading to real learning.

Saturday, December 5, 2015

Science and Conspiracy Theory: An Experiment in Human Behavior

Some political and religious views lead to interesting patterns of rejection of scientific insights, even when those insights are supported by mountains of evidence. This behavior is not difficult to explain. People cannot specialize in everything, so we tend to simplify our lives by agreeing with people we see as authorities, and we grant or withhold our trust according to how well their ideas agree with our existing concepts of the world. We also tend to feel like we are right when we are wrong. This feeling that we are right when our view of evidence is clouded by our preconceptions exhibits a form of inertia: Verifiably incorrect views can be difficult to displace, both in our own minds and in the minds of other people. Most of us are not naturally humble enough to consider that we might be wrong in areas where we feel high confidence.

As this is an education blog, I argue that part of a good education is to learn to respect the rights of others to express any point of view, no matter how wrong we might think it to be. Ideas are then open to discussion in light of the evidence and the points of view of other people. Open discussion in light of evidence would ultimately yield a better society than one in which people mainly express their views to others with whom they already agree. Any idea can be subject to such discussion, and we do ourselves no favors by avoiding discussion with those with whom we disagree. Discussion can help us refine our ideas. After all, if we are wrong, who really wants to stay that way, given that we can choose to make our views align better with the evidence?

The adherents of many views outside the mainstream of peer-reviewed science may be more likely to be wrong than those within the mainstream, but from the scientific perspective, the veracity of any idea about the natural world ultimately depends not on how many people agree, but on the continually developing stream of evidence. When they lack hard evidence to support their beliefs, people unfamiliar with scientific thinking tend to perform intellectual acrobatics, seeking for circumstantial evidence and anecdotes in support of their existing views. They sometimes even see lack of evidence, such as lines blotted out on government forms, as evidence. They somehow know what was crossed out, and they wonder why you don’t see it as well. Many people who behave this way are so convinced of the reality of their views that they rationalize their behavior or do not see it as it really is. Many people cling to such views, assuming that anyone presenting evidence to the contrary must be part of a conspiracy or must have been duped by that conspiracy. Such people are often labeled as conspiracy theorists. Of course, real conspiracies do exist, but people document them by following trails of hard evidence that would stand up in court or even peer review in a scientific journal. Conspiracy theorists build a type of intellectual immune system into their theories, designed to resist the pull of evidence that would otherwise lead people to see errors in their views. After all, how could they be wrong?

Scientific conclusions often turn out to be wrong as well. Scientific perspectives have their own type of inertia, sometimes apparently supported by a preponderance of evidence, but still, many widely regarded scientific conclusions are ultimately discredited and replaced by other views that align better with the facts. That’s the key: Scientists view new facts as we find them, and we revise our views in response. Famous scientists usually become famous by providing evidence that overturns prevailing views. Many scientists who overturn prevailing views previously accepted those views. Scientific discoveries that simply support prevailing views do not usually yield wide acclaim.

Research grants are not usually awarded for proposed projects that are intended to entirely support prevailing views. Instead, grants are awarded in support of research to test new ideas. Most often, proposed research would build new material onto prevailing views. Sometimes scientists propose to analyze new ideas that if supported by the evidence would discredit and replace prevailing views. Of course, to supplant prevailing views constructed over decades or more of accumulated evidence requires substantial hard evidence and a well-defined argument. For example, the shift in position of a star during a solar eclipse, predicted precisely by Einstein’s theory of general relativity, and measured by Sir Arthur Eddington in 1919, provided the first observational support for that theory, which supplanted Newton’s law of universal gravitation. The principal difference between the type of conceptual inertia in science and that exhibited by conspiracy theorists is that maintenance or rejection of scientific views in the scientific community depends on evidence and peer review of that evidence. Scientists are required to respond to the concerns of their reviewers. Conspiracy theorists typically work to avoid reviews by those with whom they disagree.

Conspiracy theorists tend to pile up circumstantial evidence in support of their views. For example, those who think that the Apollo moon landings were faked point to movement of a flag in a video and a handful of apparently faked images. They find it difficult to explain these things, so they assume a conspiracy. They don’t consider, for example, how a flag held out by a wire at its top, to prevent it from dangling, might rock like a pendulum for quite a while after it is staked in an environment lacking a substantial atmosphere. The same people completely dismiss overwhelming evidence that the missions really happened and were successful, including the participation of thousands of witnesses at mission control and others who were present at or involved in lift offs or earth landings, as well as the observations of hundreds or even thousands of independent scientists around the world who analyzed the rock samples and other data returned from the moon. These scientists would have been able to identify abnormalities. If these things were faked, surely someone from among these thousands would have blown the whistle with hard evidence?

I provide below a few examples of claims that are far outside of the range of mainstream science as contained in peer-reviewed literature, but that have become popular in segments of the general public. Chances are that many of you agree with at least one of these “theories”. I mean no personal offense to anyone who might agree with them. Instead, those of you who do agree should take it as a challenge to defend your perspective by following the pathway of scientific thinking: Offer for review by your peers your strongest piece of evidence and how it leads to your conclusion. Prepare your arguments carefully, and try to consider how your conclusions might be wrong. Being outside of the mainstream itself is not evidence against an idea. Yet, oftentimes those who support such ideas don’t take the time to discuss in detail the evidence for or against their ideas with those holding mainstream scientific views (who might be critical), and they think that those who disagree with them are either uninformed or tainted by the conspiracy. These perspectives limit discussion and further isolate people in their beliefs.

If you wish to mount a challenge to the prevailing scientific view, which is against these “theories”, then present the strongest piece of evidence you can identify for your perspective, and allow the discussion about that piece of evidence to take its course.

Here are a few claims to get the discussion going:
  1. The general upward trend in the average surface temperature of the earth over most recent decades has been faked, and scientific claims of climate change including global warming caused by human activities are biased by grant money and political motivations. 
  2. Genetic modification of food crops is fundamentally dangerous to humans in all its forms, and is driven entirely by profits in big industry.
  3. Long-lived vapor condensation trails that develop behind airplanes are part of a “chemtrail conspiracy” in which the government is spraying harmful chemicals on the population.
  4. Vaccines are dangerous to all children, leading to high rates of autism and other disorders. Further, vaccines do not provide any relevant protection against the diseases for which they were supposedly formulated, and incidence of these diseases has declined anyway due to cleanliness and modern nutrition.  

All of the above “theories” run directly counter to a preponderance of evidence as expressed in the peer reviewed literature, although there are caveats in the details. I include below some discussion of science in the context of these ideas along with a few caveats to the prevailing scientific perspective (my lists evidences for the scientific perspectives and of the caveats are by no means all-inclusive).

Global Warming

There is indeed a broad consensus that CO2 and methane emissions associated with human activities generate global warming. However, our confidence in the specific amount of warming that the surface of the earth is likely to achieve under doubling of CO2 is uncertain because of incomplete understanding of the balance of feedbacks that add to or subtract from the warming effects. Yet, uncertainty in the details does not imply certainty of the absence of net effects!

Some scientists do choose to study problems motivated by their politics, but this point does not influence whether their conclusions are consistent with evidence—In successful peer review, the actual evidence is what supports or refutes claims.

Other concerns that can be legitimately raised about concepts of climate change involve how the media, the public, and even some scientists describe it in order to yield action to support political agendas. Some of this behavior might be justified by the evidence, but any claims with insufficient evidential support are dishonest. For example, some politicians and reporters blame specific storm events, such as hurricane Sandy, on climate change, an assertion that few scientists have been able to demonstrate to the satisfaction of peer review. The environmental movement risks loss of public trust when they make assertions about relationships between specific types of weather events and climate change or when they make other claims that have insufficient evidence.   

Genetic Modification of Food Crops

A growing fraction of the population has become convinced that all genetic modification of food crops is dangerous, in large part due to actions of activists, labeling on organic foods, and advertising campaigns. Many people are surprised to discover that the preponderance of evidence in the scientific literature supports that nearly all genetically modified foods are safe. Simply asserting that they are dangerous and repeating that statement over and over again does not prove its truth. However, some people do raise some potentially valid concerns about genetically modified foods. I list a few of these below. I have yet to see evidence based arguments that would lead us to conclude that all genetic modification of food crops is inherently dangerous. 

a. Some genetic modification of food crops might encourage higher rates of herbicide use, which might possibly lead to health concerns. Even if true, that would not imply that genetic modification itself is fundamentally dangerous. Contrary to that view, many genetic modifications are done to reduce the need for chemicals and to make plants more disease or drought resistant. 

b. Cross-pollination (mostly within the same crop species) might spread modified genes into neighboring fields, which although not necessarily harmful to anyone’s health, might impact the ability of organic farmers to market some of their crops.

c. Some people claim that involvement of big business in some of the science of genetic modification implies that the technology is inherently bad, but this point is politically motivated and is irrelevant to whether the resulting products are in fact dangerous. Evidence must actually show the danger, and there are plenty of peer reviewers outside of the corporate funding system to provide rigorous peer review of scientific publications about technology developed in private companies (Journal editors typically choose reviewers from outside of the institution of the authors). Activists often simply assert that these foods are dangerous, and flocks of people then agree, like Columbian sheep. Many forms of genetic modification are carried out by university scientists or scientists at nonprofit organizations, independent of corporate funding.

d. Introduction of new proteins into a food supply by coding for those proteins in the DNA of plants could potentially cause allergies or other food sensitivities, but this possibility is also true for conventional plant breeding. Most genetically modified foods have been more thoroughly tested than any other types of new food crops (including crops treated by pesticides considered suitable for "organic" agriculture). Although this testing is clearly merited, to the best of my knowledge it has yet to provide any clear evidence of danger to humans.  


I am not aware of grains of truth in the “chemtrail” conspiracy theory—This rumor appears to me to be entirely fabricated, after my reading of several of the websites spreading it. Science clearly explains why some contrails last long and others do not, and none of these explanations require nefarious additives to make some of them last longer. Having a natural explanation of course does not necessarily prove that people could not use that as a cover for their nefarious deeds, but I have yet to find any evidence of a conspiracy or of the poorly defined negative impacts that would arise from whatever “they” might be spraying on us. In any case, the argument this "theory" is making is that long lasting contrails are caused by added chemicals, and that there is no natural cause of similar behavior. 


  • Vaccine injuries do occur, especially in response to allergic reactions to eggs. Yet, to date, I have never seen any source that provides verifiable evidence of claims that vaccines cause autism or that vaccines as a whole do not benefit bulk resistance of the human population to diseases that can cause harm and death. 
  • Appearance of autism symptoms the same week or even the same day on which a vaccine is administered is not evidence that the vaccine caused the autism, because the fraction of unvaccinated children exhibiting autism symptoms at the same age is not statistically different. In those cases in which autism symptoms express a few days before a vaccine administered, do we claim the opposite, that the autism caused the vaccine administration? Such a claim would of course be preposterous. More recent studies show that although major outward expression of autism symptoms ramps up near preferred times of administration of the Measles, Mumps, and Rubella vaccine, they occur in equal rates in children who do not receive the vaccine and at a similar stage in life. These points have been reviewed by scientists outside of the corporate pharmaceutical industry.
  • Experts have recently demonstrated that it is possible to diagnose autism much earlier in life, perhaps even in utero, using more specialized testing, suggesting that vaccines administered later than that time could have no impact on the statistics of autism. 
  • Many anti-vaccine activists argued that the preservative thimerosal is responsible for autism, yet, autism rates seem to be the same between those treated with vaccines with or without this additive, and with those not vaccinated at all. 
  • Furthermore, some recent research suggests that possibly all of the apparent increase in autism rates over the last two decades might result from increased rates of detection: https://www.ted.com/talks/steve_silberman_the_forgotten_history_of_autism?language=en In other words, further evidence and change in our views of that evidence over time has altered the list of symptoms that we think are consistent with the autism diagnosis, so that more people with symptoms previously not categorized as autistic now get categorized that way. So, it is possible that there is nothing abnormal about recent decades in actual autism rates: They may have always been high, but decades ago, our metrics for diagnosis were too strict, leading to many people who would be considered autistic today not being labeled that way in the past. This point makes an excellent illustration of the self-correcting nature of scientific thinking. It is not that science cannot be wrong. Instead, we extend trust to scientific thinking in general because it is self-correcting, ultimately improving on itself to yield better explanations as our understanding of the evidence improves, and we go where the evidence leads us.
  • Death rates associated with some diseases, like polio, did begin to decline prior to broad administration of the relevant vaccines. However, spreading rates of polio did not decline markedly until after the vaccine. Much of the reduction of polio death rates before vaccine use became widespread resulted from the development of the iron lung. Thus people who would have been killed by the disease previous to that invention got to continue living, but they lived lives trapped in the breathing device, crippled by their debilitating illness. I’m sure most victims of this dread disease who lived out their (usually short) lives of confinement would rather have received the vaccine and avoided their predicament. The historical record includes numerous similar examples for diseases like measles, smallpox, and others. 

Concluding Comments

If you disagree with these points, I welcome your comments and feedback, and we can exchange peer reviewed references as part of the discussion, as needed. As a scientist, my intent is to understand the workings of the natural world and how we interact with it. Optimum education is a marketplace of ideas, in which open discussion of the evidence for and against propositions is needed. No benefits come from insulting those who hold different points of view, but people should not feel insulted when other people question their views.

Sunday, November 29, 2015

Introduction to Differential Calculus for Algebra Students

My earlier blog about math education generated some offline discussion. In it, I suggested that students who are stuck on fundamental concepts should not continue forward until they understand those concepts. I also suggested that students could study principles of calculus while studying algebra. These two points seemed to some readers to generate a contradiction. I disagree. All that is required to study an advanced math topic is the set of specific fundamentals foundational to that topic. Beyond that, the traditional schedule followed in K-12 curriculum is arbitrary. An algebra student who understands how to plot a polynomial and how to find the slope of a line is prepared for differential calculus in its most fundamental form. Thus, for example, geometry and trigonometry are not fundamental to basic calculus. On the other hand, a student who does not understand the concept of slope should master that concept before attempting basic calculus.

As an illustration of how an algebra student could learn basic calculus, I include a slide show (below). Students working through the example should not simply read the slides, but should reproduce the ideas on paper and work out the algebra for themselves. Upon completion, they should understand how to find the slope of a line tangent to a continuous function, which represents the derivative of that function at that point.

Note the missing signs on slide 19: Students should take advantage of this error by filling them in themselves, then checking their result against the next slide.

Thursday, November 26, 2015

Science and the Culture of Education

I love the approach of science to learning. As a professor with a research focus in weather and climate science, my objective is to better understand aspects of the natural world. Science is a way of interrogating that world through observation, developing models of what we observe, and testing them against observations and other knowledge. This testing is necessary because we cannot simply accept our hypothetical models as fact. Fundamental to the whole scientific process is skepticism about our explanations. Successful scientists doubt their own explanations and those proposed by other scientists. Every idea is open to being discredited and discarded, even those with deep consensus, and confidence in an idea depends on the evidence presented in favor and the lack of verifiable evidence against.

In the end, the “truth” of a scientific notion or model depends not on how many scientists accept it, but on whether observed facts remain consistent with its predictions. The more evidence that piles up over years or even centuries of testing and experience raises confidence in an explanation or ultimately discredits it. Some models have been so thoroughly tested without refutation that confidence levels of most experts exceed 99%. Some aspects of quantum mechanics, the germ theory of disease, the general theory of evolution of living organisms by natural selection, and even the safety and efficacy of some algorithms of genetic modification of food crops have reached that level of confidence in the scientific enterprise, even if some political or religious movements resist or ignore the evidence. At its most fundamental level, the theory of climate change, including global warming in response to burning of fossil fuels is at a similarly high level of confidence. It is a fact, tested repeatedly in the laboratory, that CO2 absorbs infrared radiation and re emits it. In the atmosphere, it is demonstrably true that CO2 reduces the rate at which the atmosphere emits radiation into space, thereby increasing the heat retained at the surface of the earth. The direct effects of changes in CO2 concentration due to human activities is fairly small, but several known feedbacks amplify or reduce the resulting warming. Some gaps in our understanding of the size of these competing feedbacks remain. Thus the details of climate change induced by human activities, including how warm the planet will ultimately get given doubling of CO2, are not as firmly grounded as our simple knowledge that increases in CO2 concentration would raise the average temperature of the surface of the earth. In that context, the most appropriate public policy decisions with respect to climate change should be informed by our understanding of risks and the likelihoods of negative and positive outcomes, even though we are not absolutely certain at what level the altered climate will ultimately verify.

Although scientists do exist in a culture that motivates asking certain questions over others, the conclusions of science are not forced upon scientists in advance by some authority or by pre conceived notion. Instead, scientists are free to engage the data, the models of other scientists, and their own ideas, and they are free to present their ideas. Healthy scientific culture welcomes new ideas. In general, no formally submitted scientific proposition is shouted down or mocked, but new ideas or claims are brutally scrutinized through peer review. Those ideas that survive the test of time become broadly accepted.

Several aspects of the general processes of science seem natural to our youngest children. Young children are always asking questions. They observe nature and poke and prod at it, developing explanations for what they see, and they test those explanations. Of course they do not always come to conclusions that are consistent with prevailing scientific views, but most children genuinely want to understand nature. Although a small fraction of children maintain that healthy curiosity into adulthood, many of them lose it while very young, as adults squash their curiosity by suppressing their questions. They also lose interest as they begin to see science and math from the perspective enforced in public school. Many great teachers and teaching algorithms inspire interest in scientific thinking, but the system as a whole destroys that thinking, reducing it to sets of facts, rote exercises with clear pathways to a single right answer, and bubbles on standardized tests. The curriculum has become so standardized that the next steps and the next questions are almost entirely specified by the system. Thus students rarely maintain the vision of how to craft questions themselves and how to follow the evidence where it leads. The curriculum quells curiosity and excitement as a heavy wet blanket kills fire, and I am convinced that loss of these motivations for deep learning is one of the biggest tragedies of the modern world. Many heroes in education are working from within to improve the effectiveness of science curriculum, and I admire their efforts. 

I love and respect my students at the university, and nothing thrills me more than to see them ultimately buck the shackles of the system by taking back responsibility for their own learning. I teach applied mathematics, statistics, and computer programming as tools to better understand natural systems. I find that my greatest challenge is to help students learn to craft questions and algorithms to solve broadly stated problems. The education system has trained students to constantly ask authorities what they should do next. Students want the exercises set up for them. In my view, this represents the greatest failure of public education. It emerges because students are almost constantly directed by autocracy in the classroom that tells them when to do something, how to do it, and what to conclude from it.  

The real world, in contrast, requires that they learn how to pose questions, and then work out pathways to answering them when there is both too little and too much information available. They need to learn to make appropriate assumptions and how to test those assumptions. This type of learning cannot be reduced to a blank space on a worksheet or a bubble on a test form.

My own children are not perfect students, but they are curious contemplators. They left the public school system for home education years ago, and I don't recall them ever asking to go back. They spend hours each day playing, reading, computer programming, drawing, craft making, and in other pursuits. They are largely self-directed. My wife and I provide them with the topical expectations of the state, and we help them generate learning plans. We expose them to people and ideas that they might not necessarily have discovered by themselves, but only rarely do we impose our wills firmly on them. They connect with other children and adults at the park and at Yacon Village, a community-learning center in the Albany New York area. They occasionally participate in classes taught by other students and adults in the community. As one might expect, they end up behind their peers in public school in some areas and well ahead of them in others. 

We do support limited testing and assessment, by offering our children one standardized test each year. We use that test as a tool to help guide their future learning activities. Curriculum dominated by testing does not yield vibrant curiosity-driven learning. When student motivations for learning are internal, their outcomes nearly always exceed expectations. They wake up excited about what the new day will bring. They thrive on a healthy level of autonomy. Students around the world cry out for such autonomy. Let's help them achieve it.  

You may contact the author at proundy at Albany dot edu

The opinions presented here are those of the author alone and do not necessarily reflect the perspectives of my employer or the State of New York.

Tuesday, November 24, 2015

The Daily Agenda of Typical Advanced Academic Track Teens

On the average school day, the typical middle-class public-schooled teenager on an advanced academic track spends

  •          6-7 hours in school
  •          1 hour waiting for and riding the school bus
  •          3 hours on homework

Many students also participate in 1-2 hours of structured extracurricular activities. Most of them probably spend 1-2 hours preparing to go to school in the morning and eating breakfast and dinner. At the end of it all, most of them would benefit from more than 8 hours of sleep.

That leaves roughly 1-4 waking hours for their other pursuits, except that their drive for such pursuits naturally leads many of them to swipe sleep time. Most students spend their personal time networking with friends, playing online games, or participating in other entertainment.

This schedule model denies many academically motivated students what they really need most to become creative critical thinkers: Time to contemplate, to play with math, to investigate science, and to practice in the arts. Given that time for personal study, for unstructured play, for structured cooperative activities like sports, and for hobbies is so important to personal development, what can students trim to gain their best advantage possible?

My proposed solution might seem radical, but it is becoming natural for increasing numbers of students: Cut out school and the school bus!  Replace that time with educational and personal pursuits driven by the student’s actual needs, crafted by the students themselves and their parents. Academically motivated students nearly always learn better driving their own educations than following the script of public school curriculum, because they are not arbitrarily confined to continue work on topics they already understand, and they can move forward at their own paces, not slowed down by the system’s schedule. The system conditions students to think that they cannot learn certain topics without a trained teacher, but this is simply not true, especially in today’s world with so much information and free educational resources right at our fingertips.

The school culture also has deceived many students that healthy social development depends on public school, but opportunities to build social skills can be much better outside in the community than inside a school—It just takes open eyes and some determination and planning.

For those who cannot ditch the school for home education or cooperative groups, work within the system to increase the amount of time for student-driven activities at school, and for greater focus on the individual.

You may contact the author at proundy at Albany dot edu

The opinions presented here are those of the author alone and do not necessarily reflect the perspectives of my employer or the State of New York.