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    Radical Math And The Green Curriculum: Bad Ideas
    By Enrico Uva | June 30th 2012 05:00 AM | 36 comments | Print | E-mail | Track Comments
    About Enrico

    I majored in chemistry, worked briefly in the food industry and at Fisheries and Oceans. I then obtained a degree in education. Since then I have...

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    Teachers have a captive audience. It's bad enough, but somewhat forgivable, that through our shortcomings or oversimplifications, we occasionally create misconceptions regarding electronic energy levels or evolution's mechanisms. But the inoculation of curriculum with political agendas should be unacceptable in the classroom, even if the ideology seems to be on the side of the angels.  

    At a well-organized STEM symposium I attended a few days ago, a young teacher blemished his quality-presentation by recommending radicalmath.org, a "resource for educators interested in integrating issues of social and economic justice into their curriculum." They propose that rather than merely computing the population density of dandelions or the probability of encountering a red light at an intersection, we should be presenting our kids with problems like:
    1) Calculate the liquor store and fast food restaurant density. Look at how many liquor stores/fast food stores are in your neighborhood and compare them to the number of schools in the area.
    2) Explore the probability that a trafficstop should be (and is) of a person of color.
    3) If Walmart factory children workers make 30 dollars per week, what is their average wage per hour?
    (I should point out that the third problem is not necessarily from their web site, but from one workshop at the symposium.) In 2007, four hundred teachers attended a radical math conference in New York City. Another one took place this year(2012) in San Francisco and there's one coming up in January 2013. These educators seem to believe that teaching in a conventional way is too dull and that they have an antidote for what our children otherwise learn in an unfair society.

    In a similar vein, a great deal of environmental issues have found their way into all subjects. In these realms, it's difficult to dissociate the science from subjective policies, and at times the environmental science presented in high schools is riddled with factual errors.  In recent years I've seen students being fed a minestrone of nonsense including:

    (1) a French-as-a-second language article that confused the ozone hole with climate change.

    (2) a made-for-teachers booklet from the right-wing Fraser Institute, which argued that CO2 cannot possibly present a problem to humanity because its concentration in the atmosphere is below 1%.
     
    An environmental club has its place in a school. So does teaching the greenhouse effect at the appropriate level. But to force-feed uncritical minds a mixture of science and politics at the expense of the basics is not pedagogically sound. What is  fashionable in schools is to get students to fast- forward through the science, read a couple of superficial newspaper articles and have them write an essay about an environmental topic.

    Students and people in general don't suddenly and magically have worthwhile discussions about complex issues. To expect students to take a stand on topics whose surface they've barely scratched is to encourage intellectual dishonesty.

    Even when we stick to the science, students have a hard time grasping ecology without a good grounding in biology and chemistry. Pedagogues argue that exposing students to relevant, environmental issues makes it more likely for them to get turned on to science. What could happen instead is that young people might get overwhelmed and eventually desensitized to important environmental problems.













    Comments

    rholley
    Spot-on!

    Robert H. Olley / Quondam Physics Department / University of Reading / England
    vongehr
    If you beat your four women on average two times a week in total, leaving a black eye once every ten beatings, what is the proba ...

    ... well, lets be serious. I personally hated any such questions that tried to feed me Western Judeo-Christian double-morals by sneaking them through the backdoor (already as a kid when I did not even know that Judeo-Christian is - an accute sense for hypocrisy was there). Surely, I am not totally alone. So, "radical-math" alienates kids, making them hate math homework. Not a good idea.

    On the other hand, lets be honest: We have this kind of teaching all over the place already, as you wrote, for example via text selection in language training. We do not need radical-math but to be more aware about indoctrination in the other classes.
    UvaE
    On the other hand, lets be honest: We have this kind of teaching all over the place already, as you wrote, for example via text selection in language training. We do not need radical-math but to be more aware about indoctrination in the other classes. 
    Definitely. This type of teaching is easier to avoid in creating questions and exercises, but it also   happens occasionally when we're talking to students and going off on tangents, especially if we're tired, and the filters become less efficient. 
    I'm against trying to inject politics into mathematics, especially as it poses two huge problems. One, we are not spending enough time on the hard sciences as it is - most people have a very limited ability to do math (most adults can't even calculate a tip in their heads) and this is due in part to the lack of emphasis placed on it as we have increased the amount of time we spend on less important subjects, like "social studies" (fairness is important to a point, but people with degrees in "Gender Studies" don't invent biofuels or solar cells that will help mitigate global warming or grow GDP per capita). Second, teachers are almost always biased against students who challenge their political views (I encountered this repeatedly in college), and this just invites that bias into new subjects, leaving less room for dissenters to escape intellectual persecution in the soft dictatorship of academia.

    On top of that, teachers would often find that their students, at least the bright ones, reached conclusions they did not like. I can trace my philosophical shift from liberal towards libertarian to a confluence of courses in college. I was studying econometrics and advanced statistics at the same time as I was studying sociology, and decided to combine the three to prove something in my sociology class. I set out to prove a point we'd often discussed as a fact in our sociology class, namely that the death penalty is unfairly utilized to execute minorities. In a class of 28 students and a professor with a Ph.D. no one had challenged this basic assumption, and I wanted to calculate just how biased the death penalty was. Setting out to prove statistically the racism in the system (which I certainly expected to find), I ultimately found that minorities were less likely to be executed. After discussion with the professor we assumed that this was due to the prevalence of intra-racial violence (most black victims are killed by black murderers, and whites by white murderers). Again, I went back to the stats, and found that even this did not account for the disparity. The numbers, if anything, showed a system more prone to executing white perpetrators. As a scientific study, I had to accept that I'd disproven my hypothesis.

    My professor was reasonably open minded and I still got an A in that course (though she asked me not to discuss that finding in class, as she thought it might be confusing for other students), but it led to a dramatic shift in my view of the world. I'd previously considered being "open-minded" to mean "liberal", but suddenly was compelled to test even my liberal assumptions on the grounds that some of them were, perhaps, not very open-minded at all. This led me to question things I hadn't previously. It also led to uncomfortable conversations and the alienation from some of my more liberal friends (people generally dislike facts that contradict their worldview). To this day I question anything presented as a "fact" that isn't scientifically verifiable or methodologically sound (liberal, conservative, or otherwise), and I suspect teachers setting out to turn their little math students into little Marxists might find that things don't always turn out as they intend.

    UvaE
    Second, teachers are almost always biased against students who challenge their political views (I encountered this repeatedly in college), and this just invites that bias into new subjects, leaving less room for dissenters to escape intellectual persecution in the soft dictatorship of academia. 
    Just about every subject is more interesting than politics. So if teachers can be mainly preoccupied with effectively communicating the basics of their subject areas, they would not be threatened but happy to be challenged politically. 


    Teachers are not messiahs. We have to be sensitive human beings , but let's not get carried away!








    rholley
    If you beat your four women ...
    Makes me think of this ...




        source: bikyamasr.com
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    "... I personally hated any such questions that tried to feed me Western Judeo-Christian double-morals by sneaking them through the backdoor..."
    ---------------------

    It's part of the nature of culture. Every society has -- and reinforcess -- its own culture, that is, its knowledges, beliefs, language, values, art, law, morals, customs, etc. Societies do this through their institutions: government, churches, schools, markets, charities, etc.

    When a society "reinforces" its culture, it's called indoctrination. Societies do this for survival; without a shared culture, its members have nothing in common and the society falls apart. (Cultural Anthropology 101.)

    Judeo-Christian culture (AKA "Western European" culture) has been the foundation of American society since the birth of our country. Judeo-Christian values didn't sneak in through the back door. Hopefully, they're in your face everywhere you turn. Don't murder, don't steal, tell the truth, etc.

    This culture has evolved over 5,000 years. By contrast, atheist, communitarian (AKA "progressive") cultures have been around for about 100+ years and their track record isn't yet established. (Some would say their track record is established, and it's a failure.)

    So American schools reinforce Judeo-Christian values. What ELSE would you expect? Iconoclasm is not their mission. This is the United States, not the old Soviet Union.

    Individuals (such as yourself) are free to be iconoclasts. But you shouldn't expect our institutions to be. Institutions don't serve the individual. They serve the greater society -- by reinforcing a set of shared American values.

    rholley
    A bit of G.K.Chesterton is apposite here:
    But that marks their mood about the whole religious tradition: they are in a state of reaction against it. It is well with the boy when he lives on his father's land; and well with him again when he is far enough from it to look back on it and see it as a whole. But these people have got into an intermediate state, have fallen into an intervening valley from which they can see neither the heights beyond them nor the heights behind. They cannot get out of the penumbra of Christian controversy. They cannot be Christians and they can not leave off being Anti-Christians. Their whole atmosphere is the atmosphere of a reaction: sulks, perversity, petty criticism. They still live in the shadow of the faith and have lost the light of the faith.
    (The Everlasting Man: Introduction)
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    vongehr
    Judeo-Christian culture (AKA "Western European" culture) has been the foundation of American society ... Don't murder, don't steal, tell the truth, etc.
    You seem to be a good example for JC double moral - defending US american culture as being based on don't murder and don't steal while the whole is stabilized (and constructed in the first place) on daily killing and stealing all over the world (including internaly), and most importantly: distorting the truth.
    This is the United States, not the old Soviet Union.
    This, my dear, is the internet, and it is mostly Chinese by now, so you can sit at home and wallow in self pitty about the decline of your holy US all day long, but it won't change reality. History does not stop, and you guys are finished. From now on it is going to be Judeo-Christian double moral as copied by Asians who like to add a touch of "I don't even myself believe what I am saying, so what", which at least saves the bother of self-deception that Westerners waste so much resources on.
    rholley
    Sascha’s reply does raise a very salient point.  From further on in the same document:
    I do not raise in this connection the special controversy about Spain and Mexico; but I may remark in passing that it resembles exactly the question that must in some sense be raised afterwards about Rome and Carthage. In both cases there has been a queer habit among the English of always siding against the Europeans, and representing the rival civilisation, in Swinburne's phrase, as sinless ... But it is absurd to pretend that they fell lower than the other races and religions that professed the very opposite standards and ideals. There is a very real sense in which the Christian is worse than the heathen, the Spaniard worse than the Red Indian, or even the Roman potentially worse than the Carthaginian. But there is only one sense in which he is worse; and that is not in being positively worse. The Christian is only worse because it is his business to be better.
    Now somewhat against this I could quote Shakespeare:

    Lilies that fester, smell far worse than weeds.  (Sonnet 94)

    I cannot judge this matter myself, partly because I don’t have sufficient historical knowledge, but more because I cannot answer the question “what if?”  However, just to put the question in the form of an example, from the Third Crusade:

    Salah-ed-Din had to refrain from his intention to enslave all non-Moslem women and children in a city for fear of Richard the Lionheart.  However, Richard murdered 2700 hostages from the garrison of Acre, against the agreement, in order to put pressure on Salah-ed-Din in negotiations.

    Which was worse?


    Robert H. Olley / Quondam Physics Department / University of Reading / England
    No wonder American students are incapable of critical thinking. We rarely challenge them to do so. Mr. Uva underestimates the capacity of young people to accept or reject influences.

    UvaE
    Mr. Uva underestimates the capacity of young people to accept or reject influences.
    Their capacity is on a wide spectrum, and ditto for adults, but generally no one is immune from propaganda.  Jacques Ellul once pointed out that intellectuals are especially prone to it because they read so much, and due to a lack of time, do not dig deeply enough into the sources.

    Critical thinking does not have to involve politics in the classroom. Trying to design a controlled experiment involves critical thinking; so is looking for an error in a mathematical proof.
    "Critical thinking does not have to involve politics in the classroom. Trying to design a controlled experiment involves critical thinking; so is looking for an error in a mathematical proof. "

    You nailed it, imagine Tony Plato's outrage if the math lesson included a study of the stimulus' effect on unemployment. As long as your ideology is forwarded, let the kids soak it up.

    And I have seen fundamental logarithmic errors in state-approved textbooks. Should I not teach from the books? Shoot myself? Shoot the children?

    Like it or not, teachers should be well prepared specialists who know their stuff, know their kids, and have the discretion to match material to learners. That one chooses to incorporate a data set that involves issues of race and poverty into a lesson on anything from statistics to numeracy, to spreadsheet analysis does not imply that teacher has suddenly become a South American Catholic priest espousing the cause of social justice.

    Rather, it means that teacher has chosen to incorporate examples from a world his or her students might recognize. When that happens, students begin to see relevance and, in some, the spark of intellectual curiosity begins to flicker.

    The meaningfulness of the data is something a wise teacher leaves for the student to determine.

    Our problem is not too many liberal or conservative facts. It is that students are taught -- by parents, TV commentators, preachers -- that facts are either liberal or conservative.

    Our other problem is that we have far too many people who find it necessary to "control" what educators think, say and do; and far too few interested in supporting educators who attempt to teach children to think.

    Gerhard Adam
    Like it or not, teachers should be well prepared specialists who know their stuff, know their kids, and have the discretion to match material to learners.
    Sorry ... I nearly choked on my coffee when I read that line.  While there are undoubtedly exceptional teachers, let's not get too carried away with the nobility of the profession.  When a PhysEd teacher can become an algebra teacher by seniority alone, then such statements are fundamentally meaningless.
    Our problem is not too many liberal or conservative facts.  It is that students are taught -- by parents, TV commentators, preachers -- that facts are either liberal or conservative.
    No, our problem is that we think that "facts" are whatever we interpret them to be.  While "facts" may be objective, in a trivial sense.  As soon as you try to apply "facts" to a problem, you are framing the question.  "Facts", in isolation, aren't very interesting.
    Our other problem is that we have far too many people who find it necessary to "control" what educators think, say and do; and far too few interested in supporting educators who attempt to teach children to think.
    I personally think we spend too much time worrying about educational specifics, while failing to provide a solid foundation.  I hear all this concern about interests in science and mathematics, but I have to ask ... is there some shortage of scientists and mathematicians that I'm unaware of?  Some unfilled job openings that are going unanswered?

    While I don't have any specific data, I would argue that the average adult, probably operates at the 6-8 grade level at reading and the 4th grade level of arithmetic [judging by their abilities with fractions].  This suggests that other than people that are motivated for higher education [most of which they'll acquire on their own], we're wasting an awful lot of time.
    Mundus vult decipi
    I really enjoyed this article. Whenever I challenge a theory from left or right point of view, global warming being an example, I'm often met with an assumption I'm on the other side. I always indicate there are reasonable points and ares of further investigation to be done on either side and people seem to care less along the lines of "well, he doesn't get it, but at least he isnt' a complete idiot" with some pat on the head comment. Be skeptical, be open minded. Thanks for the article, excuse the grammar (posted from my phone).

    I would agree with Bill as to the relevance and value of real world mathematical problems. If I look at my own education in mathematics I found the most engaging aspects of it to be those times in which real world examples were provided. While I understood the importance of the neutral word problems presented I failed to see their value (at the time) to real world applications. This resulted in certain level of indifference and apathy on my behalf.

    I took a course in graduate school called spatial econometrics which was/is a relatively new field of study for economists. All aspects of the class focused on the positive correlations between certain characteristics within a community and the variable in focus. i.e. what effect does certain levels of community diversity have on property values, what effect does an empty lot or degraded sidewalk have on neighboring properties? What was important to me was not the political aspects of it all but whether or not further study was warranted on that particular subject and more importantly, critical thinking.

    I think the same can hold true for higher level elementary, middle, and high school students. A teacher should have the ability to provide political based math problems if they believe it will arouse the interest of students. More importantly, I believe it brings a higher level of thinking to the student. If the student finds a positive correlation between low-income neighborhoods and fast food restaurants; then they should be asking what does it mean? Is it correlation without causation, or something else? It is time to get creative with classroom curriculum rather than focus on the old ways of doing things (not that they don’t work). Change is constant and its important that the teacher has the ability to adapt standard curriculum to the students interests and demographics.

    Gerhard Adam
    I think the same can hold true for higher level elementary, middle, and high school students. A teacher should have the ability to provide political based math problems if they believe it will arouse the interest of students. More importantly, I believe it brings a higher level of thinking to the student.
    Perhaps if you're talking about a few students.  If you're talking about a classroom, then you're mistaken.  That seems to be the sticking point with most of these comments.  They are certainly applicable to a motivated student, but does anyone really believe it's going to matter to the majority?
    Mundus vult decipi
    "But to force-feed uncritical minds a mixture of science and politics at the expense of the basics is not pedagogically sound."

    I think a lot of High School students would seriously resent being referred to as "uncritical minds."

    Gerhard Adam
    I think a lot of High School students would seriously resent being referred to as "uncritical minds."
    They might, if most of them knew what it meant.
    Mundus vult decipi
    UvaE
    I think a lot of High School students would seriously resent being referred to as "uncritical minds." 
    It was not meant as an insult. It's just that most are in the process of acquiring a foundation. Without one, most can't expose too many flaws or biases in an argument or set of questions.  
    My opinion of teachers has plummeted dramatically in recent years. I, and a growing number of others, place the blame squarely on politically tinged (almost always left wing) methods such as what is described here. This brings up another question....how intelligent are the teachers teaching this if they do not realize they are slowly undermining the credibility they rely on? I say not very. Just look at how quickly the publics faith in journalism has collapsed with the introduction of blatantly partisan news outlets. At one time, being a journalist was considered, like teaching, to be a noble profession. Now, journalists routinely fine themselves feeding at the bottom of the public respect charts...alongside lawyers and politicians.

    Politics has infected and destroyed the legitimacy of many previously respected institutions. If we allow it to happen to education...and it's definately happening, then none of us are as intelligent..or more importantly, wise, as we like to think we are.

    Gerhard Adam
    ...(almost always left wing)...
    You couldn't resist.  That will really help remove partisan issues from education.
    Mundus vult decipi
    UvaE
     I, and a growing number of others, place the blame squarely on politically tinged (almost always left wing) methods such as what is described here.  
    The Fraser Institute in Canada is very right wing. So both camps are guilty. 

    Hank
    He may have a point - the examples cited certainly look suspiciously social engineering-y and that tends to be left wing people. Finding one right wing group is false balance.  In America almost 80% of teachers are left wing though it may be that Canada is more right wing than America, obviously.
    UvaE
     In America almost 80% of teachers are left wing though it may be that Canada is more right wing than America, obviously. 
    Do you have a source for that number, Hank?  I'm wondering whether it's a case of the active union leaders and representatives being more left wing than the members at large.  
    In Canada, what I can point out is that in the current student strike among college students the majority of anglophone professors and anglophone students are in favor of tuition hikes with the latter voting against the strike. But francophone teachers who tend to be more left-wing, especially if they are social studies teachers, were supporting the students.

     
    Hank
    The 2003 National Education Study found 25% of teachers were Republicans.  Now, we can choose to believe that every Independent was secretly voting Republican, even though 95% of  teacher union donations go to Democratic candidates - but then we have to believe that no teachers speaks up about how they are being made to look overtly partisan and are not.
    First, we should admit that there already are strong political agendas in the curriculum. History in most European countries is little more than a way to build common identity through creatively reinterpreting facts from the past. I imagine it's the same in the US, though it might be less apparent when your enemies haven't survived to tell their tales.

    The point is that these agendas aren't "controversial". They don't hurt anyone's immediate interests. Not anyone with a power to do something about it anyway. It does hurt the guy who believes it and ends up dying for "his" country.

    In general, leaving politics out of the classroom is preferable. But that itself becomes a political fight. People will fight against "political propaganda" that they disagree with harder than propaganda they agree with. And since the precedence of having some propaganda in the classroom is already firmly established it's going to be hard to stick to a no politics stance.

    Applying critical thinking skills to controversial issues? Why is that such a terrible thing? We need...NEED people to be able to argue their points using rational methodology, like mathematics, rather than the dogma that is usually reserved for such subjects. The "danger" of this approach is not that we'll somehow contaminate mathematics with political ideas...but that we will inject rationality into politics. And for people who hold certain views, reason is a terrifying prospect!

    Gerhard Adam
    The "danger" of this approach is not that we'll somehow contaminate mathematics with political ideas...but that we will inject rationality into politics. And for people who hold certain views, reason is a terrifying prospect!
    Sorry, but ideas like this strike me as quaint and naive.  I really don't mean to be insulting, but do you really believe that the problem in politics is the lack of rational thinkers?  How about an electorate that responds in a knee-jerk fashion to every partisan talking-point fed to them by their favorite media outlets.

    The problem is that there is absolutely zero chance of an honest politician ever being elected, let alone one that wants to have a rational discussion with the electorate.  The problem isn't with politics or politicians.  The problem rests squarely with an electorate too stupid to demand accountability from the people they elect.  Instead, they stupidly elect the same individuals term after term, and then complain about how incompetent they are.  So, who's more incompetent.  The politician in Washington, or the fool that voted for him to put him in power [for typically more than one term]?

    Mundus vult decipi
    When I say "injecting rationality into politics" I don't mean teaching politicians to be mathematicians. That's not what this article is about. I mean...if we want better politicians, we need to teach the electorate to assess them rationally. So, I think we're pretty much on the same page, Gerhard.

    I teach intro statistics in a university business school to MBAs and undergrads. I use data from climate science for examples on summary statistcs, graphs, and regression. I use local rainfall and temperature but I also give them data for global surface temperature, CO2 concentration, and solar irradiance (1978-2011). I ask the to run regressions of CO2 on temperature, solar irradiance on temperature and temperature regressed on both CO2 and solar irradiance. I also have them regress Arctic sea ice as function of time (1979-2011) using a linear and quadratic fit. It seems to stimulate their thinking about statistics and climate change. Do you object to a statistician using actual climate data for examples in class, or is that too political?

    MikeCrow
    The problem with this Gary, is the period you've selected to look at, the late 70's was the recent temp minimum, so of course starting there temps have gone up.
    You should also wonder if insolation is the only effect on earths climate from the Sun.
    Never is a long time.
    Gerhard Adam
    Do you object to a statistician using actual climate data for examples in class, or is that too political?
    That would depend now, wouldn't it?  What conclusions are you drawing from the data?  Besides these measurements, how much time has been spent in educating stupid about climate and climate modeling and behavior?

    If these are MBA's and undergrads, I can already tell you that using the data you're using is "spin city" plus.  Whatever conclusion they draw will be tainted by the fact that they don't understand the underlying science.  Your presentation of the materials makes it appear as if the science is irrelevant.  A typically failing in most statistics courses.
    Mundus vult decipi
    So your perspective is that "stupid" undergrads and MBAs should be exposed to no actual climate data unless they spend months learning about the underlying science first. I disagree. The data on atmospheric CO2 concentration, global surface temperature and solar irradiance shows a strong relationship between CO2 and temp but no relationship between CO2 and solar irradiance. It does not prove anything. They are not espected to publish scholarly papers. Still, if people in business cannot look at this data for themselves and gain some understanding from it, then we are all in big trouble. I encourage them to look at the data and think for themselves, not to believe everything they read on the internet.

    Gerhard Adam
    Still, if people in business cannot look at this data for themselves and gain some understanding from it, then we are all in big trouble.
    Newflash.  We're already in big trouble because they are looking at data they don't understand.  That's precisely the problem.  It creates the illusion that something meaningful has been accomplished, but data without the depth of proper interpretation is simply the illusion of information.  It is meaningless.

    That's my point about statistics.  I see more statistical nonsense being published on a regular basis because people think that because Excel can produce a graph, that any particular correlation of numbers must be something valid or significant. 
    Mundus vult decipi