Why is math so hard?

Why is math so hard?   What can we do about it?  Answer - give up!

More precisely,  when the approach we're using keeps on not working,  instead of doing more of it, maybe we should rethink the whole approach and give up the way that keeps not working.

I had four years of math beyond calculus and tutored many students, so I feel qualified to present an opinion on the subject.

I love math and science.  I'm very pro math.

But, I'm also pro reality.  Reality is good, even when it's inconvenient.

Most people don't like math. That's also reality.

Why is that?

I think the main reason math is so hard is that you can't get by being "mostly correct" - you have to be entirely correct.

An English paper with a grammatical error can still be excellent.  A math equation with an error is completely wrong.

Surprisingly,  if you are compulsively neat and organized,  math itself is easy, and, I love it because problems have correct answers that don't depend on what the teacher thinks.    On the other hand, I can't stand problems like "What did Hemmingway really mean by the image of the fish?" because the answer depends on the instructor.

The reason math is difficult is that most students today have no experience being the type of compulsively neat detail-obsessive workers that it demands in order to work at all.   Unless you get 100% of an solution's steps correct, the answer isn't "mostly right", it's totally wrong.

It is as if we are trying to lay precise rail-road tracks across a thinly-encrusted swamp of sloppy behavior, and, frankly,  that simply does not work, and cannot be made to work.

So, the implications of that strong assertion are enormous.  So everyone is playing "Let's pretend."

Either we bite the bullet and figure out what it takes to accomplish "self-discipline", or we should abandon all pretense that we can "teach math and science" without it.  It cannot be made to work.

There is no point trying to teach concepts to students who don't have sufficient self-control to keep a column of numbers straight on a page.   It may in fact be possible to teach the concepts, but it won't by itself result in them being able to ever "do" math or science in any socially useful sense.

If my analysis is correct, then to get STEM education to work,  we need to have wide-spread specialized remedial courses in structured work and self-discipline.   It's absurd to expect our math and science teachers to have to do that on top of teaching math and science. 

To not damage Johnny's weak self-esteem,  we keep telling him in school that 85% is "just fine" until he manages to get out in the job market, which is now international in scope,  and discovers that "85% good" doesn't even make it into the "C" pile of candidates, let alone the "A" pile, let alone land a job, let alone allow him to do the job.

In mathematics,  the passing score for any concept should be 100% - - the only exceptions being questions that were poorly designed. "Sort of knowing" something will not cut it.  Getting "most of the equation right" except for that one term there will not get most of the answer right.

This seems to come as a surprise to people, students and teachers alike.

But our concepts of discipline,  structure,  order,  routine, rigorousness are the weak spot with the approach we've been using of "national power through individual genius capacity and creativity."

OK.  Then let's be creative about this framing of the problem.   Let's stop pretending most students in K-12 today are ever going to be very good at STEM skills.    Period.  They are not.

Yes, in the long run, we should improve things, but in the short run,  don't bet on it working.

Working separately, as competing individuals,   we are very unlikely to win or even catch up and break even with the Chinese.

Isn't there ANY way to build a reliable system out of semi-reliable parts?

Yes, is the answer.   Creative redundancy.   There is a whole engineering discipline of making reliable "systems" out of unreliable and flaky components.

If we cannot make our individuals reliable,   that doesn't mean we are unable to make combinations of individuals reliable.   

If we're going  to go that direction, then the dollars, priorities, and emphasis in education needs to change from attempting to maximize individual skills and reliability to maximizing combined skills and reliability of small treams of people working on problems together.

And, just like SEAL teams in the military,  maybe these teams should persist across years, learn to work well with each other, and then go apply for jobs as a team, not as an individual, and stay together on the job.

On the job front, one way to handle the logistics would be to incorporate the team as, say, an LLC and have the LLC take a job slot as a "consultant."  That can be done with today's technology.

The problem is the educational system, oriented almost entirely around work-units of size 1, that is, "individuals."

I'll argue that it is obvious ("without proof" ) that two people, working together,  and cross-checking each other's work,  should be able to produce a math homework paper that has fewer errors on it than one person working alone.

Not only should that be "fair", it should be encouraged.

From the point of view of "business" or "commerce",    the only thing that is needed in a particular "slot" or "job" is some agent (person or company) who can take a problem and solve it in the time available. 

Already we see this in the concept "pair programming", where two people sit side by side at one computer, and together attempt to solve programming problems.    It turns out, if done correctly, this is something like 5 to 10 times more effective at generating workable programs than "dividing up the work" and having each person work in isolation on "their own piece of it."

So, here's the trade off.  To catch up to the Chinese in productivity in problem solving in math or science in the real world,  which has, in fact, no constraint of "do your own work separately",     we have two possible approaches:

• We could try to back-fill remedial high-quality self-discipline into our students and culture and also "learn math",  or
• We could try to remove the "do your own work separately" constraint and start tackling problems as pairs of somewhat-sloppy but cooperating individuals. 

Neither of these is trivial or a cake-walk, but, of the two, the second seems more likely to succeed than the first.  At a mimimum, since we're that kind of place, we should explore some of each, have some schools try to go for structure, and others go for true-pairwork.

Both of these require a cultural shift to support them.

At the current time discipline is not popular.   On the other hand "groupwork" is a dreaded four-letter work in academia as well, as in "Oh God, ... I just found out this course requires group-work. I wonder if it's too late to drop it!"

My point is, if we want to be sloppy about our personal work habits, and we appear to take that as a cultural norm,  and if we HAVE to be concerned about product reliability, which is demanded by the mission or a competitive marketplace,  then we have no choice that I have seen so far besides figuring out how cancel out that sloppiness by working together.

And,  we need to start trying to figure out how to treat a work-dyad as an acceptable filler for a "job" that currently is intended for a work-singlet. (a.k.a. employee.)

How do you pay a dyad? What about health care? Do both people always have to show up for work or can only one show up on a given day? Who cares?   If they both work "from home" does anyone even need to know it's a dyad not a singlet? If we gave the dyad a "name" and a "social security number" would that help?

That's where the problems rotate into with the dyad approach.  

Again, I didn't say it was easy -- I suggested it was easier than the alternative,  given where we're starting. 

The dyad needs a name, and a resume, just like a singlet-employee.    Presumably, the dyad needs a single paycheck.   Desk space is a problem unless the dyad works "at home."

While we're at it, let's say the dyad should be allowed to have permanent full-time access to the internet during any portion of training, education, examination, or activity during the actual job. That's realistic these days.

Here's a crucial point:  if we demand students perform amazingly well as individuals and graduate high-school and college as "singlets" before considering them for inclusion in a work team, there are two guaranteed results:

• People who would make great team members and totally boost team energy and morale, say, but are mediocre working alone will never get a chance, as they'll drop out early as "failures". 
• The people who do succeed as singlets are then supposed to do a u-turn and work as team members, which they just spent 12 or 16 years learning to avoid.

After 16 years of socializing people as fiercely competitive individuals, expecting them to make good team members is, frankly,  unrealistic.   It's as unrealistic as expecting tenured faculty members, after 7 more years of "doing their own work" in the tenure process,  to end up being "collegial."


So now the question is,  can  dyads of Americans,  with access to the world wide web, working just with each other and learning over time how to operate as a team,  trained as a team,  operating as a team,  outperform Chinese singlets working with what they learned and stuffed in their heads, without access to web?

My thought is,  yes.  

I guess, when you're coming from behind, "whatever works" is a good philosophy.  We have a lot of sports where doubling-up on your opponent is a winning strategy, don't we?

Besides .. it sure beats having to learn algebra for real.

A question that Science and Religion can come together around

As the war between sects of Islam heats up again, it becomes ever more important to find a common ground we can all move to while preserving our most crucial interests.

Sunni versus Shia,  Catholic versus Protestant,  Christian versus Muslim, Muslim versus Hindu,  it's pretty much the same old battle we've had for tens of centuries, but with frighteningly more and more advanced weaponry.

Then we have the battle heating up between all of the above and the institution of Science,  which may be losing ground far faster than it realizes.

This is not good, given that passions are high and willingness to destroy entire countries and cultures is already on the table.

So let me present an alternative.   A middle ground.   A place in which, as in the Harvard Negotiation Project's book  Getting to Yes, we can each protect our interests even if we have to relax our "positions" somewhat.

 If we take science's numbers and Drake's Law, to paraphrase Carl Sagan, there have been "billions and billions" of civilizations others than ours that not only made it to this point of technology, but did so before the Earth was even born.

Even if most of those self-destruct, at least ONE probably survived and has therefore been around for over 5 billion years. One is all it takes.

If we assume that (a) faster than light travel is possible and (b) they have the same tendency to put sensors everywhere as we do, then "they" have not only already been "here", but their sensors and probably their intervention agents are still here, busy at work around us.

For reasons of pure hubris, humans seem to want to avoid counting "1, 2, 3, ..." to get to infinity ("God"), but prefer to count "1, infinity" as if God is only one short step above mankind. That's unsupportable logic.

The far more scientific question, rather than investigating infinity with theologians, is to investigate the nature of "2", i.e., what's right here, all around us, that's higher than us but still way way lower than God?

You in the back row? No, "Congress" doesn't count as an answer.

The burden of proof, it seems to me, is on proving that we are NOT surrounded by a consciously managed framework, no more mysterious than our interventions to sustain the coral reefs.

In scientific terms, religion becomes mostly people sensing that framework and adding fanciful details.

A task on which both Science and Religion, as institutions, could and should agree on is figuring out what the shape and nature is of the real but non-mystical active and adaptive framework that surrounds us.

In fact, documenting such a framework might, in fact,  be a major step in defusing the perpetual and very destructive wars of different religions, or even different sects of different religions, over what are essentially minor cosmetic details compared to the massive framework we will find if we simply stop fighting,  develop and calibrate suitable tools for "looking" for such a framework, and take the time to look.

If nothing else,  good tools should prove their capacity by revealing a number of places where external, but very real, human agencies are messing with affairs we always suspected but couldn't prove.

* The image above is from Harvard's Kennedy School

Spiritual Solutions to Economic Problems - Baha'i Consultation

Spiritual Solutions to Economic Problems - through Baha'i consultation

( Picture from The Consultation Institute )

The Great Being saith: The heaven of divine wisdom is illumined with the two luminaries of consultation and compassion. Take ye counsel together in all matters, inasmuch as consultation is the lamp of guidance which leadeth the way, and is the bestower of understanding.
("Tablets of Bahá'u'lláh Revealed after the Kitáb-i-Aqdas" [rev. ed.], (Haifa: Bahá'í World  1982), p. 168)

All Baha'is are directed to use "consultation",  in matters great and small.  But what exactly is consultation?   Why does it work? 

Below I give my own understanding of these questions, along with some references to other sources of information about Baha'i Consultation.

Consultation is at the other end of the spectrum from the classic, legacy, Western concept of a business meeting, where each person comes with their own agenda and attempts to outmaneuver and outvote each other and their goal is to "win" the meeting and get their way on some issue.   In a typical meeting the boss runs the meeting and presents his idea first, then asks for comments and opinions.  Generally people know what's good for them and all agree.  Afterwards no one has any idea why they just spent an hour when the outcome was known before they went into the room.   Communication is very one-way, top-down.  The idea identified as the Boss's idea wins.   Opposition may be brutally hammered down, and hard feelings or resentment carried over for years after the "decision" is reached. For the most part disagreement is self-censored.  The objective is a "win", even if the "losers" are totally outraged and outmaneuvered by trickery or power.

On the other hand, Consultation involves people assembling hoping to discover what is right, not who is right.      A wide range of views and opinions is actively sought from each person in the room,  even the quiet ones, and listened to attentively and politely.   The behavior is civil if not exemplary.   One goal is that, regardless of the "outcome" of the matter under question, everyone will leave the meeting at least as good friends, and preferably stronger friends, than they were when they arrived.    Members who disagree with the views presented by others have an obligation to speak their piece as they see it.    The objective is a heartfelt unanimous realization of the right course of action, with everyone behind it.

What's interesting is that the literature of management has done a complete U-turn in the last 100 years,   from advocating very tight top-down management to advocating multidisciplinary groups given discretion to find their own pathway.

The reason for this change in industrial practices is that the problems have changed.  In 1900 it was common for the top management to be experts in everything they needed to know, and the workers simply had to follow instructions to produce good output.    As the century progressed, the competition increased dramatically,   the complexity of problems increased enormously,  the speed required for solutions shortened, and no single person could possibly know enough to solve the problem by himself.    

Companies that tried to continue the "old way" of top-down decision-making, like the auto makers General Motors and Ford,   just couldn't believe they were being outrun by participatory decision-making companies like Toyota and Honda. 

Auto companies were not unique however.   A large number of large-scale disasters of management or operation were traced back to the suppression of dissenting views or lack of diverse opinions, including such things as the Challenger Space Shuttle explosion,  Three-Mile Island meltdown,  and most airline "accidents" that resulted in loss of life.   Further investigation showed that similar problems were occurring in Hospitals, where suppression of dissenting opinions was resulting in patient harm,  amputation of the wrong arm or leg, etc. where someone knew the situation was going wrong, but was unwilling to speak up.

Current best thinking in the field is in a book titled Teaming by Amy Edmondson,  a faculty member at Harvard Business School, who discusses the key concept of "psychological safety" required for a dissenter, especially of lower rank, to speak up when they see a problem.  It turns out it is not enough to get the right people with a diverse set of knowledge and viewpoints into the room, they must feel safe from retaliation if they share their opinion.

All of which brings us back to Baha'i Consultation,  which predates the current management wisdom by 150 years and gives clear instructions as to what is required.

 The prime requisites for them that take counsel together are purity of motive, radiance of spirit, detachment from all else save God, attraction to His Divine Fragrances, humility and lowliness amongst His loved ones, patience and long-suffering in difficulties and servitude to His exalted Threshold. Should they be graciously aided to acquire these attributes, victory from the unseen Kingdom of Bahá shall be vouchsafed to them.... The members thereof must take counsel together in such wise that no occasion for ill-feeling or discord may arise. This can be attained when every member expresseth with absolute freedom his own opinion and setteth forth his argument. Should any one oppose, he must on no account feel hurt for not until matters are fully discussed can the right way be revealed. The shining spark of truth cometh forth only after the clash of differing opinions. If after discussion, a decision be carried unanimously, well and good; but if the Lord forbid, differences of opinion should arise, a majority of voices must prevail.

(`Abdu'l-Bahá, cited in a letter dated 5 March 1922 written by Shoghi Effendi to the Bahá'ís of the United States and Canada, published in "Bahá'í Administration: Selected Messages 1922-1932", p. 21-22)

So we here get the message that "intention matters."    Rather than suppressing human emotion and the role of the heart,  as in a legacy "business meeting" that should be purely rational,   consultation should include the full emotional and spiritual human capacity in a search for a pathway that looks right, feels right, and is right.

Trustworthiness,  scrupulous honesty,   and loving civility are virtues that are not just nice to have,  they are absolutely required for consultation to work successfully.     Even the famous "Toyota Way" is very clear that at the core is a a change of heart, not a change of tools.

There is a spiritual dimension as well to a perfect consultation.   While the persons consulting are present, they also need to be, effectively,  polished mirrors or hollow reeds,  reflecting the love of God into and among the persons present, to illuminate the dark corners and allow a solution to emerge.    The solution discovered is as likely to be along a totally unexpected dimension that allows a win-win-win to occur between "sides",  revealing the pathway to "unity above diversity" which more "dissolves" the problem than "solving" it.    The solution comes through the firebox of the hearts reflecting love, and not through some sort of mental or fully-rational process of mathematically ranking options or other such computations.

As Daniel Goleman's books Emotional Intelligence, and more recent Social Intelligence have documented scientifically,  humans are not really poorly functioning rational engines, but highly tuned beings hard-wired to operate in emotional synchrony with tremendous shared insight.
If there is no shared love,  there will be no solution revealed.

If there is shared love, love of God and love for each other in a shared destiny on this one planet we all inhabit,   then true miracles can be revealed through the most unlikely members,  and we can move towards the Most Great Peace.

A  summary of quotations from the Baha'i Sacred Writings can be found here:
http://bahai-library.com/compilation_consultation  and a brief informal video introduction to consultation for those who prefer video is here:
http://www.youtube.com/watch?v=8VH-4qHd3OQ . 

A classic Baha'i book is John Kolstoe's Consultation: A Universal Lamp of Guidance.

A Baha'i inspired book of techniques for handling logistics of meetings is Trip Barthel's Transforming Conflict into Concensus - 9 keys to Synergy.

Although the emotional and spiritual qualities are required for truly finding Spiritual Solutions to Economic Problems,    valuable approaches for group dynamics can be found in
 Getting To Yes (Fisher, Ury, and Patton) and
The Facilitator's Guide to Participatory Decision-Making (3rd Edition) by  Sam Kaner.

I discovered in writing this that there is a group called The Consultation Institute in the UK,  which is somewhat interesting since I was considering starting my own non-profit  501(c)(3) in the USA to do just that.     I don't know anything else about them, but here's a link to them and I do like their charter!

The Consultation Institute