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<channel>
	<title>DRS Technical Tutoring Education Blog</title>
	<link>http://drstutor.com/blog1</link>
	<description>Issues, perspectives and ideas from a tutor/engineer</description>
	<pubDate>Tue, 25 Sep 2007 19:07:05 +0000</pubDate>
	<generator>http://wordpress.org/?v=2.0.2</generator>
	<language>en</language>
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		<title>The First Rule Of Engineering</title>
		<link>http://drstutor.com/blog1/2007/09/25/the-first-rule-of-engineering/</link>
		<comments>http://drstutor.com/blog1/2007/09/25/the-first-rule-of-engineering/#comments</comments>
		<pubDate>Tue, 25 Sep 2007 19:07:05 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Things Everybody Should Know</category>
	<category>Engineering</category>
	<category>Education</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/09/25/the-first-rule-of-engineering/</guid>
		<description><![CDATA[I normally think of first rules as being positive statement.  Things like “be good” or “remember the objective.”  But engineering is ruled by Murphy&#8217;s Law (“If something can go wrong it will, at the worst possible moment and in the worst possible way.”)  So, the first rule of engineering is very simple, [...]]]></description>
			<content:encoded><![CDATA[<p>I normally think of first rules as being positive statement.  Things like “be good” or “remember the objective.”  But engineering is ruled by Murphy&#8217;s Law (“If something can go wrong it will, at the worst possible moment and in the worst possible way.”)  So, the first rule of engineering is very simple, very negative and very hard “DO NOT PANIC!.”  It should be written and expressed as “please, do not panic” but when you need it you would not remember it if it was not expressed as a shouted command.</p>
<p>The biological reason for this first rule is simply, if you panic your body is making adrenaline.   Then your response to the problem will be either a fight or flight response.  Neither of these is a solution to the problem.  Adrenaline basically shuts your brain off.  If you couldn&#8217;t think of an answer before the panic you definitely won&#8217;t think of an answer after the panic sets in.  For the geeks out there – why does Dr. Who come up with creative answers to problems?  Because he&#8217;s not panicked he can think of answers and find one that has a chance of working.  Everyone else has panicked and “lost their head.”</p>
<p>So, if you are faced with a problem you can apply this first principle of engineering by following this practice.  First, take a couple of deep cleansing breaths.  Some people disguise this step by taking a deep inhale and cursing loudly.  Second, restate the problem silently to yourself.  Third, decide what the desired solution must accomplish.  Fourth, work back from what the desired solution must accomplish back to your current problem state.  If you are really lucky, and you have some time, you might want to repeat steps 3 and 4 for a couple of different solutions.  Then you can pick the best of those solutions.  If you don&#8217;t have the luxury of lots of time pick the first solution you find and use it.</p>
<p>Cultivate this practice and you too will be seen as the strong silent nerdy type.  Oh, well you can&#8217;t always get what you want.  But you will be effective in managing a crisis.
</p>
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		<title>Proper Focus</title>
		<link>http://drstutor.com/blog1/2007/09/17/proper-focus/</link>
		<comments>http://drstutor.com/blog1/2007/09/17/proper-focus/#comments</comments>
		<pubDate>Mon, 17 Sep 2007 16:54:07 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Uncategorized</category>
	<category>Education</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/09/17/proper-focus/</guid>
		<description><![CDATA[As a tutor, I suppose I should feel grateful for “No Child Left Behind.”  It has caused enough angst to fuel the careers of many tutors.  Unfortunately, I think that angst is the problem.  The specter of failure, I think, has caused many of our children, students and adults wishing to better [...]]]></description>
			<content:encoded><![CDATA[<p>As a tutor, I suppose I should feel grateful for “No Child Left Behind.”  It has caused enough angst to fuel the careers of many tutors.  Unfortunately, I think that angst is the problem.  The specter of failure, I think, has caused many of our children, students and adults wishing to better themselves to stop very short of what they could achieve.  The most important fact is that education is an individual path.  My path took me from high school to college to graduate school, back to college and back to graduate school.  If I could have found an interesting part-time PhD program I might still be in a formal school.  But as individual interests and needs vary so do the paths that individuals take through life.  The job of a society is to lend support to people who are taking these paths.  “No Child Left Behind” envisions a world where there is only one path and it is dictated early on.  Much like the world that Huxley showed us in “Brave New World.”  I don&#8217;t want that for our children as such the sooner we give up “No Child Left Behind” the better.</p>
<p>In fact, my tenet would be students don&#8217;t fail.  The education system fails the student.  Instead of punishing failures, let&#8217;s move to rewarding success.  The bigger the success the bigger the rewards.  Maybe this way we can lose the angst and get back to raising winners.
</p>
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		<title>Keep it simple rules</title>
		<link>http://drstutor.com/blog1/2007/09/10/keep-it-simple-rules/</link>
		<comments>http://drstutor.com/blog1/2007/09/10/keep-it-simple-rules/#comments</comments>
		<pubDate>Mon, 10 Sep 2007 17:45:11 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Uncategorized</category>
	<category>Things Everybody Should Know</category>
	<category>Engineering</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/09/10/keep-it-simple-rules/</guid>
		<description><![CDATA[It seems that every time I start a new project two items determine the success of that project.  First, is that if I define the project as simply as possible.  That is, define the absolute minimum that I must have this project do.  So, if I was going to build a set [...]]]></description>
			<content:encoded><![CDATA[<p>It seems that every time I start a new project two items determine the success of that project.  First, is that if I define the project as simply as possible.  That is, define the absolute minimum that I must have this project do.  So, if I was going to build a set of shelves, I would need to know how big I could make them (basically defined by where they were going) and how strong to make them (defined by what I expect to put on them).  This gives me all I need to successfully design the shelves.  From that I can build the list of materials needed and finally build the shelves.  This is an old engineering adage “I use the KISS method, Keep It Simple (because I&#8217;m) Stupid.”</p>
<p>The second thing I need is to do the job but to do it right I need to give myself enough time to do the work (duh!).  What I really mean here is that I give myself time enough to do the job slowly.  Once you get rushed, you take short cuts, make mistakes and cause the job to take much longer.  This too has an old engineering adage “We never have time to do it right but we always have time to do it twice.”</p>
<p>Now if we only could learn the importance of these two gems of wisdom, we would never spend too much time designing a project and we would get our projects done.  The start of a school year is a great time to re-enforce these lessons to students.  Remind them to distill their assignments down to what needs to be done and take the time to do just that.  Sounds to me like a formula for a good school year.
</p>
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		<title>Day timers</title>
		<link>http://drstutor.com/blog1/2007/08/13/day-timers/</link>
		<comments>http://drstutor.com/blog1/2007/08/13/day-timers/#comments</comments>
		<pubDate>Mon, 13 Aug 2007 23:48:04 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Things Everybody Should Know</category>
	<category>Education</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/08/13/day-timers/</guid>
		<description><![CDATA[Yes, today&#8217;s middle school/high school/college student should be using a day timer  Why, with all they have going on it is an absolute wonder that they don&#8217;t explode.  OK, maybe that isn&#8217;t strictly true for college students.  Students with their first day timer should be instructed in how to use them.  [...]]]></description>
			<content:encoded><![CDATA[<p>Yes, today&#8217;s middle school/high school/college student should be using a day timer  Why, with all they have going on it is an absolute wonder that they don&#8217;t explode.  OK, maybe that isn&#8217;t strictly true for college students.  Students with their first day timer should be instructed in how to use them.  There is a lot more to a day timer entry than might first meet the eye.  And learning from your day timer can save you grief in the long run.</p>
<p>Day timers can be the most helpful tool your student has.  Encourage them to use it.  It starts out by collecting assignments and “life events” in a single place.  Just having them in one place makes them easy to find and easy to check.  By entering assignments at the time you are going to do them helps keep a student&#8217;s evening sane.  Nobody, student or parent, likes nights when the homework pushes bedtime until the wee hours.  Just keeping up with this will actually make every bodies life more sane and controlled.</p>
<p>Writing down a homework assignment in the day timer, can be a bit tricky – you want to write the assignment down when you plan on doing it!  Not when it was assigned!  So, yes the math assignment that is due in class tomorrow should be written down as a to be done tonight.  But the Chemistry lab report due next Friday can be broken into parts, some done on Tuesday, Wednesday and Thursday night.  If you end up with a huge amount of homework on Wednesday night then slipping the Chemistry lab to Thursday isn&#8217;t a crisis (or at least not yet).  Finding that you have a light homework night on Tuesday might cause you to do a bit of Wednesday&#8217;s planned Chemistry on Tuesday instead.  These kinds of decisions are possible when you work with a day timer but if you&#8217;re just working from memory things like this will just slip.</p>
<p>Building into your day timer over the weekend your important chores and practices will suddenly make it clear that you, the student, have some nights where you have lots of time to work on assignments and others where you will be hard pressed to get your work done.  So, this is the first thing that your day timer teaches you – while all days are created equal – not all days have the same number of usable hours.</p>
<p>The next thing that you can start to learn from your day timer, requires a little work on your part.  Notice, how long it takes you to do an assignment for a given class.  You might find that math homework takes you 30 minutes per assignment.  Now when you get math assignments you can block out 30 minutes of your after school hours to get it done.  If your history assignments always take an hour and a half, you can plan on that as well.  The problem comes with classes where your assignments take a widely varying amount of time (15 minutes some times and 2 hours others).  With these classes you need to look for clues in the assignment to help you predict how long the assignment will take before you do it.
</p>
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		<title>Yet another good idea</title>
		<link>http://drstutor.com/blog1/2007/08/03/yet-another-good-idea/</link>
		<comments>http://drstutor.com/blog1/2007/08/03/yet-another-good-idea/#comments</comments>
		<pubDate>Fri, 03 Aug 2007 16:40:52 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Uncategorized</category>
	<category>Education</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/08/03/yet-another-good-idea/</guid>
		<description><![CDATA[Here I am stuck in an airport, when what do my wandering eyes see?  A brief article in USA Today about how some states waive sales tax on back-to-school items!  Think of it the state waives sales tax during the month of August on text books, paper, pencils, pens and in some cases even on [...]]]></description>
			<content:encoded><![CDATA[<p>Here I am stuck in an airport, when what do my wandering eyes see?  A brief article in USA Today about how some states waive sales tax on back-to-school items!  Think of it the state waives sales tax during the month of August on text books, paper, pencils, pens and in some cases even on computers bought for children going to school.</p>
<p>I have a hard time thinking of another way that the state could physically demonstrate that it thinks it&#8217;s most important responsibility is to encourage the education of it&#8217;s citizens.  About the only other way would be for the state to actually spend more on education.  But that does not seem to be about to happen.</p>
<p>Let me know what you think about this and if I hear significant support we might try and get this to a hearing in Olympia in January&#8230;This might be a great social studies or community service or even senior project for somebody out there!
</p>
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		<title>Divide and Conquer</title>
		<link>http://drstutor.com/blog1/2007/07/30/divide-and-conquer/</link>
		<comments>http://drstutor.com/blog1/2007/07/30/divide-and-conquer/#comments</comments>
		<pubDate>Mon, 30 Jul 2007 16:56:15 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Things Everybody Should Know</category>
	<category>Mathematics Topics</category>
	<category>Engineering</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/07/30/divide-and-conquer/</guid>
		<description><![CDATA[One of the more overlooked skills that all students should have is the idea of “modularizing” a problem.  That is, breaking a problem down into component sub-problems.  I have seen this formally presented in a number of forums but mostly at the college level.  This is a trick that should be formally [...]]]></description>
			<content:encoded><![CDATA[<p>One of the more overlooked skills that all students should have is the idea of “modularizing” a problem.  That is, breaking a problem down into component sub-problems.  I have seen this formally presented in a number of forums but mostly at the college level.  This is a trick that should be formally taught at the high school or middle school level.  The first time I saw this formally presented it was called “top down design.”  Computer scientist have refined the thinking a little bit and now the concept is usually taught as “object oriented design.”  The concept is the same.  Break a big problem down into smaller manageable chunks.  If a sub-problem is to big to be solved in one step then it too is broken into smaller problems.  The design process stops when you can look at all the lowest level sub-problems and say “I know how to do that.”</p>
<p>Classically this is taught using the how do you change a tire on a car example.  We start by listing all the things we need to do to successfully change the tire.  Get tools, get spare, check spare is not flat, loosen lug nuts, jack up car, remove lug nuts, remove flat tire, put spare on, put lug nuts on, jack car down, tight lug nuts, put flat away, put tools away and at last we&#8217;re done.  Now I&#8217;ve listed these tasks pretty much in order because I&#8217;ve changed a few flats in my day.  A student, imaging this job might not list the tasks in order (or in anything close to a correct order) at this stage it doesn&#8217;t matter – in fact it doesn&#8217;t even matter if the list is complete.  The next stage of the process orders the tasks and in ordering the tasks may bring to light tasks that have yet to be defined.  Then the process defined and can be tested.</p>
<p>So, how can this be used by students?  As students get to middle school and high school they have matured from single step problems to problems that assume the student can do some things that will let them then use the new techniques they are being taught.  So when they are asked to simplify  5x + 6y -12q - 15r:<br />
it is assumed that the student knows this equation can be re-written to remove the subtraction<br />
5x + 6y + -12q + -15r<br />
now the equation can be re-arranged to<br />
5x + -15r + 6y + -12q<br />
and now we can use the distributive property to complete the problem<br />
5(x + -3r) + 6(y + -2q)</p>
<p>With time a student will do this in one step but initially this problem requires the student to do three very distinct steps.  The tool students need is to recognize if a problem requires being broken into tasks before it can be solved.  It&#8217;s not a hard concept just not something that we teach.
</p>
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		<title>Reading is still fundamental</title>
		<link>http://drstutor.com/blog1/2007/07/23/reading-is-still-fundamental/</link>
		<comments>http://drstutor.com/blog1/2007/07/23/reading-is-still-fundamental/#comments</comments>
		<pubDate>Mon, 23 Jul 2007 23:56:06 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Education</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/07/23/reading-is-still-fundamental/</guid>
		<description><![CDATA[As I&#8217;ve been out of town for most of this past month, my wife sent me the following link- CEO Libraries.  Basically something we don&#8217;t think about.  I mean the last bragging session with friends about their new houses did not include a boast about how big their personal library was.  I [...]]]></description>
			<content:encoded><![CDATA[<p>As I&#8217;ve been out of town for most of this past month, my wife sent me the following link- <a href="http://www.nytimes.com/2007/07/21/business/21libraries.html?_r=1&#038;oref=slogin">CEO Libraries.</a>  Basically something we don&#8217;t think about.  I mean the last bragging session with friends about their new houses did not include a boast about how big their personal library was.  I heard about wine cellars, viking stoves, granite, flat screen TVs and media rooms but nothing about how many books we have.  What adults talk about, what you as parents espouse as important is listened to as by your children.</p>
<p>Our personal library is about 1000 volumes, which does not include the books housed by my office desk or in my wife&#8217;s office.  My wife makes a point of reading something every night.  I tend to be a bit more hit and miss but I do read frequently.  This year has been a bit slow for me, I think I&#8217;ve read about 2-3 books per month.  (Yes, that does include reading “HP &#038; the deathly hallows” in one 14 hour sitting.)  Over time what I read has changed, in fact, I&#8217;m currently reading much more non-fiction than ever before.</p>
<p>If we had children, they would see that their parents read books.  Books as a source of entertainment and as a way to explore their world.  We need parents to talk about the importance of reading AND demonstrate the importance in their own life.  My best advice is that if you want to raise a scholar – show them how important books are to you.  Then see if you can impress your friends by the number of books you own.  Your children and your community will both profit from your pride in reading.
</p>
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		<title>Backward Problem Solving</title>
		<link>http://drstutor.com/blog1/2007/07/16/backward-problem-solving/</link>
		<comments>http://drstutor.com/blog1/2007/07/16/backward-problem-solving/#comments</comments>
		<pubDate>Mon, 16 Jul 2007 18:47:08 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Things Everybody Should Know</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/07/16/backward-problem-solving/</guid>
		<description><![CDATA[One of the most important problem solving techniques that I&#8217;ve ever used, I saw presented for the first time when I was a graduate student.  Ever since then I have wondered if it was an oversight in my training or if it was yet another thing that everybody should know how to do.  [...]]]></description>
			<content:encoded><![CDATA[<p>One of the most important problem solving techniques that I&#8217;ve ever used, I saw presented for the first time when I was a graduate student.  Ever since then I have wondered if it was an oversight in my training or if it was yet another thing that everybody should know how to do.  Today, I&#8217;ll present it as yet another thing.</p>
<p>Backward solving starts by identifying the desired end result, examining the ways to get to that result in one step.  We then repeat this step until we get to something that is totally doable.  Yeah, this doesn&#8217;t seem like rocket science, in fact, it seems to easy to ever work.  The ultimate trick here is that this method will always get you to a solution.  It will not necessarily get you to a solution quickly.  Enough hypothesis, let&#8217;s do an example.</p>
<p>The problem statement would look a little bit like this.  Sally wants to have a dinner party on her patio.  While the dinner table will have candles, the patio floor is not very even and Sally wants to make sure that the floor is sufficiently lighted to insure that her guests will not trip and fall.  The patio is about 20 feet away from the house.  Sally had thought about using Tiki torches but had decided that these would not work.  Renting a generator or running an extension cord to the patio struck her as unseemly.</p>
<p>Ultimately, Sally needs some low voltage lighting for her patio.  I could go out and buy a transformer to take house current and convert it to low voltage and attach this to pre-built low voltage walkway lights.  I could also go out and buy a set of solar powered low voltage walkway lights and install them.  Or I could get a battery pack and use it to power the low voltage walkway lights.  There may be other ways I could achieve this but we&#8217;ll stop right here.  Notice how each of these solutions is a single buy and install step away from the desired goal.  Each of these solutions should be examined in light of Sally&#8217;s problem, those that are compatible with Sally&#8217;s goals will need to be examined further.</p>
<p>The transformer to low voltage lighting solution is very much like the extension cord solution that the problem specifically rejects.  Ultimately this solution will require digging a trench, in addition, to the basic installation of the lights.  So, let&#8217;s reject this path for now.</p>
<p>Purely, solar powered lights are only on during daylight hours.  No sun means no power.    So, solar powered lights might not work for a dinner party.  So, on the surface this solution might not be a good one.  Researching some details might bring this back into consideration but for now we reject this path.</p>
<p>The last idea was to use a battery based lighting system.  While this might not be ideal, it certainly seems to meet the spirit of the problem statement.  There are two possible designs of this system.  Either the battery pack powers all the lights or each light has it&#8217;s own battery pack.  Having a single battery pack will limit the number of lights that can be powered, all the lights will have to be wired together (there&#8217;s that trench again).  The worst problem with the single battery pack solution is that discharging the batteries means all the lights will go out at once, so if the party is a real success the whole patio might be plunged into darkness.</p>
<p>The limitations on the individual battery powered lamps are that you have a lot more batteries to deal with, individual lamps may discharge earlier than expected.  The worst problem is that the individual lamps might be dimmer than the lamps in the other systems.  Notice that none of these limits is explicitly violates the restrictions in our problem statement.  Because of this it looks like the best solution is a system with individual battery powered lamps.</p>
<p>Again, the system is to find a list of methods that can get you to the ultimate solution and explore those one at a time until you find a solution that meets all the criteria of the problem.  Investigations like this may not result in highly optimized solutions.  Nor does this method get you to an answer quickly.  The kick is it will always get you to a solution (if one exists).
</p>
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		<title>Summer Learning</title>
		<link>http://drstutor.com/blog1/2007/07/05/summer-learning/</link>
		<comments>http://drstutor.com/blog1/2007/07/05/summer-learning/#comments</comments>
		<pubDate>Thu, 05 Jul 2007 21:43:54 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Things Everybody Should Know</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/07/05/summer-learning/</guid>
		<description><![CDATA[I&#8217;ve been struggling for a couple weeks about one topic.  Simply put the topic is “life time learning”, simply put anybody worth their salt is on continuous quest for more and better knowledge.  That said, the real question is how do we teach people to be life long learners?  It does not [...]]]></description>
			<content:encoded><![CDATA[<p>I&#8217;ve been struggling for a couple weeks about one topic.  Simply put the topic is “life time learning”, simply put anybody worth their salt is on continuous quest for more and better knowledge.  That said, the real question is how do we teach people to be life long learners?  It does not seem to me that we, as a society, encourage this kind of thinking.  We ask young people what they want to be when they grow up.  As if they will play one role for their entire life.  I know precious few people who can make that claim.  Even if we discount home life (and we really should not) most people have multiple careers.  The last time I heard a statistic on this it was that the average American worker switched careers 2.5 times during their working life.  <a target="_blank" href="http://www.bls.gov/news.release/pdf/nlsoy.pdf">The US Government currently reports that between 18 and 40 the Americans average 10.5 different jobs.</a></p>
<p>The long and short of this statistic is that it is nearly impossible to perfectly predict what you will be doing with your work life.  You may decide that your chosen profession is right at 21 and still right at 26 but somewhere and some when in your work life a better idea will hit you (or your boss).  At that point having been a life long learner will pay dividends.  You will be able to adapt and fit into a new work environment.</p>
<p>I like to think of the summer as the fun learning season.  This is the time you can spend exploring the edges of your current interests.  If you love music, explore the mathematics that lead to the system of notes that we use.  Look into the history of particular stamps and why our postal system delivers letters based on weight and not distance the letter travels.  Maybe even learn how to build your family&#8217;s website.  The summer is warm, lazy and full of opportunities to show your children that you did not stop learning in High School or College.
</p>
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		<title>History Lesson</title>
		<link>http://drstutor.com/blog1/2007/06/08/history-lesson/</link>
		<comments>http://drstutor.com/blog1/2007/06/08/history-lesson/#comments</comments>
		<pubDate>Fri, 08 Jun 2007 17:49:30 +0000</pubDate>
		<dc:creator>Administrator</dc:creator>
		
	<category>Education</category>
		<guid isPermaLink="false">http://drstutor.com/blog1/2007/06/08/history-lesson/</guid>
		<description><![CDATA[In the beginning we educated individuals in a one-on-one manner.  For most of human history this has been the model of education that has worked.  In the Encyclopedia Britannica I was able to find reference to Johann Heinrich Pestalozzi as one of the early expounders of group learning.   Johann Heinrich Pestalozzi [...]]]></description>
			<content:encoded><![CDATA[<p><a name="pageHeading"></a><a name="pageHeading1"></a>In the beginning we educated individuals in a one-on-one manner.  For most of human history this has been the model of education that has worked.  In the Encyclopedia Britannica I was able to find reference to Johann Heinrich Pestalozzi as one of the early expounders of group learning.   Johann Heinrich Pestalozzi died in 1827, less than 200 years ago.  Our current public schools are the result of our desire to educate all youth and the growing urbanism of our society.</p>
<p>Even in the early days of public education in this country the idea of a classroom with 20-30 students all studying the same subject at the same time, progressing in lock step was outlandish.  While some subjects lend themselves to this approach others do not.  Early on in public education the schools were small and there was a lot of one-on-one attention.  Not until large urban school districts started to arise in the early to mid-1900s did the factory educational methods we have become accustomed to become common.</p>
<p>Even when I was in high school small cohorts of students were the rule rather than the exception.  My graduating class was about 250.  Last year the same school had almost 450 graduates.  My wife&#8217;s class was about 700 students and today that district graduates almost 1500 (yes, they added another high school in the same district).  The point is that the numbers have increased to such a point that we&#8217;re seeing the limits of the factory method of education.</p>
<p>If schools produced cars then we would not see these limits.  The problem is that the inputs to the school factory vary hugely in terms of basic qualities, like curiosity, attention span and learning style.  Kind of like what would happen at a car plant if body panels came in randomly made of aluminum, stainless steel or fiberglass.  If the plant was working at a low level then the panels could be matched and the output would be perceived to be high quality.  However, if the plant ran at capacity the output quality would decline dramatically because the factory no longer had time to perform the matching operation.  In other words our schools need to make sure that every student gets the one-on-one help they need.
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