Essays On Education And Kindred Subjects (Fiscle Part- 11) by Herbert Spencer (best mobile ebook reader TXT) 📖

Publication Proposes

"To Place Before The   Student A Simple, Yet Logical Mode Of    Instruction;"

And To This End Sets Out With A Number Of    Definitions Thus:--

 

 

 

     "A Simple Line In Drawing Is A Thin Mark Drawn From One Point To

     Another.

 

 

 

     "Lines May Be Divided, As To Their Nature In Drawing, Into Two

     Classes:--

 

 

 

     "1. _Straight_, Which Are Marks That Go The   Shortest Road Between

     Two Points, As A B.

 

 

 

     "2. Or _Curved_, Which Are Marks Which Do Not Go The   Shortest Road

     Between Two Points, As C D."

 

 

 

And So The   Introduction Progresses To Horizontal Lines, Perpendicular

Lines, Oblique Lines, Angles Of    The   Several Kinds, And The   Various

Figures Which Lines And Angles Make Up. The   Work Is, In Short, A Grammar

Of Form, With Exercises. And Thus The   System Of    Commencing With A Dry

Analysis Of    Elements, Which, In The   Teaching Of    Language, Has Been

Exploded, Is To Be Re-Instituted In The   Teaching Of    Drawing. We Are To

Set Out With The   Definite, Instead Of    With The   Indefinite. The   Abstract

Is To Be Preliminary To The   Concrete. Scientific Conceptions Are To

Precede Empirical Experiences. That This Is An Inversion Of    The   Normal

Order, We Need Scarcely Repeat. It Has Been Well Said Concerning The

Custom Of    Prefacing The   Art Of    Speaking Any Tongue By A Drilling In The

Parts Of    Speech And Their Functions, That It Is About As Reasonable As

Prefacing The   Art Of    Walking By A Course Of    Lessons On The   Bones,

Muscles, And Nerves Of    The   Legs; And Much The   Same Thing May Be Said Of

The Proposal To Preface The   Art Of    Representing Objects, By A

Nomenclature And Definitions Of    The   Lines Which They Yield On Analysis.

These Technicalities Are Alike Repulsive And Needless. They Render The

Study Distasteful At The   Very Outset; And All With The   View Of    Teaching

That Which, In The   Course Of    Practice, Will Be Learnt Unconsciously.

Just As The   Child Incidentally Gathers The   Meanings Of    Ordinary Words

From The   Conversations Going On Around It, Without The   Help Of

Part 1 Chapter 2 (Intellectual Education) Pg 33

Dictionaries; So, From The   Remarks On Objects, Pictures, And Its Own

Drawings, Will It Presently Acquire, Not Only Without Effort But Even

Pleasurably, Those Same Scientific Terms Which, When Taught At First,

Are A Mystery And A Weariness.

 

 

 

If Any Dependence Is To Be Placed On The   General Principles Of    Education

That Have Been Laid Down, The   Process Of    Learning To Draw Should Be

Throughout Continuous With Those Efforts Of    Early Childhood, Described

Above As So Worthy Of    Encouragement. By The   Time That The   Voluntary

Practice Thus Initiated Has Given Some Steadiness Of    Hand, And Some

Tolerable Ideas Of    Proportion, There Will Have Arisen A Vague Notion Of

Body As Presenting Its Three Dimensions In Perspective. And When, After

Sundry Abortive, Chinese-Like Attempts To Render This Appearance On

Paper, There Has Grown Up A Pretty Clear Perception Of    The   Thing To Be

Done, And A Desire To Do It, A First Lesson In Empirical Perspective May

Be Given By Means Of    The   Apparatus Occasionally Used In Explaining

Perspective As A Science. This Sounds Alarming; But The   Experiment Is

Both Comprehensible And Interesting To Any Boy Or Girl Of    Ordinary

Intelligence. A Plate Of    Glass So Framed As To Stand Vertically On The

Table, Being Placed Before The   Pupil, And A Book Or Like Simple Object

Laid On The   Other Side Of    It, He Is Requested, While Keeping The   Eye In

One Position, To Make Ink-Dots On The   Glass So That They May Coincide

With, Or Hide, The   Corners Of    This Object. He Is Next Told To Join These

Dots By Lines; On Doing Which He Perceives That The   Lines He Makes Hide,

Or Coincide With, The   Outlines Of    The   Object. And Then By Putting A

Sheet Of    Paper On The   Other Side Of    The   Glass, It Is Made Manifest To

Him That The   Lines He Has Thus Drawn Represent The   Object As He Saw It.

They Not Only Look Like It, But He Perceives That They Must Be Like It,

Because He Made Them Agree With Its Outlines; And By Removing The   Paper

He Can Convince Himself That They Do Agree With Its Outlines. The   Fact

Is New And Striking; And Serves Him As An Experimental Demonstration,

That Lines Of    Certain Lengths, Placed In Certain Directions On A Plane,

Can Represent Lines Of    Other Lengths, And Having Other Directions, In

Space. By Gradually Changing The   Position Of    The   Object, He May Be Led

To Observe How Some Lines Shorten And Disappear, While Others Come Into

Sight And Lengthen. The   Convergence Of    Parallel Lines, And, Indeed, All

The Leading Facts Of    Perspective, May, From Time To Time, Be Similarly

Illustrated To Him. If He Has Been Duly Accustomed To Self-Help, He Will

Gladly, When It Is Suggested, Attempt To Draw One Of    These Outlines On

Paper, By The   Eye Only; And It May Soon Be Made An Exciting Aim To

Produce, Unassisted, A Representation As Like As He Can To One

Subsequently Sketched On The   Glass. Thus, Without The   Unintelligent,

Mechanical Practice Of    Copying Other Drawings, But By A Method At Once

Simple And Attractive--Rational, Yet Not Abstract--A Familiarity With

The Linear Appearances Of    Things, And A Faculty Of    Rendering Them, May

Be Step By Step Acquired. To Which Advantages Add These:--That Even Thus

Early The   Pupil Learns, Almost Unconsciously, The   True Theory Of    A

Picture (Namely, That It Is A Delineation Of    Objects As They Appear When

Projected On A Plane Placed Between Them And The   Eye); And That When He

Reaches A Fit Age For Commencing Scientific Perspective, He Is Already

Thoroughly Acquainted With The   Facts Which Form Its Logical Basis.

 

 

 

As Exhibiting A Rational Mode Of    Conveying Primary Conceptions In

Geometry, We Cannot Do Better Than Quote The   Following Passage From Mr.

Wyse:--

 

 

 

     "A Child Has Been In The   Habit Of    Using Cubes For Arithmetic; Let

     Him Use Them Also For The   Elements Of    Geometry. I Would Begin With

     Solids, The   Reverse Of    The   Usual Plan. It Saves All The   Difficulty

     Of    Absurd Definitions, And Bad Explanations On Points, Lines, And

     Surfaces, Which Are Nothing But Abstractions.... A Cube Presents

     Many Of    The   Principal Elements Of    Geometry; It At Once Exhibits

     Points, Straight Lines, Parallel Lines, Angles, Parallelograms,

     Etc., Etc. These Cubes Are Divisible Into Various Parts. The   Pupil

     Has Already Been Familiarised With Such Divisions In Numeration,

     And He Now Proceeds To A Comparison Of    Their Several Parts, And Of

     The   Relation Of    These Parts To Each Other.... From Thence He

     Advances To Globes, Which Furnish Him With Elementary Notions Of

     The   Circle, Of    Curves Generally, Etc., Etc.

 

 

 

     "Being Tolerably Familiar With Solids, He May Now Substitute

     Planes. The   Transition May Be Made Very Easy. Let The   Cube, For

     Instance, Be Cut Into Thin Divisions, And Placed On Paper; He Will

     Then See As Many Plane Rectangles As He Has Divisions; So With All

     The   Others. Globes May Be Treated In The   Same Manner; He Will Thus

     See How Surfaces Really Are Generated, And Be Enabled To Abstract

     Them With Facility In Every Solid.

 

 

 

     "He Has Thus Acquired The   Alphabet And Reading Of    Geometry. He Now

     Proceeds To Write It.

 

 

 

     "The Simplest Operation, And Therefore The   First, Is Merely To

     Place These Planes On A Piece Of    Paper, And Pass The   Pencil Round

     Them. When This Has Been Frequently Done, The   Plane May Be Put At A

     Little Distance, And The   Child Required To Copy It, And So On."

 

 

 

A Stock Of    Geometrical Conceptions Having Been Obtained, In Some Such

Manner As This Recommended By Mr. Wyse, A Further Step May Be Taken, By

Introducing The   Practice Of    Testing The   Correctness Of    Figures Drawn By

Eye: Thus Both Exciting An Ambition To Make Them Exact, And Continually

Illustrating The   Difficulty Of    Fulfilling That Ambition. There Can Be

Little Doubt That Geometry Had Its Origin (As, Indeed, The   Word Implies)

In The   Methods Discovered By Artizans And Others, Of    Making Accurate

Measurements For The   Foundations Of    Buildings, Areas Of    Inclosures, And

The Like; And That Its Truths Came To Be Treasured Up, Merely With A

View To Their Immediate Utility. They Would Be Introduced To The   Pupil

Under Analogous Relationships. In Cutting Out Pieces For His

Card-Houses, In Drawing Ornamental Diagrams For Colouring, And In Those

Various Instructive Occupations Which An Inventive Teacher Will Lead Him

Into, He May For A Length Of    Time Be Advantageously Left, Like The

Primitive Builder, To Tentative Processes; And So Will Learn Through

Experience The   Difficulty Of    Achieving His Aims By The   Unaided Senses.

When, Having Meanwhile Undergone A Valuable Discipline Of    The

Perceptions, He Has Reached A Fit Age For Using A Pair Of    Compasses, He

Will, While Duly Appreciating These As Enabling Him To Verify His Ocular

Guesses, Be Still Hindered By The   Imperfections Of    The   Approximative

Method. In This Stage He May Be Left For A Further Period: Partly As

Being Yet Too Young For Anything Higher; Partly Because It Is Desirable

That He Should Be Made To Feel Still More Strongly The   Want Of

Part 1 Chapter 2 (Intellectual Education) Pg 34

Systematic Contrivances. If The   Acquisition Of    Knowledge Is To Be Made

Continuously Interesting; And If, In The   Early Civilisation Of    The

Child, As In The   Early Civilisation Of    The   Race, Science Is Valued Only

As Ministering To Art; It Is Manifest That The   Proper Preliminary To

Geometry, Is A Long Practice In Those Constructive Processes Which

Geometry Will Facilitate. Observe That Here, Too, Nature Points The   Way.

Children Show A Strong Propensity To Cut Out Things In Paper, To Make,

To Build--A Propensity Which, If Encouraged And Directed, Will Not Only

Prepare The   Way For Scientific Conceptions, But Will Develop Those

Powers Of    Manipulation In Which Most People Are So Deficient.

 

 

 

When The   Observing And Inventive Faculties Have Attained The   Requisite

Power, The   Pupil May Be Introduced To Empirical Geometry; That

Is--Geometry Dealing With Methodical Solutions, But Not With The

Demonstrations Of    Them. Like All Other Transitions In Education, This

Should Be Made Not Formally But Incidentally; And The   Relationship To

Constructive Art Should Still Be Maintained. To Make, Out Of    Cardboard,

A Tetrahedron Like One Given To Him, Is A Problem Which Will Interest

The Pupil And Serve As A Convenient Starting-Point. In Attempting This,

He Finds It Needful To Draw Four Equilateral Triangles Arranged In

Special Positions. Being Unable In The   Absence Of    An Exact Method To Do

This Accurately, He Discovers On Putting The   Triangles Into Their

Respective Positions, That He Cannot Make Their Sides Fit; And That

Their Angles Do Not Meet At The   Apex. He May Now Be Shown How, By

Describing A Couple Of    Circles, Each Of    These Triangles May Be Drawn

With Perfect Correctness And Without Guessing; And After His Failure He

Will Value The   Information. Having Thus Helped Him To The   Solution Of

His First Problem, With The   View Of    Illustrating The   Nature Of

Geometrical Methods, He Is In Future To Be Left To Solve The   Questions

Put To Him As Best He Can. To Bisect A Line, To Erect A Perpendicular,

To Describe A Square, To Bisect An Angle, To Draw A Line Parallel To A

Given Line, To Describe A Hexagon, Are Problems Which A Little Patience

Will Enable Him To Find