Repository: UIHistories Project: Mathematical Models Construction and Use of Mathematical Models (Fehr & Hildebrandt) [PAGE 3]

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MATHEMATICS

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LIBRARY I* Introduction

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One of the principles often cited as basic in our system of e l e m e n t a r y as w e l l as s e c o n d a r y e d u c a t i o n is "learning b y a c t i v i t y " , or "learning b y d o i n g " * .In m a t h e m a t i c s t e a c h i n g in the p r i m a r y g r a d e s , this p r i n c i p l e is u s e d in i n t r o d u c i n g the concept of n u m b e r and f a m i l i a r i t y w i t h g e o m e t r i c shapes and f i g u r e s , In the junior h i g h school g r a d e s , it h a s n o t always b e e n true that l e a r n i n g h a s c o n t i n u e d b y m e a n s of experimentation, and exploration* Y e t c h a r a c t e r i s t i c of the junior h i g h s c h o o l s t u d e n t is that h e loves to e x p e r i m e n t , h e likes "to see it work",h e w a n t s to create and h e enjoys e x p l o r i n g . One c r i t i c i s m that m a y be o f f e r r e d of m u c h of our m a t h e m a t i c s t e a c h i n g is that we h a v e n o t p e r m i t t e d enough o p p o r t u n i t i e s for e x p l o r a t i o n and d i s covery * Y e t m a t h e m a t i c s , m o r e t h a n any other s u b j e c t , w i t h p e r h a n s the e x c e p t i o n of s c i e n c e , is r i c h w i t h s u c h p o s s i b i l i t i e s • A simple m o d e l or d e v i c e , m a d e b y an o t h e r w i s e u n i n t e r e s t e d stud e n t , m a y be the m e a n s w h e r e b y h e is able to u n d e r s t a n d r e l a t i o n s h i p s , w h o s e m a s t e r y leads to further i n v e s t i g a t i o n s * A m o n g the m o d e l s and d e v i c e s w h i c h offer the b e s t o p p o r t u n ities are those w h i c h can b e m a d e f r o m simple and i n e x p e n s i v e m a t e r i a l s , such as c a r d b o a r d , w o o d , s t r i n g , e l a s t i c s , s t i c k s , p a p e r , e t c . T h e s e can and should be m a d e by e v e r y s t u d e n t . They are a p p r o x i m a t e in s t r u c t u r e and of ca t e m p o r a r y n a t u r e , b u t c r e a t e i n t e r e s t and d e v e l o p the I m a g i n a t i o n * Later, permanent m o d e l s c a n b e m a d e f r o m g l a s s , m e t a l , c e l l o p h a n e , • wood> e t c . , w h i c h are n e a t , a c c u r a t e , and strong in s t r u c t u r e . M o d e l s of this t3^pe m a y b o c o n s t r u c t e d as p r o j e c t s b y v a r i o u s pupils and should f o r m a p a r t of a p e r m a n e n t m a t h e m a t i c a l c o l l e c t i o n for the s c h o o l . T h e y should lend t h e m s e l v e s to r a t h e r severe h a n d l i n g and b e u s e d for e x h i b i t i o n and d e m o n s t r a t i o n p u r p o s e s • Besides promoting a "spirit of discovery" and "creative t h i n k i n g " , the a c t u a l c o n s t r u c t i o n of a m o d e l r e q u i r e s a student to apply n u m e r i c a l and g e o m e t r i c p r i n c i p l e s p r e v i o u s l y s t u d i e d , aui thus g i v e s an i n s i g h t Into a p p l i e d m a t h e m a t i c s . W i t h this there can come a far b e t t e r a p p r e c i a t i o n of t h e - p a r t p l a y e d b y m a t h e m a t i c s in our m o d e r n I n d u s t r i a l and scientific a g e . Stud e n t s w h o cannot r e a d i l y g r a s p a b s t r a c t ideas and r e l a t i o n s h i p s , o f t e n sense t h e m q u i c k l y w h e n p r e s e n t e d in c o n c r e t e s i t u a t i o n s . This pamphlet has been written to call to attention the v a l u e of m o d e l s In m a t h e m a t i c s i n s t r u c t i o n . The t r e a t m e n t is b y n o m e a n s c o m p l e t e or e x h a u s t i v e . M a n y of the d e v i c e s m a k e the a c t u a l t e a c h i n g of m a t h e m a t i c s easier and the s u b j e c t m a t t e r f a s cinating* T h e y lead students to n e w Ideas and d i s c o v e r i e s , w h i c h in t u r n lead to still o t h e r s , "it Is f u n to l e a r n b y doing*" II* Surveying Instruments 1, The Transit..* Many junior high school textbooks cont a i n c h a p t e r s on i n d i r e c t measurement--!* I n d i n g i n a c c e s s i b l e d i s tances b y m e a n s of a h o m e - m a d e t r a n s i t and a scale d r a w i n g * D i r e c t i o n s for m a k i n g a t r a n s i t are I n c l u d e d in m a n y b o o k s .