A System Which Allows Students to Explore Algorithms

T h i s p a p e r d i s c u s s e s t h e p r o b l e m s o f mak ing a l g o r i t h m s ' t r a n s p a r e n t ' . The app roach t a k e n has been t o d e f i n e a Forma l Language f o r t h e p r o b l e m doma in w h i c h d e s c r i b e s t h e m a i n s t e p s i n t h e a l g o r i t h m under d i s c u s s i o n . T h i s Forma l Language has been used i n a sys tem w h i c h a l l o w s t h e s t u d e n t t o e n q u i r e a b o u t s e l e c t e d p a r t s o f t h e a l g o r i t h m and i n a f a c i l i t y w h i c h comments o n t h e s t u d e n t ' s e x p l a n a t i o n s o f c e r t a i n p a r t s o f t h e a l g o r i t h m . Some i n d i c a t i o n i s g i v e n a s t o how t h e s y s t e m ' s f a c i l i t i e s can b e e x t e n d e d t o answer a f u r t h e r r ange o f q u e s t i o n s , b u t i t i s c o n c l u d e d t h a t i n o r d e r t o make s u b s t a n t i a l p r o g r e s s i n t h i s p u r s u i t a s i n g l e r e p r e s e n t a t i o n f o r a l g o r i t h m s i s r e q u i r e d w h i c h can be b o t h e x e c u t e d and used as a b a s i s f o r e x p l a n a t i o n s . 1 . I n t r o d u c t i o n T h e r e a r e c l e a r l y two m a j o r d r i v i n g f o r c e s i n t h e f i e l d o f g e n e r a t i v e CAI (Computer A s s i s t e d I n s t r u c t i o n ) ; n a m e l y , t h e p r a c t i c a l one o f i m p l e m e n t i n g sys tems w h i c h a r e c a p a b l e o f p r o d u c i n g t e a c h i n g m a t e r i a l , and s e c o n d l y t h e i n t e r e s t o f t h e A I ( A r t i f i c i a l I n t e l l i g e n c e ) p r a c t i t i o n e r s who seek t o r e p l i c a t e v a r i o u s f a c e t s o f i n t e l l i g e n t b e h a v i o u r ( t e a c h i n g c l e a r l y b e i n g one such a c t i v i t y ) , G e n e r a t i v e CAI sys tems have used e s s e n t i a l l y two t y p e s o f know ledge b a s e s : Semant i c Ne t s and A l g o r i t h m s . I n t h i s paper w e s h a l l b e c o n c e r n e d o n l y w i t h t h e l a t t e r t y p e and w e s h a l l see t h a t , g i v e n a n a l g o r i t h m w h i c h i s a b l e t o s o l v e p r o b l e m s i n a p a r t i c u l a r d o m a i n , i t e n a b l e s t h e sys tem t o o f f e r a r ange o f t e a c h i n g modes. These c a p a b i l i t i e s can b e d i v i d e d i n t o t h r e e l e v e l s o f s o p h i s t i c a t i o n w h i c h a r e r e p r e s e n t e d b y t h e a b i l i t y t o : ( i ) T e l l t h e s t u d e n t whe the r o r n o t h i s s o l u t i o n i s c o r r e c t . ( i i ) Show t h e s t u d e n t how t h e a l g o r i t h m w o u l d s o l v e t h e same p r o b l e m ( t h i s i s e s s e n t i a l l y showing t h e s t u d e n t t h e t r a c e o f t h e a l g o r i t h m ) . ( i i i ) Debug t h e s t u d e n t ' s e x p l a n a t i o n o f how t h e a l g o r i t h m , o r p a r t o f t h e a l g o r i t h m w o r k s . * T h i s i s a r e v i s e d v e r s i o n o f a paper g i v e n a t t h e SSRC "Compute rs i n E d u c a t i o n " Seminar h e l d a t t h e U n i v e r s i t y o f W a r w i c k , UK, J u l y 1976. The ma in p r o b l e m w i t h l e v e l one sys tems i s d e c i d i n g w h e t h e r o r n o t t h e answer g i v e n b y t h e s t u d e n t i s e q u i v a l e n t t o t h a t g e n e r a t e d b y t h e a l g o r i t h m . I n g e n e r a l , t h i s i s a n o n t r i v i a l t a s k : b u t s o f a r a r e a s have been chosen where t h e answer r e q u i r e d i s a number o r a s i m p l e l i t e r a l and hence t h i s d i f f i c u l t y has been a v o i d e d (see f o r i n s t a n c e U h r [ 1 ] ) . P e p l i n s k i l 2 ] has imp lemen ted a second l e v e l sys tem w h i c h g i v e s s t u d e n t s l i n e a r e q u a t i o n s t o s o l v e and r e q u i r e s them t o r e s p o n d w i t h t h e v a l u e f o r t h e unknown. A f t e r a number o f u n s u c c e s s f u l a t t e m p t s , t h e p rog ram p r e s e n t s t h e s t u d e n t w i t h a l l t h e s t e p s w h i c h t h e a l g o r i t h m p e r f o rms i n s o l v i n g t h e p r o b l e m . I n t h i s pape r w e s h a l l d i s c u s s a sys tem w h i c h p r e s e n t s t h e s t u d e n t w i t h t h e t r a c e o f t h e a l g o r i t h m and t h e n a l l o w s h im t o d i s c u s s c e r t a i n a s p e c t s o f t h i s i n f o r m a t i o n . F u r t h e r , w e w i s h t o c o n s i d e r t h e t h i r d and m o r e c h a l l e n g i n g p r o b l e m o f d e s i g n i n g a sys tem t o comment o n (debug) t h e s t u d e n t ' s e x p l a n a t i o n s . The sys tem we have i m p l e m e n t e d assumes t h a t t h e s t u d e n t s a r e f a m i l i a r w i t h t h e a l g o r i t h m b u t may need some a s s i s t a n c e i n e x t r a c t i n g t h e e s s e n t i a l i n f o r m a t i o n f r o m t h a t p r e s e n t e d f o r a p a r t i c u l a r p r o b l e m , and t h a t t h e s t u d e n t s may need some h e l p i n Processing t h i s i n f o rma t i on . Suppose t ha t the given a lgor i thm conta ins *N' sequent ia l processes, P1 to Pn: suppose t h a t the essen t i a l fea tu re of the f i r s t N-1 processes is t h a t each ca l cu la tes the value of a v a r i a b l e , say V1 to V n 1 , and f u r t h e r suppose t h a t the essen t i a l fea tu re of the Nth p ro cess is to c a l c u l a t e the value of a f u r t h e r va r iab le , Vn using the values of the va r i ab les V1 to V n 1 . I f the student requests help about t h i s a l go r i t hm , it seems reasonable to present him w i t h a TRACE which cons is ts of N-l f ac t s ( va r iab le values) and a s ing le DEDUCTION, the value of the Nth v a r i a b l e . (This in fo rmat ion is r e f e r r e d to as the S y s t e m ' s TRACE and t h i s f a c i l i t y as the HELP mode.) C l e a r l y , the form of the TRACE w i l l depend upon the a lgor i thm being discussed and w i l l usua l l y be a ser ies of in terspersed FACTS and DEDUCTIONS. On the other hand, whatever the form of the TRACE i t is poss ib le t h a t the HELP provided would not be at a s u f f i c i e n t l e v e l of d e t a i l and so the student would want to ask some subs id ia ry quest ions about the var ious s t a t e ments. This can be viewed as the student asking f o r more d e t a i l e d in fo rmat ion about one of the p ro cesses. I d e a l l y , the student would be able to f u r t h e r query t h i s secondlevel i n fo rmat ion and so on u n t i l a l l h i s quer ies are answered.