�e io C

IMPORTANCE OF DIAGNOSTIC ASSESSMENTS AS A

PRECURSOR TO DIFFERENTIATED LEARNING

I porta e of Diag osi Assess e tsAssess e ts a e esse ial to dete i e ho

u h a hild has lea t. The a e e ui ed i o de to p o ide a o plete pi tu e of lea i g, i fo aio o lea i g p og ess of the stude t, to diag ose spe ii st e gths a d eak esses i a stude t s lea i g, a d to oi ate fu the lea i g. Assess e t is a o i uous a d a o goi g p o ess.

Diag osi assess e ts help to i d out the thought p o ess of the hild, his easo i g fo a pa i ula a s e . The help dete i e the le el of k o ledge a d skill of the hild. I ou loud ased Adapai e Math Lea i g Tool alled Mi dspa k a diag osi test o de i al o pa iso has ee i t odu ed ased o esea h D . Ka e �ta e f o The U i e sit

of Mel ou e, Aust alia. The test, alled

Ksha a Chak a a th

De i al Co pa iso Test DCT , hi h has ee ate pted o e stude ts i � ea s, lassiies stude ts i to a ious is o epio odes ased o thei thi ki g hile o pa i g

pai s of de i als. The a e take th ough spe ii e edial paths a d i all gi e a post -DCT to he k thei lea i g.

DCT De i al Co pariso Test : �tude ts u de sta di g of de i al u e aio is apped usi g a sho t test alled the De i al Co pa iso Test DCT , he e stude ts ha e to hoose the la ge u e f o ea h of pai s

of de i als. The pai s a e a efull hose so that f o the pate s of espo ses, a stude t s isu de sta di g a e diag osed as elo gi g to o e of a u e of lassii aio s e io ed late sho i �tep i Figu e A

 

Figu e A: Illust ated Flo of stude ts i Mi dspa k s De i al odule

74

This is follo ed a ga e alled Hidde Nu e s he e stude ts a e p ese ted ith t o de i al u e s ith digits hidde ehi d losed

doo s; the task is to i d hi h u e is la ge ope i g as fe doo s as possi le. ‘e ui i g

si ila k o ledge to that e ui ed fo the su ess o DCT, the ga e also highlights the pla e alue p ope t that the ost sig ii a t digits a e those to the let. sho i �tep � i Figu e A

The ga e helps us disi guish the t o ajo

Classii aio a d details of the ode:

PRIMARY SECONDARY HOW DOES THE STUDENT THINK? SO.. WHAT’S

MISCONCEPTION MISCONCEPTION HIS/ HER ANSWER?

‘TYPE’ ‘TYPE’

Whole u e T eats de i al po io as a othe hole u e . . < . as <

thi ki g L,L Nu e ato fo used thi ki g hooses . > . as > , hile �t i g le gth thi ki g hooses . < . as has digits a d has t o.

)e o- akes- s alle ate a de i al poi t akes the u e s alle . Co e tl hooses

thi ki g + Colu Co side s . as te ths a d . as te ths. . < .� ut

O e lo Thi ki g L,L� i o e tl hooses . < . as te ths < te ths.

‘e e se thi ki g L,L Belie es ight ost olu s ha e la gest pla e alue, . < . as hu d ed

so o pa es f o the ight- ost olu i st. te s > te s

De o i ato fo used ‘eads a o e digit de i al as a u e of te ths, . > . thi ki g �,� a t o digit de i al as a u e of hu d edths a d . > .

the i o e tl ge e alises the fa t that te th is g eate tha hu d edth to a u e i the te ths is g eate tha a u e i the hu d edths .

‘e ip o al thi ki g o T eats de i al po io as so ethi g a alogous to . � < .

egai e thi ki g �,� the de o i ato of a f a io o as a u e o as / � < / o as the othe side of ze o o less tha ze o. - � < - .

Lo ge - is- la ge

L

�ho te - is- la ge

�

Difere t groups of de i al pairs to help lassify the stude ts **To disi guish et ee the L* fails g oup , passes g oup � a d �*- t pe passes g oup , fails g oup �

To disi guish a o g L,L * fails g oup , passes g oup , L,L� * passes oth g oup a d a d L,L * fails oth g oup a d .

G‘OUP G‘OUP �

. / . . / .

G‘OUP G‘OUP

. �/ . . �/ .�

Lea i g Cu e, August �

a s of thi ki g stude ts ha e- lo ge is la ge the g eate the le gth of the de i al,the la ge

its alue a d sho te is la ge the lesse the le gth of the de i al, the la ge its alue . Fu the spe ii uesio s a d espo se of the stude t help us ide if the logi ehi d thei thi ki g.

Based o the is o epio u ket the stude t is lassiied i to, he/ she is p ese ted ith a spe ii o de of uesio s a d lea i g ga es that ill help lea his/ he is o epio s.

75�e io C

hi h p odu es e o s is that a stude ts i ludi g hole u e thi ke s a e u a le

to i se t a u e et ee , sa , . a d . as the thi k these a e o se ui e u e s. I o e of the stude t t ials, � stude ts e e ade to pla the ga e agai ate the had i ished a d this i e the e e a le to pla e a u e

et ee . a d . � a d also e plai f o hat the o se ed that . a d . � a e

the sa e as . a d . � espe i el a d he e . ould o e i et ee . Wo ki g o o e uesio s like this, he e the s ste sho s de i als that e ist et ee the gi e � de i als, halle ges thei thi ki g a d a stude ts a e a le to look at de i als i the t ue light.

O e stude ts ha e o pleted thei e ediaio path, the ha e a post- DCT pai s of de i als

he e the la ge de i al should e hose - de i als d a i all ge e ated to e o d the odes agai a d he k i p o e e t if a .

The o heade s o espo d to the is o epio odes i p e test a d olu heade s o espo d

to is o epio odes i post test.

 

To disi guish et ee �� * fails g oup , passes g oup a d ���* fails oth g oup a d .

G‘OUP G‘OUP

. �/ . . / .�

**‘efe to appe di fo details o ho the u e s a e ge e ated i ea h g oup

Re ediaioThe e ediaio path, o e is o epio odes a e ge e ated, o sists of lea i g u its

o de i als o epts hi h is i ed as ell as e tai ga es depe da t o the is o epio ode that help stude ts lea the fu a

a d lea thei is o epio s. Fo e a ple, a stude t ho has got the ode L,L Whole Nu e Thi ke s ill i iiall get a ga e alled De i alie s hi h is a lassi shooi g ga e desig ed to li k a ious ep ese taio s of the alue of digits i a de i al u e . Fo e a ple,

the i the u e . is to e ide iied as ep ese i g te ths, . , / as ell as i o e

dii ult ep ese taio s e ui i g eu iisi g as hu d edths, thousa dths.

�tude ts ith hole u e thi ki g ill e helped this ga e he e the ealize that the pla e alue of i . is . a d ot as pe ei ed

hole u e thi ke s.

This is follo ed a ga e alled Fl i g Photog aphe ate ate pi g a fe uesio s o de i als he e stude ts photog aph a a i al li ki g he a heli opte passes a spe iied u e o a u e li e. This task e ui es u de sta di g of de i al u e aio

a d elai e size of de i al u e s. Whole u e thi ke s usuall e pe t .� to e e la ge a d a e su p ised to see it lose to

ze o .

The e t ga e that appea s agai ate o ki g o so e uesio s o de i als is Nu e Bet ee . The ga e is pla ed o a u e li e,

he e stude ts ha e to t pe i a u e et ee a gi e pai of e d poi ts. The ai situaio

76

O ser aio s: ‘oughl % of the stude ts a e Appa e t E pe ts AE i o pa iso of de i als.

� LL� )e o- akes s alle + Colu o e lo a d �� De o i ato Fo used Thi ki g see to e the ajo is o epio s a o g stude ts ith % a d % p o i e e espe i el .

Out of stude ts i LL� p e , e ai ed i LL� hile o ed to AE i the post test. ha e o ed to � atego .

Out of �� stude ts i �� p e , e ai ed i �� hile o ed to AE i the post test. ha e o ed to L atego .

Stude t I ter ie O ser aio s:�tude ts used a ious ethods/ thi ki g to o pa e t o de i als-

Gi e � de i als, see hi h o e is lose to the e t hole u e o hat should e added to i g it to the e t hole u e �tude ts a o a ot a s e o e tl ith this easo i g .

� Add ze oes to ake the � de i als of the sa e st i g le gth a d the o pa e the �.

Co pa e the hole u e . If sa e o pa e the te ths, hu d edths et i that o de .

Fe e digits is the g eate de i al . �o e a lea l e plai this is e ause te ths is

g eate tha hu d edths

Ate the de i al poi t the u e hi h is lesse is the g eate de i al. He e the look at the alue he eas i the p e ious ase the look at the u e of digits ate the poi t .

Lea i g Cu e, August �

Ha d ite espo ses of so e stude ts a out ho the hoose the la ge de i al i a gi e pai .

Poi ts to o side fo Ve sio � The u e t fo at does ot lassif a stude t i to � dife e t is o epio s. He is eithe put u de UN U lassiied atego o , i ase he is lassiied u de L o � a d the e has uliple o g u de sta di gs, is lassiied i to L,UN a d �,UN espe i el .

A p o isio to let stude ts e lassiied i to o e tha o e is o epio t pe should e

o side ed.

� Hidde Nu e s a e used as a diag osi test i the iddle of the e edial path to he k fo stude t s lea i g a d u de sta di g ate a ouple of ga es, so that the path a e

odiied i ase his is o epio has shited f o o e to the othe du i g the ou se of e ediaio .

 

77�e io C

GROUP EXAMPLES DESCRIPTION

G‘OUP . / . A1 > B

1 + , B� f ee o A

1 = B

1 + & B� <

L-� . / . � X, Y elo g to [ , ], keep <

G‘OUP � . / . A1 > B

1 + , o A

1 = B

1 + & B� <

L-� . �/ . X elo gs to [ , ], Y elo gs to [ , ] keep > .

G‘OUP . �/ . B1 = , A

1 <= B�, X, Y elo g to [ , ], keep <

.� / .

G‘OUP . �/ . A1 = B

1 < , A� = B� < , A < , B < A , keep >

. �/ .

G‘OUP . / .� A1 > B

1, X, Y elo g to [ , ], keep =

. / .

G‘OUP . �/ .� A1 > B

1 + , A� < B�, A < B , =

. / .

Kshama has a Master’s degree i Mathe ai s fro IIT Madras. She as a Edu aio al Spe ialist at Edu aio al I iiai es P t. Ltd. for 3 ears i the o te t de elop e t tea of Mi dspark, a o puter ased lear i g progra e for stude ts fro Classes to , i Mathe ai s. Her ork i luded uilizi g e perise to de elop oferi gs that ould help i i pro i g tea hi g a d lear i g sta dards i s hools de elopi g i o ai e tests a d e er ises, orga isi g orkshops, de elopi g i o ai e tea hi g aterials a d produ io of resear h reports. She ill soo e pursui g the M.A i Edu aio progra e at Azi Pre ji U i ersit , Ba galore. She a e o ta ted at ksha a. hakra arth @ei-i dia. o

Appe di

A .A1A�….A is the la ge de i al u e

B .B1B�….B is the s alle de i al u e