Prompt

Chicago Public Schools conduct annual, standardized testing for third, sixth and eighth graders. These are high$-$stakes tests, because a student$$s promotion to the higher grade depends on its result. The schools are held responsible for poor performance and if a school fails to produce $$good$$ results, it is sanctioned or possibly shut down. The original dataset consists of $700,000$ sets of test answers and around $100$ million individual answers $(1993-2000).$ For this activity we just examine a specimen of the answers chosen by sixth graders for these tests from a particular classroom. Class A shows curious performance $($right$).$

Individual student answer strings for class A are provided below. Investigate why an entire roomful of students in the classroom suddenly got very smart one year and very dim the next.

d $4$ a $2341$ c a c b d d a d $3142$ a $2344$ a $2$ a c $23421$ c $00$ a d b $4$ b $3$ c b

$1$ b $2$ a $34$ d $4$ a c $42$ d $23$ b $141$ a c d $24$ a $3$ a $12$ d a d b c b $4$ a $2134141$

d b a a b $3$ d c a c b $1$ d a d b c $42$ a c $2$ c c $31012$ d a d b c b $4$ a d b $40000$

d $12443$ d $43232$ d $32323$ c $213$ c $22$ d $2$ c $23234$ c $332$ d b $4$ b $300$

d b $2$ a b a d $1$ a c b d d a $212$ b $1$ a c d $24$ a $3$ a $12$ d a d b c b $400000000$

d $4$ a a b $2124$ c b d d a d b c b $1$ a $42$ c c a $3$ a $12$ d a d b c b $423134$ b c $1$

$1$ b $33$ b $4$ d $4$ a $2$ b $1$ d a d b c $3$ c a $22$ c $000000000000000000000$

d $43$ a $3$ a $24$ a c b $1$ d $32$ b $412$ a c d $24$ a $3$ a $12$ d a d b c b $422143$ b c $0$

$313$ a $3$ a d $1$ a c $3$ d $2$ a $23431223$ c $000012$ d a d b c b $400000000$

d b $2$ a $33$ d c a c b d $32$ d $313$ c $21142323$ c c $300000000000000$

d $43$ a b $4$ d $1$ a c $3$ d d $43421240$ d $24$ a $3$ a $12$ d a d b c b $400000000$

d b $223$ a $24$ a c b $11$ a $3$ b $24$ c a c d $12$ a $241$ c d a d b c b $4$ a d b $4$ b $300$

d b $4$ a b a d c a c b $1$ d a d $3141$ a c $212$ a $3$ a $1$ c $3$ a $144$ b a $2$ d b $41$ b $43$

$1142340$ c $2$ c b d d a d b $4$ b $1$ a c d $24$ a $3$ a $12$ d a d b c b $43$ d $133$ b c $4$

$214$ a b $4$ d c $4$ c b d d $31$ b $1$ b $2213$ c $4$ a d $412$ d a d b c b $4$ a d b $00000$

$1423$ b $4$ d $4$ a $23$ d $24131413234123$ a $243$ a $2413$ a $21441343$

$3$ b $3$ a b $4$ d $14$ c $3$ d $2$ a d $4$ c b c a c $1$ c $003$ a $12$ d a d b c b $4$ a d b $40000$

d b a $2$ b a $21$ a c $3$ d $2$ a d $3$ c $4$ c $4$ c d $40$ a $3$ a $12$ d a d b c b $400000000$

d $122$ b a $2$ c a c b d $1$ a $13211$ a $2$ d $02$ a $2412$ d $0$ d b c b $4$ a d b $4$ b $3$ c $0$

$144$ a $3$ a d c $4$ c b d d a d b c b c $2$ c $2$ c c $43$ a $12$ d a d b c b $4211$ a b $343$

a$,$ b$,$ c and d constitute correct answers.

$0$ is for no answer

$1,2,3$ and $4$ are for incorrect answers where $1$ corresponds to a$,2$ to b and so on$.$