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Fostering a Good Mathematical Disposition

by Glenda Lappan, NCTM President 1998-2000

NCTM News Bulletin, September 1999

I suppose it is because nearly all children go to school nowadays, and

have things arranged for them, that they seem so forlornly unable to

produce their own ideas.

--Agata Cristie

!"ery September, #e ret$rn t% s&%%l #it a 'eeling %' rene#al, %pe, and

anti&ipati%n( And #it ea& %' tese Septembers, #e begin #it a pr%'essi%nal plan '%r te year(

)$r plans in&l$de identi'ying te matemati&s &%ntent #e are g%ing t% try t% tea& better, te

ideas #e are g%ing t% $se t% streamline %$r &$rri&$l$m, and %# #e are g%ing t% b$ild %n %$r

st$dents* matemati&s +n%#ledge( T% tat #%$ld add, as te Agata Cristie $%te implies, tat

#e need t% plan t% elp st$dents de"el%p ealty disp%siti%ns t%#ard matemati&s(

.e&ently, as+ed a matemati&ian 'riend %' mine #at e #%$ld m%st li+e '%r st$dents &%ming int%

&%llege t% +n%# in matemati&s( e/pe&ted t% get te $s$al list %' spe&i'i& matemati&al

pr%&ed$res, te&ni$es, r$les '%r s%l"ing e$ati%ns, and s% '%rt( nstead, e t%$gt '%r a min$te

and said, $st send tem t% $s +n%#ing %# t% st$dy matemati&s and %# t% be %rganied and

#it a #illingness t% try tings in matemati&s tat re$ire s%me e''%rt( Tis #as an eye-%pener

'%r me( And tin+ e is rigt(

St$dents need disp%siti%ns tat #ill enable tem t% perse"ere in m%re-&allenging pr%blems, t%

ta+e s%me resp%nsibility '%r teir %#n learning, and t% de"el%p g%%d #%r+ abits in matemati&s(

3n'%rt$nately, #e tend t% red$&e learning matemati&s t% s%meting tat tea&ers #%r+ e/tremely

ard t% elp st$dents d% #ile st$dents #ait '%r tea&ers t% ma+e it simple en%$g t% s$r"i"e te

test %n 4riday(

T%se 4riday tests are imp%rtant '%r assessment, b$t tey al%ne are n%t en%$g, espe&ially i' tey

are n%t al#ays &allenging( 4%rt$nately, many tea&ers are beginning t% in&%rp%rate assessment

s$ggesti%ns 'r%m te NCTM Standardsby gi"ing st$dents a "ariety %' %pp%rt$nities t% s%# $s

#at tey +n%# and are able t% d% in matemati&s( Still, it*s &lear #e need t% ma+e m%re e''%rts t%

empasie assessing matemati&al disp%siti%ns and #%r+ abits--s% tat #en st$dents g% %n t%

&%llege %r &areers, tey a"e te essential desire t% s%l"e di''i&$lt pr%blems(

Part %' te &allenge '%r tea&ers is te di''i&$lty %' assessing s$& aspe&ts %' st$dents* pr%gress(

5$t m$& %' te s%$r&e %' te &allenge is tat #e a"e n%t traditi%nally ta+en m$& resp%nsibility

'%r '%stering st$dents* attit$des t%#ard matemati&s and teir per&epti%ns %' teir %#n r%le in

learning te s$b6e&t(

S% #at &an #e d% ab%$t tis state %' a''airs7 e &an begin by realiing tat #e play a r%le in

&anging st$dents* minds ab%$t #at is in"%l"ed in learning matemati&s( Already s%me tea&ers

a"e been #%r+ing %n #ays t% en&%$rage better matemati&al disp%siti%ns and #%r+ abits--and

t% e"al$ate %n te basis %' tese #%r+ abits( )ne e''e&ti"e t%%l, %n&e tea&ers a"e t%ld st$dents

%' teir e/pe&tati%ns, is st$dent sel'-e"al$ati%ns $sed as a reg$lar &%n&l$si%n t% a tea&ing $nit( As

a s$pplement t% tests and pr%6e&ts, st$dent sel'-assessments &an sed ligt '%r b%t te st$dent

and te tea&er %n $esti%ns s$& as te '%ll%#ing

Mathematical Dispositions::%# d% st$dents resp%nd t% matemati&al &allenges7 :%# d% tey

see temsel"es as learners %' matemati&s7 Are tey #illing t% perse"ere in attempting t% ma+e

sense %' a pr%blem, a pr%&ed$re, a &%n&ept, %r s%me %ter imp%rtant aspe&t %' matemati&s7 Are

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tey a&&$m$lating a set %' g%%d matemati&al e/amples tat tey &an $se t% elp remember %r

re&%nstr$&t imp%rtant ideas7

Work Habits:Are te st$dents able t% %rganie and s$mmarie teir #%r+7 ;% tey see te big

ideas in #at tey are learning7 Are tey see+ing &%nne&ti%ns am%ng ideas tat tey are st$dying7

Can tey $se pre&ise matemati&s lang$age and appr%priate representati%ns t% elp &%mm$ni&ate

teir ideas7 Are tey pr%gressing in be&%ming independent learners7 Are tey able t% learn 'r%m,

and &%ntrib$te t%, te learning %' %ters7

Tese g%als '%r te matemati&s &lass migt seem t% already %"erb$rdened tea&ers li+e te stra#

tat br%+e te &amel*s ba&+( 5$t tea&ers #%*"e tried tis tell me tat a'ter a 'e# m%nts %'

str$ggling t% '%&$s st$dents %n teir r%le in learning matemati&s tr%$g tese sel'-re'le&ti%ns,

tey see real &anges in st$dents* engagement in teir &lassr%%ms( Teir st$dents n%t %nly learn

matemati&s better b$t als% gain a sel'-a#areness tat gi"es tem te &%n'iden&e t% &%ntin$e t%

learn( S% as te s&%%l year begins and ne# &allenges emerge, try t% gi"e y%$r st$dents a gi't

tat #ill &arry tem '%rt t% '$t$re matemati&s and li'e s$&&esses--elp tem learn t% pr%d$&e

teir %#n ideas(

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