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Development of Visual Mathematics Literacy Self-efficacyScale for Prospective Teachers

Author(s):Baa! "al#! (presentin$)% &eim "apa Ay'#n (presentin$)

onference:* +,.% The Past% the Present an' the /uture of 'ucational *esearch

0et1or!:+.2 Mathematics 'ucation *esearch

/ormat:Paper (opy for 3oint Session)

Session 4nformation

24 SES 04 JS, Teaching, Learning and Assessment in Higher Education

Paper Session% 3oint Session 05 ++ an' 05 +.

Time:+,.-,6-,7

,6:,,-,:7,

*oom:B,7, Anfiteatro

hair:Tam8s 9oma

ontri;ution

Development of Visual Mathematics Literacy Self-efficacy Scale for

Prospective Teachers

4n the last century% ne1 thou$hts an' inventions come to life 'ay ;y 'ay as a result of !no1le'$e

transmission an' pro'uction 1hich are important elements in people<s lives 1hile teachers< roles

are prominent in this process2 They shoul' have some capa;ilities to ;e $oo' role mo'els for

in'ivi'uals2 This assumption ;rin$s some terms an' concepts to min's that shoul' ;e ac=uire' ;y

every teacher2 4n this perspective% >literacy? term o;tains a concession over others e@plaine' as the

capacity of in'ivi'uals to fin' an' use of !no1le'$e% s!ills ;esi'es analyin$% u'$in$ an' also

solvin$ an' ma!in$ sense of pro;lems in 'ifferent areas (D% +,+)2 Mathematics literacy has

;ecome one of the $oals of mathematics teachin$ 'ue to chan$es at technolo$y an' mathematics

as a result of transition from in'ustrial to information society (9aiserC 5illan'er% +,,)2 4t is

'efine' as >an in'ivi'ual<s capacity to i'entify an' un'erstan' the role that mathematics play in the

1orl'% to ma!e 1ell foun'e' u'$ements an' to use an' en$a$e 1ith mathematics in 1ays that

meet the nee's of that in'ivi'ual<s life as constructive% concerne' an' reflective citien? (D%

+,,E)2n the other han'% visual literacy as a 'ifferent type of literacy 'efine' ;y 5ileman (667)

as? the a;ility to turn information of all types into pictures% $raphics or forms that help

communicate the information?2 4t is an interrelate' concept inte$ratin$ theory% visual lan$ua$e an'

presentational perspective an' technolo$ical 'evelopment (9or'i$el A;erse!% +,,F)2 The

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importance of inte$ration of various 'isciplines in e'ucation to provi'e meanin$ful learnin$ is

emphasie' (Ta!#n an% antGr! C Hn$el% +,,) so inter'isciplinary relations an' loo!in$ the

pro;lems from multi-perspectives $ains hi$h attention2 Ience% t1o literacy types 1ill ;e consi'ere'

as one type of literacy% visual math literacy2 ach in'ivi'ual ma!es use of visual ima$es in their

'aily lives% especially solvin$ mathematical pro;lems an' concretiin$ the a;stract concepts 1ith

this 1ay is supporte' ;y many researchers (Polya 6J7K Ium;ree% 66+K 9arC pe!% +,,6) havin$positive effect on mathematics achievement of stu'ents2 Duchastel (6F,) mentione' the functions

of visuals un'er 'ifferent cate$ory names such as lo$ical- mathematical an' 'ata presentation

implyin$ the relationship of visual literacy 1ith mathematical literacy2 se of 'ia$rams an' charts in

or'er to e@plain mathematical relationship is 'escri;e' in the former cate$ory 1hile visual

presentation of 'ata is $iven as an e@ample of the latter one2 Be!'emir an' Duran (+,+) stu'ie'

on this concept an' 'efine' it as >the mastery to 'efine% interpret% evaluate an' use the pro;lems

in 'aily life 1ithin visual frame1or! an' to 'efine% interpret% evaluate an' use the visual or spatial

information in mathematical terms2? To ;e literate in visual mathematics% in'ivi'uals< affective

characteristics play a prominent role 'ue to the nature of the constructs2 Self -efficacy is one of the

affective constructs 'escri;e' ;y Ban'ura (66J) as >the ;eliefs in one<s capa;ilities to or$aniean' e@ecute the courses of action re=uire' pro'ucin$ $iven attainments? (p2 7)2 Since visual math

literacy is a novel term% teachers an' prospective teachers< self efficacy ;eliefs to1ar' this concept

shoul' ;e consi'ere' ;eforehan' ;ecause they shoul' have re=uire' capa;ilities to1ar' the $iven

era ;efore assessin$ ho1 stu'ents are2 Teachers< self efficacy perceptions are consi'ere' one of the

factors 1hich 'irectly influence their =uality of instructions in the lon$ run (Tschannen-Moran%

5oolfol! Ioy% +,,J)2 There is no such a scale 1hich assesses efficacy ;eliefs of teachers or teacher

can'i'ates to1ar' visual mathematics literacy term that mi$ht ;e 'ue to its recent use in the

literature2 Thus% the purpose of this stu'y is to 'evelop a vali' an' relia;le scale to assess self

efficacy ;eliefs of prospective teachers to1ar' visual mathematics literacy2

Method

The accessi;le population of the stu'y is un'er$ra'uate stu'ents in 'ucation /aculty of Mi''le

ast Technical niversity in An!ara% Tur!ey2 onvenience samplin$ proce'ure 1as utilie'2 The

sample consiste' of 76 teacher can'i'ates inclu'in$ 'ifferent fiel's of stu'y an' $ra'e levels2 /or

the instrument 'evelopment part% the literature relate' to mathematics% visual% visual mathematics

literacy an' self efficacy constructs 1ere e@amine' carefully to $enerate initial item pool2 Besi'es

loo!in$ the literature% ei$ht open en'e' =uestions 1ere as!e' to si@ mathematics e'ucation

$ra'uates2 After revie1in$ the literature an' o;tainin$ the responses to =uestions% the elementary

an' secon'ary school mathematics curricula 1ere analye' ;ecause content of the su;ect 1as

concerne' as one of the 'imension for the $iven construct (Be!'emir CDuran% +,+)2 Base' on the

literature revie1% current scales an' responses to open en'e' =uestions% .+ items 1ere 1ritten in

the initial item pool2 Then% co$nitive intervie1s 1ere 'one 1ith t1o teacher can'i'atesK e@pert

opinion 1as ta!en from one e@pert in the fiel' an' one measurement an' e'ucation specialist 1ith

PhD 'e$rees to provi'e content vali'ity of the instrument2 Base' on the e@pert opinions an'

co$nitive intervie1s% E items 1ere eliminate' an' some of the items 1ere revise' 'ue to content

irrelevance% pro;lems relate' to 1or'in$ an' or$aniation of items for the sa!e of the instrument<s

clarity an' un'erstan'a;ility2 onse=uently% the scale as a self-report instrument comprise' of +E

items on a nine point Li!ert scale ran$in$ from () >insufficient? to (6) >very sufficient?2 The first

part of the scale is a;out the 'emo$raphic information as!in$ =uestions a;out $en'er% fiel' ofstu'y% $ra'e level% the $ra'uate' hi$h school% NPA an' the status of ta!in$ a math course 'urin$

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university e'ucation2 The secon' part involves items pointin$ out prospective teachers< self efficacy

;eliefs to1ar' visual math literacy2Sample items mi$ht ;e $iven as% Io1 1ell can you estimate the

perimeter of a placeO K Io1 1ell can you 'evelop a proect in your 'iscipline ;y $ettin$ ;enefit

from mathematics an' visual 'isciplinesOK Io1 1ell can you 'etermine the similarities of

$eometrical shapes aroun'O

Expected Outcomes

After the a'ministration of the scale% factor analysis 1as con'ucte' to o;serve the

interrelationships amon$ the varia;les an' to 'iscover factor structure of the scale2 @ploratory

/actor Analysis (/A) 1as utilie'2 Base' on the multivariate normality assumption% Principal A@is

/actorin$ e@traction metho' 1as use'2 Then% the correlation matri@ 1as e@amine' to see the

relationships ;et1een items2 ach item correlate' each other 1ith a value of 27, or hi$her2 Barlett<s

Test of Sphericity fin'in$s 1ere si$nificant in'icatin$ the 'ifference of correlation matri@ from the

i'entity matri@ 1hile 9aiser Meyer l!in (9M) value is 26 2E, an' the sample sie is ten times$reater than the num;er of items2 Three factors 1ere o;serve' accor'in$ to scree plot

results2;li=ue rotation 1as use' to simplify an' clarify the 'ata ;ase' on the assumption that

factors are correlate' 1ith each other2 Pattern matri@ 1as e@amine' an' accor'in$ to results% item

an' + 1ere 'eci'e' to ;e eliminate' 'ue to cross loa'in$s an' uninterpreta;le contri;ution of

items to relate' factor an' /A 1as e@ecute' a$ain 1hich reveale' three factors2 The final version

of the scale involves +. items clustere' aroun' three 'imensions name' as >comprehension of

visual mathematics !no1le'$e?% >actuality? an' >$eometrical fi$ures C shapes?2 Actually% fin'in$s

correspon' 1ith the literature in a 1ay that confirms the vali'ity of the scale2 E+2E.Q of variance is

e@plaine' ;y these three 'imensions 1hich also sho1 that self-efficacy of visual mathematics

literacy is a multi'imensional construct2 /actors are also intercorrelate' 1hile relia;ility coefficients

of each factor as 26.% 2FE an' 2F6 are consi'era;ly hi$h2 All in all% althou$h the >Visual Mathematics

Literacy Self fficacy Scale? 'isplays the ;asic properties of a relia;le an' vali' scale for teacher

can'i'ates% it nee's to ;e vali'ate' in the lon$ run 'ue to continuity of vali'ation process of the

scale 'evelopment2

Reerences

Ban'ura% A2 (66J)2 Self-efficacy: The e@ercise of control2 0e1 &or!: /reeman2 Be!'emir% M2 C

Duran% M2 (+,+)2 Development of a visual math literacy self efficacy perception scale for

elementary stu'ents2 3ournal of n'o!u May#s niversity 'ucation /aculty% 7()% F6-2

Duchastel% P2 2 (6F,)2 *esearch on 4llustrations in 4nstructional Te@ts2 Bryn Ma1r% Pa2: The

American olle$e% Department of *esearch an' valuation2 (*4 Document *epro'uction Service

0o2 D + 7+.) Ium;ree% *2 (66+)2 @periments an' relational stu'ies in pro;lem solvin$: A

meta-analysis2 3ournal for *esearch in Mathematics 'ucation% +7 (7)% +.+-+J72 9aiser% N2 C

5illen'er% T2 (+,,)2 Development of mathematical literacy: *esult of an empirical stu'y2 Teachin$

Mathematics an' its Applications% +.(+-7)% .F-E,2 9ar% T2 C pe!% A2 S2 (+,,6)2 Matemati! tarihin'e

sRel pro;lemlerin RGmGn'e $Rrsel temsillerin !ullan#lmas# se of visual representations on

solvin$ 1or' pro;lems on mathematics historyU2 3ournal of af=a niversity% +F% 7F-.J2

9or'i$el A;erse! (+,,F)2 Visual literacy-one of +st century literacies for science teachin$ an'

learnin$2 Pro;lems of 'ucation in the +st entury% % 6-J2 D ( r$aniation for conomico-operation an' 'evelopment)2 (+,,E)2 Assessin$ scientific% rea'in$ an' mathematical literacy% A

8/19/2019 Development of Visual Mathematics Literacy Self

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/rame1or! for P4SA +,,E2 *etrieve' from the 5orl' 5i'e 5e;: http:WW1112oec'-

ili;rary2or$W'ocserverW'o1nloa'W6F,E,7e2p'fO

e@piresX76+F+.6Ci'Xi'CaccnameXoci'.7,+76Cchec!sumX6BADEDD+B77.DDD6/

,/FBA D ( r$aniation for conomic o-operation an' 'evelopment)2 (+,+)2 P4SA +,+

asessement an' analytical frame1or!% matehematics% rea'in$% science% pro;lem solvin$ an'

financial literacy2 *etrieve' from 5orl' 5i'e 5e;: http:WW1112oec'2or$WpisaWpisapro'uctsWP4SAQ+,+,+Q+,frame1or!Q+,e-;oo!Yfinal2p'f Polya% N2 (6J7)2 Io1 to solve it% a ne1 aspect of

mathematical metho'2 0e1 3ersey: Princeton niversity Press2 Ta!#n an% B2% antGr! NGnhan%

B2C Hn$el r'al% S2 (+,,)2 /en ;il$isi RZretmen a'aylar#n#n fen 'erslerin'e matematiZin

!ullan#m#na yRneli! Ryeterli! inanlar#n#n incelenmesi The e@amination of self efficacy ;eliefs of

science teacher can'i'ates to1ar' the use of mathematics on science lessonsU2 3ou#rnal of

Pamu!!ale niversity 'ucation /aculty% J% .J[+2 Tschannen-Moran% M2 C 5oolfol! Ioy% A2

(+,,J)2 The 'ifferential antece'ents of self efficacy ;elefs of novice an' e@perience' teachers2

Teachin$ C Teacher 'ucation% +7(E)% 6..-6E2 5ileman% *22 (667)2 Visual communicatin$2

n$le1oo' liffs% 0e1 3ersey: 'ucational Technolo$y Pu;lications2

Author 4nformation

Baa! "al#! (presentin$)

Mi''le ast Technical niversity% Tur!ey

&eim "apa Ay'#n (presentin$)

Mi''le ast Technical niversity% Tur!ey