UEBReady?Day2:

TechnicalMaterials

August2016FrancesMaryD’Andrea,Ph.D.literacy2@mindspring.com

WithmanythankstoLorraineBanks,DarleenBogart,JamesBowden,JosieHowse,PhyllisLandon,Holly

Lawson,JennyMcFadden,JanetReynolds,andCatherineWest

Objectives

Bytheendofthistraining,parBcipantswillbeableto:•  demonstrateunderstandingofbasicprinciplesofUEBbybraillingexamplesentences.

•  brailletechnicalcodesymbolsforSTEM(science,technology,engineering,andmath)content

•  usereferenceswithintheUEBGuidelinesforTechnicalMaterialmanualandotherresourcestoproduceintermediateandadvancedlevelsofSTEMcontent

•  describeanduseappropriategradeoneindicatorswithintechnicalandmathemaBcaltranscripBon.

Remember:

•  TechnicalmaterialsinUEBfollowthesamesymbolsandrulesfornontechnicalmaterials•  •consistencyofrulesacrosscontexts•  •followspacingofprint(mostly)•  •"standalone"rule(whenisitacontracBon?)•  •grade1moderules

Thereisno"UEBMathCode"—it'sallONEcode.•  othercountriesthathaveadoptedUEBareusingitonly•  theUSistheonlycountrythatismaintainingitsoldmathcodeinaddiBontoadopBngUEBsowehavenomodeltofollow

TwoImportantRules!

•  Standalonerule:SecKon2.6•  “AleSerorleSers-sequenceisconsideredtobe‘standingalone’ifitisprecededandfollowedbyaspace,ahyphen,oradash.”(Canbeeitheraregulardashorlongdash.)Thisisimportantbecauseithelpsyoudecideif/whenyouneedtousegrade1indicators.

•  Grade1Mode:SecKon5.1•  “Agrade1indicatorisusedtosetgrade1modewhenthegrade1meaningofasymbolcouldbemisreadasacontracBonmeaningoranumericmeaning.”

•  Somesymbolshavea“grade1meaning”andthereforeneedagrade1indicator.

•  Note:“Uncontractedbrailleisdifferentfromgrade1mode.”SecBon2.5.2

TheReaderRules!•  InUEB,youmustalwaysthinkfromthebraillereader'sviewpoint—whatwillpotenBallybeconfusedormisread?That'swhytheStandingAloneRuleandtheGrade1rulesaresoimportant.•  Tocheckyourwork,alwaysask:"Couldthissymbolbeconfusedwithsomethingelse?"•  Thatalsomeansthatintechnicalcontexts,theremaybemorethanonewaytodosomething.•  Thebasicruleofthumb:Trytominimizeindicatorsinthemiddleofanexpression.

UniCicationofLiteraryandMathematicalTexts

•  UEBisdesignedtounifysignsacrossliteraryandmathemaBcalcontexts.

•  Numbersandsymbolsarethesameinallcontexts.

blue "6 yell[ "7 gre5

blue+yellow=green.

,simple z #a "6 #a "7 #b4

Simpleas1+1=2.

#a"6#a "7 #b

1+1=2

Numbers

•  Numericmodeindicatorisconsidereda“prefix”inUEBandletsthereaderknowthatwhatfollowsarenumbers.Itsets“numericmode.”Itisdots3-4-5-6#

•  Theonlysymbolsthatmaybeusedinnumericmodeare:digits,decimalpoint(period),comma,simplefracKonline,numericspace(dot5),andthelineconKnuaKonindicators(usedwhendividingverylongnumbersbetweenbraillelines).Anythingelseterminatesit!

Numbers•  Thenumericindicatoristerminatedbyaspace,signsofoperaBon,hyphen,dash,colon,apostrophe,ellipsis,parentheses,slash,etc.somustberepeated.Here'swhy:

,an #h-cab fleet ,! vote 0 #h-#cab4

An8-cabfleet Thevotewas8-312. •  Thenumericindicatoralsosignifies“grade1”modesocan’tuse“th”and“st”contracBonsalernumbers•  #ast floor 1stfloor

Grade1ModeandNumericIndicator

•  Thenumericindicatoractsasagrade1indicator.Thismeansthatwhatfollowsanumbersignhasitsuncontractedmeaning.

•  Asymbolthatdoesn'tfollowanumericindicatorandcouldbeamisreadasanumberorcontracBonneedsthegrade1indicator.

•  InUEB,a"word"isdefinedas"stringofsymbols"calledasymbols-sequence.Itisterminatedbyaspace(orthegrade1terminator).

Grade1Indicators

;indicatesthefollowingsymbolisingrade1;; indicatesthefollowingwordisingrade1;;; indicatesthefollowingpassageisingrade1 ;' (dots5-6,3)terminatesthegrade1passage.Whengrade1modeissetbythenumericindicator,itisterminatedbyaspace,hyphenordash.Theeffectofanumbermaybeterminatedbutgrade1modeconBnues.Inotherwords,morethingsterminatenumericmodethanterminategrade1mode.

Grade1Indicators

•  Ifabraillesymbolalsohasacontractedmeaningthenthegrade1indicatormustbeusedunlessgrade1modeisalreadysetorifthere’snoambiguitywhenfollowingUEBrules:

3g 3G 3m3m

Grade1Indicators

•  Ifabraillesymbolalsohasacontractedmeaningthenthegrade1indicatormustbeusedunlessgrade1modeisalreadysetorifthere’snoambiguitywhenfollowingUEBrules:

•  #c;g #c,g #cm #c ;m

3g 3G 3m 3m

Grade1IndicatorsBecausethereisnoambiguity,agrade1indicatorisnotrequiredwhenanycapitalleSeroranyoftheleSersk-zfollowanumber.AsimplearithmeBcequaBongenerallywillnotneedgrade1indicators. Anyalgebraexpressionmayneedagrade1wordindicatoror,ifitincludesspaces,agrade1passageindicator.

SignsofOperationandComparison

"6 + (plus) "- - (minus)

"8 x (multiplication sign) "4 � (multiplication dot)

"/ ÷ (division sign) "7 = (equals) @< < (less than) @> > (greater than)

OtherUsefulSigns

",- long dash (centered line) 3+1 = — .- underscore 3+1 = _

+ general omission/"visible space" 3 + 1 =

#= infinity ∞ .p Pi π ,* therefore ∴ .=" continuation indicator for long expressions (dot 5) See your UEB Rulebook for additional symbols.

10VerySimpliCiedRulesKISSforUEB1.  +-x÷=alltakedot52.  moneysymbolstakedot4andarefollowedbynumbersign(but

canalsostandalone!)3.  operaBonsignsareunspacedbothsides4.  comparisonsignsarespacedbeforeandaler5.  greaterthanandlessthansignstakedot46.  simplefracBonline–/ 7.  mixednumerals–repeatnumbersign8.  superscript–changelevelup(9)9.  subscript–changeleveldown(5)10.  squareroothastoopenandclose(% +)

Source:HitchhikersGuidetoUEB(NewZealand)

SimpleArithmetic#ab"6#ce "7 #dg

#ej"/#e "7 #aj

#h"4#c "7 #bd

#ib @> #hc

SimpleArithmetic#ab"6#ce "7 #dg

12+35 = 47 #ej"/#e "7 #aj

50÷5 = 10 #h"4#c "7 #bd

8�3 = 24 #ib @> #hc

92 > 83

SpacingofMathProblems

•  Thereissomeflexibilityinspacing.•  Ingeneral,spacingconformstoprint,however...•  ThereisastrongpreferencenottospaceoneithersideofasignofoperaBonandaspaceonbothsidesofasignofcomparison.

•  Ifpreparingsimpleproblemsforyoungchildren,permissibletospacearoundsignofoperaBon.

SimpleFractionsandMixedNumbers

.=/ simplenumericfracBonline

.=./ generalfracBonline

.=( generalfracBonopenindicator

.=) generalfracBoncloseindicator

.=_/slashmark

Fractions

•  A true fraction has one number written above another number: use the simple numeric fraction line.

•  In fractions with numerals, there is no need to repeat the numeric indicator after the fraction line (because it’s allowed in numeric mode along with commas, decimals).

•  Mixed fractions are treated as two unspaced numeric items. •  Follow print to differentiate between a fraction line or slash.

Examples

#a/c #b#a/b #b4e/c4e

Examples

2 1213

#a/c #b#a/b #b4e/c4e

2.53.5

FractionsinOrdinaryPrint

Used when the print fraction is written with the numerator and denominator written horizontally or linearly instead of vertically. In this case, the slash mark is used:

5/6 of the class can go. #e_/#f ( ! class c g4

Model A257/6 has new features. ,model ,a#beg_/#f has new f1tures4

7/6 #g_/#f Date?Somethingelse?

GeneralFractionIndicatorsinUEB

ForfracBonsthatdonotmeetthedefiniBonofasimplefracBon,thatis,“verBcal”fracBonsthatincludeanythingotherthananumber,acomma,adecimal(“notenBrelynumeric”),usegeneralfracKonindicators:

( )

;(x./#b) ;;;y "7 (x./#b);'

y = x2

€

x2

GeneralFractionIndicatorsinUEB

WithgeneralfracBons,youneedto"open"and"close"itandusethegeneralfracBonline.Youmayalsoneedtousegrade1indicatorsifleSersarestandingalone,orifindicatorscanbeconfusedwithcontracBons.Inotherwords,yousimplyapplythesamerulesaswithanyothercontext.

GeneralFractions,cont.•  SomeBmesit'sonlynecessarytousethegrade1symbolindicator.•  Intheseexamples,the"opengeneralfracBon"indicatorcouldlooklike"of"soitneedsagrade1symbolindicator.The"closegeneralfracBon"isundertheinfluenceofthenumericindicatorsodoes

notneedagrade1symbol.

;(x./#b) ;(x"6y./#b)

x2

x + y2

GeneralFractions,cont.

•  SomeBmes,it'seasierandlessobtrusivetousethegrade1"word"indicator.

•  Pusngthe"word"indicatorinfrontmeansthatallthesymbolshavetheir"uncontracted"meaning.Andthatwayyoudon'thavetointerrupttheexpressiontokeeppusnginsymbols.

•  The"word"isterminatedatthespace.

;;(a./b) a

b

GeneralFractions,cont.•  Eveningrade1wordmode,youmayhavetoincludeagrade1symboltodisBnguishaleSera-jfromanumber.

;;(#c./#ab;d)

312d

GeneralFractions,cont.

•  AndsomeBmesit'sbesttoputtheenBreexpressioninagrade1passage.Thatway,thereaderknowstheenBreexpressionisuncontractedunBlthepassageterminatorisused.

•  ThepassageishandyforequaBonsbecauseitgoesacrossspaces.

;;;y "7 (x./#b);'

y = x2

Keepinmind...

•  Thinkthroughwhetherit'sbesttouseagrade1passageindicatororgrade1symbolindicators.

•  Trytokeepexpressionsononeline.Ifthat'snotpossible,dividetheexpressionatthegeneralfracBonlineusingtheconBnuaBonindicator(dot5).

•  Theonlythingsthatterminategrade1modethathasbeensetbyanumericindicatorarethespace,hyphen,ordash!

SuperscriptsandSubscriptsinUEB

.=9 .=5

levelchangeup levelchangedownsuperscript subscriptdots3-5 dots2-6

SuperscriptsandSubscripts

Inordertopreventconfusionwiththelowergroupsigns,inoren,usethegrade1indicator.

Vitam9 ,b;5#f

#i yd;9#b

#cm9#b

SuperscriptsandSubscripts

Inordertopreventconfusionwiththelowergroupsigns,inoren,usethegrade1indicator.

Vitam9 ,b;5#f vitaminB6

#i yd;9#b 9yd2

#cm9#b 3m2

BrailleGroupingSymbolswithSuperscriptandSubscriptandConceptofanItem

Theeffectofthelevelindicatoronlyappliestotheitemornextindividualsymbol. .=<braillegroupingopen.=> braillegroupingclose

a.  An"item"includes:•  •EnBrenumberwithcomma,decimalpoint•  •EnBrefracBon•  •EnBreradical•  •Anarrow•  •Anarbitraryshape•  •AnythinginbraillegroupingindicatorsOtherwisethe"item"isthenextindividualsymbol.(11.4.1)

Groupingindicators

•  KeepanexpressiontogethersothereaderknowstheenBreexpressioniswithinasuperscriptorsubscript.NegaBvesuperscriptsandsubscriptsmustbeenclosedinbraillegroupingsymbols.

#e9#bx #e9<#bx> #d9<"-#c>

52 x 4−352 x

RadicalsinUEB

.=% openradical(root)

.=+ closeradical(root)LikethegeneralfracBonindicators,radicalscomeinpairs.Whatyouopen,youmustclose.SomeBmesinprint,thevinculumdoesn'thavethehorizontalline:√

ThereisaUEBsymbolforthis:"%

RadicalsinUEB

• Placetheopenradicalsignbeforetheexpressioninsidethesquareroot(radicand).•  Theradicanditselfmaybeanyexpressionwhatsoever,andmaythereforecontainradicalsaswellasothermathemaBcalstructures.•  SinceboththeopeningandclosingradicalsignshavealternaBvecontractedmeaningsusethegradegrade1indicators,asneeded.

SimpleRadicalsinUEB

;%#af+ ;;%x"6y+ ;;%x9#b"6#c+

;;%(x./y)+

#e%a+

16

yx+

yx

a5

x2 +3

CubeRoots•  Iftheradicalindexisprintedaboveandtotheleloftheradical,inbraillethatindexisplacedasasuperscriptimmediatelyfollowingtheopeningradicalsymbol.

3√8 mn√xy

;;%9#c#h+ ;;%9<mn>xy+ [Note:Intheseexamples,thereshouldbeahorizontallineovertheradicand.Annoyingly,PowerPointwouldn'tletmedothis!!!!]

Keepinmind...

•  Thinkthroughwhetherit'sbesttouseagrade1passageindicatororgrade1symbolorwordindicators.Generally,ifit'sanequaBon,usethepassage.•  Trytokeepmathexpressionsononeline.Ifthat'snotpossible,dividetheequaBonatsignofcomparison.•  Theonlythingsthatterminategrade1modethathasbeensetbyanumericindicatorarethespace,hyphen,ordash!Thinklikeabraillereader.

Parallel,PerpendicularandBasicShapes

#l parallel to ∥#- perpendicular to ⊥$ shape indicator : shape terminator $#c regular (equilateral) triangle △$#d square

¨

$= circle ¡

RulesforShapeIndicators• Usethegrade1indicatorbeforeashapeindicatorunlessnumericmodeisalreadyset.• DonotuseashapeterminaBonsigniftheshapeisfollowedbyaspace.• UseashapeterminaBonsignwhentheshapeisfollowedbyapunctuaBonmarkorothersymbols.

Examples

;$#c ,,abc

;$#c:,,abc

NoBcehowthesecondexampleisunspaced.

Examples

;$#c ,,abc △ABC

;$#c:,,abc △ABC

NoBcehowthesecondexampleisunspaced.

GeometryExamples•  Followprintforusingothersymbols.AB||CD AB||CD ;,,AB #l ;,,CD ,,AB#_,,cd

XY⊥GH,,XY #- ,,GH

∠ ABC=45º_[,,ABC "7 #de~j

Trigonometry• Generallyspeaking,followprintintheuseofsymbols.• WhenconsideringtheabbreviaBonforsine(usuallywriSenas"sin")thinkaboutwhetheritisingrade1modeornot.Spellingitoutcanbehelpfulsothe"in"isnotconfusedwiththesuperscript.• KnowyourGreekleSersymbols!Seep.10inHHGandSecBon4.5intheUEBRulebook.

Othermath• Calculus,matrices,vectors,settheory,grouptheory,barsover,andarrowscanallbedoneinUEB.•  SymbolstobrailletheseexpressionscanbefoundintheUEBRulebookAppendix3(thesymbolslist)andintheGuidelinesforTechnicalMaterials.

Calculus

;;!x9#b;dx ∫x2dx

;;!(dx./%#a"-x9#b+) ∫dx√1-x2

SetTheory

.6 .8 ~e union intersecBon isanelementof

_<#a1 #b1 #c_>.8_<#b1 #c1 #d_> "7 _<#b1 #c_>

Chemistry

,ions ,h;9"61 ,cl;9"- & ;;,Ca9<#b"6>

IonsH+,Cl-andCa2+

SpatialMathIfthemathproblemispresentedspaBallyandnotlinearly,generallyfollowprint.

However,theUEBRulebookallowsfortheAustralianconvenBonofpusngthesignofoperaBonalerthefirstnumber.

YoucanalsousethenumericpassageindicatorbeforethespaBalproblemandterminateitattheend.Youcanalsodothisforaseriesofproblemsonapage.

ThreeExamples:

1. 2. 3. #abc #abc "6 "6# ad # ad ## "333 "333 adie #acg #acg "8 bc "3333 ddhe biij

"33333

cdche

#'

Canceling

•  Usethe"linethroughpreviousitem"symboltoshowcancellaBon

.=`: 15 315 320= 204=4

## c

ae ae`: c

"33– "7 "3333 "7 "3

bj bj`: d

d

#,

NemethIntheUS• NemethCoderemainsanofficialcodeintheUnitedStates.• ResoluBonspassedbybothACBandNFBin2012.• MoBononwhichtheUSmembersofBANAvotedcanbefoundontheBANAwebsite.• BANAconBnuestosupportNemethcodeandhasanacBveMathTechnicalCommiSeeaswellasaChemistryCommiSee.

Nemeth-UEBTaskForce•  RecogniBonthatincurrentNemethcodetranscripBons,thenonmathemaBcaltextthatsurroundsthemathemaBcsisbasedonEnglishBraille,AmericanEdiBon(EBAE),whichisbeingreplacedbyUnifiedEnglishBraille(UEB).

•  BrailleuserswouldneedknowtwosetsofrulesforcontracBons,capitalizaBon,emphasis,punctuaBon,spacing,andsoon.

•  NeedforaccuratetranslaBonbothfromprinttobrailleandfrombrailletoprintbecomesanincreasinglycriBcalconsideraBonwithmoreelectronicfiles.

•  Developmentofaprovisionalguidancedocument,thenmadeaddiBonsandclarificaBons.BANAMathCommiSeecreatedafinaldocument.

GuidanceDocument•  “GuidanceforTranscripBonUsingtheNemethCodewithinUEBContexts”• UseofacodeswitchingsymbolforgoingintoandoutofNemeth.•  SymboladdedtoUEBRulebookin2013.(SeeSecBon14inUEBRulebookformoreinformaBon.)• GuidancedocumentonBANAwebsite.

BANAFall2015Boardmeeting

•  Lengthydiscussionregardingtechnicalmaterials.Passedoverwhelmingly.

•  "TheBrailleAuthorityofNorthAmerica(BANA)recognizesand

appreciatesthegenuineconcernsfromthebraillecommunityregarding

thetransiBontoUnifiedEnglishBraille(UEB).BANAstandsbyouroriginal

moBontoadoptUEBasacompletecodeaswellastheimplementaBon

statementissuedin2014inwhichweexpressedthattheNemethCode

remainsintegraltobrailleintheUnitedStates.TheBoardofBANAcould

notreachconsensusregardingtheestablishmentofasinglestandard

codefortechnicalmaterialsforbrailleintheUnitedStates.Thedecision

touseUEBortheNemethCodewithinUEBcontextfortechnicalmaterials

shouldbemadebasedonbraillereaders'individualneeds."

Indiana:ConsiderationsforNemethandUEB•  DevelopedbyIndianaUEBTransiBonTeamtoprovideguidanceforIEPteams.

•  ConsideraBons:•  InstrucBon•  Ageofonset(whenswitchingfromprinttobraille)•  CogniBvefactors•  InterestsandapBtude•  Currentbrailleskills•  Otherfactors(moBvaBon,Bmetocompletetasks,etc.)

•  LinkisontheBANAwebsite.

BANAWebsite• BANAmaintainsadynamicwebsiteofconBnuouslygrowingresources,materials,news,andlinksinaccessibleformats

• Newareaforbraillereaders

• Newareaforteachers&transcribers

• NumerousBANApublicaBonsareavailableonthewebsite

• Visitusatwww.brailleauthority.org

TranscriberTraining• NLStranscribercourse hSps://n�.org/braille-transcribing

• NLSexaminaBontooaddaleSerofUEBproficiencytoexisBngcerBficaBon.

hSps://n�.org/ueb-resources

Training•  LinkstotrainingcoursesandotherresourcesforpracBBonerswhoknowEBAE:• Hadley• CNIBcourse• ManualsfromAustralia&NewZealand• ABCsofUEBcomparesEBAEandUEB(Risjord)• UEBtoEBAECompanionresource(Lhotka)• WisconsinCenterfortheVisuallyImpaired• UEBotonlinecoursefromNorthernIllinois

Resources:Training

• Morelinkswillbeaddedtowebsoon

• UEBPREPfromPortlandStateinprocess

•  Forpeoplewhodon’tknowEBAE:• UEBOnlinefromAustralia(linkonBANAwebsite)

• AshcrolbookforuniversiBesfromSCALARSPublishing

• NLSTranscribingmanual

ResourcesandSupport•  SCALARS:BrailleEnthusiast’sDicJonaryupdatecomingsoon

• AFBPress:BurnsBrailleGuideupdateForReaders:

•  NBPmaterialsinUEBsuchasSyndicatedColumnistsWeekly

•  UEBMaterialsfromNLSavailableinBARD

•  "ListofFrequentlyUsedSymbols"onwebsite

ForTeachers&Students• AmericanPrinBngHousefortheBlind:BuildingonPaNerns,manyothers

• NaBonalBraillePress:Children'sBrailleDicJonary,andtheirBrailleBookClub

•  Seedlingsbooks•  "UEBToo"supplementtoBrailleTooand"SixDotCelebraBons"frombrl2.com

•  LessonsonthePerkins'PathstoLiteracysite•  "UEB/EBAEchecklist"(Peaslee)• BrailleChallengeacBviBesmovingtoUEB

Resourcesformathmaterials

•  ICEB'sGuidelinesforTechnicalMaterials:hSp://www.iceb.org/ueb.html• NewZealandresource:TheHitchhiker'sGuidetoUEBMaths• hSp://www.banzat.org.nz/documents/HHGMaths.pdf

•  CanadianresourceguidebyHeatherHarlandandCherylRoberts:"UnifiedEnglishBrailleforMathforSightedLearners."hSps://www.prcvi.org/files/braille/UEB_Braille_for_Math_2014.pdf

Resourcesformathmaterials

•  AvailablefromAPH:•  Feel'nPeel:BasicMathSymbols,sBckersformathavailableinUEBaswellasNemeth.

• BothUEBandNemethoutputareavailableontheOrionTI-84Plusversion2calculatorthatconnectstoaBaumorAPHRefreshabraille18.

• MathRobotAppforiPadsupportsbothUEBandNemethcodes.

• MathWindowkitsavailableforbothNemethandforUEB.www.mathwindow.com

AssessmentIssues• Needsofstudentsinthestate

• Assessmentsshouldbeinthecode(s)studentsareusingfortheirschoolwork

• AssessmenttranscripBonprocess

•  Thinkingahead,planningahead

• Assessmentdecision-making

• AddressduringIEPprocess

•  Teamdiscussionanddecision

Collaboration&Communication

}  DiscusswithteachersandparentsthegoalsofUEBinstrucBon

}  ShareawriSenplanofinstrucBonforusingUEBduringthetransiBon

}  ScheduleinstrucBon,includingamountofparBcipaBoninclassroomacBviBesandamountof“pullout”fordirectinstrucBon(forolderstudents)

}  Discussandplanforongoingassessmentofliteracylearning.

PlanforStudentTransition

• Don’tassumestudentswilllearnUEBwithoutinstrucBon.CreateaplanfortransiBon.

• Collectprogressdatatodocumentstudent’sacquisiBonofUEBskill/knowledge

• AdvocatefordirectinstrucBonBme

• Don’tletfocusoncodederailfocusonreading,wriBngandmathemaBcscontent!

• OurfirstjobistoensuresuccessingeneralcurriculumandECC

FinalThoughts• Renewedinterestinbrailleliteracy!

• Developmentofnewbrailletrainingtools

• MoreconversaBonsaboutinstrucBonalstrategiesforSTEMacademicareas

• MorecollaboraBonwithinstatesandnaBonally.

References•  Bogart,D.,D’Andrea,FM,Koenig,A.(2004).Acomparisonofthefrequencyofnumber/punctuaBonandnumber/leSercombinaBonsinliteraryandtechnicalmaterials.RetrievedfromhSp://www.brailleauthority.org/research-ueb/contentanalysisfinal11-15-04.pdf.

•  Gentle,F.,Steer,M.,&Howse,J.(2012).NewdotsDownunder:TheimplementaJonofUnifiedEnglishBrailleinAustralianschools.BriBshJournalofVisualImpairment,30,197-200.

•  Herzberg,T.S.,&Rosenblum,L.P.(2014).PrinttoBraille:PreparaBonandAccuracyofMathemaBcsMaterialsinK-12EducaBon.JournalOfVisualImpairment&Blindness,108(5),355-367.

•  Holbrook,M.C.,&MacCuspie,P.A.(2010).TheUnifiedEnglishBrailleCode:ExaminaBonbyScience,MathemaBcs,andComputerScienceTechnicalExpertBrailleReaders.JournalOfVisualImpairment&Blindness,104(9),533-541.

•  Holbrook,M.C.,D'Andrea,F.M.,Sanford,L.(2014).AshcroU'sProgrammedInstrucJon:UnifiedEnglishBraille(API-UEB).Germantown,TN:SCALARSPublishing.

References•  InternaBonalCouncilonEnglishBraille.(2014).GuidelinesforTechnicalMaterial.RetrievedfromhSp://www.iceb.org/ueb.html.TheBrailleAuthorityofNewZealandAotearoaTrust.(2013).

•  InternaBonalCouncilonEnglishBraille.(2013).UEBRulebook,2ndEdiJon.RetrievedfromhSp://www.iceb.org/ueb.html.

•  TheHitchhiker'sGuidetoUEBMathemaJcs.RetrievedfromhSp://www.banzat.org.nz/documents/HHGMaths.pdf

•  UBCEvaluaBonReportUSA.(1991).RetrievedfromhSp://www.iceb.org/ubcevus.html.