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7/26/16
1
UEBReady?Day2:
TechnicalMaterials
August2016FrancesMaryD’Andrea,[email protected]
WithmanythankstoLorraineBanks,DarleenBogart,JamesBowden,JosieHowse,PhyllisLandon,Holly
Lawson,JennyMcFadden,JanetReynolds,andCatherineWest
Objectives
Bytheendofthistraining,parDcipantswillbeableto:• demonstrateunderstandingofbasicprinciplesofUEBbybraillingexamplesentences.
• brailletechnicalcodesymbolsforSTEM(science,technology,engineering,andmath)content
• usereferenceswithintheUEBGuidelinesforTechnicalMaterialmanualandotherresourcestoproduceintermediateandadvancedlevelsofSTEMcontent
• describeanduseappropriategradeoneindicatorswithintechnicalandmathemaDcaltranscripDon.
Remember:
• TechnicalmaterialsinUEBfollowthesamesymbolsandrulesfornontechnicalmaterials• •consistencyofrulesacrosscontexts• •followspacingofprint(mostly)• •"standalone"rule(whenisitacontracDon?)• •grade1moderules
Thereisno"UEBMathCode"—it'sallONEcode.• othercountriesthathaveadoptedUEBareusingitonly• theUSistheonlycountrythatismaintainingitsoldmathcodeinaddiDontoadopDngUEBsowehavenomodeltofollow
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TwoImportantRules!
• Standalonerule:SecKon2.6• “AleUerorleUers-sequenceisconsideredtobe‘standingalone’ifitisprecededandfollowedbyaspace,ahyphen,oradash.”(Canbeeitheraregulardashorlongdash.)Thisisimportantbecauseithelpsyoudecideif/whenyouneedtousegrade1indicators.
• Grade1Mode:SecKon5.1• “Agrade1indicatorisusedtosetgrade1modewhenthegrade1meaningofasymbolcouldbemisreadasacontracDonmeaningoranumericmeaning.”
• Somesymbolshavea“grade1meaning”andthereforeneedagrade1indicator.
• Note:“Uncontractedbrailleisdifferentfromgrade1mode.”SecDon2.5.2
TheReaderRules!• InUEB,youmustalwaysthinkfromthebraillereader'sviewpoint—whatwillpotenDallybeconfusedormisread?That'swhytheStandingAloneRuleandtheGrade1rulesaresoimportant.• Tocheckyourwork,alwaysask:"Couldthissymbolbeconfusedwithsomethingelse?"• Thatalsomeansthatintechnicalcontexts,theremaybemorethanonewaytodosomething.• Thebasicruleofthumb:Trytominimizeindicatorsinthemiddleofanexpression.
UniCicationofLiteraryandMathematicalTexts
• UEBisdesignedtounifysignsacrossliteraryandmathemaDcalcontexts.
• 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
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Numbers
• Numericmodeindicatorisconsidereda“prefix”inUEBandletsthereaderknowthatwhatfollowsarenumbers.Itsets“numericmode.”Itisdots3-4-5-6#
• Theonlysymbolsthatmaybeusedinnumericmodeare:digits,decimalpoint(period),comma,simplefracKonline,numericspace(dot5),andthelineconKnuaKonindicators(usedwhendividingverylongnumbersbetweenbraillelines).Anythingelseterminatesit!
Numbers• Thenumericindicatoristerminatedbyaspace,signsofoperaDon,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”contracDonsamernumbers• #ast floor 1stfloor
Grade1ModeandNumericIndicator
• Thenumericindicatoractsasagrade1indicator.Thismeansthatwhatfollowsanumbersignhasitsuncontractedmeaning.
• Asymbolthatdoesn'tfollowanumericindicatorandcouldbeamisreadasanumberorcontracDonneedsthegrade1indicator.
• InUEB,a"word"isdefinedas"stringofsymbols"calledasymbols-sequence.Itisterminatedbyaspace(orthegrade1terminator).
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Grade1Indicators
;indicatesthefollowingsymbolisingrade1;; indicatesthefollowingwordisingrade1;;; indicatesthefollowingpassageisingrade1 ;' (dots5-6,3)terminatesthegrade1passage.Whengrade1modeissetbythenumericindicator,itisterminatedbyaspace,hyphenordash.Theeffectofanumbermaybeterminatedbutgrade1modeconDnues.Inotherwords,morethingsterminatenumericmodethanterminategrade1mode.
Grade1Indicators
• Ifabraillesymbolalsohasacontractedmeaningthenthegrade1indicatormustbeusedunlessgrade1modeisalreadysetorifthere’snoambiguitywhenfollowingUEBrules:
3g 3G 3m3m
Grade1Indicators
• Ifabraillesymbolalsohasacontractedmeaningthenthegrade1indicatormustbeusedunlessgrade1modeisalreadysetorifthere’snoambiguitywhenfollowingUEBrules:
• #c;g #c,g #cm #c ;m
3g 3G 3m 3m
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Grade1IndicatorsBecausethereisnoambiguity,agrade1indicatorisnotrequiredwhenanycapitalleUeroranyoftheleUersk-zfollowanumber.AsimplearithmeDcequaDongenerallywillnotneedgrade1indicators. 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.
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10VerySimpliCiedRulesKISSforUEB1. +-x÷=alltakedot52. moneysymbolstakedot4andarefollowedbynumbersign(but
canalsostandalone!)3. operaDonsignsareunspacedbothsides4. comparisonsignsarespacedbeforeandamer5. greaterthanandlessthansignstakedot46. simplefracDonline–/ 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
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SpacingofMathProblems
• Thereissomeflexibilityinspacing.• Ingeneral,spacingconformstoprint,however...• ThereisastrongpreferencenottospaceoneithersideofasignofoperaDonandaspaceonbothsidesofasignofcomparison.
• Ifpreparingsimpleproblemsforyoungchildren,permissibletospacearoundsignofoperaDon.
SimpleFractionsandMixedNumbers
.=/ simplenumericfracDonline
.=./ generalfracDonline
.=( generalfracDonopenindicator
.=) generalfracDoncloseindicator
.=_/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.
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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?
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GeneralFractionIndicatorsinUEB
ForfracDonsthatdonotmeetthedefiniDonofasimplefracDon,thatis,“verDcal”fracDonsthatincludeanythingotherthananumber,acomma,adecimal(“notenDrelynumeric”),usegeneralfracKonindicators:
( )
;(x./#b) ;;;y "7 (x./#b);'
y = x2
€
x2
GeneralFractionIndicatorsinUEB
WithgeneralfracDons,youneedto"open"and"close"itandusethegeneralfracDonline.Youmayalsoneedtousegrade1indicatorsifleUersarestandingalone,orifindicatorscanbeconfusedwithcontracDons.Inotherwords,yousimplyapplythesamerulesaswithanyothercontext.
GeneralFractions,cont.• SomeDmesit'sonlynecessarytousethegrade1symbolindicator.• Intheseexamples,the"opengeneralfracDon"indicatorcouldlooklike"of"soitneedsagrade1symbolindicator.The"closegeneralfracDon"isundertheinfluenceofthenumericindicatorsodoes
notneedagrade1symbol.
;(x./#b) ;(x"6y./#b)
x2
x + y2
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GeneralFractions,cont.
• SomeDmes,it'seasierandlessobtrusivetousethegrade1"word"indicator.
• Pusngthe"word"indicatorinfrontmeansthatallthesymbolshavetheir"uncontracted"meaning.Andthatwayyoudon'thavetointerrupttheexpressiontokeeppusnginsymbols.
• The"word"isterminatedatthespace.
;;(a./b) a
b
GeneralFractions,cont.• Eveningrade1wordmode,youmayhavetoincludeagrade1symboltodisDnguishaleUera-jfromanumber.
;;(#c./#ab;d)
312d
GeneralFractions,cont.
• AndsomeDmesit'sbesttoputtheenDreexpressioninagrade1passage.Thatway,thereaderknowstheenDreexpressionisuncontractedunDlthepassageterminatorisused.
• ThepassageishandyforequaDonsbecauseitgoesacrossspaces.
;;;y "7 (x./#b);'
y = x2
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Keepinmind...
• Thinkthroughwhetherit'sbesttouseagrade1passageindicatororgrade1symbolindicators.
• Trytokeepexpressionsononeline.Ifthat'snotpossible,dividetheexpressionatthegeneralfracDonlineusingtheconDnuaDonindicator(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
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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:• •EnDrenumberwithcomma,decimalpoint• •EnDrefracDon• •EnDreradical• •Anarrow• •Anarbitraryshape• •AnythinginbraillegroupingindicatorsOtherwisethe"item"isthenextindividualsymbol.(11.4.1)
Groupingindicators
• KeepanexpressiontogethersothereaderknowstheenDreexpressioniswithinasuperscriptorsubscript.NegaDvesuperscriptsandsubscriptsmustbeenclosedinbraillegroupingsymbols.
#e9#bx #e9<#bx> #d9<"-#c>
52 x 4−352 x
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RadicalsinUEB
.=% openradical(root)
.=+ closeradical(root)LikethegeneralfracDonindicators,radicalscomeinpairs.Whatyouopen,youmustclose.SomeDmesinprint,thevinculumdoesn'thavethehorizontalline:√
ThereisaUEBsymbolforthis:"%
RadicalsinUEB
• Placetheopenradicalsignbeforetheexpressioninsidethesquareroot(radicand).• Theradicanditselfmaybeanyexpressionwhatsoever,andmaythereforecontainradicalsaswellasothermathemaDcalstructures.• SinceboththeopeningandclosingradicalsignshavealternaDvecontractedmeaningsusethegradegrade1indicators,asneeded.
SimpleRadicalsinUEB
;%#af+ ;;%x"6y+ ;;%x9#b"6#c+
;;%(x./y)+
#e%a+
16
yx+
yx
a5
x2 +3
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CubeRoots• Iftheradicalindexisprintedaboveandtothelemoftheradical,inbraillethatindexisplacedasasuperscriptimmediatelyfollowingtheopeningradicalsymbol.
3√8 mn√xy
;;%9#c#h+ ;;%9<mn>xy+ [Note:Intheseexamples,thereshouldbeahorizontallineovertheradicand.Annoyingly,PowerPointwouldn'tletmedothis!!!!]
Keepinmind...
• Thinkthroughwhetherit'sbesttouseagrade1passageindicatororgrade1symbolorwordindicators.Generally,ifit'sanequaDon,usethepassage.• Trytokeepmathexpressionsononeline.Ifthat'snotpossible,dividetheequaDonatsignofcomparison.• Theonlythingsthatterminategrade1modethathasbeensetbyanumericindicatorarethespace,hyphen,ordash!Thinklikeabraillereader.
Parallel,PerpendicularandBasicShapes
#l parallel to ∥#- perpendicular to ⊥$ shape indicator : shape terminator $#c regular (equilateral) triangle △$#d square
¨
$= circle ¡
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RulesforShapeIndicators• Usethegrade1indicatorbeforeashapeindicatorunlessnumericmodeisalreadyset.• DonotuseashapeterminaDonsigniftheshapeisfollowedbyaspace.• UseashapeterminaDonsignwhentheshapeisfollowedbyapunctuaDonmarkorothersymbols.
Examples
;$#c ,,abc
;$#c:,,abc
NoDcehowthesecondexampleisunspaced.
Examples
;$#c ,,abc △ABC
;$#c:,,abc △ABC
NoDcehowthesecondexampleisunspaced.
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GeometryExamples• Followprintforusingothersymbols.AB||CD AB||CD ;,,AB #l ;,,CD ,,AB#_,,cd
XY⊥GH,,XY #- ,,GH
∠ ABC=45º_[,,ABC "7 #de~j
Trigonometry• Generallyspeaking,followprintintheuseofsymbols.• WhenconsideringtheabbreviaDonforsine(usuallywriUenas"sin")thinkaboutwhetheritisingrade1modeornot.Spellingitoutcanbehelpfulsothe"in"isnotconfusedwiththesuperscript.• KnowyourGreekleUersymbols!Seep.10inHHGandSecDon4.5intheUEBRulebook.
Othermath• Calculus,matrices,vectors,settheory,grouptheory,barsover,andarrowscanallbedoneinUEB.• SymbolstobrailletheseexpressionscanbefoundintheUEBRulebookAppendix3(thesymbolslist)andintheGuidelinesforTechnicalMaterials.
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Calculus
;;!x9#b;dx ∫x2dx
;;!(dx./%#a"-x9#b+) ∫dx√1-x2
SetTheory
.6 .8 ~e union intersecDon isanelementof
_<#a1 #b1 #c_>.8_<#b1 #c1 #d_> "7 _<#b1 #c_>
Chemistry
,ions ,h;9"61 ,cl;9"- & ;;,Ca9<#b"6>
IonsH+,Cl-andCa2+
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SpatialMathIfthemathproblemispresentedspaDallyandnotlinearly,generallyfollowprint.
However,theUEBRulebookallowsfortheAustralianconvenDonofpusngthesignofoperaDonamerthefirstnumber.
YoucanalsousethenumericpassageindicatorbeforethespaDalproblemandterminateitattheend.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"symboltoshowcancellaDon
.=`: 15 315 320= 204=4
## c
ae ae`: c
"33– "7 "3333 "7 "3
bj bj`: d
d
#,
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NemethIntheUS• NemethCoderemainsanofficialcodeintheUnitedStates.• ResoluDonspassedbybothACBandNFBin2012.• MoDononwhichtheUSmembersofBANAvotedcanbefoundontheBANAwebsite.• BANAconDnuestosupportNemethcodeandhasanacDveMathTechnicalCommiUeeaswellasaChemistryCommiUee.
Nemeth-UEBTaskForce• RecogniDonthatincurrentNemethcodetranscripDons,thenonmathemaDcaltextthatsurroundsthemathemaDcsisbasedonEnglishBraille,AmericanEdiDon(EBAE),whichisbeingreplacedbyUnifiedEnglishBraille(UEB).
• BrailleuserswouldneedknowtwosetsofrulesforcontracDons,capitalizaDon,emphasis,punctuaDon,spacing,andsoon.
• NeedforaccuratetranslaDonbothfromprinttobrailleandfrombrailletoprintbecomesanincreasinglycriDcalconsideraDonwithmoreelectronicfiles.
• Developmentofaprovisionalguidancedocument,thenmadeaddiDonsandclarificaDons.BANAMathCommiUeecreatedafinaldocument.
GuidanceDocument• “GuidanceforTranscripDonUsingtheNemethCodewithinUEBContexts”• UseofacodeswitchingsymbolforgoingintoandoutofNemeth.• SymboladdedtoUEBRulebookin2013.(SeeSecDon14inUEBRulebookformoreinformaDon.)• GuidancedocumentonBANAwebsite.
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BANAFall2015Boardmeeting
• Lengthydiscussionregardingtechnicalmaterials.Passedoverwhelmingly.
• "TheBrailleAuthorityofNorthAmerica(BANA)recognizesand
appreciatesthegenuineconcernsfromthebraillecommunityregarding
thetransiDontoUnifiedEnglishBraille(UEB).BANAstandsbyouroriginal
moDontoadoptUEBasacompletecodeaswellastheimplementaDon
statementissuedin2014inwhichweexpressedthattheNemethCode
remainsintegraltobrailleintheUnitedStates.TheBoardofBANAcould
notreachconsensusregardingtheestablishmentofasinglestandard
codefortechnicalmaterialsforbrailleintheUnitedStates.Thedecision
touseUEBortheNemethCodewithinUEBcontextfortechnicalmaterials
shouldbemadebasedonbraillereaders'individualneeds."
Indiana:ConsiderationsforNemethandUEB• DevelopedbyIndianaUEBTransiDonTeamtoprovideguidanceforIEPteams.
• ConsideraDons:• InstrucDon• Ageofonset(whenswitchingfromprinttobraille)• CogniDvefactors• InterestsandapDtude• Currentbrailleskills• Otherfactors(moDvaDon,Dmetocompletetasks,etc.)
• LinkisontheBANAwebsite.
BANAWebsite• BANAmaintainsadynamicwebsiteofconDnuouslygrowingresources,materials,news,andlinksinaccessibleformats
• Newareaforbraillereaders
• Newareaforteachers&transcribers
• NumerousBANApublicaDonsareavailableonthewebsite
• Visitusatwww.brailleauthority.org
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TranscriberTraining• NLStranscribercourse hUps://n�.org/braille-transcribing
• NLSexaminaDontooaddaleUerofUEBproficiencytoexisDngcerDficaDon.
hUps://n�.org/ueb-resources
Training• LinkstotrainingcoursesandotherresourcesforpracDDonerswhoknowEBAE:• Hadley• CNIBcourse• ManualsfromAustralia&NewZealand• ABCsofUEBcomparesEBAEandUEB(Risjord)• UEBtoEBAECompanionresource(Lhotka)• WisconsinCenterfortheVisuallyImpaired• UEBotonlinecoursefromNorthernIllinois
Resources:Training
• Morelinkswillbeaddedtowebsoon
• UEBPREPfromPortlandStateinprocess
• Forpeoplewhodon’tknowEBAE:• UEBOnlinefromAustralia(linkonBANAwebsite)
• AshcrombookforuniversiDesfromSCALARSPublishing
• NLSTranscribingmanual
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ResourcesandSupport• SCALARS:BrailleEnthusiast’sDicJonaryupdatecomingsoon
• AFBPress:BurnsBrailleGuideupdateForReaders:
• NBPmaterialsinUEBsuchasSyndicatedColumnistsWeekly
• UEBMaterialsfromNLSavailableinBARD
• "ListofFrequentlyUsedSymbols"onwebsite
ForTeachers&Students• AmericanPrinDngHousefortheBlind:BuildingonPaNerns,manyothers
• NaDonalBraillePress:Children'sBrailleDicJonary,andtheirBrailleBookClub
• Seedlingsbooks• "UEBToo"supplementtoBrailleTooand"SixDotCelebraDons"frombrl2.com
• LessonsonthePerkins'PathstoLiteracysite• "UEB/EBAEchecklist"(Peaslee)• BrailleChallengeacDviDesmovingtoUEB
Resourcesformathmaterials
• ICEB'sGuidelinesforTechnicalMaterials:hUp://www.iceb.org/ueb.html• NewZealandresource:TheHitchhiker'sGuidetoUEBMaths• hUp://www.banzat.org.nz/documents/HHGMaths.pdf
• CanadianresourceguidebyHeatherHarlandandCherylRoberts:"UnifiedEnglishBrailleforMathforSightedLearners."hUps://www.prcvi.org/files/braille/UEB_Braille_for_Math_2014.pdf
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Resourcesformathmaterials
• AvailablefromAPH:• Feel'nPeel:BasicMathSymbols,sDckersformathavailableinUEBaswellasNemeth.
• BothUEBandNemethoutputareavailableontheOrionTI-84Plusversion2calculatorthatconnectstoaBaumorAPHRefreshabraille18.
• MathRobotAppforiPadsupportsbothUEBandNemethcodes.
• MathWindowkitsavailableforbothNemethandforUEB.www.mathwindow.com
AssessmentIssues• Needsofstudentsinthestate
• Assessmentsshouldbeinthecode(s)studentsareusingfortheirschoolwork
• AssessmenttranscripDonprocess
• Thinkingahead,planningahead
• Assessmentdecision-making
• AddressduringIEPprocess
• Teamdiscussionanddecision
Collaboration&Communication
} DiscusswithteachersandparentsthegoalsofUEBinstrucDon
} ShareawriUenplanofinstrucDonforusingUEBduringthetransiDon
} ScheduleinstrucDon,includingamountofparDcipaDoninclassroomacDviDesandamountof“pullout”fordirectinstrucDon(forolderstudents)
} Discussandplanforongoingassessmentofliteracylearning.
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PlanforStudentTransition
• Don’tassumestudentswilllearnUEBwithoutinstrucDon.CreateaplanfortransiDon.
• Collectprogressdatatodocumentstudent’sacquisiDonofUEBskill/knowledge
• AdvocatefordirectinstrucDonDme
• Don’tletfocusoncodederailfocusonreading,wriDngandmathemaDcscontent!
• OurfirstjobistoensuresuccessingeneralcurriculumandECC
FinalThoughts• Renewedinterestinbrailleliteracy!
• Developmentofnewbrailletrainingtools
• MoreconversaDonsaboutinstrucDonalstrategiesforSTEMacademicareas
• MorecollaboraDonwithinstatesandnaDonally.
References• Bogart,D.,D’Andrea,FM,Koenig,A.(2004).Acomparisonofthefrequencyofnumber/punctuaDonandnumber/leUercombinaDonsinliteraryandtechnicalmaterials.RetrievedfromhUp://www.brailleauthority.org/research-ueb/contentanalysisfinal11-15-04.pdf.
• Gentle,F.,Steer,M.,&Howse,J.(2012).NewdotsDownunder:TheimplementaJonofUnifiedEnglishBrailleinAustralianschools.BriDshJournalofVisualImpairment,30,197-200.
• Herzberg,T.S.,&Rosenblum,L.P.(2014).PrinttoBraille:PreparaDonandAccuracyofMathemaDcsMaterialsinK-12EducaDon.JournalOfVisualImpairment&Blindness,108(5),355-367.
• Holbrook,M.C.,&MacCuspie,P.A.(2010).TheUnifiedEnglishBrailleCode:ExaminaDonbyScience,MathemaDcs,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.
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References• InternaDonalCouncilonEnglishBraille.(2014).GuidelinesforTechnicalMaterial.RetrievedfromhUp://www.iceb.org/ueb.html.TheBrailleAuthorityofNewZealandAotearoaTrust.(2013).
• InternaDonalCouncilonEnglishBraille.(2013).UEBRulebook,2ndEdiJon.RetrievedfromhUp://www.iceb.org/ueb.html.
• TheHitchhiker'sGuidetoUEBMathemaJcs.RetrievedfromhUp://www.banzat.org.nz/documents/HHGMaths.pdf
• UBCEvaluaDonReportUSA.(1991).RetrievedfromhUp://www.iceb.org/ubcevus.html.