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! ! ! !
Facilitators Guide
Improving Accessibility inMiddle Grades Mathematics:
Language in theMath Classroom
Produced!by:!
!
!
!
Education!Development!Center,!Inc!
!
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!2009!Education!Development!Center,!Inc.! ! 2!
Improving!Accessibility!in!Middle!Grades!Math:!Language!in!the!Math!Classroom!
!
Improving!Accessibility!in!Middle!Grades!Mathematics:!Language!in!the!Math!
Classroom!was!developed!at!Education!Development!Center,!Inc!(EDC)!in!Newton,!
MA.!This!tool!is!part!of!the!Mathematics!Improvement!Toolkit,!a!project!of!the!
National!Forum!to!Accelerate!Middle!Grades!Reform,!and!was!supported!by!The!U.S.!
Department!of!Education's!Comprehensive!School!Reform!Quality!Initiative,!grant!#!
S332B060005.!Opinions!expressed!are!those!of!the!authors!and!not!necessarily!those!
of!the!Department.!
!
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!2009!Education!Development!Center,!Inc.! ! 3!
Improving!Accessibility!in!Middle!Grades!Math:!Language!in!the!Math!Classroom!
SECTION!1!
WELCOME.............................................................................................................................................!4!
INTRODUCTION!AND!OVERVIEW..................................................................................................................!4!
WHO!SHOULD!FACILITATE!THIS!WORKSHOP?!...............................................................................................!4!
WHO!SHOULD!PARTICIPATE!IN!THIS!WORKSHOP?!.........................................................................................!5!
WORKSHOP!DESIGN!AND!TOPICS!...............................................................................................................!5!
WORKSHOP!GOALS!.................................................................................................................................!6!
HOW!TO!PREPARE!FOR!THE!WORKSHOP!.......................................................................................................!7!
WORKSHOP!PLANNING!CONSIDERATIONS!....................................................................................................!7!
LOGISTICS!..............................................................................................................................................!8!
WORKSHOP!MATERIALS!...........................................................................................................................!9!
PHOTOCOPYING!RECOMMENDATIONS!.......................................................................................................!11!
FACILITATION!TIPS!.................................................................................................................................!12!
WORKSHOP!AGENDA!AND!PACING!SUGGESTIONS!.........................................................................................!14!
WORKSHOP!AGENDA!"!BROAD!VIEW!.....................................................................................................!14!
WORKSHOP!AGENDA!!DETAILED!VIEW!................................................................................................!15!
PACING!SUGGESTIONS!............................................................................................................................!17!
SLIDE!NOTES!GUIDE!...............................................................................................................................!18!
APPENDICES:!ADDITIONAL!FACILITATION!RESOURCES!......................................................................................!75!
APPENDIX!1:!OPTIONAL!WORKSHOP!INTERIM!ACTIVITIES!.............................................................................!76!
HANDOUTS!A1"A2................................................................................................................................!76!
APPENDIX!2:!SAMPLE!EMAIL:!WORKSHOP!ANNOUNCEMENT!.........................................................................!78!
APPENDIX!3:!SAMPLE!EMAIL:!WORKSHOP!REMINDER!..................................................................................!79!
APPENDIX!4:!FACILITATION!CHECKLIST!......................................................................................................!80!
APPENDIX!5:!PACING!GUIDE!...................................................................................................................!82!
APPENDIX!6:!SAMPLE!VOCABULARY!PLANNER!............................................................................................!84!
WORKSHOP!HANDOUTS!...........................................................................................................................!1!
!
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!2009!Education!Development!Center,!Inc.! ! 4!
WELCOME!
We!are!pleased!to!offer!you!this!workshop,!Improving!Accessibility!in!Middle!Grades!
Mathematics:!Language
!in
!the
!Math
!Classroom.!The!workshop!is!designed!to!help!math!and!
special!education!teachers!improve!access!for!students!to!the!language!they!need!in!order!
to!learn!middle!grades!mathematics!concepts.!
This!workshop!was!developed!at!Education!Development!Center,!Inc.!(www.edc.org)!in!
Newton,!MA.!This!workshop!is!part!of!the!Mathematics!Improvement!Toolkit,!a!project!of!
the!National!Forum!to!Accelerate!Middle!Grades!Reform!(www.mgforum.org),!and!was!
supported!by!The!U.S.!Department!of!Education's!Comprehensive!School!Reform!Quality!
Initiative,!Grant!#!S332B060005.!Opinions!expressed!are!those!of!the!authors!and!not!
necessarily!those!of!the!Department.!!This!workshop!builds!on!the!work!of!the!Addressing!
Accessibility!in!Mathematics!project:!edc.org/accessmath.!
!
INTRODUCTION!AND!OVERVIEW!
This!guide!is!designed!to!support!the!facilitator!of!the!workshop.!While!this!guide!focuses!
more!heavily!on!the!content!of!the!workshop!than!it!does!on!the!development!of!
facilitation!
skills,!
facilitators!
with!
a!
range!
of!
experience!
can!
use!
these!
materials!
to!
prepare!
and!conduct!the!workshop.!
!
WHO !SHOULD!FACILITATE !THI S!WORKSHOP?!
Facilitators!might!be!experienced!math!or!special!education!teachers,!teacher!leaders,!or!
curriculum!specialists.!The!facilitators!do!not!have!to!be!experienced!in!facilitating!
workshops.!Since!this!workshop!aims!to!build!collaboration,!it!works!particularly!well!when!
co"facilitated!by!two!individuals,!one!with!expertise!in!teaching!math!and!one!with!special!
education!teaching!expertise.!
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!2009!Education!Development!Center,!Inc.! ! 5!
WHO!SHOULD!PARTICIPATE !IN !THIS!WORKSHOP?!
This!workshop!is!intended!for!teachers!of!middle!grades!mathematics!who!work!in!inclusive!
classrooms!
with!
students!
with!
mild!
to!
moderate!
learning!
disabilities!
receiving!
the!
regular!
mathematics!curriculum.!This!includes!general!and!special!education!teachers.!The!
workshop!may!also!be!appropriate!for!teachers!who!teach!in!a!self"contained!classroom,!
resource!room!or!pull"out!program!for!mathematics,!as!it!focuses!on!strategies!for!
supporting!students!in!making!sense!of!the!language!used!in!math!instruction!in!order!to!
improve!access!to!math!concepts.!!
!
WORKSHOP!
DESIGN!AN D!
TOPICS!
This!workshop!is!designed!to!be!interactive!and!to!provide!opportunities!for!teachers!to!
learn,!discuss,!practice,!reflect!and!bring!their!learning!back!to!their!own!practice.!!The!
workshop!begins!with!brainstorming!and!reflection!on!the!language!demands!and!
challenges!present!in!the!mathematics!classroom.!!It!then!moves!to!a!focus!on!vocabulary!
as!a!point!of!intersection!of!the!four!key!language!processes:!reading,!writing,!speaking!and!
listening.!Finally,!the!workshop!explores!research"based!strategies!for!vocabulary!
instruction!and!tools!for!planning!vocabulary!instruction.!The!workshop!is!structured!
around!four!key!elements:!
1. Information!The!facilitator!will!provide!some!direct!instruction!in!language!processes!and!
demands,!research,!and!planning.!!This!will!provide!a!launching!pad!for!further!
examination!and!exploration!by!participants.!
2. Video!Participants!will!watch!real!video!footage!of!classroom!instruction.!!This!is!used!to!
provide!examples!of!the!implementation!of!strategies!intended!to!make!the!
language!of!mathematics!accessible!and!spark!reflection,!discussion!and!learning!for!
workshop!participants.!
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!2009!Education!Development!Center,!Inc.! ! 6!
3. Activities!Participants!will!try!strategies,!apply!their!ideas!and!build!skills!by!participating!in!
individual,!partner!and!group!activities.!These!are!designed!to!provide!interactive!
learning!experiences!and!opportunities!to!connect!the!content!of!the!workshop!to!the!participants!own!classroom!practice.!
4. Discussion!Participants!will!have!further!opportunities!to!share!their!ideas,!learn!from!
colleagues!and!build!understanding!through!small"!and!large"group!discussion!
structured!around!specific!goals!and!questions.!
!
WORKSHOP!GOALS!
In!the!workshop,!participants!will:!
! Deepen!their!understanding!of!the!language!demands!in!mathematics.!! Learn!about!research!on!vocabulary!instruction!and!difficulty!for!students!with!
disabilities.!
! Learn!ways!to!plan!and!implement!vocabulary!instruction!and!writing!activities!in!the!mathematics!classroom.!
! Share!perspectives!and!strategies!and!collaborate!to!improve!access!to!language!and!math!learning.!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 7!
HOW!TO !PREPARE!FOR!THE!WORKSHOP!
This!guide!provides!information!and!materials!to!assist!the!facilitator!in!planning!and!
facilitating!this!workshop.!This!section!outlines!the!steps!for!preparation,!including:!
workshop!planning,!logistics,!and!materials.!
!
WORKSHOP!PLANNING !CONSIDERATIONS !!
SCHEDULING !
The!workshop!may!be!offered!as!one!6!hour!session,!or!split!into!two!3!hour!sessions.!If!you!
will!be!using!two!sessions!to!complete!the!workshop,!it!is!suggested!that!the!two!sessions!be!held!within!4!to!6!weeks!of!one!another.!Optional!interim!activities!designed!to!link!the!
two!sessions!are!provided!(Appendix!1).!!
!
PARTICIPANTS !
The!intended!audience!for!this!workshop!is!middle!grades!mathematics!teachers!and!special!
education!teachers.!This!workshop!is!designed!for!a!group!of!ranging!8"30!participants.!If!
your!staff,!is!much!larger!than!30,!you!should!consider!running!the!workshop!with!an!
additional!facilitator!or!breaking!into!two!groups.!!
The!workshop!is!enriched!through!the!dialog!of!teachers!with!different!perspectives,!so!a!
range!of!grade!levels!(6"8),!and!a!variety!of!teaching!roles!is!ideal.!This!workshop!would!also!
be!useful!for!teacher!aides!and!other!paraprofessionals!who!work!with!students!in!
mathematics.!!!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 9!
6. Be!sure!you!have!the!required!equipment!and!materials.!!A!materials!list!is!provided!in!the!next!section!of!this!guide.!
1"3!Days!in!advance,!the!facilitator!should:!
1. Do!a!technology!test"run!with!the!computer/projector/dvd!player!to!ensure!that!you!know!how!to!operate!each!and!switch!between!them!as!needed.!
2. Plan!snacks!or!meals!if!you!will!provide!either.!3. Establish!partner!and/or!grouping!assignments.!4. Ensure!that!workshop!handouts!and!materials!are!ready.!Make!Ground!Rules!and!
Parking!Lot!and!carousel!posters!(refer!to!slide!4!and!61!of!the!Slide!Notes!Guide).!
5. Do!a!final!practice!of!the!workshop!using!all!of!the!materials.!On!the!day!of!the!workshop,!the!facilitator!should:!
1. Set!up!the!meeting!space:!! Arrange!tables!or!desks!in!groupings!and!with!a!view!of!the!screen.!! Set!up!Parking!Lot!area!and!post!Ground!Rules.!!! Set!up!and!test!computer!equipment!and!DVD!player.!! Set!up!sign"in!area!and!name!tags.!! Arrange!place!for!breakfast,!snacks!or!lunch!(if!provided).!! Distribute!handout!packets.!
Are!you!ready?!Complete!the!facilitation!checklist!provided!(Appendix!4).!
WORKSHOP!MATERIALS!
This!Facilitation!Guide!includes!most!of!the!information!required!for!the!workshop,!
including!background!information,!facilitation!tips,!workshop!agendas,!and!handouts.!!!
! In!addition,!the!PowerPoint!presentation!for!the!workshop!is!provided!on!the!Mathematics!Improvement!Toolkit!website:!www.middlegrademath.org!
! The!required!DVD!must!be!ordered!separately!using!the!instructions!on!the!same!website:!www.middlegrademath.org!
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Here!is!the!list!of!materials!needed!to!facilitate!the!workshop!in!your!school!or!district:!
! This!facilitation!guide!! PowerPoint!presentation!" DVD!entitled!Improving!Access!to!Middle!Grades!Mathematics:!Language!in!the!
Math!Classroom!
" Computer!with!DVD!player!&!speakers.!!Alternatively,!you!could!show!the!DVD!using!a!DVD!player!and!television.!You!will!need!a!computer!to!show!the!power!point!
presentation.!!
" LCD!projector!and!screen!" Whiteboard/chalkboard!or!easel!with!chart!paper!and!chalk!or!markers!" Charts!for!Carousel!Sharing:!!5!large!pieces!of!poster!or!easel!paper,!each!with!one!
of!these!five!questions:!
! What!are!good!strategies!for!introducing!and!developing!understanding!of!vocabulary?!! What!are!good!strategies!for!embedding!vocabulary!in!math!instruction?!! What!are!good!strategies!for!reviewing!vocabulary?!! Which!vocabulary!strategies!are!particularly!helpful!for!students!with!disabilities?!! How!do!our!curriculum!materials!support!vocabulary!instruction?!What!further!
supplements!would!be!beneficial?!
" Packet!of!workshop!handouts!for!each!participant.!The!handout!masters!can!be!found!in!this!guide!and!on!the!Mathematics!Improvement!Toolkit!website:!
www.middlegrademath.org!
" Highlighter!or!marker!for!each!participant!" Colored!stickers!for!Gallery!Walk!(optional;!see!Slide!Notes!Guide,!slide!62)!" Name!tags,!marker!and!sign"in!sheet,!if!using!" Lessons!or!units!from!your!curriculum!materials.!!You!will!be!asking!participants!to!
bring!these,!but!it!would!be!helpful!to!provide!some!resources!in!case!any!
participant!forgets!to!bring!what!is!needed.!
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PHOTOCOPYING !RECOMMENDATIONS !
You!will!need!to!provide!a!set!of!handouts!to!each!participant.!The!handout!masters!are!
provided!
in!
the!
back!
of!
this!
guide.!!
For!
ease!
of!
use!
of!
the!
handouts,!
it!
is!
best!
to!
organize!
them!for!participants!as!follows:!
1. Photocopy!Handout!1,!page!1!(Warm!Up)!on!colored!paper,!if!possible.!!Keep!this!handout!separate!from!the!other!handouts!and!distribute!it!to!tables!or!desks!
before!the!participants!arrive!at!the!workshop.!
2. Staple!Handouts!1,!page!2!through!Handout!16!together!in!numerical!order!as!one!packet!of!handouts.!
3. Photocopy!Handout!17!separately!and!reserve!this!document!to!distribute!at!the!end!of!the!workshop.!!This!is!the!feedback!form.!4. Photocopy!Handout!12!(I!have,!Who!has?)!on!card!stock!and!cut!into!cards.!Note:!
You!will!need!1!set!of!cards!for!every!12!participants.!
!
!
!
!
!
!
!
!
!
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FACILITATION!TIPS!
The!following!is!a!list!of!suggestions!to!keep!in!mind!when!you!are!facilitating!the!
workshop.!
#Learn!about!the!participants!in!the!group!you!are!facilitating.!What!are!their!areas!of!expertise?!What!professional!development!experiences!have!they!had?!
#If!you!are!unfamiliar!with!the!participants,!or!they!with!each!other,!consider!opening!the!session!with!an!icebreaker!activity!in!addition!to!the!Warm"Up.!
#Circulate!as!participants!work!on!small!group!activities.!Observe!and!listen!to!them!to!determine!if!they!understand!the!task!and!have!successfully!gotten!
started.!
#Listen!to!identify!themes!or!particular!approaches!and!ideas!that!youd!like!to!incorporate!into!the!follow"up!discussion.!!
#Articulate!the!purpose!and!intended!results!of!the!session!and!the!component!parts.!!Keep!these!goals!central!as!you!present.!!
#Small!group!work!is!designed!to!for!teachers!to!learn!from!one!another.!Stimulate!discussion!among!participants!and!get!them!actively!involved.!Listen!and!pose!
questions!to!move!their!discussion!forward.!!!
#Be!flexible.!Plan!in!advance,!but!be!ready!to!change!or!adapt!to!meet!the!needs!of!the!group.!
#Look!for!places!to!connect!the!work!to!your!specific!district!situation.!!#Watch!your!pace!!Pacing!suggestions!are!provided!as!guidelines,!but!try!to!gauge!
the!needs!of!the!group.!!A!pacing!guide!is!provided!(Appendix!5).!
#Know!yourself!!Do!you!tend!to!move!and!talk!quickly?!Slowly?!!Want!the!details!or!just!the!big!picture?!!As!you!prepare,!mark!reminders!to!yourself!such!as!keep!
this!brief!or!slow!down.!!
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#Avoid!simply!reading!through!the!presentation!slides!as!you!present.!Practice!the!presentation!so!that!you!are!able!to!use!the!information!on!the!slide!to!remind!
you!of!the!key!ideas.!Do!not!talk!about!every!point!on!the!slide.!
#Anticipate!the!issues!or!problems!that!could!arise!in!the!workshop!and!plan!how!you!would!respond!to!them.!!
#Consider!inviting!feedback!at!the!close!of!the!session!to!help!you!improve!your!facilitation!or!modify!the!workshop.!An!optional!feedback!form!is!included!with!
the!handouts.!
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WORKSHOP!AGENDA!AND!PACING!SUGGESTIONS!
WORKSHOP!AGENDA!"!BROAD!VIEW! !!!!!
Time!
(min)!
Workshop!
Segment!
Description!
5! Warm"Up!
Activity!
Gets!participants!thinking!about!the!topic!of!language!in!the!mathematics!
classroom!
20! Introduction!! Outlines!the!agenda,!goals!and!ground!rules!for!the!workshop.!
25! Language!
Demands!in!
Mathematics!
Explores!the!importance!of language!in!mathematics!learning!and!uses!
classroom!video!to!examine!the!language!demands!present!in!a!middle!grades!
mathematics!lesson.!
45! Vocabulary!
Challenges!in!
Mathematics!
Vocabulary!is!the!intersection!of!the!four!main!language!processes:!reading,!
writing,!listening!and!speaking.!!This!segment!explores!the!kinds!of!vocabulary!
students!need!and!the!challenges!of!learning!vocabulary.!
10! Break! !
!
60!
Vocabulary!
Strategies,!!
Part!1!
Shares!video!examples!of!vocabulary!strategies!and!provides!information!on!
the!research!on!teaching!vocabulary.!
30! Vocabulary!
Strategies,!!
Part!2!
Shares!instructional!activities!for!teaching!vocabulary!in!mathematics!and!
provides!an!opportunity!for!participants!to!apply!these!strategies!to!their!own!
practice!
! Lunch! END!OF!PART!I
30! Embedding!
Vocabulary!
Shares!a!video!example!of!a!lesson!that!reinforces!vocabulary!by!embedding!it!
into!the!lessons!tasks!20! Reviewing!
Vocabulary!
Focuses!on!strategies!for!reinforcing!and!reviewing!vocabulary.!
30! Writing!in!
Mathematics!
Explores!ways!to!support!student!understanding!and!writing!in!mathematics!by!
examining!student!writing!and!discussing!instructional!strategies.!
40! Planning!
Vocabulary!
Instruction!
Introduces!a!model!for!planning!for!the!vocabulary!instruction!in!the!math!
classroom!and!provides!an!opportunity!for!participants!to!do!some!planning!for!
their!own!instruction.!
10! Wrap"Up! Summarizes!the!key!messages!of!the!workshop!and!allows!participants!to!
provide!feedback.!!
! ! !
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WORKSHOP!AGENDA!!DETAILED !VIEW!
Time!
(min)!
Activity! PPT Slides Materials!(Handouts/Video)
5! Warm"up:!! *** H"1,!page1!(Language!in!the!
Math!Classroom)!!
20!
!
Introduction
! Schedule!! Workshop!Topics!and!Goals!! Ground!Rules!! Discuss!Warm"Up!
17!
PowerPoint!Handout!for!
note"taking!(optional)!
!
Handout1,!page!1,!2!
25! Language!Demands!in!Mathematics
Why!is!language!important!to!learning!
mathematics?!
What!language!demands!are!present!in!a!!!math!
lesson?!
Background/Goal!of!Using!Video!!
!"#$%&'()*+')+,-.+/.",(&.*+#0"11&''2+
1. Watch!video!segment!2. Discuss!at!table!groups!3. Reflect!on!your!own!situation!4. Whole!Group!Sharing!
!
8"16!
H"2!(Focus!Question)!
45!
!
!
Vocabulary!in!Mathematics!
! Vocabulary!as!the!intersection!of!4!language!processes:!reading,!writing,!
listening!and!speaking!
! Key!vocabulary!in!lesson!! Types!of!word!knowledge!! Activity:!Identify!and!Classify!Vocabulary!
Words!
! Share!ideas!! Vocabulary!Challenges!Activity!! Vocabulary!Issues!for!Students!with!
Disabilities!
! Review!a!sample!Math!Lesson!
!
17"37!
!
!
H"2!!(Focus!Questions)!
!
H"3!(Identify!and!Classify!
Vocabulary)!
!
H"4!(Vocabulary!Challenges)!
!
!
H"5!(A!Math!Lesson)!
10! Break!
!
60!
Vocabulary!Strategies,!Part!1
Viewing!Video!!
!Review
!
focus!
question!
! Show!Video!Segment:!The!Warm"Up!and!Have!participants!fill!out!related!blocks!on!
video!recording!sheet!
! Discussion!National!Reading!Panel!Research!
!
38"44!
H"6!(Focus!Question)!
!
DVD!Warm"Up!
!
H"7!(Research"based!Strategies)!
!
H"8!(Reflect!on!Video)!
!
!
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Time!
(min)!
Activity! PPT Slides Materials!(Handouts/Video)
! Consider!recommended!strategies!for!special!education!population!
! View!Video!Segment:!Main!Investigation!! Discussion!
Teacher!Interview!
DVD!Main!Investigation
DVD!Teacher!Interview!
30! Vocabulary!Strategies,!Part!2
Exploring!Instruction!Activities:!
! Visual!Definition!! 4"Block!
Partner!Discussion:!!
! How!would!this!activity!benefit!students?!What!might!be!challenging?!How!could!you!
make!it!more!accessible?!
!
45"52!
!
H"9!(Practice!Strategies)!
! End!of!Part!1/Lunch!
!
!
30!
Embedding!Vocabulary!
String!Shapes!Lesson!!
! Lesson!Background!! Show!Video!Embedding!Vocabulary!! Carousel!Sharing!!
!
53"62!
H"10!(Focus!Question)
!
Video!
Embedding!Vocabulary!
!
!
20!
Reviewing!Vocabulary!
! Watch!Video!Segment!Reviewing!Vocabulary!
! Matching!!! I!Have;!Who!Has?!
63"71!
H"10!(Focus!Question)
!
DVD!Reviewing!Vocabulary!
!
H11!(Matching!Cards)!
H12!(I!Have;!Who!Has?)!
!
!
30!
Writing!in
!Mathematics
!
! Analyze!problem!! Examine!student!writing!! Discuss!strategies!! Whats!Missing!Activity!
!
72"77!
H"13!(Examine!a!Math
!Task)
H"14!(Whats!Missing?)!
H"15!(Strategies!for!Writing!
in!Math)!
40! Planning!Vocabulary!Instruction
! Planning!Activity!! Share!Plans!With!Group!
!
78"81!
H"16!(Planning!Instruction)!!
10! Wrap"Up! 82"84 H"17!(Feedback!Form)
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!2009!Education!Development!Center,!Inc.! ! 17!
PACING!SUGGESTIONS!
Sometimes!the!pacing!of!a!workshop!does!not!go!as!expected.!Perhaps!an!activity!or!
discussion!takes!you!in!a!different!direction!or!requires!more!time!than!you!planned.!If!you!
find!yourself!running!behind!schedule,!you!will!need!to!make!some!decisions!about!what!to!
shorten!or!eliminate.!Below!are!some!guidelines!to!support!your!decision"making.!
Workshop!
Segment!Adjustments!
Approx.!
Savings!
(min)!
Reinforcing!
Vocabulary!
Omit!Slides!62"66!and!accompanying!activities!and!video.!!
This!is!an!example!of!embedding!vocabulary!
!
15"20!
Planning!
Vocabulary!
Instruction!
Planning!is!a!very!valuable!part!of!the!workshop.!!This!offers!
the!best!opportunity!for!participants!to!process!their!
learning!and!apply!it!to!their!own!situation.!!It!also!enables!
them!to!more!readily!bring!the!professional!development!
experience!back!to!their!classroom!practice.!!For!this!
reason,!it!is!not!recommended!that!you!eliminate!the!co"
planning!segment.!!Further,!you!need!to!provide!at!least!30!
minutes!for!productive!planning.!Do!not!cut!this!segment!
shorter!than!that.!!You!could!cut!the!sharing!out!of!the!plans!
and!do!this!at!another!time.!
!
!
10!
Writing!in!
Mathematics!You!could!omit!this!section!entirely!to!save!time!or!do!it!at!a!
separate!time.!
30!
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!2009!Education!Development!Center,!Inc.! ! 18!
SLIDE!NOTES!GUIDE!
PART !1!
INTRODUCTION !! 7 !SLIDES,!APPROXIMATELY !20 !MINUTES !Slide!1!
!
Handout!1!!Language!in!the!Math!
Classroom!
!
Purpose:!!
To!welcome!and!situate!participants!and!to!engage!them!
in!the!subject!of!the!workshop!by!providing!some!
individual!reflection!prior!to!the!start!of!the!workshop!
Action:!
!In!advance!of!the!workshop,!type!your!name,!contact!
information!and!any!other!relevant!details!after!
Facilitator:!!
Display!this!slide!as!participants!are!arriving.!Have!the!
Warm"Up!available!for!them!to!complete.!
If!desired,!have!participants!sign!attendance!sheet.!
Talking!Points:!
Please!read!the!slide!which!provides!some!details!about!
getting!started.!!In!advance!of!the!start!of!the!workshop,!
please!work!individually!on!the!warm"up.!!Well!have!a!
chance!to!discuss!this!page!early!in!the!workshop.!
!
!
!
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Slide!2!
Purpose:!To!establish!the!workshop!goals!
Talking!Points:!!
Here!is!what!we!aim!to!accomplish!as!goals!today.!!
[read!slide]
!
Slide!3!
Purpose:!To!outline!the!topics!of!the!workshop!
Talking!points:!!
Lets!look!at!the!key!topics!of!the!workshop.!The!
workshop!begins!by!looking!at!the!language!demands!
present!in!the!!mathematics!classroom.!!!
Then,!it!moves!to!a!focus!on!developing!and!
implementing!vocabulary!and!language!strategies!
designed!to!improve!math!learning.!Next!the!workshop!
will!address
!some
!strategie
!to
!support
!students
!in
!
writing!in!mathematics.!!The!workshop!concludes!with!
an!opportunity!for!collaborative!planning.!!
!
!
!
!
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Slide!4!
!
Purpose:!To!establish!guidelines!for!working!together!
Talking!Points:!!
Ground!Rules!help!facilitate!the!work!of!groups!in!
achieving!particular!goals.!It!is!important!to!review!them!
and!to
!convey
!that
!they
!represent
!our
!hopes
!for
!how
!to
!
work!together.!!This!helps!to!get!everyone!on!the!same!
page.!Here!are!the!ground!rules!I!am!suggesting.![read!
slide]!
Action:!Invite!clarifying!questions!and!additions!to!this!list!
of!ground!rules.!!!
Action:!Point!out!the!Parking!Lot.!
Talking!Points:
!!The!Parking!Lot!is!where!we!note!subjects!that!come!up!
(such!as!related!but!tangential!topics)!that!we!would!like!
to!pursue!further.!It!helps!us!stay!on!track!to!complete!
the!workshop!while!honoring!the!important!issues!that!
may!come!up!as!we!work!today.!If!we!keep!track!of!them!
here,!we!can!make!a!plan!to!discuss!them!further!at!
another!time.!
Action:!You!can!ask!participants!if!anyone!uses!this!
strategy!in!their!classroom.!
Note:!!In!advance!of!the!workshop,!post!these!ground!rules!in!
the!room!where!participants!can!view!and!refer!to!them!
throughout!the!session.!You!can!also!modify!the!list!as!the!
group!decides.!!
Also,!designate!an!easel!with!chart!paper,!a!posted!piece!of!
easel!paper,!or!a!section!of!a!whiteboard!for!maintaining!the!
list!of!parking!lot!items.!!Entitle!the!area!PARKING!LOT!!
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!2009!Education!Development!Center,!Inc.! ! 21!
Slide!5!
Handout!1,!page!2!!
Language!in!the!Math!
Classroom!
!
Talking!Points:!
Lets!look!at!the!warm!up!problem!on!Handout!1,!page!1.!
Did!you!have!enough!time!to!work!on!the!problem?!!!
!
Note:!
If!
many!
have!
not!
finished,!
provide!
more!
time.!!
If!
only!a!few!have!not!finished!or!arrived!late!and!did!not!do!
it,!you!could!have!them!make!a!group!of!three!for!the!
next!part!of!the!warm"up.!!They!can!observe!and!offer!
their!observations!in!the!discussion.!
!
Talking!Points:!
Now!lets!go!to!the!next!page!of!Handout!1.!
With!a!partner,!you!are!going!to!describe!how!you!
approached!the!problem.!But!there!are!some!rules!""""!
you!cannot!point!to!your!work!or!show!it!and!you!cannot!
use!certain
!words.
!!These
!are
!listed
!on
!the
!page.
!After
!
you!have!each!had!a!turn!to!explain!your!approach,!
discuss!question!#2.!Then,!well!come!back!together!and!
talk!about!this!experience.!
!
!
!
!
!
!
!
!
!
!
!
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Slide!6!
!
!
!
!
Talking!Points:
Lets!talk!together!now!about!your!experiences.!!What!was!
it!like!to!try!to!describe!something!with!your!word!choice!
limited?!
!
[Possible!Follow
!up
!questions]
!
! How!did!you!feel!when!you!were!doing!this?!! What!did!it!make!you!think!about?!! How!would!it!have!been!different!if!you!could!have!
used!any!words!you!wanted?!
! What!do!you!think!the!point!of!our!doing!this!is?!!
The!purpose!of!the!warm"up!was!to!simulate!how!it!feels!to!
try!to!explain!something!with!a!limited!vocabulary.!!You!
might!have!been!successful!in!solving!the!problem!but!
struggled!to!explain!your!thinking.!Students!with!language!
disabilities!sometimes!experience!challenges!in!explaining!
themselves!when!they!cannot!access!the!vocabulary!they!
need.!!
!
!
!
!
!
!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 23!
LANGUAGE!DEMANDS!IN !MATHEMATICS! 9 !SLIDES,!APPROXIMATELY !25 !MINUTES !Slide!7!
!
Talking!Point:!
Here!
is!
a!
little!
example!
to!
illustrate!
how!
students!
sometimes!interpret!language!very!literally!in!
mathematics.!Here!the!student!has!found!x!and!circled!it!
when!the!problem!really!means!for!the!student!to!solve!
for!the!value!of!x.!
!
Slide!8!
!
!
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Slide!11!
!
Talking!Points!
David!Allsopp!has!done!quite!a!bit!of!research!related!to!
teaching!mathematics!to!students!with!disabilities.!!!
Here!are!a!couple!of!findings!about!language!that!he!
shares!in
!a!book
!called
!Teaching
!Mathematics
!
Meaningfully.!![read!slide]!
!
!
!
!
!
Slide!12!
!
Talking!Points!
Language!Proficiency!can!affect!math!learning.!
Here!are!just!a!few!examples!that!illustrate!what!might!
go!wrong!when!students!are!not!proficient!in!language.!!
[Read!slide]!
!
I!wonder!if!you!have!any!experiences!to!share!about!
how!language!proficiency!effects!math!learning?!
[allow!time!to!participants!to!share!their!stories]!
!
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!2009!Education!Development!Center,!Inc.! ! 27!
Slide!15!
!
!Video!
Introduction!
!Handout!2!
Focus!Questions!for!
Video!
!
!
Talking!Points:!
In!order!to!focus!our!discussion,!I!am!going!to!give!you!
a!question!or!two!for!each!segment!of!video!that!we!
watch.!!On!Handout!2!you!can!record!your!observations!
if!you
!wish.
!This
!may
!be
!helpful
!when
!we
!discuss
!it
!
after.!If!you!prefer!to!just!watch!with!the!question!in!
mind,!that!is!fine!too.!
As!you!watch!consider!the!question:!
What!does!this!lesson!demand!in!terms!of!language!
skills?!
Youll!also!see!a!space!on!the!recording!sheet!for!you!to!
jot!down!vocabulary!you!hear!that!you!think!is!
important.!
Action:!Show!clip!called!Introduction.!
!
Pacing!Note:!This!video!clip!is!approximately!5!minutes!in!
length.!
!
!
!
!
!
!
!
!
!
!
!
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Slide!16!
!
Purpose:!To!discuss!the!language!demands!in!a!math!
lesson!using!the!video!as!a!launching!pad!
Talking!Point:!
Now,!at!your!table!group,!please!discuss!your!
observations!about!the!language!demands!in!the!lesson!
clip!we!just!watched.!!!Then,!after!everyone!has!had!a!
chance!to!share,!discuss!the!second!question!on!the!
slide.!
!
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VOCABULARY !IN !MATHEMATICS! 21 !SLIDES, !APPROXIMATELY!45 !MINUTES!Slide!17!
!
Talking!Points:!
These!
are!
4!
language!
processes!
that!
are!
used!
in!
most!
middle!grades!math!classes.!!Listening,!Speaking,!
Reading,!and!Writing!!
I!think!all!of!you!identified!demands!of!the!lesson!that!
fell!into!each!of!these!categories.!
!
!
!
!
Slide!18!
!
Purpose:!To!establish!a!workshop!focus!on!vocabulary!as!
the!intersection!of!4!language!processes!
Talking!Point:!
Vocabulary!is!at!the!intersection!of!these!processes!
because!each!process!requires!the!use!of!vocabulary.!!
!In!teaching!math!there!are!some!unique!issues!related!
to!vocabulary.
!!We
!are
!going
!to
!focus
!on
!this
!next.
!
!
!
!
!
!
!
!
!
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Slide!19!
!
Talking!Points:!
Lets!look!at!vocabulary.!!We!can!break!vocabulary!use!
into!two!areas:!
Receptive!"""vocabulary!that!which!you!receive,!such!as!
when!you
!are
!reading
!or
!listening
!to
!someone
!speak.
!
Expressive!""vocabulary!used!to!convey!ideas!in!writing!
or!speaking.!
Here!are!the!demands!of!receptive.!!Reading!and!
listening!requires.[read!slide]!
!
Here!are!the!demands!of!expressive.!!Reading!and!
writing!requires[read!slide]!
!
Slide!20
!
!
See!handout!on!next!page!
!
Talking!point:!
Lets!talk!about!the!vocabulary!you!identified!in!the!
video.!
Im!going!to!record!the!words!that!you!heard.!!You!can!
just!call!them!out!as!I!record.!![on!chart!paper!or!white!
board]!
Action:!As!participants!call!out!words,!place!them!in!three!
columns!(specific!math!vocab,!context!vocab,!process!
vocab)!but!dont!label!the!columns!yet.!Its!okay!if!you!
dont!have
!responses
!in
!all
!of
!the
!columns.
!
Talking!point:!
You!probably!noticed!that!I!grouped!the!words!as!I!
recorded!them.!!Does!anyone!see!a!pattern!in!how!I!
have!grouped!them?!!How!might!you!label!the!columns?!
!
Facilitator!Notes:!It!is!okay!if!you!use!different!labels!for!the!
columns.!!The!titles!themselves!are!not!as!important!as!the!
idea!that!there!are!different!kinds!of!vocabulary!that!students!need!in!math.!
!
!
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Slide!20!(continued)!
!Handout!2!
Focus!Questions!for!
Video!
!
!
Slide!21!
!
Purpose:!to!underscore!the!different!types!of!vocabulary!
knowledge!and!students!need!for!math!
Talking!Points:!
Here!are!the!labels!that!I!will!be!using!to!distinguish!
different!types!of!vocabulary!present!in!the!math!class.!
The!vocabulary!of!the!math!class!could!be!broken!into!
three!categories.!
[read!each
!bullet
!including
!the
!examples.
!You
!can
!add
!
other!examples!if!youd!like.]!
!
!
!
!
!
!
!
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Slide!22!
!
!Handout!3!
Identify!and!Classify!
Vocabulary!
!
Note:!this!handout!has!4!pages!
Purpose:!The!goal!of!this!activity!is!for!participants!to!
practice!examining!a!task!for!the!range!of!vocabulary!and!
to!prioritize!importance!of!the!language!in!order!to!make!
instructional!decisions.!
Talking!Point:!
Next,!were!going!to!examine!some!vocabulary!in!math!
problems.!!Id!like!you!to!work!in!pairs!or!groups!of!three!
and!do!the!following:!
!
[read!the!slide.]!
!
Im!going!to!provide!different!problems!to!different!
groups,!so!that!there!is!variety.!!Some!groups!will!be!
working!on
!the
!same
!problem.
!!
Action:!After!groups!have!had!about!20!minutes!to!work,!
direct!participants!to!join!up!with!a!pair!or!group!who!
worked!on!the!same!problem!they!did.!Ask!them!to!
discuss!their!ideas.!
!
Facilitation!Note:!Five!problems!(Problems!3a"3e)!are!provided!
for!this!activity.!!You!should!select!no!more!than!3!to!use.!!
Assign!each!pair!one!problem!to!work!on.!!Be!sure!that!two!
groups!have!the!same!problem,!so!that!they!can!discuss!it!at!
the!end.!!If!you!prefer,!you!might!select!only!one!problem!and!have!everyone!use!the!same!one.!!Additionally,!if!you!would!
like!to!personalize!the!workshop,!you!could!replace!these!
problems!with!a!problem!or!problems!from!your!own!
curriculum!materials!or!state!assessment.!!Be!sure!to!select!
problems!that!are!language"rich!and!contain!a!variety!of!types!
of!vocabulary.!
!
!
!
!
!
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Slide!23!
!
!
!
Action:!After!groups!have!had!a!chance!to!share!with!
another!group,!ask!the!whole!group!to!consider!these!
questions.!Facilitate!a!whole"group!discussion!
Facilitation!Note:!Some!ideas!that!may!emerge!or!that!you!
may!want!to!bring!up:!
Some!process!words!are!words!that!students!come!across!
routinely!in!constructed!response.!If!students!do!not!answer!a!
question!well,!it!may!be!that!they!need!support!with!these!
process!words.!What!does!it!mean!to!explain!your!thinking!
or!show!your!work,!for!example?!How!is!this!different!from!
other!subject!areas?!
Other!math!vocabulary!words!might!be!content"specific.!!
These!are!usually!quite!essential!to!success!in!solving!a!
problem.!Building!understanding!behind!the!definition!is!important!to!helping!students!retain!and!retrieve!the!
definition!later.!!!
Context!words!may!or!may!not!be!essential!for!solving!a!
problem.!But,!even!if!students!dont!need!to!know!the!
meaning!of!a!word!to!solve!a!problem,!they!might!give!up!on!a!
problem!if!they!dont!know!the!word.!So,!they!dont!need!to!
know!what!a!whole!number!is!to!answer!the!multiple!choice!
question.!!Nor!do!they!need!to!know!what!a!florist!is.!But,!
knowing!these!words!may!make!it!easier!to!envision!the!
situation!and!more!likely!that!they!will!stick!with!the!problem.!!!
Slide!24
!
!
Purpose:!To!provide!an!example!of!a!strategy!to!make!
language!accessible!
Talking!Points:!
This!is!an!actual!item!from!the!8th!grade!Colorado!State!
Math!Assessment.!!In!addition!to!the!text!of!the!
problem,!the!definitions!of!two!words!are!provided!as!
shown!here.![Read!slide]!
The!developers!of!this!test!dont!want!context!
vocabulary!to
!be
!an
!obstacle
!to
!showing
!math
!
understanding.!!
So,!their!strategy!is!to!provide!definitions!as!a!resource!
to!students.!!
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Slide!25!
!
!
!
!
!
!
Slide!26
!
!
Talking!Points:!
One!reason!students!struggle!when!reading!
mathematics!is!!!
[read!slide]!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
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Slide!27!
!
Talking!Point:!
Here!is!a!comparison.![read!fiction!example!and!then!the!
math!text]!
Action:!Ask
!for
!comments
!from
!the
!group
!on
!the
!question
!
at!the!bottom!of!the!slide.!
!
Slide!28
!
!
Talking!Point:!Another!challenge!is!that!math!has!symbols!to!learn!in!
addition!to!words.!!Learning!math!vocabulary!means!
learning!symbols,!too.!
!
!
!
!
!
!
!
!
!
!
!
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Slide!29!
!
!
Talking!point:!
[Read!slide.]!
When!was!the!last!time!you!heard!these!words!outside!
of!math!class?!
This!means
!students
!have
!probably
!not
!heard
!the
!word
!
very!often.!
!
Slide!30!
!
See!handout!on!next!page!
!
!
!
!
!
!
Purpose:!The!goal!of!this!activity!is!to!think!about!why!
language!is!uniquely!challenging!in!the!math!classroom.!!!
Talking!point:!
Lets!do!an!activity!now!to!dig!deeper!into!the!
challenges!of!vocabulary!in!the!math!classroom.!!Youll!
be!using!Handout!4!for!this!activity.!
!
[Review!the!steps!of!this!activity!as!outlined!on!the!
slide.]!!
Action:!!As!you!circulate!during!the!group!work,!make!
sure!that!participants!know!that!they!do!not!need!to!
come!up!with!an!example!for!each!category.!
!
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Slide!30(continued)!
!Handout!4!
Vocabulary!Challenges!!
!
Slide!31!
!
Purpose:!!To!conclude!a!discussion!of!common!
vocabulary!challenges!and!begin!to!shift!focus!to!
strategies!
!
Talking!points:!
Lets!talk!now!together!about!your!experiences!and!
strategies.!
!
Action:!Read!the!two!questions!and!facilitate!a!discussion.!!
You!could
!record
!their
!ideas
!and
!strategies
!if
!youd
!like.
!
Sometimes!creating!a!list!encourages!responses.!This!
should!be!a!brief!5"minute!discussion.!
!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 38!
Slide!32!
!
!
Slide!33
!
!
Purpose:!To!provide!information!about!three!areas!of!
difficulty!in!vocabulary!for!students!with!disabilities!
Talking!Points:!
We!know!that!vocabulary!can!be!challenging!for!all!
students,!and!now!I!want!to!!focus!us!on!students!with!
disabilities.!
Here!are!a!few!areas!of!difficulty!for!students!with!
disabilities.!!Well!talk!a!bit!about!each!of!these!on!the!
upcoming!slides.!
!
[Read!three!bullet!points]!
!
!
!
!
!
!
!
!
!
!
!
!
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Slide!34!
!
Talking!Point:!!
Some!students!with!disabilities!have!trouble!with!
decoding!""!that!is,!the!use!of!phonics!to!decipher!print!
patterns!and!translate!them!into!the!sounds!of!
language.!In!math,!students!are!called!upon!to!do!a!lot!
of!decoding.!Whats!involved!in!decoding!in!math?!
[Read!bullet!points]!
So,!decoding!in!math!involves!an!even!higher!demand!of!
thinking!and!processing!than!other!subject!areas.!!Its!
more!involved!than!just!decoding!words.!
!
Slide!35
!
!
Talking!points:!
Now!this!is!an!interesting!thing!to!consider.!!We!all!have!
experiences!with!students!who!struggle!with!story!or!
word!problems.!!Think!about!how!the!structure!of!these!
is!different!from!the!reading!students!experience!in!
other!subjects.!
!
[Share!first!bullet]!
!
The!structure,!in!math,!is!turned!upside!down.!!So,!we!
need!to
!support
!students
!in
!learning
!this
!different
!
structure!and!perhaps,!in!reorganizing!the!information!
so!they!can!tackle!the!problem.!
Solving!problems!requires!students!to!determine!the!
necessary!information.!
!
[share!second!bullet]!
!
!
!
!
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Slide!36!
!
Talking!Point!
Lets!think!about!expressive!language.!
!
[Read!slide.]!
!
Slide!37
!
!
See!handout!on!next!page!
!
!
!
!
!
!
!
Talking!points:!
We!are!going!to!watch!some!more!video.!!First,!though,!I!
want!you!to!be!familiar!with!the!math!content.!!So,!
using!Handout!5,!Id!like!you!to!do!the!following:!
!
[Read!bullets]!
!
Then!discuss!your!answers!with!a!partner!at!your!table.!
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Slide!37!(continued)!
!Handout!5!
A!Math!Lesson!
!Note:!This!handout!has!4!pages.!
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VOCABULARY !STRATEGIES:!PART!1 ! ! 7!SLIDES,!APPROXIMATELY !60 !MINUTES !Slide!38!
!
Video!
Warm!Up!
!Handout!6!
Focus!Question!for!Video!
!
Talking!Points:!
Now,!
well!
shift!
to!
the!
video!
to!
look!
for!
strategies!
to!
support!the!learning!of!vocabulary.!
Once!again,!you!can!use!Handout!6!to!record!their!
observations!if!youd!like.!!You!dont!have!to!write!down!
your!ideas.!!This!is!primarily!provided!to!keep!the!
question!in!the!forefront!for!viewing.!
[Read!slide]!
Action:!Show!clip!called!Warm!Up!Activity!
Pacing!Note:!This!video!clip!is!3!!minutes!in!length.!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
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Slide!39!
!
Talking!Point:!
Now,!turn!to!a!partner!and!share!two!strategies!that!
you!observed.!
!
!
!
!
Slide!40!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 44!
Slide!41!
!
!
Handout!7!
Research"based!
Strategies!for!Teaching!
and!Learning!Vocabulary!
!
Talking!Points:!
So!what!does!the!research!say!about!teaching!
vocabulary?!
The!National!Reading!Panel!was!convened!in!1997!by!a!
request!from
!Congress.
!Its
!charge
!was
!to
!assess
!the
!
effectiveness!of!different!approaches!used!to!teach!
children!to!read.!In!2000,!the!NRP!concluded!its!work!
and!submitted!"The!Report!of!the!National!Reading!
Panel:!Teaching!Children!to!Read,"!at!a!hearing!before!
the!U.S.!Senate!Appropriations!Committee's!
Subcommittee!on!Labor,!Health!and!Human!Services,!
and!Education.!
That!report!offered!findings!and!determinations!for!
many!topics!related!to!reading,!including!vocabulary.!!
They!are
!included
!on
!Handout
!7.
!
Heres!what!they!found.!!!
!
[Review!the!slide.]!
!
The!research!says!its!important!to!deliberately!teach!
the!vocabulary.!In!todays!workshop,!well!explore!how!
to!incorporate!these!recommendations!in!instruction.!!
Notes:!Embedding!instruction!in!rich!contexts:!!students!can!access!
the!vocabulary!more!successfully!when!it!is!included!in!situations!
which!students!can!relate!to.!!This!embedding!supports!learning!and!retrieval!of!vocabulary!
Incidental!opportunities!"""these!are!the!situations!in!which!the!
vocabulary!might!not!be!central,!but!students!can!hear!it!and!even!
apply!it!to!a!situation.!
!
!
(For!more!information!on!the!report,!visit!
http://www.nichd.nih.gov/publications/nrp/findings.cfm)!!
!
!
!
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Slide!42!
!
Video!
Main!Investigation!
!Handout!7!
Research"based!
Strategies!for!Teaching!
and!Learning!Vocabulary!
!
!
Talking!Point:!
Were!going!to!watch!the!main!lesson!now.!!Here!is!the!
focus!question:!!
!
[read!bullet]
!
!
You!can!use!Handout!7!to!record!your!observations!and!
ideas.!!!
Action:!Show!clip!called!Main!Investigation!
Pacing!Note:!This!video!clip!is!7!minutes!in!length.!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
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Slide!43!
!
!
Handout!8!
Reflect!on!the!Video!
!
Talking!Point:!
Now,!Id!like!to!give!you!more!time!to!dig!into!these!NRP!
strategies!by!completing!Handout!8!with!a!partner.!
Discuss!these!two!questions.![read!slide.]!
After!we!have!completed!this!section,!well!watch!the!
teacher!interview!clip.!
!
!
!
!
!
!
!
!
!
!
!
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Slide!44!
!
Video!
Teacher!Interview!
!Handout!8!
Focus!Questions!for!
Video!
!
!
Purpose:!To!summarize!the!messages!of!this!section!and!
hear!about!the!teachers!thinking!
Talking!point:!!
[Read!slide]!!
At!the!very!bottom!of!Handout!8,!there!is!a!space!for!
notes.!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 48!
VOCABULARY !STRATEGIES:!PART!2! 8 !SLIDES,!APPROX.!30 !MINUTES !
Slide!45!
!
Talking!Points:!
Were!
going!
to!
talk!
about!
a!
process!
for!
teaching!
vocabulary!in!mathematics!so!that!it!is!better!undersood!
and!retreived.!
!
Its!helpful!to!think!about!these!three!steps:!
First[read!first!bullet]!
Second[read!second!bullet]!
Third[read!third!bullet]!
!
!
!
Slide!46!
!
Talking!Point:!
Well!start!by!looking!at!strategies!designed!to!build!
and!refine!definitions!of!key!vocabulary!terms.!
!
!
!
!
!
!
!
!
!
!
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Slide!47!
!
Talking!Points:!
One!way!to!help!students!learn!vocabulary!is!to!build!
understanding!through!visuals.!!In!this!case,!the!shapes!
are!grouped!as!polygons!and!not!polygons.!
!
The!teacher!can!provide!more!shapes!and!ask!the!
students!if!they!think!they!are!polygons!or!not.!Once!
students!get!a!bigger!group!of!shapes!sorted,!they!can!
try!to!create!a!definition!for!the!word.!
!
!
Slide!48!
!
!
Talking!Point:!
Another!strategy!for!teaching!vocabulary!is!called!a!
Vocabulary!4"Block!
!
[Read!top!of!slide]!
Here!are!some!details!about!what!kinds!of!things!might!
go!in!each!of!the!blocks.!!This!doesnt!need!to!be!too!
prescriptive.!!There!might!be!some!variability!in!what!is!
contained!in!a!space!depending!upon!the!word.!!But,!
here!is
!one
!example.
!!!You
!have
!the
!term
!written
!in
!the
!
middle!and!here!are!the!four!blocks.!
!
[Read!the!descriptors!for!each!block]!
!
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Slide!49!
!
Talking!Point:!
Here!is!an!example!of!a!4"block!created!by!a!student!for!
the!term!!median!
[Read!what!is!contained!in!each!of!the!blocks]!
!
!
!
!
!
Slide!50!
!
See!handout!next!page!
!
!
!
!
!
!
!
!
!
!
!
!
!
Talking!Point:!
Now!you!will!have!a!chance!to!try!out!planning!one!of!
these!strategies.
!!!
!
Heres!what!Id!like!you!to!do!.!
First,!locate!Handout!9.!!You!are!going!to!.!
!
[read!slide]!
!!
!
!
!
!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 51!
Slide!50!(continued)!
!Handout!9!
Practice!Strategies!
!
Note:!This!handout!has!2!pages!
Slide!51!
!
!
Talking!Points:!
Okay,!now!Id!like!to!give!you!a!chance!to!share!your!
work!and!discuss!the!experience!with!a!partner.!
Please!turn!to!a!partner!and!explain!your!strategy.!
After!you!have!shared!your!strategy,!discuss!these!
questions.!
!
[read!questions]!
!
Then,!at!the!end!of!your!partner!discussion!,!Id!like!you!
to!identify!one!idea!from!your!discussion!to!share!out!
with!the!whole!group.!
!
!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 52!
END!OF!PART !1!
Slide!52!
!
!
!
Talking!Point:!
!
[Read!
slide]!
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Slide!55!
!
Talking!Points!
What!do!we!mean!by!this!and!why!would!we!do!this?!
Well,!it!is!important!to!use!vocabulary!in!ongoing!work!.!
Using!vocabulary!in!context!anchors!the!vocabulary!
within!a!real
!situation.
!!Knowing
!the
!definition
!of
!median
!
is!one!thing;!being!able!to!calculate!the!median!from!a!
data!set!and!draw!a!conclusion!is!more!mathematically!
sophisticated!and!powerful.!!The!context!can!also!help!
reinforce!the!meaning!of!the!vocabulary!and!assist!
students!in!retrieval!of!that!information!later.!
!
Secondly,!embedding!vocabulary!that!has!already!been!
taught!will!provide!more!opportunities!for!the!students!
to!see,!use,!hear!and!write!the!vocabulary.!!This!
repetition,!in
!varied
!language
!modalities,
!as
!we
!
discussed,!is!critical!to!learning!and!retaining!vocabulary.!
Slide!56!
!
Talking!Point:!
Next!we!are!going!to!look!at!a!classroom!video!example!
of!a!lesson!that!embeds!vocabulary.!It!is!called!String!
Shapes!and!is!featured!in!the!upcoming!video!clip.!
Heres!some!information!about!the!lesson:!
!
[read!bullets]!
!
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Slide!57!
!
Purpose:!To!familiarize!participants!with!the!math!activity!
and!problem!featured!in!the!video!
Talking!
Points:!
Here!is!the!problem!that!students!are!working!on!in!the!
video.!!The!curriculum!materials!call!them!clues.!!Your!
job!is!to!discuss!whether!you!can!make!a!shape!that!fits!
the!given!criteria.!
[Read!slide]!
!
Slide!58!
!
!
Talking!Point:!
Next!we!are!going!to!watch!a!video!of!a!class!working!on!
the!string!shapes!lesson.!!Here!is!some!background.!
!
[read!slide]!
!
!
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Slide!59!
!
[Read!Slide]!
Slide!60!
!
Video!!
Embedding!
Vocabulary!
!
See!handout
!on
!next
!page
!
!
!
Talking!Point:!
Now!well!watch!the!video!of!the!lesson.!
Please!use!handout!10!for!your!note"taking.!!Just!the!top!
part.!!The!bottom!is!for!the!next!video!segment.!This!is!the!
question!for!you!to!focus!on:!
!
[Read!question]!
!
Action:!Show!clip!called!Embedding!Vocabulary!
!
Pacing!Note:!This!video!clip!is!approximately!5!minutes!in!
length.!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 57!
Slide!60!(continued)!
!Handout!10!
Focus!Questions!for!
Video!
!
!
!
!
!
!
Slide!61!
!
!
!
!
!
Talking!Point:!
Youll!see!chart!paper!posted!around!the!room.!!Each!
poster!has!a!question!for!you!to!consider.!
This!is!the!procedure.!!!
[read!bullets]!
!
Note:!Youll!need!to!announce!the!pairs!or!groups!of!three!and!
assign!them!a!poster!at!which!to!start.!!Youll!also!need!to!make!
the!
posters!
in!
advance!
of!
the!
workshop.!!!
!
Pacing!Note:!!Allow!groups!approximately!3!minutes!at!each!
chart.!!Signal!when!its!time!to!move!by!ringing!a!bell!or!calling!
out!Time!to!move!to!the!next!chart.!
!
Carousel!Questions!(5!pieces!of!chart!paper)!
!
1.!What!are!good!strategies!for!introducing!and!developing!
understanding!of!vocabulary?!
!
2.!What!are!good!strategies!for!embedding!vocabulary!in!math!instruction?!
!
3.!What!are!good!strategies!for!reviewing!vocabulary?!
!
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Slide!65!
!
Video!
Reviewing!Vocabulary!
!Handout!10!
Focus!Questions!for!
Video!
!
!
Talking!Point:!
Lets!pick!back!up!with!the!class!we!watched!doing!the!
string!shapes!lesson.!!They!have!moved!on!in!their!unit!of!
study.!
Here!
is!
the!
focus!
question!
on!
Handout!
10.!
[Read!slide.]!
Action:!Show!clip!called!Reviewing!Vocabulary!
Pacing!Note:!This!video!clip!is!approximately!2!minutes!in!
length.!
Note:!The!DVD!contains!one!more!clip!entitled!"Students!Share!
Thinking.!This!video!clip!is!not!used!in!the!workshop!but!is!
provided!for!your!use!at!another!time!should!you!choose.!A!
focus!question!for!use!with!this!clip!is:!!"What!vocabulary!do!
students!use!to!share!their!understanding!of!the!mathematics?"!
This!video!segment!is!completely!optional!and!has!not!been!
integrated!into!the!workshop.!
!
!
!
!
!
!
!
!
!
!
!
!
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Slide!66!
!
Talking!Point:!!
Please!turn!to!!a!partner!and!discuss!this!question.![read!
slide.]!
!
!
Note:!If!youd!like!to!get!participants!up!and!moving!a!little,!you!
can!ask!them!to!find!someone!with!the!same!color!shirt!(or!close!
to!the!same!color!if!there!is!not!a!match!)!with!whom!they!
havent!had!a!chance!to!work!yet!today.!
!
Slide!67!
!
See!Handout!on!next!page!
!
!
!
!
!
!
!
!
!
!
Talking!Point:!
Here!is!an!example!of!cards!that!can!be!used!to!
reinforce/review!vocabulary.!
Some!teachers!provide!the!card!with!the!term!and!blank!
cards!for!the!students!to!create!the!definition!and!picture.!
Others!provide!the!completed!cards!to!students!to!match.!
!
The!students!add!new!sets!of!matching!cards!to!their!set!
as!they!explore!new!vocabulary.!Then,!they!can!use!the!
cards!for
!reference
!and
!review.
!
Handout!11!!shows!the!layout!and!another!example!of!
this!matching!activity.!
!
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Slide!67!(continued)!
Handout!13!
Examine!a!Math!Task!
!
!
Slide!68!
!
Talking!Point:!
The!next!activity!is!called!I!Have,!Who!Has?!!Is!anyone!
familiar!with!the!activity?!!!
Let!me!share!an!example!with!you.!
[read!slide.]!
!
!
!
!
!
!
!
!
!
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!2009!Education!Development!Center,!Inc.! ! 63!
Slide!69!
!
!Handout
!14
!Activity!Cards!
!
Note:!This!handout!has!2!
Talking!Point:!
So!lets!get!started.!!Ill!be!dividing!you!up!into!groups!
shortly.!!Let!me!tell!you!what!you!will!do!to!get!started!
and!to!play!the!game!with!your!group.!
[Read!
the!
steps!
on!
the!
slide]!
!
You!may!never!have!taught!some!of!this!vocabulary.!!So,!
when!you!get!your!card,!if!you!dont!remember!what!the!
term!means,!ask!someone!to!help!you!before!the!game!
starts.!
Action:!To!set!up!this!activity:!
1. Create!groups!of!6"12!participants.!!If!you!have!a!larger!group,!youll!need!multiple!groups!and!sets!of!cards!
2. Have!participants!stand!in!a!circle.!Distribute!all!of!the!cards.!(Some!people!may!have!more!cards!than!others.!
Thats!okay.!You!MUST!distribute!all!of!the!cards!or!the!
activity!wont!work!)!
Note:!In!advance!of!the!workshop,!create!Activity!Cards!from!
Handout!12.!If!you!have!some!participants!with!experience!with!
this!activity,!you!might!want!to!distribute!them!among!the!
groups!to!help!guide!the!activity.!
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Slide!70!
!
Handout!12
!
I!Have,!Who!Has?!Activity!
Card!Master!
!
Note:!This!handout!has!2!pages.!
Talking!Point:!!
The!master!for!a!set!of!cards!is!provided!on!Handout!12.!
This!activity!can!be!used!in!a!variety!of!ways.!!Here!are!
some!examples.!!!
[read!top
!part
!of
!slide]
!
Action:!Facilitate!a!discussion!using!the!questions!on!the!
slide.!This!should!take!no!more!than!5"10!minutes.!
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Slide!71!
!
Talking!Points:!
To!summarize!what!we!have!been!discussing,!here!are!a!
few!things!to!keep!in!mind![read!slide.]!
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!2009!Education!Development!Center,!Inc.! ! 66!
WRITING!IN !MATHEMATICS! 6!SLIDES,!APPROXIMATELY !30 !MINUTES !Slide!72!
!
!
!
!
!
Slide!73!
!
Talking!Point:!
Writing!is!helpful!to!students!in!learning!mathematics!as!it!
can:![read!bullet!points!on!slide.]!
While!it!has!many!benefits,!writing!also!poses!barriers!for!
some!students.!
!
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Slide!74!
!
Handout!13!
Examine!a!Math!Task!
!
Talking!Point:!
To!better!understand!potential!barriers,!lets!examine!the!
math!task!on!Handout!13.!
[read!slide]
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Slide!76!
!
Talking!Point:!
Here!is!an!example!of!how!the!students!response!might!be!
strengthened!with!the!inclusion!of!mathematical!
vocabulary.!!
[read!the!bottom!example!on!the!slide.]!
!!
Slide!77
!
!
See!handout!on!next!page!
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!
Talking!Point:!!!
In!summary,!lets!look!at!some!strategies!for!helping!
students!with!writing!in!mathematics.!Well!be!using!
Handout!15!which!provides!a!list!of!strategies.!!!
[read!slide.]!
!
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Slide!77!(cont.)!!
!Handout!15!
Strategies!for!Writing!in!Math!
!
Note:!This!handout!has!3!
pages.!
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!2009!Education!Development!Center,!Inc.! ! 71!
PLANNING!VOCABULARY !INSTRUCTION! 4 !SLIDES,!APPROXIMATELY !40 !MINUTES !Slide!78!
!
!
!
!
Slide!79!
!
Talking!Point:!
Before!we!go!on!to!do!some!actual!collaborative!planning,!
lets!review!some!key!messages!of!todays!work.!!Here!are!
some!main!points!to!remember!while!planning!for!
vocabulary!instruction.!
[read!slide]!
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Slide!80!
!
!
Handout!
16!
Planning!Instruction!of!
Vocabulary!
!
Note:!This!handout!has!3!pages!
Talking!Point:!!
Now,!youll!have!a!chance!to!do!some!planning.!!I!asked!
you!to!bring!some!curriculum!materials!for!this!activity!
and!I!also!have!some!resources!here.!!This!is!the!general!
flow!of
!the
!planning.
!Youll!
!
[Read!bullets]!
!
Lets!look!at!Handout!16.!!This!handout!structures!a!
process!for!developing!your!plan.!
!
!
!
Note:!!Have!people!plan!in!teams!of!math!and!special!education!
teacher!together!where!possible.!
!
For!your!reference!in!gaining!an!image!of!what!a!completed!
planner!might!look!like,!see!the!sample!planner!in!Appendix!6.!
Slide!81!
!
Talking!Point:!!!
Lets!take!some!time!to!share!plans!now.!!Please!join!up!
with!another!pair!and!do!the!following.!
[Read!Slide]!
!
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!2009!Education!Development!Center,!Inc.! ! 74!
Slide!83!(cont.)!
!Handout!17!
Feedback!Form!
!Slide!84!
!
Note:!This!slide!provides!information!on!the!funding!
source!and!developer!of!this!workshop.!
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!2009!Education!Development!Center,!Inc.! ! 75!
APPENDICES:!ADDITIONAL!FACILITATION!RESOURCES!
APPENDIX!1:!OPTIONAL!WORKSHOP!INTERIM!ACTIVITIES!..............................................................................!76!
APPENDIX!2:!SAMPLE!EMAIL:!WORKSHOP!ANNOUNCEMENT!.........................................................................!78!
APPENDIX!3:!SAMPLE!EMAIL:!WORKSHOP!REMINDER!..................................................................................!79!
APPENDIX!4:!FACILITATION!CHECKLIST!.......................................................................................................!80!
APPENDIX!5:!PACING!GUIDE!....................................................................................................................!82!
APPENDIX!6:!SAMPLE!VOCABULARY!PLANNER!.............................................................................................!84!
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APPENDIX!1: !OPTIONAL!WORKSHOP!INTERIM !ACTIVITIES!
HANDOUTS!A1"A2 !
!
Handout!A1:!Language!in!the!Math!Classroom!Interim!Activity!
Please!choose!one!of!the!four!activities!below!to!complete!in!preparation!for!the!next!
workshop!session!on!______________________________.!!!Please!bring!any!relevant!
supporting!documents!such!as!plans,!reflection/goal!setting!forms!and/or!sample!
student!work!to!the!next!session!to!share!with!your!colleagues.!
!
1. Plan!and!teach!a!lesson!or!part!of!a!lesson!using!a!vocabulary!instructional!strategy!from!the!session!or!from!your!experience.!After!planning/teaching!the!lesson,!
complete!the!Reflection!Questions.!Handout!A2.!!!
2. Choose!a!math!task!of!the!lesson!featured!in!the!video.!How!might!you!make!the!language!of!this!lesson!accessible!to!a!range!of!learners?!!!Consider!what!vocabulary!
instruction!you!would!use!and!how!you!might!assess!student!learning!of!the!
vocabulary!and!the!math!concepts.!!
!
3. Go!back!to!Problems!3a"3e!(Handout!3)!from!the!workshop.!!Choose!one!of!those!problems!and!plan!some!instruction!to!support!students!in!accessing!the!language!of!
the!problem.!!Have!you!maintained!the!integrity!of!the!mathematics?!!Create!a!
follow"up!problem!for!students!to!solve!after!the!instruction!and!completion!of!the!
problem!from!Handout!3.!
!
4. Reflect!upon!the!strategies!that!you!observed!and!discussed!during!todays!workshop!session.!Are!you!inspired!to!try!a!particular!strategy!in!your!own!teaching!
situation?!!Describe!a!plan!to!do!so!and!record!some!notes!on!your!progress!to!bring!
to!the!next!meeting.!
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APPENDIX!3: !SAMPLE!EMAIL:!WORKSHOP !REMINDER!
!
Workshop!Reminder!
!
As!you!know,!our!upcoming!workshop!Improving!Accessibility!in!Middle!Grades!
Mathematics:!Language!in!the!Math!Classroom!!is!only!___(one!week)_____away.!This!will!
be!a!great!opportunity!for!math!and!special!education!teachers!to!work!together!to!
promote!learning!in!the!math!classroom.!We!are!looking!forward!to!this!and!expect!it!to!be!
a!very!productive!session.!!Here!are!some!details!to!help!you!prepare!and!get!the!most!out!
of!the!session.!
!
1. [Date!and!Start!and!End!Time]!2. [Locationinclude!any!pertinent!details!such!as!parking!instructions!or!reminders!such!as!Bring!a!sweater!since!this!room!is!sometimes!cool.]!
3. [Lunch!details!!""when,!how!long,!should!they!bring!their!own!or!will!it!be!provided?]!4. What!to!bring:!!Since!a!segment!of!this!workshop!will!be!devoted!to!planning!for!your!own!classroom,!youll!need!to!bring!some!curriculum!materials!to!the!workshop.!!
Please!bring!a!lesson!or!set!of!lessons!that!you!have!recently!taught!or!will!be!teaching!
in!the!next!few!weeks.!!You!do!not!have!to!have!taught!the!lesson!in!advance!of!the!
workshop.!!You!do!not!need!to!bring!sample!student!work,!however!you!should!bring!
any!teacher!support!materials!related!to!the!lesson,!such!as!a!teacher!guide.!
5. !Any!other!details?!!
I!am!excited!that!we!will!have!the!opportunity!to!explore!the!topic!of!language!and!math!
and!look!forward!to!your!participation.!!Please!be!in!touch!if!you!have!any!questions.!
!
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APPENDIX!5: !PACING!GUIDE!! !
Start!
Time!
End!
Time!
Workshop!
Segment!
Slides!
Presented!
Video/!!Discussion! Activity/!
Discussion!
Total!
Time(min)!
Materials!
! ! Warm"Up! Slide!1! ! ! 5! Handout!1!
! !
!
Introduction!
Slides!1"7!
!
!
Ground!Rules/!!
Parking!Lot!
2"5!minutes!
!
20!
!
Handout!1!
Parking!Lot!!
! !
Language!Demands!
!
!
Slides!8"16!
!
Watch!Video!and!Discuss!!
10!minutes!!!
!
25!
!
Handout!2!
DVD:!Introduction!
! !
Vocabulary!in!Math!Slides!17"37!
!
!
Handouts!2!&!3!
15!minutes!
Handout!4!
10"12!minutes!
H"5!
10!minutes!
45!
Handout!3!
Handout!4!
Handout!5!
! !
Vocabulary!Strategies,!
Part!I!
!
Slides!38"44!
!
Warm!Up/Handout!6!
10"15
!minutes
!
Main!Investigation!H"7!&8!
20!minutes!
Interview!H"8!
4"5!minutes!
!
!
60!
Handout!6!
Handout!7!Handout!8!
DVD:!Warm!Up!
! !
Vocabulary!Strategies,!
Part!II!
Slides!45"52!
minutes!!
H"9!Practice!
Strategies/Discuss!
15"20!minutes!
30!
!
Handout!9!
End!of!Part!1!
!
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Start!
Time!
End!
Time!
Workshop!
Segment!
Slides!Presented Video/!!Discussion Activity/!Discussion Total!Time!
(min)!
Materials
! !
Embedding!
Vocabulary!
Slide!53"62!
!
H"10!Embedding!
Vocabulary!
8!minutes!
!
String!Shapes!Lesson!
10!minutes!
Carousel!Sharing!
12!minutes!
30! Handout!10!
! !
!
Reviewing!
Vocabulary!
!
!
Slides!63"71!
!
!
I!Have!Who!Has!
10"15!minutes!!
20!
Handout!11!
Handout!12!
!
!
! !
!
Writing!in!
Mathematics!
!
!
Slides!72"77!
!
!
H"13/14!Whats!Missing!
15!minutes!
H"15!Writing!Strategies!
10!minutes!
!
!
30!
Handout!13!
Handout!14!
!!!!!Handout!15!
!
! !
Planning!
Vocabulary!
Instruction!
Slides!78"81!
!
!
H"16!Planning!
25!minutes!
Share!Plans!
10!minutes!
!
40!
Handout!16!
!
! !
!
Wrap"Up
!
Slides!82"84!
!
!
!!!!!Feedback!Form!
8"10
!minutes
!
!
10!
!
Handout!17!
!
End!of!Part!2
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APPENDIX!6: !SAMPLE!VOCABULARY!PLANNER!
Main!Math!Goals!for!Unit!or!Chapter!
! Determine!intervals!and!create!coordinate!plane!grid!! Plot!data!points!in!the!coordinate!plane!! Analyze!data!and!determine!correlation!
Key!Vocabulary!Words!!(Choose!2!to!4!words!from!an!upcoming!lesson!or!unit)!
x"axis!!!!!!!!y"axis!!!!!!!!!ordered!pair!!!!!!!!!correlation!
!
Students!Prior!Experiences!with!the!Vocabulary!
a)!How!much!experience!have!your!students!had!with!these!vocabulary!words?!!!None!!!A!little!!!!Some!!!!A!lot!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! correlation!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!x"axis;!y"axis;!ordered!pair!
!
b)!If!you!have!already!provided!instruction!on!these!vocabulary!words,!what!did!you!do?!!The!students!have!created!vocabulary!4"blocks!for!x"
axis,!y"axis!and!ordered!pair;!they!have!also!had!quite!a!bit!of!experience!plotting!ordered!pairs.!
c)!What!kinds!of!difficulties!did!students!have!with!these!vocabulary!words?!!!If!students!are!given!an!ordered!pair!and!asked!to!plot!it,!most!
understand!what!they!are!supposed!to!do.!!When!they!are!given!a!point!plotted!in!the!coordinate!plane!and!asked!to!describe!it!as!an!ordered!
pair,!some
!dont
!know
!what
!this
!means.
!!Some
!students
!have
!typical
!confusion
!over
!which
!axis
!is
!which.
!!Correlation
!is
!a!new
!concept
!this
!year.
!!It!is!a!new!word!for!nearly!all!students,!too.!Check!if!they!have!worked!with!this!in!science.!
d)!What!phases!of!instruction!would!you!like!to!provide!on!these!vocabulary!words?![You!will!make!plans!in!the!next!section.]!
! Introduce/Explore![First"time!instruction!of!the!term)!!!!correlation!! Refine!and!Practice!(students!have!some!understanding!of!the!word!and!are!working!to!strengthen!that!understanding)!!others!! Review!(students!should!have!a!good!understanding!of!the!word!through!previous!instruction)!
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!
Plan!Instruction.!!
Describe!what!you!will!do!for!the!phase!of!instruction!you!are!planning.!What!will!you!do!in!math!class?!What!are!your!suggestions!for!ways!to!
help!students!with!this!vocabulary!in!other!settings,!such!as!a!mathematics!support!class?!
!
1.!Introduce/Explore!(First!exposure!to!vocabulary!words.)!
2.!Refine!&!Practice!(Students!working!to!build!understanding!and!
practicing!using!terms)!
3.!Review!(Reinforcing!established!vocabulary)!
CORRELATION!Present!examples!and!non"examples!and!
have!students!work!on!building!their!
understanding.!
!
!
!
!
!
!
!
!
!
!
!Refine!examples!to!those!that!represent!
positive!correlation!and!those!that!represent!
negative!correlation!
!
Have!them!create!vocabulary!4"block!of!
positive!correlation!&!negative!correlation!to!
add!to!their!binder!section.!
x"axis;!y"axis;!!!!!!!!!!!
Return!terms!to!word!wall!and!preview.!
Emphasize!these!terms!in!discussing!
correlation.!
!Include!past!state!test!items!on!correlation!in!
mixed!practice!problem!sets!for!continued!
practice!and!review.!
!
Add!these!terms!to!matching!cards!set!for!
review!later.!
!
!
ORDERED!PAIR!
Preview!term!in!math!support!class;!practice!
plotting!and!describing!ordered!pairs!being!
sure!to!use!this!term!in!directions!&!
explanations.!
Strategies!to!Consider!
Visual!Definition!
Example/non"example!
Vocabulary!4"Block!
Word!Wall!
!
Journal!
Matching!Cards!
I!Have;!Who!Has?!
Kinesthetic!Activity!
!
Mnemonic!Strategy:_____________________ !
Writing!Exercise!
Multiple!Exposure!"!!How?!
Direct!Instruction!(How!will!students!practice?)!
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!2009!Education!Development!Center,!Inc.! ! 1!
WORKSHOP!HANDOUTS!
HANDOUT!1:!LANGUAGE!IN!THE!MATH!CLASSROOM!.........................................................................................!2!
HANDOUT!2:!FOCUS!QUESTION!FOR!VIDEO!....................................................................................................!4!
HANDOUT!3:!IDENTIFY!AND!CLASSIFY!VOCABULARY!LANGUAGE!IN!THE!MATH!CLASSROOM!.........................................!5!
HANDOUT!4:!VOCABULARY!CHALLENGES!.......................................................................................................!9!
HANDOUT!5:!A!MATH!LESSON,!PAGE!1!......................................................................................................!10!
HANDOUT!6:!FOCUS!QUESTION!FOR!VIDEO!..................................................................................................!14!
HANDOUT!7:!RESEARCH"BASED!STRATEGIES!FOR!...........................................................................................!15!
HANDOUT!8:!REFLECT!ON!THE!VIDEO!.........................................................................................................!16!
HANDOUT!9:!PRACTICE!STRATEGIES!...........................................................................................................!17!
HANDOUT!10:!FOCUS!QUESTIONS!FOR!VIDEO!...............................................................................................!19!
HANDOUT!11:!MATCHING!CARDS!EXAMPLE!.................................................................................................!20!
HANDOUT!12:!I!HAVE,!WHO!HAS?!ACTIVITY!CARD!MASTER!............................................................................!21!
HANDOUT!13:!EXAMINE!A!MATH!TASK!.......................................................................................................!23!
HANDOUT!14:!!WHATS!MISSING?!............................................................................................................!24!
HANDOUT!15:!STRATEGIES!FOR!WRITING!IN!MATH!........................................................................................!25!
HANDOUT!16:!PLANNING!INSTRUCTION!OF!VOCABULARY,!PAGE!1!.....................................................................!28!
HANDOUT!17:!FEEDBACK!FORM!...............................................................................................................!31!
!!
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!2009!Education!Development!Center,!Inc.! ! 2!
Handout!1:!Language!in!the!Math!Classroom,!Page!1!
!
1. Solv