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TESOL 2010 - Friday, March 26, 2010

Christine Prosch proschc@fccps.org

M ath Vocabulary: Use It or Lose It

Christine Prosch, ESOL Teocher Fa lls Church City Public Sd1ools, Falls Church, VIrginia

M ary Ellen Henderson Middle School

· Moth Remediation fOf 8e; tnner to Advanced Etls -Drodos S, 6 & 7, Mom S lhrO<>Dh Pro-Algebra

• Co-Teod1, MomS, 6 & 7

• Push-In, Mom 5, 6 & 7

• Sheltered Moth - for beglnner ELls & .. cotch~up" d ou e s

Why is language important ...

to mathematical understanding & higher order thinking?

o NCTM* Standards Ex: Reasoning and Proof Standard lnstruc1ional programs from p ro- K - 12 should enable all aludonla to:

a make and investigate mo1'tlemotlcol (OniedVres

a d evelop and evaluate mom.motic:cl argument'S and proofs

a select and u.se various types of reasoning and me thods of proof.

· National Coundl of Teachers of Mathematics

. Why is language imF-rlont .. .

Massachusetts Objectives*

$tadot•tt di[IIJf iiJ ,nlbJt• .... ,fl .. ··-·--·· ... -... - ... -...... _ ... ,, . fO"'M~fUUil•f.o l"tMMiltl , t•Mttfoet. ...

.. ..-....-:.~"-~ rtprtnllri•l., tU,t

... .... -HOe .((!ll• c:t •rt~ •'1-.tlla• d•~~ '-i!'coiiMNat~

-..tl-ll~fl:r•NI m.b llrtmtllt, Wt'Vt''ll 01 t~l)trir'l'ltt'!U, • 116 -----........ ........... .. """*" ·~· _.,. , • ...,..,t 4•tt

a;;u:.e;~ ...... - ...... ~ ... ., ....... • r'Oo'n'IUII tt 0,\l .. tbN, .. ·-----...-.. - ... ... _ .. ______ .,.., ___ / ....... _. ........... __ .~ ..... ~

I ~f~i."1ff!ilJilfn;i.clP:Z-~t~ .5Hl9.M•• .... -. ' ~ . __ ... _. oll)~"";.t'::M:"".;i.'t'~;!":;. , ·--· .. •---~-4 ... ---···--... -- ... .. - .. - .... ... - - •

.,. __ ,.. _____ ow......._o..nw

Are we providing our ELLs with in ferior /earning opportunities in moth clas.ses?

a low-level clones or groups ~

a instruction in rote methods J

o oveny reduced language * o minimal problom solving opportunllles'

a spiraling wrricu1um assumptions ;

JIONI>I'I.t'~ 9.. , ~·

,11{). 3

13.1/ ) /3.()11

What does the first one soy?

Uh, 24 is ... less than 3 Is it~

No, 24 Is greater than 3~

Language is only part of the good mathematics leu on ...

a Manipu1otln s

o Modeling

a bp• ,lmenforion

a Proc.edures a Practice

a Cont~4ctiont ro bodcground knawJedge

a Collaboration- ESL/ESOL & Content Teod1ets

Let's talk, write and read ...

practical considerations o Level of ELL

a beg inner - intermediate - advanced o Timing ?

a daily a integrated into lessons a 5 to 20 minutes per class depending on lesson & strategy used

o Which words ? o Consider frequency of use across mathematics & previous knowledge a General suggestions

• first verbs (add. compare, solve) & quantifiers (least. most) • then: unit specific language {triangle, perimeter, length, parallel) • last: naming {the commutative property is the one that.. .)

o Assessment - opportunities dally - by individual Ieamer

Journaling: Doing and Writing

l'1me: I Witte thes• numben on th1 nui'T'Ibtr llnt In the CQfrtoet plilee

2.8 1.4 0.2

• ! ~ f ! ! ! ! ! I I ! ~ i I f I i ! i i I f ! ! ~ ! ~ ! : ~ ! ! !• 0 I l )

Wh••$h0lllcf 1 .85 IDO" the ,..,mbtflnt' ~'\l\t"/f:/4M be:S-t (edl.latedlsueu ltld wntt ill On l.ht ftiiJ~Ine. (~If- how }'0\1 ~ .,.het• to Pill .\ (Of tooowyou -nlde 'fOY p u ).

Journaling: Doing ond Writing

-· ~VIfl(td lt "fl.

.......... il!diO u lUll» . ... 1 9 Wlbl. \ llltl'i 110 on• 11'1<1 tl~ •rei on rM cr.rn&!lt!ltl tO ,..., to J"' • "n ... ,.._.

s.o IIIUilllwf9.'

IOIIf•a.tMUJ•h.- ........ ....... te-11 ,...1-' lnllll'l'l'\tdl-'1 .. ... . :

ltsiJlllf8lpCN n ..... ..... t ..... h~'

~Iii 00 .. .,.,) 1 hilltiO 11\e t....o ~

I I"J Ofttl r ~~2..-...ot_. ~,.~.,._~,

,1'4~ llh t W!Jbl'

·~-------- ... &.~..: ' !Uti IN (In lhe Qlll!lR!tJal !t ...oflfloMilflll, It yo., gO 10h, 00 ~ 10 t • "*" .. ,.., llalb Of fi:W!lZdbt ~

Journoling: Doing and Writing

'!t4 !o'ftt•.,..a;o- Jioo o41<_,....,.

,.... -~-~~rtoiOJf_....,_

., ... .,.. ........ ~111 ___ _ _ _ _ _ _ _ _ _ _

~-.: w .. _ ,__..,._,..

~Iii" :011(» 100 • 11

Journallng: Doing and Writing I can use division when I

~·-· ........ ' I 4-tila II!. l'l'lon.y II\ 0'11 !Wty ._ P"" Qt,lllft.,..."

' , ci!'IICt~IUianO: I ._., .. ~~-~~ ..... b ...

' . ....,.n I • t nt 10 ~;. I I !lid t OI'It iNr<Q ~01'19 n.e dlvldh O IN~-­

IntoM!I".,._ ii'Wl

• ,.,.,, oooii• • ,.'"' ""'l~tr'ldt.•

1 11-~~CU'e~tD· ,...,...:

t~l.rmM••~ · ....... .,..~"~· • wt niiOt.ll t iL (lt.-71tr pro"'P'I 'orm<wt) lt.st c:clns to lhll on • u ""r• lll ~· ,....2$ ·) ·~

Journaling: Doing and Writing _, ' THINK HARD-

1377+13= A. 2 9 If you havo no ldeu afl<lr 3

J B. 29 minutes you can asl< lore h.,l

TRY SOMET~ING (on pol*)

C. ~ I I One an ower is correct Explain how you J ./\.

know which anawer It corrood even d (" /) I you do not do the division problem ~,/ ]1 ~»eWthett- LS Gtr.-e:t "GQ""'C~\'

I··· r

Journaling: Doing and Writing ,_, r·:;! . ..... ,..., ..... ... .... ~WI I ll« •!~ !

...... ,.. ___

'I r::. I II

... < ..

I 1 )n•lJ,;:

·~---

Hf < " '

Journoling: Connecting to

I n.. • ...,. ... .., • peri"'*• _..., W!e trt.- tHM <•11141"'"­

-~ l "-II>IIN,..... _... -.-4...., ptclmt'tr llf ttM , ..,.

I H_ .. _ , . .. .... , ... - ....... ...... " M

-.. .. .....,PM _.,.._ .,,...

.. , .. ca.. ... r

I ,.,_ """,___....... ptt!n mw .. tM _._, It• .,..."

I o."'-...'""'"'-"'-""""--""""""' .., -----

I I I

J011rnaling: Connecting to Common Usage of language

Wrt'fe )'OW own~ 01' l*"imet• f'.ol world p!'Obfem.

advanced level: When a teacher wants to put a border around a chalk board she have to measure it hke: What Is the perimeter?

Intermediate level: ~

If you want to get a tatoo on ·t!·· your hand they have to t measure the inside to see ~ how big to get It ,

Journaling: Connecting to Common Usage of Language

Revltw the VocabuJary & the Process think - sl/empt- discuss __ ..,.. .... _ ..., .... .. - •• ,..,. .11 ........... ~-~ ..... -·-... -, ....

__ 4x - t 2lt __

Journaling: Connecting to

~ ,_...iciiiolt.miilmiioiiin...,u11s aiiiigiiliei.oiiif.iLiiiiaii.niigilu aiiiigii.ie-.-1

~ .... ..,.. 3._.__, ..... . ---- .... -

Journaling: Connecting to Common Usage of Language

-~--------------~

LMk .. tiM l ..... y. ~ II- dlt,..,. ... ~~vt• • ftoO'oll • tt thoey~ 111!11'? • Th-e IINQ-tw 11bd !.tl.n.ot&W d~.t-"'lltlfl tii.INI!I'"I • Dll~ P,op.ny: 2{,11 ..... 2J. • '1141

Journaling: Connecting to Common Usage of Language

t1ow it an opetation in math hkt en oper~tlon h\ the hO&pital?

advanced level: • a operation at the hospital Ia like which bone Is

connected to which end operttlon In math ia tile same because you have to connect botn number together." with addition11l discussion ldenlf!ed t~t opttltlon u addition

early-intermediate level : 'The doctor going to add more medicone and minus injections tnat equals you feel better.

Journaling: Connecting to

Common Usage of Language

~~----------------~ ' running on empty" and "nun out of steam" are both called expressions. •

2y +19x - 54 is also called an exprus/on What are the same about both of these ways that

expression Is used? Explain

Subject is to sentence as expression is to equation.

Journallng: Connecting to Common Usage of Language

---~~~------~ Subject is to sentence as exproasion is to equation.

'because the subject Is the most Important part of a sentence:

These students have only seen expressions on one side of an equalion -+ 3x- 12 ~ -6

Journallng: Connecting to

11• :~eua~ . Oll.,•Oon • ""'" • dl'rt~nu

-~--- ..... ~. --- - lllt.!ll!dlt

2 + 30=32

Crp_.,..., ~"'-, ... -~ . ...... _ _ - - - - - -

Journaling: Error Corrections

o Intermediate to Advanced ELLs -

a Problem solving and higher order thinking a Focus on key vocabulary with a WOfd Box a Add s&ntence starters for needed scaffolding a Motivating - students like it

Journaling: Error Corrections

Explain the mlsn.lce that the student made. Woa .. .. all• t >411"'"•

You mustuse at lust 2:of thue words~ :\c ftld• mooJ&• rci.._. ..t~tn rh£ . ..

hfl, tt. U n ... - loN4Httb.lt ll• - "u v.lq t.erwe . .

lliJll n. ••. .,. ,..,w ...... ..,*" ;-11 l'bllt • ... . .. dim~Jwldbl<lo; III..W.: ~~t.belfl.d.,. _ _ e • .w..n~4<~ - (ad lltll) ..

Find lh£ !l'!ea.tl f«< th~ .nt of dc.to.

ZS. U , 19, 20, 21. Z) , 23 fi?5." vv - ./ -1 3'1 101 r,W

lj .;( " 16'1·0

J' ~ 3'1 ..fl. ·30 ,3 'I ""';j ~

~ ~

Journaling: Error Corrections

-- I The student made a mistake when slhe . .. First, the student . .. I could see that the mean was wrong because .. . There is a problem with the part where slhe .. .

Journo ling: with Cloze PowerPoint

c All Levels of Ells -

o Focus on key vocabulary for a concept a Allows customizatlon to population a Can be altered for review or extension

Word Walls

o Beginner Ells -word & example

a Aids fistemng, speaking, writing and memoty a Flexible - easy to add or delete a Magnetic - students cen sort, men1pulate

Example

dillldend

Word Walls

o Intermediate to Advanced ELLs -

,.. ' ....

word • definition - diagram/example a Aids speaking, writing and memory a Student-created definitions;

higher order thinking & ownership a Permanent, color-coded by concept a Refer back to in future lessons

Personal Math Dictionary

.... ~n-•••·· 1 -... (klk-Y r·- ·~••

I II I

I I[ I -

VA Standards of Learning: Year-End Assessment Problem Problem #2 The area of a rectangle Is between 1,500 and 2,000 square Inches. Which could be the length and width of the rectangle?

F 72 ln. x 36 in. G 60 ln. x 30 in. H 40 ln. x 30 in. J 181n. x321n.

2006 Released Test Items. Plain English Math, 6"' Grade 0 C0fnfl'IO(!W$8!Ih d Wgil'l.• , De~, of E<IJeallon

Additional Resources & References

a For gamea and teacl\lng ~as that can geMrato meaningful dlscuoolon and teaming in math class: Brad Fu~on and Bill Lombard have a serieS of boob . Simply Groat Explorations in Geometl)' I Number Sense I Fractions, Oecimals, & Porcenls I AlpebnJ Readiness websHe: www,I!IDn>ss com

a For sample math prompts that have some acxompanyinq scaffolding- avaRable In different grade levels: O'Connell, S. (2001 ). Math tho Wnte Way: Th1nking and W)'ifll)gAbout Msth. Grand Rapids. McGraw-Hill CN!dren's PubJishlng.

o For practice with nuency in saying the "math word..-: Pappas, T. (1991). Math Toll<: ~fhemalical k»asln Poem! tor 1Wo Voices. San Ca~os, CA: Wo~ Wide Publishing.

a For samples of Wllal good discussion In math class should look like: Holben. J. (1997). Making Ssnio: Tei>Ching end Leaming Metheroolics with Ullderslanding. Port•mouth, NH: Heinemann.

a NCTM (National Council of T10chen1 of Malhemalfcs) webs~e: www nc!m.grg a Virginia Standards of Leor"A'JBo w&bsae:

http:/fflww doe.yirofnja gov E/lnslrudfpnlsol htrrn

o Masaaehusetts CurriculUm Frameworks website: hrtp 1/yNt« doe ma».o<futlramewori(lleuatnt htmJ

go to: http://bit.ly/csolmath - you can send a comment - ask for matcrinls to be cm:.til~d · j oin a group to share ideas