math summative assignment

8/20/2019 Math Summative Assignment

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Bowering 1

Summative Math Assignment

Adam Bowering

March 4, 2016

1. Teaching Mathematics to Students withLearning Disai!ities " Annotated

Bi!iogra#h$%%%%%.Page 2

Instructional Design in Mathematics for Students with Learning Disabilities…….2-3

Math interventions for students with learning disabilities: mths and realities…....2-!

Mathematics and learning disabilities……………………………………………....!

Investigating elementar mathematics curricula: focus on

students with learning disabilities………………………………………………......!-"

#re$aring teachers to teach mathematics to students withlearning disabilities…………………………………………………………………"-%

Mathematics instruction for elementar students with learning disabilities………..%-&

2. A &ritica! 'eview o( )&TM Artic!es

*+ractions%..age -. 'eview o( Math

Mani#u!atives%%%%%%%%..Base-ten

Blocks……………………………………………………………………………………………………

Pattern

Blocks……………………………………………………………………………………………

………..

Money……………………………………………………………………………………………

…………………...

Fraction

Tiles………………………………………………………………………………………………

……….

Two-SidedCounters…………………………………………………………………………………………

….

4. Mathematics and

Techno!og$%%%%%%%%%.Smartboard lesson !n "ntroduction to

Fractions………………………………………………


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#ideo $sing regrou%ing &or addition and subtraction using base ten

blocks…….

Big book Fall "nto

Counting………………………………………………………………………………

/. ther Areas o(nterest%%%%%%%%%%%%%'lementary Mat(ematics course )ournal

entries……………………………………………..

Science obser*ation +ournal gra%(s……………………………………………..

…………………..

Cool ,ebsites and *ideo related to mat(ematics conce%ts………………………..

………………………………………………………………………………

1.Teac(ing Mat(ematics to C(ildren wit(

earning isabilities - !nnotated Bibliogra%(y

Mathematics is regularl seen as an area of struggle for man students. 'his is es$eciall

true for students with learning disabilities. Mathematics content can be overwhelming to these

students since there are man strategies and s(ills the must ac)uire in a relativel short amount

of time for their cognitive $rocesses. I believe it is u$ to the educator to ta(e note of these

differences* and ad+ust their instruction accordingl. 'hroughout the following annotated

bibliogra$h* I highlight some articles that I have found interesting that introduce a$$licable

was of teaching mathematics content to children with learning disabilities.

,arnine* D. &. Instructional Design in Mathematics for Students with Learning

Disabilities. Journal of Learning Disabilities, 30/20* 31-!.

'he author suggests that there are multi$le causes for low achievement

level for students with learning disabilities. ne such cause is the mismatch


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Bowering /

between the students learning and design of instruction. Students with learning

disabilities ma have difficult with memor* and strateg ac)uisition. 4hen

conce$ts are introduced at a ra$id $ace that students are not able to (ee$ u$ with*

these students often become overwhelmed and disinterested in the material.

Students with learning disabilities benefit more when the design is centered on big

ideas* strategies* efficient use of time with mani$ulatives* clear and e5$licit

instruction* and $ractice and review. 6nother strateg for instruction is to use

strand organi7ation for lessons. 'he idea is to design lessons around strands to

address different big ideas in "-1 minute $eriods. 4hen teachers a$$l these

design $rinci$les* it could have a $ositive effect on achievement for students with

learning disabilities.

8leischner* 9. .* ; Manheimer* M. 6. &. Math interventions for students with learning

disabilities: mths and realities. School Psychology Review, 26 /30* 3&-!3.

'wo t$es of learning disabilities are discussed in this $a$er. 'he include

dscalculia* and verbal learning disabilities* which are referred to as


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the recall of information. ,alculators are also $resented b the authors* who sa

that calculators are encouraged b the >,'M. 'hese devices serve as a wa to

verif answers. Students should also have smbols that re$resent o$erations in

math* and $ictorial and concrete re$resentation of the material to strengthen their

s(illset.

4hen children learn to read* the are usuall $laced in grou$s of students

at the same level as them* which is not often done in mathematics. 'he authors

suggest that this should also be done in math so teachers can use s$ecific

instruction for students with learning disabilities* rather than a one-si7e fits all

class instruction.

?ear* D. 211!. Mathematics and learning disabilities. Journal of Learning Disabilities,

37 /0* !-".

,hildren with Learning disabilities often have trouble with numbers*

counting* and arithmetic. ,ounting $rinci$les and the $rinci$les of $roblem

solving tended to be lac(ing in the children used in this stud. 'he stud also goes

on to sa that children with learning disabilities continue to have difficulties in

retrieving arithmetic facts from their long-term memor* which did not im$rove

over time. 'he stud found that children with LD had interru$tions in attentional

information $rocessing. 'his resulted in difficulties with information

mani$ulation with math language. Students with learning disabilities re)uire more

time to $rocess information* which is +ust as true for math content. #roviding

students with the time to $rocess new information allows these students to have a

better understanding of conce$ts li(e counting and basic arithmetic.


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@ord* ,.* ; >ewton* 9. 6. 21!. Investigating elementar mathematics curricula: focus on

students with learning disabilities. School Science an !athe"atics, ##$/!0* -21.

'he $ur$ose of this stud was to e5amine curricula to see if there was a

wa to $rovide more o$$ortunities for engagement for students with LD. 'he

stud focused on three mathematics curricula that $ut a s$otlight on accessibilit

in regards to challenges in wor(ing memor for these students. Instruction that

was used in this stud included the em$hasis of visuals* math conversations* and

develo$ing metacognitive s(ills. 'he finding was that teachers must consider how

their curriculum outcomes $rovide effective instruction for the storage and

organi7ation of information for these students. 'eachers must also ta(e into

account how the outcomes develo$ students thin(ing $rocesses and their overall

understanding of mathematical conce$ts. 'his s$ecific stud concluded that the

curriculum areas were effective in teaching students with LD to solve multi-ste$

$roblems. @owever* su$$lemental materials should be used in con+unction with

curriculum to meet the needs of students with LD.

#armar* A.* ; ,awle* 9. &. #re$aring teachers to teach mathematics to students with learning

disabilities. Journal of Learning Disabilities, 30/20* BB-&.

Several standards are $ut forth in this stud which reflect the wa in which

teachers need to $re$are to teach children with learning disabilities. Standard one

is to model good mathematics teaching. 'eachers need to have (nowledge of the

curriculum* and the variet of instructional techni)ues available to them.

'eachers shouldnt +ust focus on one area to strengthen their teaching* the must

focus on a well-rounded a$$roach when teaching mathematics. 6 collaborative


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a$$roach between the teacher and s$ecial education teacher is suggested when

teaching children with LD. 6n e5$ectation of this a$$roach would be enhanced

)ualit of education* allowing students to reach higher levels of $roblem solving*

reasoning* and connections with the mathematics content.

Standard two is for students to have the a$$ro$riate (nowledge of

mathematics. 'e5tboo(s have gotten longer* and therefore more com$le5.

Crea(ing the information down into finer details will decrease the time for

coverage of the content. 'eachers need a balanced a$$roach to $rovide students

with an understanding of the meanings* $rocesses* and $rinci$les of mathematics.

'he stud stressed that activities need to be $lanned around real-life

$roblem solving and big ideas. >ew teachers must constantl (ee$ in contact with

other teachers and staff* creating a collaborative a$$roach when focusing on

a$$ro$riate instruction. 'his stud also cited the >,'M as one of the

organi7ations to use as a reference for teachers.

'hornton* ,.* Langrall* ,.* ; 9ones* ?. &. Mathematics instruction for elementar students

with learning disabilities. Journal of Learning Disabilities, 30/20* !2-"1.

T(is study (ig(lig(ts t(e need &or teac(ers to constantly be

3uestioning t(eir long standing belie&s w(en it comes to

teac(ing4 learning4 and using curriculum. Common %ractice in

today5s classroom re6ects a narrow &ocus on com%utation. T(e

%a%er s%eaks about (ow t(e 7CTM %ro%osed 8*e goals to ret(ink

mat( teac(ing and learning. T(ey include instilling *alue o& mat(


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on students4 increasing con8dence in t(eir ability to do mat(4

become mat(ematical %roblem-sol*ers4 to reason

mat(ematically4 and to communicate using mat(. Teac(ers

s(ould do t(is by decreasing t(eir %encil-and-%a%er com%utation

and rote memori:ation o& t(e content. Students s(ould be gi*en

multi%le ways to re%resent t(e same answer. T(is could be

t(roug( illustration or mani%ulati*e use.

"n t(e end4 t(e article suggests t(at teac(ers need to (a*e

a balanced a%%roac( w(en teac(ing mat(ematics4 engaging

students in meaning&ul tasks4 accommodating &or t(e di*erse

ways in w(ic( students learn4 and to allow students to discuss

and +usti&y t(eir %roblem-sol*ing strategies. Teac(ers need to

%ro*ide students time to engage in and s(are t(eir own solutions

to meaning&ul %roblems.

2. A &ritica! 'eview o( )&TM Artic!es "

+ractions

Artic!e 1 "

5!mbrasio4 B. ;


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second source o& diGculty many students did not see t(e

additi*e nature o& t(e decimal %laces. T(e last4 and most

im%ortant4 diGculty is t(at relying on %rocedures &or ordering

decimals can mask a student5s true understanding o& t(e relati*e

si:e o& decimal numerals. 5!mbrosio and


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Artic!e 2 *


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Bowering 11

. 'eview o( Math Mani#u!atives

Base-10 blocks

"mage sourceI (tt%IJJwww.ama:on.comJearning-Kesources-Plastic-Base-

StarterJd%JB>>>F@#BB


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Base ten blocks are *ery *ersatile mani%ulati*es t(at can be used to

re%resent many abstract conce%ts in mat(ematics. T(ey can be used to

illustrate addition4 subtraction4 multi%lication4 and di*ision %roblems. " would

use base ten in any grade4 since t(ey (a*e suc( a range o& use. T(ey can be

used to introduce %lace *alue to lower grades4 and decimal %oints in u%%er

elementary. uring my student interns(i%4 " introduced base ten to my grade

2 class. " started wit( t(e basics. $nits were 8rst4 &ollowed by rods w(ic( "

associated wit( being 1> units. T(is was a toug( conce%t &or students to

gras% at 8rst4 since t(ey couldn5t 3uite understand t(e *alue o& eac( unit. "

would use base ten blocks &or any o& t(e abo*e mentioned to%ics.

Pattern Blocks

"mage SourceI (tt%IJJwww.mat(ed%age.orgJanglesJ

!s t(e %icture illustrates abo*e4 a set o& %attern blocks consist o& a blue

r(ombus4 green triangle4 tan r(ombus4 orange s3uare4 yellow (eagon4 and

t(e red tra%e:oid. T(ese mani%ulati*es can be used to meet a number o&

curriculum outcomes. Students can use %attern blocks to e%lore basic

geometric s(a%es or %ut t(em toget(er to build more intricate or com%le


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Bowering 1/

s(a%es. T(ese blocks allow students to see t(at larger s(a%es are com%osed

o& smaller ones4 w(ic( relates to &ractions. T(ese blocks would also be a

great tool &or students to create and identi&y %atterns. " would use t(em to

indicate conce%ts4 like teac(ing about t(e %attern core to lower 'lementary

students. T(ese mani%ulati*es also %ro*ide students wit( a way o&

identi&ying and disco*ering 2 s(a%es in a (ands on way. Pattern blocks are

an educational tool t(at students (a*e &un using4 w(ic( makes t(eir learning

more engaging. T(ey are *ery *ersatile and are &ound in most sc(ools. ne

cool t(ing about t(ese s(a%es is t(at you can dis%lay t(em on t(e smart

board at t(e same time t(at t(e students are mani%ulating t(em at t(eir

desks4 creating a re&erence w(en you a teac(ing conce%ts to t(e class.

Money as Manipulatives

"mage sourceI (tt%sIJJwww.rainbowresource.comJ%rodlist.%(%L

sub+ectMat(ematicsJ1>;categoryMoneyN-NMaterialsNO2NMani%ulati*esJ2A

https://www.rainbowresource.com/prodlist.php?subject=Mathematics/10&category=Money+-+Materials+%26+Manipulatives/2569https://www.rainbowresource.com/prodlist.php?subject=Mathematics/10&category=Money+-+Materials+%26+Manipulatives/2569https://www.rainbowresource.com/prodlist.php?subject=Mathematics/10&category=Money+-+Materials+%26+Manipulatives/2569https://www.rainbowresource.com/prodlist.php?subject=Mathematics/10&category=Money+-+Materials+%26+Manipulatives/2569


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Bowering 10

"n a ty%ical set o& money mani%ulati*es4 you will 8nd %ennies4 nickels4

dimes4 3uarters4 loonies4 toonies and bills. Money is a tangible mani%ulati*e

since it is somet(ing students will use in t(eir e*eryday li*es. T(e

mat(ematic skills related to money are necessary &or all ages. ne im%ortant

note to make as a teac(er is t(at %ennies do not eist anymore4 w(ic( would

be somet(ing you would (a*e to teac( to lower 'lementary students. T(is

mani%ulati*e can be used to establis( a &urt(er understanding o& addition4

subtraction4 di*ision and multi%lication. T(is mani%ulati*e would bene8t

students in t(eir e%loration o& decimals and &ractions as well. T(ere are

dollars4 w(ic( are w(oles4 and cents4 w(ic( are %arts o& a w(ole. T(is (el%s

to su%%ort students understanding o& decimals and &ractions. T(e &raction

can be re%resent like t(isI 0J1>>4 wit( 0 being t(e cents4 and 1>> being a

dollar. T(e &act t(at students use t(is mani%ulati*e in a real li&e content

strengt(ens its ability to connect students to t(e content.

Fraction Tiles


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Bowering 1

"mage sourceI (tt%sIJJwww.enasco.comJ%roductJTB1@11T

!s seen in t(e %icture abo*e4 a &ull set o& &raction tiles consists o& one

w(ole4 two (al*es4 t(ree t(irds4 &our 3uarters4 8*e 8&t(s4 si sit(s4 eig(t

eig(t(s4 ten tent(s and twel*e twel&t(s. Fraction tiles are an ecellent way

&or students to e%lore and understand (ow %arts make u% a w(ole. " would

use t(e sim%ler &ractions at 8rst w(en " am introducing &ractions4 and

gradually introduce &ractions wit( a greater denominator as students become

more com&ortable wit( t(is ty%e o& mani%ulati*e. T(is mani%ulati*e also

&urt(ers students understanding o& addition4 subtraction4 multi%lication and

di*ision o& &ractions. T(ese mani%ulati*es gi*e students a concrete

re%resentation o& an abstract conce%ts. Since a lot o& students belie*e t(at

eac( number in a &raction is diHerent4 t(ese %ro*ide clarity on t(at issue by


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Bowering 1

getting students to see t(e set o& numbers as a w(ole. Being able to see t(e

%ro%ortions o& t(ese &ractions makes it easier &or students to com%are4 order4

and eamine e3ui*alent &ractions. Some &raction tiles also (a*e decimal

notations on t(e o%%osite side4 w(ic( is ecellent &or seeing t(e relations(i%

between decimals and &ractions w(ic( is bene8cial in t(e u%%er %rimary

grades. " c(ose t(is mani%ulati*e to re*iew because " &eel as t(oug( it

%ro*ides a great *isual &or students w(en t(ey are learning &ractions. "t5s

im%ortant t(at students see conce%ts and are able to e%lore t(em in a

(ands-on way. Students struggle wit( understanding &raction si:es. Many

c(ildren mig(t belie*e t(at 1J9 is bigger t(an 1J/ sim%ly because t(e 9 is

larger t(an t(e /. T(e mani%ulati*e %ro*ides students a way to see t(ese

&ractions &or w(at t(ey truly are.

To-!ided Counters

"mage sourceI (tt%IJJwww.ama:on.comJearning-!d*antage-921>-Magnetic-

CountersJd%JB>>1$>B)@

Two sided counters are anot(er *ersatile mani%ulati*e t(at can be used

in so many diHerent ways. First oH4 t(ey (el% students wit( counting4

diHerentiating between sets o& ob+ects4 addition and subtraction4 or

multi%lication and di*ision. " used counters in my %eer teac(ing module to

diHerentiate between diHerent sets o& &ractions using ten &rames. " asked &or

students to use one colour to re%resent /J1>4 and anot(er colour to re%resent


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Bowering 19

2J1>. T(is allowed me to bridge into t(e addition o& &ractions as well4 since

t(e two sets could be combined. " also use t(em to teac( about t(e multi%le

ways a number good be re%resented using addition. For eam%le4 i& students

were looking &or t(e number QR4 " would ask students to dro% t(eir

counters on t(eir desks to see (ow many diHerent ways t(is number could

be re%resented.

" really en+oyed using counters. T(ey %ro*ide students wit( so many

easy ways to re%resent abstract conce%ts. " would use t(ese as a regular %art

o& my mat( teac(ing in my classroom.


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Bowering 1@

4. Mathematics and Techno!og$

!martboard lesson " #n introduction to $ractions T(e &ocus o& t(e &ollowing lesson is (ow to introduce &ractions at a

basic le*el. T(is lesson is intended &or a grade / introduction. T(e &oundation

o& &ractional conce%ts is so im%ortant in mat(4 as t(ese conce%ts etend into

ot(er mat( areas. "n t(is lesson4 " s%eak about t(e a%%ro%riate *ocabulary to

use w(en talking about &ractions4 and t(e way in w(ic( students s(ould be

associating &ractions to real-li&e a%%lication.


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Bowering 1A

%sing Manipulatives $or &egrouping

Base-ten blocks are a &antastic way to illustrate addition and

subtraction %roblems using a tec(ni3ue called regrou%ing. T(is tec(ni3ue

%ro*ides a sim%le and concrete way &or students to (a*e a *isual

re%resentation o& a %roblem. "n t(e &ollowing *ideo4 " talk about t(e

ad*antages o& using t(is tec(ni3ue4 and t(e ste%s to &ollow to com%lete t(is

tec(ni3ue.


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Bowering 2>

Fall into Counting " Big book T(e aim o& t(is big book was to %ro*ide students wit( multi%le

re%resentations o& counting using &amiliar ob+ects. !s t(e aut(ors4 we wanted

to include an element o& interacti*ity wit( t(e book so t(at students could

use a (ands-on a%%roac( w(en counting. Students will also be eercising

t(eir literacy skills4 re3uiring t(em to listen to (ear t(e %roblem t(at t(ey

must sol*e on eac( %age. ,e also introduced a sim%le way to include

addition wit(in some o& t(e %roblems.


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Bowering 21

/. ther Areas o( nterest Journal entries from my math methods course.

'iscussion (uestions

3amine $our own regions curricu!um document. 5hat are the

!earning e3#ectations (or numer (or chi!dren in indergarten

to grade 27 &om#are these e3#ectations with ideas #resented

in this cha#ter. 5hat ideas are stressed7 Did an$thing sur#rise

$ou7

T(e learning e%ectations are similar to t(ose in t(is c(a%ter. C(ildren are

e%ected to ski% count by 2s4 4 and 1>s4 count on &rom a number4 count by

ones &rom a gi*en number and count &orwards and backwards. C(ildren are

also e%ected to count using coins. T(is last e%ectation sur%rised me since

money is an abstract conce%t. Students must 8rst learn to associate t(e

corres%onding wort( o& eac( coin to t(e coins %resented in a mat( %roblem.

T(is could ser*e to be %roblematic at 8rst since c(ildren at t(is stage (a*e

only learned to count ob+ects based on (ow many ob+ects t(ere are. 7ow4

ob+ects (a*e diHerent 3uantities associated wit( t(em4 %enny being one4

nickel being 8*e4 and a dime being ten. C(ildren (a*e been learning using

singular mani%ulati*es to t(is %oint4 so adding t(is conce%t o& coins being

wort( more t(an ot(ers may be con&using to c(ildren in t(e beginning.


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Bowering 22

Dowe*er4 t(is is an im%ortant skill since c(ildren will e*entually be using

money in t(e real world.

8ouve noticed that a student $ou are woring with is counting

o9ects with an accurate se:uence o( numers words, ut is

not attaching a numer to each o9ect. There(ore, the

students ;na! count is inconsistent and inaccurate. 5hat

wou!d $ou #!an to he!# this student deve!o# a etter gras# o(

one*to*one corres#ondence7

T(ere a cou%le o& strategies " mig(t use to (el% t(is c(ild wit( one-to-one

corres%ondence. T(e 8rst strategy would be to (a*e a set o& 6as( cards wit(

t(e corres%onding number. !s t(e student counts t(e ob+ect4 t(e 6as( card

wit( t(e correct number could be located underneat( t(at ob+ect so t(e

student could associate t(e number wit( t(e ob+ect. !not(er strategy would

be to use a calculator or counter. !s t(e student counts eac( ob+ect4 (a*e

t(em record t(e number on t(e calculator or counter so t(ey are associating

t(at number wit( t(e ob+ect in t(e se3uence.

3#!ore a we*ased #rogram (or dri!!ing asic (acts. 5hat

(eatures does the #rogram have that are good7 )ot so good7


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Bowering 2/

T(is article contains web-based %rograms o& basic mat( &acts and ot(er

sub+ectsI (tt%sIJJ+r.brain%o%.comJ

T(is %rogram (as sim%le mat( e3uations t(at student can interact wit(. "

&ound t(at students would become (ig(ly engaged in t(e content once t(ey

were able to use t(is sort o& %rogram be&ore e%loring t(e conce%ts in real

li&e. "n terms o& limitations in tec(nology4 i& t(ere were only 2 com%uters in

t(e class4 t(e teac(er could sim%ly %ose 3uestions during w(ole grou%

instruction. Students can s(are ideas wit( t(e class as to w(at t(ey t(ink t(e

answer would be. T(e teac(er would use t(e answer on t(e website to see i&

it would be correct or not.

5hat is the im#ortance o( menta! mathematics and

com#utationa! estimation (or dai!$ !iving7 5hat are the

advantages o( eing a!e to estimate in #u!ic situations and

settings7

Mental mat(ematics aids in t(e e*ery mat( conce%t t(at we use in a real li&e

contet. ,e use mat( to count money w(en we buy groceries &rom t(e store4

or we use mental mat( to count our (ours we5*e worked during t(e week.

,e use mental mat( w(ile %laying s%orts to add u% scores to determine w(o

de&eats w(o. T(e ad*antage o& being able to estimate in %ublic situation

s(ows your com%etency wit( being able to %er&orm sim%le mat( %roblems

wit(out t(e use o& a calculator or ot(er de*ice t(at %eo%le tend to de%end

u%on. T(is is es%ecially true wit( t(e use o& cell %(ones. Most o& t(ese de*ice

https://jr.brainpop.com/https://jr.brainpop.com/


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Bowering 20

come e3ui%%ed wit( a ready to use calculator4 making t(em easy and

con*enient4 w(ic( (am%ers our ability to use our mental mat( skills.

Science Observation Journal

T(e &ollowing images de%ict gra%(s t(at " created in a %ro+ect t(at we

com%leted as %art o& my 'lementary science course. T(e 8rst %(otogra%(

s(ows a line gra%(4 w(ic( com%ares two diHerent sets o& tem%eratures o*er

a s%an o& 1 days. " gat(ered t(e data &rom a t(ermometer outside o& Brian

Mulroney Dall on t(e ST$ cam%us4 as well as &rom t(eweat(ernetwork.com.


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Bowering 2

"n t(is second %(otogra%(4 " c(ose to use a bar gra%( to s(ow t(e diHerent

3uantities and ty%es o& garbage " &ound in t(e (abitat we were in*estigating.

T(is kind o& gra%( gi*es a good re%resentation o& t(e ty%e o& data " collected.

For t(is 8nal illustration4 we (ad to ma% t(e area we were studying4 and

measure t(e total area using lengt( widt(. " &ound t(is acti*ity easy4 and

&ound t(at it would easily be translated into a classroom acti*ity.

Cool websites and videos!

(tt%IJJwww.a%lusmat(.comJ

http://www.aplusmath.com/http://www.aplusmath.com/


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Bowering 29

T(is website %ro*ides a ton o& cool and interacti*e games to (el% students

wit( t(eir mat( skills. T(ere are also works(eets4 digital 6as(cards4 and

*ideos

(tt%IJJwww.coolmat(-games.comJ

T(is is anot(er cool and &un interacti*e 8lled wit( in&ormation on *arious

to%ics in mat(ematics.

! UouTube *ideo &or decimalsI
http://www.coolmath-games.com/http://www.coolmath-games.com/

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