A Cl

Receive

doi:10.5

Abstra

The purpre-servmathemclass. Tanalysiswritten problemsemesteparticipcategorproblemThe maorganizreal situskills udistribualgebraan apprequationbasic ge

Keywoteacher

lassific

P

ed: February

5296/jei.v6i

ct

rpose of thivice mathem

matical modThe current s. The databy 59 seni

ms and soler period ppants themsically as fo

ms, “Future athematical ze the data, wuation mathused are geution and cic rational

ropriate matns in 1 vareometry inf

rds: Mathcandidate

ation o

Prospec

A

Me

y 26, 2020

i1.16566

is research imatics teach

delling skillsstudy is a q

a of the stuior mathemlutions. Thprior to theselves prodollows: “Wprediction”modelling write depen

hematically enerally; tocolumn graexpressionsthematical friable, estabformation, d

hematical m

of Math

ctive M

Alattin Ural

ehmet Akif

E-mail: ura

Accepte

URL: h

is to classifyhers in terms and mathequalitative rudy was ob

matics teache participa

e research. duced. The

Which optio” problems askills used

ndent and inor geometribe able to

aph, write s, write/solvfunction expblish propordraw and int

modelling,

98

hematic

Mathem

(Correspon

f Ersoy Univ

al@mehme

d: March 3

https://doi.o

fy the mathems of the nematical skresearch andbtained fro

hers. They wants took m

The proble mathematn is more and “Relatioare as follo

ndependent vically, use mo do four algebraic

ve equationplaining thertion, use tterpret a 1st

Mathemati

cal Mod

matics T

nding autho

versity, Turk

etakif.edu.tr

1, 2020 P

org/10.5296

ematical monumber of vkills used ind the data w

om the matwere given mathematicaems are thtical modeleconomica

onship betwows: to be abvariables, wmathematicoperations expression,

n and inequae data relatetrigonometrt degree ine

ical model

Journal o

deling P

Teachers

r)

key

Published: A

6/jei.v6i1.16

odelling provariables ann solving thewas analyzehematical ma 1-week p

al modellinhe original lling probl

al” problemween two quble to colle

write fixed val conceptswith ration

, do arithmality in 1 ored to the datic ratios inquality in 2

lling probl

of EducationISSN 2

2020, Vol.

www.macroth

Problem

s

April 10, 20

6566

oblems prodnd to determhe problemsed using desmodelling pperiod to wng course

problems lems produ

ms, “Profit-muantities” prect appropriavalues, visua. The mathenal numbermetic operar 2 variable

ata, solve 1sn right trian2 variables.

lems, Math

nal Issues 2377-2263

6, No. 1

hink.org/jei

ms of

020

duced by mine the in each scriptive problem

write the for one that the

uced are making” roblems. ate data, alize the ematical rs, draw ation in es, write st degree ngle, use

hematics

1. Intro

Mathemreal-lifemodelincollectsvariableare donThe solgeneral

Mathemreadingcalculathandlin& HainZverkovmay be of the previouabout thcountriebetweenpracticefor succpoint heit was rsolving

Mathemexperimcomputmodelli(Berry &

Blum mathem

oduction

matical mode situations ng process is and analyes necessaryne and a malution obtainized for oth

matical mog-understandtion, etc. (N

ng real-life snes, 2004; Hva, 2001). Naffected bystudent, the

us experienche situationes, Klymchn the real wes before. Tcessful mode observed revealed tha

modeling p

matical modmental modeter-based ining is asked& Houston,

(1991) revmatical topic

delling proband contain

is to undersyses the apy to solve thathematical ned is interp

her problem

deling is ding, thinkNiss, 2003)situations thHaines, CroNiss (2001)y the teachine motivatioces. Galbrain in the conhuk and Zvworld and thTanner and Jdeling, studthat the stu

at students hproblems.

delling probelling. Whinformation,d by giving, 1995; Kap

vealed the cs.

blems are nn different ptand the rea

ppropriate dhis problemmodel is c

preted in res (Berry &

linked to king and . Several sthat require aouch, & Da

stated that ng approachon of the teith and Stillntext also aerkova (200he mathemaJones (1995dents shoul

udents had dhad significa

blems can bile theoretic, in experig informati

pur, 1982).

table bel

99

non-routine possible solal-life probldata. The n

m. After thiscreated, its eal life. At tHouston, 1

other mathapplying ptudies havea mathematavies, 2001the perform

h, the probleacher and lman (2001

affects their01) revealeatical world5) observedld know whdifficulty. Inant difficult

be grouped ucal modellinimental moion about e

low regard

problem silutions. Thelem. Here thnext stage s stage, the naccuracy anthe last stag995).

hematical problem soe shown thatical solutio; Ikeda &

mance of stuem situationthemselve

) stated thar modelinged that studd because td that knowhat knowledn the study ties in using

under two mng includesodelling, thexperiment,

ding real-w

Journal o

tuations thae first step ihe person dis the stagnecessary mnd suitabilitge, the mode

skills sucholving straat students on (ChristianStephens, 2udents in thn given in ts, the effor

at students’ skills. In th

dents found hey had noledge alonedge to use conducted b

g the concep

main headins mathemathe solution

observatio

world exam

of EducationISSN 2

2020, Vol.

www.macroth

at express cin the mathe

defines the pge of choosmathematicaty are inveel is develo

h as matheategies, reahave difficunsen, 2001;2001; Klymhe modelingterms of thert shown ageneral kno

heir studiesdifficult to

ot experience was not suwhere, and

by Erdoğanpt of functio

ngs; theorettical, statistn of matheon and their

mples and

nal Issues 2377-2263

6, No. 1

hink.org/jei

complex ematical problem, sing the al works stigated.

oped and

ematical asoning, ulties in Crouch

mchuk & g process e interest nd their owledge s in nine o switch ced such ufficient d at this n (2010), on while

tical and tical and ematical r results

related

Table 1

Real-w

variou

chemic

absorp

rainbo

genetic

rates o

price in

income

electio

social

traffic

biking

chairop

gambli

paintin

musica

Solvingcompet

• C

• C

• C

• C

• Cnec

Jensen Degree degree spectrumlevel, incan intedomainexampl

. Real-worl

world examp

us growth and

cal reactions

ption, decay o

w

cs

of interest

ndex

e tax

ons

classes

flow

g

plane

ing

ng

al scales

g mathematence. Accor

Competence

Competence

Competence

Competence

Competencecessary.

(2007) statof coveragof autonomm of contexndicating hoegrate relev

n of situatioe, the fact

ld examples

les

d decay proc

s, spread of e

of beer froth

tical moderding to Blu

to understa

to create a

to solve ma

to interpret

e to questi

ted three de indicating

my with whxts and situaow conceptuvantly in a

ons in whichthat someo

s and related

esses: popul

pidemics, wa

and so on

elling problum (1996), m

and real life

mathematic

athematical

t mathemati

ion the sol

dimensions g which aspich this actations in whually and tectivating thh someone

one is very

100

d mathemati

ation growth

arming/cooli

lems is remathematic

problems a

cal model fr

problems i

ical results f

lution and

to assess sects of the ctivation takehich someonechnically ahe competecan performcompetent

ical topics

Relat

h,

ing,

funct

geom

arithm

algeb

arithm

arithm

arithm

arithm

finite

algeb

linear

stoch

geom

arithm

lated to oncal modellin

and create a

rom real life

n the mathe

for real life;

perform a

someone’s competencyes place. Rne can activ

advanced theency. The rm mathemawhen it co

Journal o

ted mathema

ions, calculu

metry, calculu

metic, probab

bra

metic, functio

metic, algebr

metic, functio

metic, geome

e maths, prob

bra

r algebra, fun

hastics, finite

metry, algebra

metic, algebr

ne’s matheng competen

real model

e model;

ematical mo

;

another mo

possession y someone cadius of ac

vate the come mathematadius of ac

atical modelomes to dev

of EducationISSN 2

2020, Vol.

www.macroth

atical topics

us, linear, alg

us

bility, (linear

ons, calculus

ra, functions

ons, calculus

etry, stochast

bability, linea

nctions, calc

e maths

a

ra, functions

ematical mncies are tho

l;

odel;

odelling pro

of a compcan activatection, indicampetency. Ttics is that sction addrelling activitveloping an

nal Issues 2377-2263

6, No. 1

hink.org/jei

gebra

r)

s

s

tic

ar

ulus

modelling ose:

ocess if

petency: e and the ating the

Technical someone sses the ties. For nd using

optimizsame cokind of These tpossessdimensimathem

Figure

Most omodelinmathemresearchmodelinmathemparticipthis gapcontribu

2. Meth

The purpre-servmathemclass. Tanalysis

zation modeompetence

f mathematithree dimension of a coions when

matical mod

e 1. Geome

of the mathng compete

matical modh has beenng problem

matical modpants in a hop. In additiute to the pr

hods

rpose of thivice mathem

matical modThe current s. The data

els in everywhen it cocs someonensions haveompetence i

we attempelling comp

etrically visu

hematical mencies of thdeling educan found in

ms produceddels, problolistic way.ion, it is throcess of de

is research imatics teach

delling skillsstudy is a q

a of the stu

yday shoppomes to dese can use ane been visus representet to suppor

petency, am

ualized threand

modeling rhe participaation on stun the literad by studenlems and Thus, a co

hought that evelopment

is to classifyhers in terms and mathequalitative rudy was ob

101

ing situatiosign problemnd how flex

ualized geomed by a volrt the deve

mong a group

ee dimensiontechnical le

researches ants, the difudents’ concature regardnts. In thismathematic

ontribution the results of the math

fy the mathems of the nematical skresearch andbtained fro

ons, for exams. The tec

xible they armetrically ilume. We nelopment ofp of student

ns (degree oevel)

in mathemfficulties thceptual devding the cs study, it cal modellwill be madobtained f

hematical m

ematical monumber of vkills used ind the data w

om the mat

Journal o

ample, doeschnical levere in their un Figure 1.

need to pay f a competets.

of coverage

matics educahey face anvelopment ilassificationis focused ling skills de to the litfrom the cu

modelling ed

odelling provariables ann solving thewas analysehematical m

of EducationISSN 2

2020, Vol.

www.macroth

s not guaravel addresseuse of math. In this mattention to

tence, for e

e, radius of a

ation is abnd the effecin matheman of matheon classifyproduced

terature in turrent reseaducation.

oblems prodnd to determhe problemsed using desmodelling p

nal Issues 2377-2263

6, No. 1

hink.org/jei

antee the es which ematics. odel the o all the example,

action,

bout the ct of the atics. No ematical ying the

by the terms of

arch will

duced by mine the in each scriptive problem

written the Matmathema 1-weethat thenumberclass wused.

3. Find

A classion the ntype omathem

3.1 Non

Preservof real some ccollectinwere un

3.1.1 Pr

The catparticip

• Ttriethe(for

• Tear

3.1.2 M

Gatheri

3.1.3 M

4 opera

3.2 One

3.2.1 Pr

The catfollows

by 59 maththematics T

matical modek period toe participantr of variabl

were examin

dings

ification of number of v

of the mamatical skills

n-variable S

vice teacherslife proble

conditions ang some da

nable to put

roblem Typ

tegories crepants are as

he problemed to find ouy used are ar 4-year uni

The problemrn money”, “

Mathematica

ing appropri

Mathematica

ations with r

e Variable M

roblem Typ

tegories cres:

hematics teaTeacher Traidelling courso write the pts themselves used in

ned in terms

mathematicvariables us

athematical s.

Solutions (L

s in this catems they prand requireata and takforward a m

es

eated regarfollows:

ms of “whichut which ofas follows: iversity term

ms of “earni“earning sta

al Modelling

iate data, or

al Skills Use

rational num

Mathematica

es

eated regard

acher candiining Prograse for one sproblems an

ves producedmathematics of the ma

cal models psed is given

modelling

evel 0)

tegory creatroduced. Hos variable ing some amathematic

ding the co

h option is mf the two op“carboy or

m)”, “rent o

ing money”atus of a flo

g Skills Use

rganizing da

ed

mbers, distri

al Models (L

ding the co

102

dates. The pamme of Fasemester pernd solutionsd. The probcal models.athematics t

produced byn below. Eag problems

ted a solutioowever, theuse. Pre-se

average valucal model.

ontent of th

more econoptions would

water purifor buy”.

”: “at least hower greenh

ed

ata, mathem

ibution and

(Level 1)

ontent of th

participantsaculty of Edriod before s. The problblems were Then, the topics and m

y prospectivach class cos, mathem

on without e solution oervice teachues based o

he modellin

mical”: in sd be more efier”, “farm

how many house”, “par

matical skills

column cha

he 1-variab

Journal o

s were the 4ducation. Ththe researchlems are thefirst classifmathematic

mathematic

ve mathemaonsists of thatical mod

using variaof such prohers did noon these da

ng problem

such problemeconomical.

for meat or

ratings shourking prices

s.

art.

le modellin

of EducationISSN 2

2020, Vol.

www.macroth

4th grade stuhe participah. They wee original pfied in termcal models

cal modellin

atics teachehree sub-catdelling ski

ables in the oblems depot use variaata. Therefo

ms produced

ms, the part. The probler milk”, “bu

uld a seriess”.

ng problem

nal Issues 2377-2263

6, No. 1

hink.org/jei

udents at ants took re given

problems ms of the

in each ng skills

ers based tegories: ills and

solution pends on ables by ore, they

d by the

ticipants em titles us or car

s take to

s are as

• Texaproor (for

• Tmodep“wh

• Tconpasbe p

• Tmathebet“W

3.2.2 M

To be aindepenproblemand use

3.2.3 M

In additarithmeunknowthe dataequationgeometr

3.3 Two

3.3.1 Pr

The catfollows

• T“Ca“Mcar

The problemamined the oblem titles water purifr 4-year uni

The problemodel in suchpending on hen does th

The problemnditions for ssengers shoproduced to

The problemathematical y used are

tween numbWeight loss”,

Mathematica

able to gathndent variabm, interpret e the needed

Mathematica

tion to the metic operatiown equationa (such as 2n, establishry knowled

o Variable M

roblem Typ

tegories cres:

The problemarboy water

Making pomer (for 4-year

ms of whichconditions they use ar

fier”, “anti-iversity term

ms of predich problemstime. The p

he lake dry”,

ms of profa job to be

ould be at leo make mon

ms of relatiorelationship

e as followsber of touri, “How muc

al Modeling

her appropribles, write the model

d mathemati

al Skills Use

mathematicons with al

n or inequali2nd degree h proportiondge.

Mathematica

es

eated regard

ms of which r or water pegranate sor university

h option is mfor which

re as followlime tablet

m)”, “drip o

ction of futus in order tproblem title, “use rate o

fit-making: e profitable. east for gainney”, “Sun p

onship betwp between ts: “Relationsts and incoch fuel is th

Skills Used

iate data, oconstant v

in terms ofical concept

ed

al skills in lgebraic ratity, write thpolynomialn, use trigo

al Models (L

ding the co

option is mpurifier”, “4

our at home term)”, “Re

103

more econoof the two

ws: “rechargor magneti

or normal irr

ure: The pato make pres they usedof recycling

In such p The problen”, “At leaspanel”, “Mi

ween two qutwo quantitnship betwome”, “Rel

here in the fu

d

organize thevalues, conf real life, vts in the pro

3.1.3, to betional exprehe most appl, exponentionometric r

(Level 2)

ontent of th

more econom4 season tir or buying”ent or buy a

omical: In suoptions woeable or baic anti-limerigation”.

articipants trredictions ad are as fol

g”.

problems, them titles usest how manyinimum adv

uantities: Thties in such

ween distanclationship buel tank”.

e data, to benvert the revisualize theocess of solu

e able to wressions, estapropriate maial functionratios in the

he 2-variab

mical: “stonre or winter”, “Which fa fleet”.

Journal o

uch problemould be morttery-operat

e for dishwa

ried to presabout a qualows: “max

he participaed are as foy kilograms

vertising cos

he participanproblems.

ce and heigbetween pop

e able to weal probleme real situatution.

ite algebraiablish and athematical

n), solve 2nde right trian

le modellin

ne block pavr and summfleet rental c

of EducationISSN 2

2020, Vol.

www.macroth

ms, the partre economited”, “carboasher”, “bu

sent a matheantity that ximum hair

ants examiollows: “Hos of bananast”.

nts investigThe proble

ght”, “Relapulation an

write dependm to mathetion mathem

ic expressiosolve 1st d function red degree 1-ngle, use th

ng problem

vement or amer tire sepacompany”,

nal Issues 2377-2263

6, No. 1

hink.org/jei

ticipants cal. The oy water us or car

ematical changes length”,

ined the ow many s should

gated the em titles ationship d time”,

dent and ematical

matically

on, make degree 1 egarding -variable he basic

s are as

asphalt”, arately”, “Bus or

• Tadvstat“Hoyeathatypminitse

3.3.2 M

To be aindepenproblemand use

3.3.3 M

In addiexpressdegree value).

3.4 Mul

3.4.1 Pr

The catfollows

• Tcig

• Tand

• T“Mmewoweedrivsho

3.4.2 M

To be aindepen

The problemvertising cotion for cheow many taars later doeat a dormitopes of coffenimum costelf”.

Mathematica

able to gathndent variabm, interpret e the needed

Mathematica

ition to thesions, establ2 unknown

ltivariate M

roblem Typ

tegories cres:

The problemgarette”, “Ho

he problemd price”.

he problemMaximum pr

et the demauld be morek in orderving licenseould be on th

Mathematica

able to gathndent variab

ms of profitst”, “3rd breap fuel”, “ables and ches a dishwaory make me to make mt”, “when d

al Modeling

her appropribles, write the model

d mathemati

al Skills Use

e mathematlish 1st degn inequality

Mathematica

es

eated regard

ms of whichomemade to

ms of relation

ms of profit-mrofit”, “Saviand at minire economir to make the courses”, he breakfas

al Modeling

her appropribles, write

t-making: Tridge: how m“At least hohairs must basher amort

money”, “Wmaximum woes a solar

Skills Used

iate data, oconstant v

in terms ofical concept

ed

tical skills gree 2 unkny, use speci

al Models

ding the con

h option is omato paste

nship betwe

making: “Wing the costimum cost”ical”, “Howhe most pro“Obtainingt plate for a

Skills Used

iate data, oconstant v

104

The problemmany yearsow many yebe producedtise itself”,

What types oweekly earnpanel recov

d

organize thevalues, conf real life, vts in the pro

in 3.2.3, tnown inequial defined

ntent of the

more econe production

een two qua

Water vendot of jacketin

”, “Under ww many pieofit”, “profig the most pa child with

d

organize thevalues, con

m titles useto recover”

ears later dd to make th“At least h

of componenings”, “Prover itself”, “

e data, to benvert the revisualize theocess of solu

o be able uality, drawfunctions (

e multivaria

nomical: “Nn”.

antities: “Re

r’s gain funng”, “Produ

what conditieces of clotit-making stprofit with m

minimum c

e data, to benvert the re

Journal o

ed are as fo”, “Should h

does jacketinhe gain the mow many s

ents should oduction of“when does

e able to weal probleme real situatution.

to write 2 w and interp(such as ab

ate modellin

Normal ciga

elationship

nction”, “Couction of clons buying thing shoultatus of a cminimum cocost”.

e able to weal problem

of EducationISSN 2

2020, Vol.

www.macroth

follows: “Mhe go to theng amortisemost”, “Ho

students shobe mixed i

f tahini-mols the capital

write dependm to mathetion mathem

variable apret a graph

bsolute valu

ng problem

arette or el

between pa

ost functionleaning matg a room theld be producompany givost”, “Whic

write dependm to mathe

nal Issues 2377-2263

6, No. 1

hink.org/jei

Minimum e remote e itself”, ow many ould live into two lasses at l recover

dent and ematical

matically

algebraic h of 1st

ue, exact

ms are as

lectronic

ackaging

of diet”, terials to ermostat uced per ving the ch foods

dent and ematical

problem

3.4.3 M

To be aarithmeinequal

4. Resu

When lhad no 2-variab

The pro

Table 2

The the

Profit-m

Which

Relatio

Future

Total

When thand “Pr

The resnumber

m, the neede

Mathematica

able to do etic operatioity system (

ults

ooked at thvariable (o

ble and 22%

oblems prod

. The Them

eme of the pr

making

option is mo

onship betwe

prediction

he table is arofit elimina

ults regardir of variable

ed mathema

al Skills Use

arithmetic oons with alg(aim functio

he models only arithme

% of them w

duced by the

mes of the Pr

roblem

ore profitable

een two quan

analyzed, itation” are a

ing mathemes are shown

atical concep

ed

operations gebraic and on),

f mathematetic operatiowere multiva

e participan

roblems

Non-

Solut

5

e 5

ntities

10

is seen thatcommon pr

matics topicsn generally

105

pts in the pr

in rational rational ex

tics teacher ons); 31% oariate.

nts are prese

-variable

tions

1-

M

4

5

5

4

1

at the probleroblem type

s and mathein Table 3.

rocess of so

numbers, wpressions, w

candidates;of them had

ented catego

-variable

Models

2

M

1

8

8 1

ems of “Whe in each ca

matical mo

Journal o

olution.

write algebrwrite max th

; it was seend 1-variable

orically in th

2-variable

Models

M

M

0 9

3

1

8 1

hich option itegory.

delling abil

of EducationISSN 2

2020, Vol.

www.macroth

raic expreshree variab

n that 16% e, 31% of th

he Table 2.

Multivariate

Models

9

3

1

13

is more eco

lities on the

nal Issues 2377-2263

6, No. 1

hink.org/jei

sion, do le linear

of them hem had

Total

28

21

6

4

59

onomical”

basis of

Table 3variable

Number

Variable

0

1

2

Min 3

When th(Non-vaother h(Non-vaknown,be consmodelinmodels)

When ththe modmodelliTherefomodellilimited the matthan levtypical below:

The Cothe amohe wishestablis

. Mathemates

r of

es Mathem

Four op

(Level 0

and 4 o

unknow

function

function

1-variab

of geom

(Level 1

1st deg

absolute

(Level

expressi

he table is eariable modhand, it is ariable mod mathemati

sidered togeng skills ar) and Level

he solutionsdel increaseing skills usore, the nuing skill. Hoto writing a

thematical svel 2. Therexample of

mpany wanount of profhes to buy sh a partners

tics topics a

matics Topics

peration in Q, di

0+) 1st degree

operations, rat

wn equation or

n such as 2nd

n and graph o

ble equation, ra

metry and trigon

1+) 1st degree

gree 2 unknow

e value and exa

0+) 4 operatio

ions, linear ineq

examined; mdels), Level

seen thatdels), Levecal modelin

ether. Therere leveled a-2 (2-variab

s of the pared from 0 tosed by the pumber of vaowever, cona gain/aim fsubjects andefore, it wof mathemat

nts the total fit he plans

at least 50ship in the f

and mathem

istribution and c

1 unknown alg

ional expressio

inequality, ba

degree polyno

f them, solutio

atio-proportion,

nometry in the r

2-variable alge

wn inequality

ct value functio

ons with algeb

quality system

mathematic-1 (1-variab

mathematel-1 (1-variang skills incefore, on theas follows: ble models)

ticipants weo 2, it was sparticipants ariables in nsidering thfunction (ind mathematould be apptical modell

risk not to to make fro

0,000 TL sfuture. Acco

106

matical mod

column graph

gebraic expressi

ons, 1st degre

asic knowledge

omial, exponen

on of 2nd deg

, basic knowle

right triangle

ebraic expressio

and graph of

ons

braic and ratio

al modelingble models)tical skills able modelclude mathee basis of thLevel-0 (N.

ere examineseen that theincreased inthe model

hat the modenequality systical modelpropriate toling using a

exceed 0.12om this inveshares fromording to th

delling abili

Mathem

To colle

ions

e 1

e of

ntial

gree

edge

(Level 0

independ

visualize

convert

problem

interpret

ons,

f it, (Level 1

model

onal

g skills can , Level-2 (m(math top

ls) and Levematical skihe findings

Non-variable

ed; as the nue mathematin the mannel also showels with 3 ostem with 1ling skills u evaluate tha minimum

2 as per its estment is a

m the Compe above dat

Journal o

ties on the

matical Modellin

ct appropriate d

0+) to be able

dent variables,

e the real sit

the real prob

m, solve the m

t the model

1+) to determin

be leveled min 2-variabpics) are level-2 (2-varlls, so theseof this rese

e models), L

umber of vaical subjecter that covews the leveor more vari degree); it

used in thishis category

m of 3 varia

investment at least 25,0pany 3, whta, let’s crea

of EducationISSN 2

2020, Vol.

www.macroth

basis of nu

ng Abilities

data, organize th

to write depen

write constan

tuation mathem

oblem to math

mathematical

ne some restric

as follows: ble models)eveled as riable mode two resultearch; matheLevel-1 (1-

ariables incts and matheer the previoel of matheiables are gt cannot be ss category ay within lev

ables was pr

policy. In a000 TL. In ahich he thinate a model

nal Issues 2377-2263

6, No. 1

hink.org/jei

umber of

he data

ndent and

nt values,

matically,

hematical

problem,

cts of the

Level-0 ). On the Level-0

dels). As s should ematical -variable

cluded in ematical ous level. ematical

generally said that are more vel 2. A resented

addition, addition, nks may that will

maximi

X1 = st

X2 = st

X3 = st

X4 = st

X5 = st

Gain Fu

Restrict

X1+X2

X1.0,15+XX

Z = 0.2

X3≥50

X1,X2,X5. Discu

The proprofit-mpredictimodelliequationfunctiontrigonomskills udistingumake asin the geometr

Anothermodel imodelliTherefomathem

When cduring mathemlevel (mteachingto use situation

ize the profi

tock of the c

tock of the c

tock of the c

tock of the c

tock of the c

unction: Z =

tions: +X3+X4+X2.0,12+X3.0,03+X1+X2+X3+X

23X1+0.16X

0.000 (restri

X3,X4,X5≥ussion and

oblems promaking, whion of futuring problemns or inequn, 2nd degmetric ratio

used by theuish betweessumptionsmathemati

rically, to in

r result obtincreased fring skills usore, it can bmatical mod

considered their educa

matical modmost of themg, students mathematicn.

it of the com

company 1

company 2

company 3

company 4

company 5

= 0.23X1++X5≤250.0

+X4.0,05+X5.0,1

X4+X5

X2+0.04X3

iction of the

≥0

Conclusion

oduced by thich optionre. The matms are thouality in 1 gree polynoos in orthoge participanen depende, to write coical solutionterpret the

tained fromfrom 0 to 2sed by the pbe said thatelling skills

the matheation life; itdelling werem are at the learn the mcal concept

mpany.

(HS1)

(HS2)

(HS3)

(HS4)

(HS5)

0.16X2+0.

000 (capita

18 ≤ 0.12 (r

3+0.08X4+e company 3

n

the participn is more thematical tose: algebr

or 2 unknomial, 2nd onal triangl

nts in the ment and indonstant valuon stage, tmodel.

m the study , it was see

participants t the numbes.

ematics subt was seen e the mathelevel of mi

mathematicalts in which

107

04X3+0.08

al restriction

risk restricti

+0.28X5≥23)

pants are thprofitable

topics invoraic expresnown, colum

degree eqle and Pythamathematicdependent vues, to use tto visualize

is that as en that the increased in

er of variab

bjects that that the so

ematical coiddle school

al concepts ih contexts.

8X4+0.28X

n)

ion)

25.000 (pro

hematically, relationsh

olved in thessions, ratiomn or line

quation in agorean relaal modellinvariables, tothe matheme the real

the numbermathematic

n the mannebles in the m

mathematicolutions theoncepts and l). As knowin a procedu

This resul

Journal o

X5

ofit restrictio

as followship betwee solution oonal expres

graph, lin1 unknownation. Mathng process o collect ap

matical concesituation

r of variablcal subjectser that covemodel also

cs teacher ey presented

skills at mwn, in the prural way anlt can be s

of EducationISSN 2

2020, Vol.

www.macroth

on)

s: the proben two quof the mathessions, 1st

near or expn, ratio-pro

hematical mare as foll

appropriate epts and opmathematic

les includes and matheer the previo

shows the

candidates d in the pro

most at highrocess of trand do not lestemmed fr

nal Issues 2377-2263

6, No. 1

hink.org/jei

blems of uantities, ematical

degree ponential oportion,

modelling lows: to data, to

perations cally or

d in the ematical ous level. level of

learned ocess of h school aditional arn how

rom this

Anothersolutionpre-servschool able to Ural (20mathemschool.

Blum ((Table among Differenthemed and arisubject

The durgiven 1importamodelinModelleactivitieschool Considedepartmthere islonger-tand skiThus, th

Referen

Berry, J

Blum, ArgumemathemEngland

Blum, WSchrifte

ChristiaMatos, ICTMAPublish

r important ns by using vice mathemcurriculum use these c020). If stud

matical conc

1991) revea1). It was sthe real-li

ntly, in the problems a

ithmetic weof trigonom

ration, cont hour a we

ant factor ong process eme Eğitimes in the bolevels. Theering that

ment and res no signifiterm matheills, studenthe types of p

nces

J., & Housto

W. (1991).ents and Ins

matical modd.

W. (1996). enreihe Dida

ansen, I. (20W. Blum, K 9: Applic

hing. https://

point in thionly arithm

matics teacsuch as va

concepts is adents are recepts in rea

aled a table seen that thife problemcurrent stu

are includedere also incmetry was u

tent and teaeek, throughof the maththey did. T

mi (Mathemook require erefore, a c

the particeceived suffficant limitaematical mots may be aproblems pr

on, K. (1995

. Applicatiostructional Adelling and

Anwendunaktik der M

001). The efK. Houston

cations in s/doi.org/10.

is context ismetic operathers who sariable, algealso anothe

equired to seal life prob

regarding rhe problemsms in this udy, “profit-d. In terms cluded in t

used in a few

aching methh one semehematical m

The content atical Modemathemati

change in thcipants werficient mathation for thodeling eduasked to prroduced and

5). Mathem

ons and MAspects. Inapplication

ngsbezüge iMathematik,

ffect of taskn, & S. Carscience and1533/97808

108

s that 12% otions withoushould haveebraic expr

er finding. Set mathemablems shou

real-world es of “growttable, are

-making” anof mathem

the current w problems.

hod of mathester, is a simodeling prof the coureling Educaical knowlethese factorre senior hematical mhe participaucation requroduce and d the mathe

matical mode

Modelling inn M. Niss, Wns (pp. 10-

im Mathem23, 15-38.

k organisatiorreira (Eds.)d technolog857099655.

of pre-serviut using vare acquired ression, equSimilar findatical modelld be emph

examples anth process”also inclu

nd “relationmatics topics

research. D.

hematical mignificant liroblems tharses consistation)” writedge and skrs may affestudents o

modeling edants. For fuuired by hig

solve mathematical ski

elling. Brist

n MathemaW. Blum &29). Ellis H

matikunterric

on on classr), Modellinggy (pp. 31.5.311

Journal o

ice mathemariables (algthe subject

uation, ineqdings were f

ling at a gohasized, at

nd related m” and “priceuded in thenship betwes; functions,Differently,

modeling edumitation ofat students ed of the btten by Ura

kills at the sect obtaininof the matducation; it uture studiegher mathehematical mlls may diff

tol: J. W. Ar

atics TeachI. Huntley

Horwood L

cht. Trends

room modelg and math1-320). Ch

of EducationISSN 2

2020, Vol.

www.macroth

atics teachegebra). The ts of the sequality werefound in a sood level, th

least from

mathematicae index” whe current reen two qu, algebra, g, in this stu

ucation, whf the researc

produced book “Matemal (2018). Msecondary ang differentthematics tt can be staes, at the eematical knomodeling prfer.

rrowsmith L

hing: A Re(Eds.), Tea

Limited, Ch

s und Persp

lling activithematics edhichester: H

nal Issues 2377-2263

6, No. 1

hink.org/jei

ers made fact that

econdary e not be study by he use of

m middle

al topics hich are

research. antities”

geometry udy, the

hich was ch as an and the matiksel

Modeling and high

results. teaching ated that end of a owledge roblems.

Ltd.

view of ching of ichester,

pektiven.

ies. In J. ducation, Horwood

Crouchworld ahttps://d

Erdoğantools. Pj.sbspro

Galbrai(Eds.), M

Haines,Matos, ICTMAPublish

Ikeda, modellimathem10.1533

Jensen, GalbraiEnginee

Kapur, Journalhttps://d

KlymchCarrieraPublish

Niss, Myears ofof mathAcadem

Niss, MKOM PEducati

Tanner,modelliAdvanc61-70).

Ural, A

, R., & Haand the mdoi.org/10.1

n, A. (2010Procedia So.2010.03.72

ith, P., & StiModelling a

, C., CrouchW. Blum, K 9: Applic

hing. https://

T., & Steping. In J. F.

matics educ3/97808570

T. H. (20ith, W. Bluering and E

J. N. (198l of Mathdoi.org/10.1

huk, S., & a (Eds.), M

hing. https://

M. (2001). f experiencehematics a

mic Publishe

M. (2003). MProject. In ion (pp. 115

H., & Jing—A socices and pers

Yorklyn: W

. (2018). M

aines, C. (2mathematical1080/00207

0). Primary Social and 23

illman, G. (and Mathem

h, R., & DaK. Houston

cations in s/doi.org/10.

phens, M. . Matos, W.cation (pp. 099655.5.38

007). Assesum, & S. KEconomics. C

2). The arthematical 1080/00207

Zverkova, Modelling /doi.org/10.

University es with the

at universityers.

MathematicA. P. Gag

5-124). Athe

Jones, S. io-contructispectives in

Water Street

Matematiksel

2004). Matl model. In390310001

teacher eduBehaviora

(2001). In Jmatics. Chic

avies, J. (20n, & S. Carscience and1533/97808

(2001). Th. Blum, S.

381-400). 81

ssing matheKhan (Eds.)Chichester:

t of teachinEducation 398201302

T. (2001). and mathe1533/97808

mathematiRoskilde m

ty level: an

cal competeatsis (Eds.)ens: The He

(1995). Divist interprn the teachin

Mathemati

l Modelleme

109

thematical mnt. J. Math638322

ucation studal Sciences,

. F. Matos, chester: Hor

001). Underrreira (Eds.)d technolog857099655.

he effects K. Houston

Chicheste

ematical m), Mathema Horwood.

ng the art oin Scien

210

In J. F. Mematics edu857099655.

cs based omodel. In D.n ICMI st

encies and t), 3rd Medellenic Math

Developing retation. In Cng of mathecs.

e Eğitimi. A

modelling: h. Educ. S

dents’ability, 2, 4518-4

W. Blum, Srwood Publ

rstanding st), Modellinggy (pp. 366.5.366

of studentn, & S. P. Cer: Horwoo

modellibg catical Mod

of mathemance and T

Matos, W. Bucation (p. .4.227

on problem-. Holton (Edtudy (pp. 4

the learningditerranean hematical S

metacogniC. Sloyer, Wematical mo

Ankara: Anı

Journal o

Transitionsci. Technol

y to use fun4522. https

S. K. Houstoishing.

tudents’ mog and math6-380). Ch

s’discussionCarreira (Edod Publishin

ompetency.elling (ICT

atical modelTechnology,

Blum, S. K.227). Chi

-oriented std.), The tea405-422). D

g of mathemConferenceociety.

itive skillsW. Blum, &odelling an

Publishing.

of EducationISSN 2

2020, Vol.

www.macroth

s between l., 35(2), 1

nctions as ms://doi.org/1

on, & S. P.

odelling skihematics edhichester: H

n in matheds.), Modelling. https://

. In C. HaTMA12) Ed

lling. Intern 13(2), 1

. Houston, hichester: H

tudent projaching and lDordrecht:

matics: Thee on Mathe

s in mathe& I. Huntleynd applicati

.

nal Issues 2377-2263

6, No. 1

hink.org/jei

the real 197-206.

modeling 10.1016/

Carreira

lls. In J. ducation, Horwood

ematical ling and /doi.org/

aines, P. ducation,

national 185-192.

& S. P. Horwood

ects: 25 learning Kluwer

e Danish ematical

ematical y, (Eds.), ons (pp.

Ural, AEnglishStudies,

Copyri

Copyrigthe jour

This is Commo

A. (2020). h and Turki, 6(10).

ight Disclai

ght for this rnal.

an open-aons Attribut

A comparaish undergr

imer

article is re

access articltion license

ative study raduate mat

etained by t

le distribute(http://crea

110

of mathemthematics st

the author(s

ed under thativecommo

matical modtudents. Eu

s), with firs

he terms anons.org/licen

Journal o

delling comuropean Jou

st publicatio

nd conditionses/by/3.0/

of EducationISSN 2

2020, Vol.

www.macroth

mpetences burnal of Ed

on rights gr

ons of the C/).

nal Issues 2377-2263

6, No. 1

hink.org/jei

between ducation

ranted to

Creative