The representation of prospective teachers in solving math problems affects the results solving math problems faced, so that representation is an important aspect of building an understanding of mathematical concepts. This research uses a qualitative approach with a case study method. 7 out of 112 mathematics education teacher candidates were selected as research subjects. Algebra assignments and interview sheets that have been validated by two experts in mathematics, and use think aloud and field notes as data collection tools. Triangulation data sources were used as data reliability. The findings in this study are two ways that prospective teachers use area measurements (geometric representations) to solve algebraic problems, namely direct algebraic-geometric translation and algebraic-geometric translations based on the results of factorization. The process of emerging geometric representations is based on the pre-existing knowledge of prospective teachers. In addition, from the stages of the geometric representation process, a similar pattern was found that could be used for further research. The patterns are in the form of perception, appearance, strategy, and re-check. We recommend to carry out further research related to the geometric representation process associated with information processing theory and to develop learning models that can improve the representation of geometrics in solving mathematical problems. For the learning process, teachers do not realize the importance of geometric representation, because they may feel that students are not able to complete tasks using representations and are not trained to develop tasks involving geometric representations. The implication for learning is that it can help develop the mathematical abilities of students and prospective teachers.
REFERENCES
1.
Cankoy
O
, Özder
H.
The Influence of Visual Representations and Context on Mathematical Word Problem Solving Başlam ve Görsel Anlatımların Matematiksel Sözel Problem Çözümüne Etkisi.
2011
;30
:91
–100
.2.
Chang
BL
, Cromley
JG
, Tran
N.
Coordinating Multiple Representations in a Reform Calculus Textbook
. Int J Sci Math Educ.
2016
;14
(8
):1475
–97
.3.
Sajadi
M
, Amiripour
P
, Rostamy-Malkhalifeh
M.
The Examinig Mathematical Word Problems Solving Ability under Efficient Representation Aspect
. Math Educ Trends Res.
2013
;2013
:1
–11
.4.
Akyuz
& Stephan
. National Council of Teachers of Mathematics A Proposed Instructional Theory for Integer Addition and Subtraction A Proposed Instructional Theory for Integer Addition and Subtraction.
2012
;43
(4
):428
–64
.5.
Crespo
SM
, Kyriakides
AO
. To Draw or Not to Draw : Exploring Children’s Drawings for Solving Mathematics Problems.
2007
;14
(2
):118
–25
.6.
Elia
I
, Gagatsis
A
, Panaoura
A
, Zoulinaki
F.
Geometric and algebraic approaches in the concept of “ limit ” and the impact of the “ didactic contract
.” 2009
;(July 2007):765
–90
.7.
Mcgee
EO
. Robust and Fragile Mathematical Identities : A Framework for Exploring Racialized Experiences and High Achievement Among Black College Students.
2016
;46
(5
):599
–625
.8.
Duval
R.
A cognitive analysis of problems of comprehension in a learning of mathematics.
2006
;103
–31
.9.
Montenegro
P
, Costa
C
, Lopes
B.
Transformations in the Visual Representation of a Figural Pattern Transformations in the Visual Representation of a Figural Pattern
. Math Think Learn [Internet].
2018
;20
(2
):91
–107
. Available from: 10.
Adu-gyamfi
& Bosse
. Processes and reasoning in representations of linear functions.
2013
;(March).11.
Afriyani
D
, Sa’Dijah
C
, Subanji
S
, Muksar
M.
Students’ construction error in translation among mathematical representations
. J Phys Conf Ser.
2019
;1157
(3
):0
–6
.12.
Leikin
R
, Leikin
M
, Waisman
I
, Shaul
S.
Effect of the Presence of External Representations on Accuracy and Reaction Time in Solving Mathematical Double-Choice Problems By Students of Different Levels of Instruction
. Int J Sci Math Educ.
2013
;11
(5
):1049
–66
.13.
Fujita
T
, Kondo
Y
, Kumakura
H
, Kunimune
S.
Students ’ geometric thinking with cube representations : Assessment framework and empirical evidence
. J Math Behav [Internet].
2017
;46
:96
–111
. Available from: 14.
Sa’dijah
C
, Afriyani
D
, Subanji
S
, Muksar
M.
Characteristics of Students’ Mathematical Understanding in Solving Multiple Representation Task based on Solo Taxonomy
. Int Electron J Math Educ.
2018
;13
(3
):281
–7
.15.
Lowrie
T
, Logan
T
, Hegarty
M.
The Influence of Spatial Visualization Training on Students’ Spatial Reasoning and Mathematics Performance
. J Cogn Dev [Internet].
2019
;20
(5
):729
–51
. Available from: 16.
Ferdianto
F
, Hartinah
S.
Analysis of the Difficulty of Students on Visualization Ability Mathematics Based on Learning Obstacles.
2020
;429
(Icasseth 2019):227
–31
.17.
Miyazawa
Atsushi
, Nakayama M
and
, Keio Fujishiro
Issei
. An Immersive Virtual Environment for Visualization of Complex and/or Infinitely Distant Territory. In: Goos Gerhard
HJ
, editor. Transactions on Computational Science XXXVI Special Issue on Cyberworlds and Cybersecurity [Internet]
. Germany: Springer
; 2020
. p. 64
–78
. Available from: https://www.springer.com/series/818318.
Hawes
Z
, Moss
J
, Caswell
B
, Seo
J
, Ansari
D.
Relations between numerical, spatial, and executive function skills and mathematics achievement: A latent-variable approach
. Cogn Psychol [Internet].
2019
;109
(December 2018
):68
–90
. Available from: 19.
Isa
Irawan
M, Mukhlash
I
, Adzkiya
D
, Darmadi
, Sanusi
. Development of trigonometric visualization concepts to increase the study motivations of SMK students
. J Phys Conf Ser.
2019
;1218
(1
).20.
Perumal
L
, Tso
CP
, Leng
LT
. Analysis of thin plates with holes by using exact geometrical representation within XFEM
. J Adv Res [Internet].
2016
;7
(3
):445
–52
. Available from: 21.
Handayani
UF
, Sa’Dijah
C
, Sisworo, Sa’Diyah
M
, Anwar
L.
Mathematical creative thinking skill of middle- ability students in solving contextual problems
. AIP Conf Proc.
2020
;2215
(April).22.
Duval
A.
The representation selection problem: Why we should favor the geometric-module framework of spatial reorientation over the view-matching framework
. Cognition [Internet].
2019
;192
(March 2018
):103985
. Available from: 23.
Sirajuddin
; Cholis
Sa’dijah
; I Nengah
Parta
; Sukoriyanto
. Multi-representation raised by prospective teachers in expressing algebra
. J Educ Gift Young Sci.
2020
;8
(2
):857
–70
.24.
Britt
MS
, Irwin
KC
. Algebraic thinking with and without algebraic representation: A three-year longitudinal study
. ZDM - Int J Math Educ.
2008
;40
(1
):39
–53
.25.
Blanton
M
, Stephens
A
, Knuth
E
, Gardiner
AM
, Isler
I
, Kim
J
, et al. The Development of Children ’ s Algebraic Thinking : The Impact of a Comprehensive Early Algebra Intervention in Third Grade.
2015
;46
(1
):39
–87
.26.
Jupri
A
, Drijvers
P
, van den Heuvel-Panhuizen
M.
Difficulties in initial algebra learning in Indonesia
. Math Educ Res J.
2014
;26
(4
):683
–710
.27.
Bulut
N
, Bulut
M.
Development of Pre-Service Elementary Mathematics Teachers’ Geometric Thinking Levels Through an Undergraduate Geometry Course
. Procedia - Soc Behav Sci [Internet].
2012
;46
(1986
):760
–3
. Available from: 28.
Suwito
A
, Yuwono
I
, Parta
IN
, Irawati
S
, Oktavianingtyas
E.
Solving Geometric Problems by Using Algebraic Representation for Junior High School Level 3 in Van Hiele at Geometric Thinking Level.
2016
;9
(10
):27
–33
.29.
Pauwels
P
, Krijnen
T
, Terkaj
W
, Beetz
J.
Enhancing the ifcOWL ontology with an alternative representation for geometric data
. Autom Constr [Internet].
2017
;80
:77
–94
. Available from: 30.
31.
Creswell
JW
. Educational research: Planning, conducting, and evaluating quantitative and qualitative research
. Vol. 4
, Educational Research.
2012
. 673
p.32.
Fraenkel
, Jack R
; Wallen
, Norman E
; Hyun
HH
. How to Design Research in Education and Evaluate Research in Education (8th ed) [Internet]
. 8th ed. Kiefer
S
, editor. New York
: McGraw-Hill Education
; 2011
. Available from: http://93.174.95.29/main/08038F0AEC758396BA27A57C51A6A6D533.
Subanji
S.
Teori Berpikir Pseudo Penalaran Kovariasional [Internet].
2016
. Available from: https://www.researchgate.net/publication/309287861%0ATeori34.
Huang
R
, Kulm
G.
Prospective middle grade mathematics teachers’ knowledge of algebra for teaching
. J Math Behav.
2012
;31
(4
):417
–30
.35.
Polya.
How to Solve it: A New Aspect of Mathematical Method
. Expanded P. John H.
Conway
, editor. America
; 2004
.36.
Thom
JS
, Mcgarvey
LM
. The act and artifact of drawing ( s ): observing geometric thinking with, in, and through children ’ s drawings
. ZDM.
2015
;47
(3
):465
–81
.37.
Mamolo
A
, Ruttenberg-Rozen
R
, Whiteley
W.
Developing a network of and for geometric reasoning
. ZDM Math Educ.
2015
;38.
Yang
KL
, Li
JL
. A Framework for Assessing Reading Comprehension of Geometric Construction Texts
. Int J Sci Math Educ.
2018
;16
(1
):109
–24
.39.
Dogan-dunlap
H.
Linear algebra students ’ modes of reasoning : Geometric representations
. Linear Algebra Appl [Internet].
2010
;432
(8
):2141
–59
. Available from: 40.
Sandoval
I
, Possani
E.
An analysis of different representations for vectors and planes in R 3 Learning challenges
. Educ Stud Math [Internet].
2016
;(1
):109
–27
. Available from: 41.
Alghtani
OA
, Abdulhamied
NA
. The effectiveness of geometric representative approach in developing algebraic thinking of fourth grade students
. Procedia - Soc Behav Sci [Internet].
2010
;8
(5
):256
–63
. Available from: 42.
Mamolo
A
, Ruttenberg
R.
Developing a network of and for geometric reasoning.
2014
;43.
Long
Z
, Meng
H
, Li
T
, Li
S.
Compact geometric representation of qualitative directional knowledge
. Knowledge-Based Syst [Internet].
2020
;195
:105616
. Available from: 44.
Karakok
G.
Making connections among representations of eigenvector: what sort of a beast is it?
ZDM - Math Educ [Internet].
2019
;(0123456789
). Available from: 45.
Beckmann
S
, Izsak
A.
Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities
. J Res Math Educ.
2015
;46
(1
):17
–38
.46.
Lepak
JR
, Wernet
JLW
, Ayieko
RA
. Capturing and characterizing students ’ strategic algebraic reasoning through cognitively demanding tasks with focus on representations
. J Math Behav [Internet].
2018
;(October 2017):0
–1
. Available from: 47.
Rahayuningsih
S
, Nusantara
T
, As
A
, Susanto
H.
Cognitive Styles: Characterization of College Students’ Creative Mathematical Thinking
. Int J Humanit Soc Sci Educ.
2019
;6
(3
):50
–60
.48.
Karakok
G
, Stephenie
HS
, Dyben
A.
Secondary teachers ’ conception of various forms of complex numbers.
2014
;
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