Discriminant Analysis of Students' Spatial Ability in Understanding Flat-Sided Geometric Shapes

Muh. Khaedir Lutfi, Tatang Herman, Endang Cahya Mulyaning A

Abstract


Spatial ability is a crucial aspect that supports students in visualizing and understanding abstract mathematical concepts, particularly flat-sided geometric shapes in geometry learning. This study aims to identify the factors that differentiate students with low and high spatial abilities through discriminant analysis. The factors analyzed include Mental Rotation, Spatial Orientation, Visualization, Spatial Relation, and Spatial Perception, measured using a spatial ability test. The test instrument consisted of five questions developed based on the spatial ability framework offered by Maier and validated by mathematics and learning evaluation experts. A total of 34 ninth-grade students from a junior high school in Tangerang Regency were selected through purposive sampling. The analysis results showed that Visualization, Spatial Relation, and Spatial Perception were the main predictors that significantly differentiated the two groups. Visualization supports the ability to imagine geometric objects, Spatial Relation facilitates the understanding of relationships between objects, and Spatial Perception aids in recognizing the position and relationship of geometric elements. The resulting discriminant model had an eigenvalue of 13.967, indicating a strong discriminant power in separating student groups. Understanding these differentiating factors provides a foundation for designing effective learning strategies, such as the use of augmented reality (AR) applications and 3D modeling tools to enhance students’ comprehension of spatial figures. Furthermore, interventions using physical or virtual manipulatives can be tailored to students’ needs, assisting them in mastering the concept of flat-sided geometric shapes.


Keywords


Discriminant Analysis, Mental Rotation; Spatial Orientation; Spatial Perception; Spatial Relation;

Full Text:

PDF
rticle

References


Andriani, A., Dewi, I., & Manurung, N. (2022). Analysis of student’s mathematical spatial abilities in solving geometric problems. Proceedings of the 4th International Conference on Innovation in Education, Science and Culture, ICIESC 2022, 11 October 2022, Medan, Indonesia. https://doi.org/10.4108/eai.11-10-2022.2325388

Anwar, & Juandi, D. (2020). Studies of level visual thinking in geometry. 1470(1), 12095. https://doi.org/10.1088/1742-6596/1470/1/012095

Battista, M. T., Frazee, L. M., & Winer, M. L. (2018). Analyzing the Relation Between Spatial and Geometric Reasoning for Elementary and Middle School Students (pp. 195–228). https://doi.org/10.1007/978-3-319-98767-5_10

Benelli, G., Caporali, M., Rizzo, A., & Rubegni, E. (2001). Design concepts for learning spatial relationships. 22–30. https://doi.org/10.1145/501516.501522

Budiarto, M. T., Khabibah, S., & Firdaus, A. M. (2020). Misconception Of Junior High School Students On Two-Dimentional Figure Materials. Journal of Database Management, 8(1), 1–8. https://doi.org/10.26858/JDS.V8I1.13316

Chen, Y. C., Yang, F. Y., & Chang, C.-C. (2020). Conceptualizing spatial abilities and their relation to science learning from a cognitive perspective. Journal of Baltic Science Education, 19(1), 50–63. https://doi.org/10.33225/JBSE/20.19.50

Cui, X., & Guo, K. (2022). Supporting mathematics learning: a review of spatial abilities from research to practice. Current Opinion in Behavioral Sciences, 46, 101176. https://doi.org/10.1016/j.cobeha.2022.101176

Dick, A. O. (1976). 7 – Spatial Abilities (pp. 225–268). https://doi.org/10.1016/B978-0-12-746302-5.50014-1

Fiantika, F. R., Maknun, C. L., Budayasa, I. K., & Lukito, A. (2018). Analysis of students’ spatial thinking in geometry: 3D object into 2D representation. Journal of Physics: Conference Series, 1013(1). https://doi.org/10.1088/1742-6596/1013/1/012140

Girma, D. D. (2015). Students’ Learning Experiences When Using a Dynamic Geometry Software.

Gómez-Tone, H. C., Martín-Gutiérrez, J., Bustamante-Escapa, J., & Bustamante-Escapa, P. (2021). Spatial Skills and Perceptions of Space: Representing 2D Drawings as 3D Drawings inside Immersive Virtual Reality. Applied Sciences, 11(4), 1475. https://doi.org/10.3390/APP11041475

Handayani, R. (2023). Analisis kemampuan spasial visualization siswa sekolah dasar dalam pemecahan masalah geometri. Didaktik: Jurnal Ilmiah PGSD STKIP Subang, 9(1), 717–725. https://doi.org/10.36989/didaktik.v9i1.663

Hazen, N. (1983). Spatial Orientation: A Comparative Approach (pp. 3–37). https://doi.org/10.1007/978-1-4615-9325-6_1

Hidayat, S., Yanti, Y., & Imswatama, A. (2022). Analisis Kesulitan Siswa Dalam Memecahkan Masalah Dan Kemampuan Pemahaman Konsep Bangun Ruang Sisi Datar Pada Pembelajaran Jarak Jauh. Jurnal PEKA (Pendidikan Matematika), 6(1), 20–28. https://doi.org/10.37150/jp.v6i1.1683

Hodgkiss, A. (2019). The role of spatial cognition in children’s science learning.

Judd, N., & Klingberg, T. (2021). Training spatial cognition enhances mathematical learning in a randomized study of 17,000 children. Nature Human Behaviour, 5(11), 1548–1554. https://doi.org/10.1038/S41562-021-01118-4

Juliana, A., Nurjanah, & Usdiyana, D. (2022). The learning obstacles in solving geometry problems based on spatial ability in term of Van Hiele level. Nucleation and Atmospheric Aerosols. https://doi.org/10.1063/5.0117208

Kim, J. H. (2019). Multicollinearity and misleading statistical results. Korean Journal of Anesthesiology, 72(6), 558–569. https://doi.org/10.4097/KJA.19087

Koustriava, E., & Papadopoulos, K. (2010). Mental Rotation Ability of Individuals with Visual Impairments. Journal of Visual Impairment & Blindness, 104(9), 570–575. https://doi.org/10.1177/0145482X1010400910

Kurnia, A. N., & Hidayati, N. (2022). Analisis kemampuan berpikir geometri berdasarkan tahap berpikir van hiele pada pembelajaran matematika siswa smp. EduMatSains : Jurnal Pendidikan, Matematika Dan Sains, 6(2), 419–430. https://doi.org/10.33541/edumatsains.v6i2.3618

Kusnadi, D., & Barumbun, M. (2023). Analisis kemampuan spasial siswa melalui teori belajar van hiele pada pembelajaran matematika di sekolah dasar. Jurnal Mathematic Paedagogic, 7(2), 146–157. https://doi.org/10.36294/jmp.v7i2.3100

Liu, Q.-T., Ma, J., Yu, S., & Wu, L. (2022). Geometry Wall: An Embodied Gesture-based Game for Supporting Spatial Ability. 258–263. https://doi.org/10.1109/TALE54877.2022.00050

Lutfi, M. K., Cahya Mulyaning, E., & Annisa Kusumastuti, F. (2024). Analysis of Students’ Geometrical Thinking from Geometry Task Related to HOTS from PISA. KnE Social Sciences, 2024, 943–952. https://doi.org/10.18502/kss.v9i13.16020

Lutfi, M. K., & Jupri, A. (2020). Analysis of junior high school students’ spatial ability based on Van Hiele’s level of geometrical thinking for the topic of triangle similarity. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032026

Lutfi, M. K., & Kusumastuti, F. A. (2024). Integrasi Augmented Reality berbantuan Geogebra sebagai Media Pembelajaran Interaktif dalam Pembelajaran Materi Bangun Ruang. Social, Humanities, and Educational Studies (SHES), 7(3).

Lutfi, M. K., Kusumastuti, F. A., Akib, I., & Rohmawati, A. (2023). Media E-Learning Bangun Ruang Sisi Datar: Kelayakan pada Pembelajaran Daring. Edu Komputika Journal, 9(2), 78–87. https://doi.org/10.15294/edukomputika.v9i2.54743

Ma’rifatin, S., Amin, S. M., & Siswono, T. Y. E. (2019). Students’ mathematical ability and spatial reasoning in solving geometric problem. 1157(4), 42062. https://doi.org/10.1088/1742-6596/1157/4/042062

Maier, P. H. (1991). Spatial Geometry and Spatial Ability - How to Make Solid Geometry Solid. 69–81. http://webdoc.sub.gwdg.de/ebook/e/gdm/1996/maier.pdf

Manovich, L. (2011). What is visualisation. Visual Studies, 26(1), 36–49. https://doi.org/10.1080/1472586X.2011.548488

McCarthy, R. A. (1990). 4 – Spatial Perception (pp. 73–97). https://doi.org/10.1016/B978-0-12-481845-3.50007-2

Muhammad, N., Rehman, D. S., & Naeemullah, D. M. (2022). An Investigation into Spatial Ability in Geometry among Secondary School Students. Sir Syed Journal of Education & Social Research, 5(3), 22–28. https://doi.org/10.36902/sjesr-vol5-iss3-2022(22-28)

Ngirishi, H., & Bansilal, S. (2019). An exploration of high school learners’ understanding of geometric concepts. 77(1), 82–96. https://doi.org/10.33225/PEC/19.77.82

Noor Muhammad, Dr. Sajid Rehman, & Dr. Muhammad Naeemullah. (2022). An Investigation into Spatial Ability in Geometry among Secondary School Students. SJESR, 5(3), 22–28. https://doi.org/10.36902/sjesr-vol5-iss3-2022(22-28)

Novita, R., Putra, M., Rosayanti, E., & Fitriati, F. (2018). Design learning in mathematics education: Engaging early childhood students in geometrical activities to enhance geometry and spatial reasoning. 1088(1), 12016. https://doi.org/10.1088/1742-6596/1088/1/012016

Owens, K., & Clements, M. A. (Ken. (1998). Representations in Spatial Problem Solving in the Classroom. The Journal of Mathematical Behavior, 17(2), 197–218. https://doi.org/10.1016/S0364-0213(99)80059-7

Özçakir, B., & Cakiroglu, E. (2021). Fostering spatial abilities of middle school students through augmented reality: Spatial strategies. Education and Information Technologies, 1–34. https://doi.org/10.1007/S10639-021-10729-3

Palobo, M., & Juniati, D. (2022). The geometric thinking process of students in constructing the concept of area. International Journal of Research - Granthaalayah, 10(5), 75–87. https://doi.org/10.29121/granthaalayah.v10.i5.2022.4613

Prayitno, L. L., Purwanto, Subanji, S., Susiswo, S., & As’ari, A. R. (2020). Exploring Student’s Representation Process in Solving Ill-Structured Problems Geometry. 7(2), 183–202. https://doi.org/10.17275/PER.20.28.7.2

Ramesh, V. M. (2018). Spatial abilities in early childhood. 1–7. https://doi.org/10.1109/FIE.2018.8658655

Riastuti, N., Mardiyana, & Pramudya, I. (2017). Analysis of students geometry skills viewed from spatial intelligence. AIP Conference Proceedings, 1913. https://doi.org/10.1063/1.5016658

Saad, M. N., Muda, Z., Ashaari, N. S., Hamid, H. A., & Hasan, N. H. binti A. (2015). The spatial relation features for describing objects relationships within image. 126–131. https://doi.org/10.1109/ICEEI.2015.7352482

Sabil, H., Simanjuntak, S. M. O. U., Iriani, D., & Junita, R. (2024). Analysis of Students ’ Spatial Ability in Geometry Material. 13(3), 436–448.

Salsabilah, A. S., Nur Afifah, N. P., & Putri Herdiansyah, R. F. (2023). Analisis Kesulitan dalam Menyelesaikan Soal Luas Bangun Datar Gabungan Siswa Kelas IV SD. Journal on Education, 6(1), 2601–2608. https://doi.org/10.31004/joe.v6i1.3290

Sorby, S. A., Duffy, G. A., & Yoon, S. Y. (2022). Math Instrument Development for Examining the Relationship between Spatial and Mathematical Problem-Solving Skills. Education Sciences, 12(11), 828. https://doi.org/10.3390/educsci12110828

Stuchlík, A. (2003). Space and spatial orientation. Chekhoslovatskaia Fiziologiia, 52(1), 22–33.

Sumarni, S., & Prayitno, A. T. (2016). Kemampuan visual-spatial thinking dalam geometri ruang mahasiswa universitas kuningan. 2(2). https://doi.org/10.25134/JES-MAT.V2I2.349

Suprayo, T., Sugiman, S., Pujiastuti, E., Setiyani, S., & Oktoviani, V. (2023). Analisis kesulitan siswa smp dalam menyelesaikan soal bangun ruang sisi datar. Jurnal Lebesgue, 4(1), 352–363. https://doi.org/10.46306/lb.v4i1.203

Tadeo, D., & Yoo, J. (2022). Students’ Recognition of Concepts of Reflection and Refraction in Multiple Representational Formats. Jurnal Pendidikan Fisika, 10(2), 75–92. https://doi.org/10.26618/jpf.v10i2.7639

Yu, M., Cui, J., Wang, L., Gao, X., Cui, Z., & Zhou, X. (2022). Spatial processing rather than logical reasoning was found to be critical for mathematical problem-solving. Learning and Individual Differences, 100, 102230. https://doi.org/10.1016/j.lindif.2022.102230

Zakelj, A., & Klančar, A. (2022). The Role of Visual Representations in Geometry Learning. European Journal of Educational Research, 11(3), 1393–1411. https://doi.org/10.12973/eu-jer.11.3.1393




DOI: https://doi.org/10.20961/ijpte.v9i1.98297

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Muh. Khaedir Lutfi, Tatang Herman, Endang Cahya Mulyaning A

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

miya4d

toto togel

andri dapat freespin saat lagi ngabuburit di mahjong ways 2

rp 6.500.000 dari spin terakhir samsul di mahjong ways

cerita damar ngopi di teras terus meledak di mahjong ways 2

scatter hitam bikin gilang kesenangan di kosan malam itu

rp 19.200.000 cuma dari satu freespin bikin haris kaget

pasca putus cinta firman nemu hoki di mahjong ways

rp 14.000.000 lewat scatter hitam faisal nggak nyangka

pengalaman unik hamid main mahjong ways pakai wifi warung

jefri penasaran coba mahjong ways 2 dan untung besar

cerita tomi dapat scatter pas sedang ngantuk berat

paul dapat rp 1.000.000 dari spin iseng di mahjong ways

rahasia kemenangan anton saat sedang santai di teras rumah

galang beli scatter sekali dan tembus rp 12.400.000

rendi ngabuburit di teras dan dapat keuntungan besar

detik detik kemenangan raka di mahjong ways 2

rp 9.800.000 dari mahjong ways saat main di terminal

dimas nonton bola sambil spin malah dapat freespin 4x di mahjong ways

roni berhasil tebak pola mahjong dan menang banyak

taufik lagi ngopi di warung malah dapat rp 10.600.000 di mahjong ways 2

zaky main mahjong ways di lapak pasar malam dan tembus jutaan

cerita nyata edi dapat freespin 3x di mahjong ways 2 malam hari

raka gak nyangka scatter mahjong muncul saat lagi beresin kamar

scatter hitam di mahjong ways bikin ramzi jadi senang seharian

pas lagi nyantai di angkringan andre malah dapat freespin

spin pertama mahjong ways 2 bikin yusuf bingung dan kaya

dapat rp 8.300.000 di mahjong ways saat rangga bosan di kantor

jam 2 subuh alwi cuma niat ngecek mahjong ways tapi malah cuan

spin mingguan anton di mahjong ways 2 bikin heboh satu warung

cerita yusuf menang mahjong ways 2 saat hujan deras

galih ternyata hoki di mahjong ways saat lagi di kos teman

anggoro ngebet main scatter hitam dan dapat rp 9.900.000

kenangan pertama irwan spin mahjong dapat rp 8.200.000

mahesa main mahjong ways pas ngantuk dan bikin heboh tetangga

cerita rasyid spin di pinggir danau kena freespin mahjong

berkah fajar di freespin pertama mahjong ways 2

rp 11.400.000 saat putra coba polanya sendiri di mahjong

langkah nekat jefri beli scatter mahjong ways 2 sekali dan menang

zidan nggak ngerti cara main mahjong tapi menang juga

pengalaman cuan besar aldi dari spin acak mahjong

momen hoki bima dari spin tak terduga mahjong ways

penjual mie sop di kampung cilacap mendadak beli motor baru berkat strategi mahjong ways koi800

buk rusmi borong barang elektronik dan buka warung baru setelah raih jackpot mahjong ways koi800

terungkap bocoran room mahjong koi800 yang bikin buk rusmi dapat jp puluhan juta dalam semalam

modal 20 ribu berbuah jackpot 72 juta buk rusmi beberkan trik dan pola mahjong koi800

ibu ibu kampung bongkar tips menang mahjong ways di koi800 usai beli motor dan kulkas baru

viral di grup facebook penjual mie sop raih jackpot mahjong koi800 dan buka usaha sambal rumahan

trik main mahjong ways versi buk rusmi jadi bahan perbincangan di tiktok setelah menang jutaan

kisah ibu rusmi dari kampung ke kios sendiri dengan rekomendasi room gacor mahjong koi800

rumus gacor mahjong ways koi800 berhasil bikin buk rusmi cairkan wd 68 juta dalam 2 hari

bocoran mahjong koi800 dari grup whatsapp bikin buk rusmi sukses buka warung baru di garasi

anak surabaya bongkar bocoran pola mahjong ways di gojek800 yang bikin orang tua bangga

trik rahasia anak lajang surabaya raih jackpot mahjong ways hingga ratusan juta di koi800

sukses di usia muda anak surabaya bagikan strategi mahjong ways paling ampuh di gojek800

rekomendasi pola dan rumus mahjong ways dari anak surabaya yang cairkan wd di koi800

pengakuan anak surabaya terkait trik dan bocoran jackpot mahjong ways di gojek800

strategi main mahjong ways yang dipakai anak surabaya di gojek800 bikin netizen terkejut

anak surabaya viral setelah temukan pola menang mahjong ways di koi800 ini buktinya

bocoran langka mahjong ways di gojek800 ditemukan anak surabaya ini penjelasannya

tips main mahjong ways ala anak surabaya berhasil bawa pulang cairan rp86 juta dari koi800

rumus rahasia mahjong ways dari anak surabaya bikin netizen pada ikutan main di gojek800

anak surabaya menjadi sorotan karena raih jackpot mahjong ways dengan trik koi800

strategi cuan anak surabaya main mahjong ways di gojek800 ini kata orang tua nya

pola jitu dari anak surabaya bikin mahjong ways di koi800 auto gacor dan cair

bocoran paling ditunggu anak surabaya raih jackpot di gojek800 pakai pola mahjong ways

tips dan strategi mahjong ways bikin anak surabaya dipuji warganet setelah cair di koi800

anak surabaya ungkap rekomendasi rumus mahjong ways yang bikin kemenangan di gojek800

trik rahasia diungkap anak surabaya setelah mahjong ways meledak di koi800

mahjong ways di gojek800 bikin anak surabaya cairkan wd dan bawa bangga ke orang tua

kisah anak surabaya raih jutaan dari mahjong ways pakai bocoran gojek800

rahasia kemenangan mahjong ways di koi800 versi anak surabaya ini tipsnya untuk pemula

buk rusmi ngaku menang puluhan juta dari mahjong koi800 berkat strategi pagi dan jeda spins

penjual mie sop pensiun dini setelah raih jackpot mahjong ways koi800 berkat pola ini

pola mahjong ways koi800 jadi viral usai buk rusmi menang jutaan dan borong alat masak

rekomendasi slot mahjong ways dari buk rusmi bikin warga kampung ikut berburu jackpot koi800

strategi main mahjong ways saat subuh bikin buk rusmi cairkan wd ratusan juta di koi800

kisah buk rusmi beli motor honda vario setelah raih jp di koi800 berkat tips mahjong gacor

warga miskin jadi punya tabungan usai rajin main mahjong ways dengan trik khusus di koi800

ibu rusmi dari kampung sentolo jadi trending karena menang mahjong ways koi800 lewat bocoran teman

setelah pakai rumus tembak ganda di mahjong ways buk rusmi raih jackpot dan beli lahan kosong

pengakuan buk rusmi soal pola auto spin dan jeda 10 detik di mahjong koi800 berbuah cairan jutaan

SLOT DANA

SLOT DANA

KASTATOTO

toto slot

situs toto

arista88

slot toto

situs slot gacor

mahjong

magnum188

Dewaslot88

laetoto

spaceman

agen toto play

slot

slot777

bonus new member 100

mahjong slot

Manjur55

spaceman

mdg188

pstoto99

visi4d

slot gacor

slot777

DPRBET

dollar4d

dewaslot88.eu.com

roda4d

mcmbola

hoki99

situs slot

roda4d

toto slot

situs slot gacor

dewahoki

tiga37

PSTOTO99

levis4d

batmantoto

erek erek

slot gacor

qqpulsa

mastogel

batmantoto

Situs Toto

slot gacor

slot88

https://nanostix.co.id/sp2/

lagi4d

https://malcolmhurst.com/

https://xinuosco.com/

https://reportertatu.com/

situs toto

kosmik 4d

bandar togel

situs togel

DUNIATOTO

indo911

situs toto

dewagaruda

coktogel

coktogel

miya4d

Toto Togel

erek erek

levis4d

javtogel

slot

https://micromaterialsresearch.com/

https://tvwesal.com/

toto slot

AMARTOTO

slot

paitogel

ceri123

slot

spaceman slot

Slot777

Situs Slot Gacor

miya4d

slot longhoki

MOM4D

omtogel

toto slot

paitogel

  

International Journal of Pedagogy and Teacher Education

Print ISSN: 2597-7792
Online ISSN: 2549-8525
Website: https://jurnal.uns.ac.id/ijpte/index
Email: ijpte@mail.uns.ac.id
Published by: Faculty of Teacher Training and Education, Universitas Sebelas Maret
Ir. Sutami Street, No. 36A, Surakarta, Jawa Tengah Indonesia

toto togel

slot gacor

tokowin99

titan777

988slot

988bet