Dewi Risalah
1Introduction
Spatial reasoning is the processing of non-verbal information in the form of images or symbols [16] to solve problems. According to [9]
it is stated that spatial thinking or reasoning, physically and mentally involves us, the location and movement of objects. Spatial reasoning is very important in informing cognitive abilities to investigate and solve problems, especially problems in mathematics.
In solving a problem, someone will do a mental process by using all the perceptual knowledge that is owned and determine the right strategy to solve the problem. There is an organizational theory of perception about understanding in solving problems, namely the Gestalt Theory. [15] stated that in making a model of perceptual models, people need a continuity of good spatial reasoning from Gestalt Theory. Previous writers have argued that Gestalt principles provide a useful guiding framework for categorizing multi-sensory displays [1] Gestalt is one of the schools of psychology that studies a phenomenon as a whole or totality, wherein it contains four laws namely proximity law, closeness law, equality law, and continuity law.
These four laws will support spatial reasoning.
Spatial reasoning is very important in informing our ability to investigate and solve problems, especially problems in mathematics. [8], states that spatial reasoning is not only important in mathematics but also in all fields of study. In the Ontario curriculum it combines spatial and mathematics sense into one unit because both are related to each other. In line with the curriculum, [10] states the importance of spatial reasoning skills in STEAM, mathematics, measurement, and problem solving both inside and outside of school.
Mathematics is one of the materials in mathematics that has been taught to students in junior high schools. Mathematics is the study of shapes and images. Without spatial ability, students cannot fully appreciate
1 IKIP PGRI Pontiaanak
nature [4] In mathematics students are required to be able to imagine, manipulate, and compare objects in solving problems. For example, if students are asked to find the broad shaded comparisons of a mathematics, then what students can do is imagine and manipulate the shape of the mathematics is one way to solve it.
In the process of solving a problem someone will do a mental process by using all the knowledge that is owned and determine the right strategy to solve the problem. [11] reveals two kinds of problems, namely (a) problems to find, can be theoretical or practical, abstract, or concrete including riddle, and (b) problems to prove, to show that a statement is true or false (not both). In mathematics, problems are usually in the form of mathematical problems, but not all math problems are problems. [5]
explained that a question is called a problem depending on the knowledge someone has therefore, a question is a problem for person, but it might not be a problem for others.
The approach in research is qualitative used to describe student reasoning based on the Gestalt law in solving mathematics problems.
The subjects in this research were students who had studied mathematics lessons. Subjects were taken from several of these students based on students' spatial reasoning abilities.
The researcher initially gave the subject mathematics problem solving task to the subject to find out the spatial reasoning of students. From the results of the answers given by this subject, the researcher will see whether there are students who use spatial reasoning, namely imagining, manipulating, or comparing objects. All the components of spatial reasoning will be associated using Gestalt law. The data obtained from this research are the results of tests and the results of interviews between researchers and interview subjects. Every data obtained are analyzed during and after data collection.
After the instrument was validated by an expert validator, the researcher corrected the instrument in accordance to the feedback given by the validator who was then consulted again with the supervisor. Then the instrument was used by researchers to collect data from predetermined research subjects. In the instrument, students were asked to determine the comparison of the area shaded with the whole geometry.This instrument is given to students to find out the possibility of a reasoning flow that is different from the research subject.
Based on the above background, the formulation of the problem in this research is "How is spatial reasoning based on Gestalt law to solve
mathematic problems?". By knowing this spatial reasoning, it is expected to be able to give ideas for teacher in improving mathematic lesson by paying attention to students’ spatial reasoning so it will be more directed.
Discussion
Based on the results of data exposure above, students who have spatial reasoning are students who are able to imagine, manipulate and compare an object. This is in line with [13] stating that spatial reasoning includes mental rotation (imagine) and mental transformation (manipulate) where in the mental manipulate there is the ability to reason by comparing. [12]
also stated that spatial reasoning includes mental rotation (imagine) and mental translation (manipulate). Related to the components that exist in spatial reasoning, there are 4 Gestalt laws that support this, namely proximity law, closeness law, similarity law and continuity law.
From the results and process of the analysis above, there are several indications of word/sentence indications on spatial reasoning which indicate Gestalt laws. In the component of spatial reasoning, when the subject imagines an object, there are several indications of words/sentences such as imagining any mathematics shapes, whole mathematics, rotate, parallel, mathematics, in the same direction, opposite, get, part. This is in line with [7] stating that imagining objects is the process of transforming all objects in the mind. Then when the subject manipulates an object, there are several indications of words/sentences such as seeing the shaded part, moved, united, form, parallel, shaded, unshaded, position, forming geometrical shapes, rotation, winding, ignoring, there is a center point, rotated , there are parts, opposite, parts, get, size and shape, length of side.
This is in line with [7] stating that object manipulation happens when only parts of the object are transformed. Furthermore, when the subject compares an object, there are several indications of words/sentences like I do a comparison, mathematics, the length of the side of , is congruent. This is in line with [6] stating that comparing objects can occur when we have two or more things at the same time that are good for the purpose of having a better understanding of the relationship between them or for the purpose of having a better choice.
Regarding the indication of words/sentences that exist in spatial reasoning, there is a Gestalt law that supports this. In words/sentences such as seeing shaded parts, there are shapes, shaded, position, moved, there are parts, parallel, size and shape, united, unshaded, side length, parts, are indications of proximity law. This is in line with [14,3] stating that things that are close together in time or place tend to be regarded as a totality. In
words/sentences such as imagining any mathematics, whole mathematics figure, contained in it, rotated, in the same direction, opposite, seeing any mathematics shapes, forming a mathematics, position, apit, there is a center point, based on the image, an indication of closeness law. This is in line with [14,3] stating that things that tend to close will form an impression of its own totality. In words/sentences such as mathematics, move, put together, there are shapes, flaps, comparisons, lengths of sides , congruent, the same size and shape, based on the image, are indicators of similarity law. This is in line with [14,3] stating that with regard to things that are similar to each other, people tend to perceive as a group or a totality. Furthermore, in words/sentences such as rotation, ignoring form, I make comparisons , it is already done, the results of the comparison obtained is, are some indication of continuity law. This is in line with [14,3] stating that people will tend to assume a pattern of continuity on existing objects.
Based on the description above, on the subject's spatial reasoning when imagining, there are four Gestalt laws, namely, proximit law, closeness law, similarity law, and continuity law. Then, the subject's spatial reasoning when manipulating is divided into four categories based on Gestalt laws namely proximity, closeness, similarity and continuity.
Furthermore, the subject's spatial reasoning when is related to two gestalt laws, namely similarity and continuity. However, from several laws that exist when the subject does spatial reasoning when imagining, there is one Gestalt law that dominates it, namely closeness law. This is because, when the subject is asked to explain how to understand and solve the problem, the subject sees more things that tend to close like when the subject says the whole word/sentence, looks at any shapes formed. This is in line with [7] stating that imagining objects is the process of transforming all objects in the mind. Then, when the subject does spatial reasoning when manipulating, there is one Gestalt law that dominates it, proximity law.
This is because when a subject is asked to explain how to understand and solve a problem, the subject sees more things that are close together in a time or place that tends to be considered a totality such as when the subject says a word/sentence there is a part, of any mathematics. This is in line with [7] stating that object manipulation happens when only parts of the object are transformed. Whereas from several laws that exist when the subject does spatial reasoning when comparing, there is one Gestalt law that dominates it, namely similarity law. This is because, when a subject is asked to explain how to understand and solve a problem, the subject sees more things that tend to be identical to something similar to each other
like when the subject says words/sentences congruent to those geometries.
This is in line with [6] stating that comparing objects can occur where we have two or more things at the same time that are good for the purpose of having a better understanding of the relationship between them or for the purpose of having a better choice.
From the discussion above, there are findings that the researcher got, namely when the subject uses spatial reasoning by imagining, there will be an indication of closeness law that arises when subject does spatial reasoning. This occurs because most of the subject's thoughts refer to things which tends to close by seeing the whole object as its own totality. Then, when the subject uses spatial reasoning by manipulating, there will be an indication of proximity law that arises when the subject is doing spatial reasoning. This occurs because most of the subject's thoughts refer to things that are close together by seeing parts of the object as separate totality . Whereas, when the subject uses spatial reasoning by comparing, there will be indication of similarity law that arises when the subject performs spatial reasoning. This occurs because the subject tends to perceive an object with identical things similar to each other as a separate totality. We can see other findings on Figure 15 and Figure 16 [17] .
1.
Figure 15. The flow of spatial reasoning on subject with closeness law From Figure 15, it is explained that the subject reasoning process begins when the subject is able to change the overall orientation of the form in his mind (imagining), then the subject is able to do so by moving each part of the object to create a new form (manipulating). From the new form, the subject is then able to solve the problem given by comparing parts of the shape with the overall shape (comparing). From the process, subjects tend to see objects as a whole that close together as something intact because there is no part that is ignored in solving problems.
2.
Figure 16. The flow of spatial reasoning on subject with proximity law From Figure 16, From Figure 16, it is explained that the subject reasoning process begins when the subject is able to change the orientation of the form that looks the same and close together by moving each part of the object to create a new shape (manipulate). From the new form, the subject is then able to solve the problem given by comparing parts of the
closeness law
Proximity law
closeness law
Proximity law
shape with the overall shape (comparing). From the process, the subject tend to see parts that are close together as something intact because there are parts that are ignored in solving problems.
Conclusion
Based on the findings and results of the discussion described previously, the research summarizes the following points:
When the subject solves the problem through the process of imagining, manipulating, then comparing, there is a law for the subject to use the closeness law when solving problems, because the subject tends to see the entire object that closes together as something intact.
When the subject solves the problem through the process of manipulating then comparing, there is a law for the subject to use proximity law when solving problems because the subject tends to see parts of objects that are close together as something intact.
References
[1] Chang, D. & Nesbitt, K. 2005. Developing Gestalt-Based Design Guidelines For Multy-Sensory Display. The Proceeding Of NICTA- Hcsnet Multimodal User Interaction Workshop, The ACS Conference In Research And Practice In Information Tecnology CIRPIT, 57: 9-16.
[2] Creswell, W. J. 2014. Research Design: Qualitative, Quantitative And Mixed Methods Approaches, California: Saga Publication.
[3] Faizi., Mohsen, Shahbazi., Mahtiam, Heidari., & Ali, Akbar. 2013.
The Effect of Gestalt Conceptual Theory on City Planning. International Journal of Advanced Research, Vol.1, Issue 7, 675-685. ISSN NO 2320-5407.
[4] Guven, B; Kosa, T. (2008). The Effect of Dynamic Mathematics Software on Student Mathematics Teachers Spatial Visualization Skill. The Turkish Online Journal of Education Technology. ISSN:
1303-6521 articel 11, 7 (4).
[5] Hudojo, Herman. (2003). Pengembangan Kurikulum dan pembelajaran matematika (Curriculum development and mathematics learning). Malang: State University of Malang.
[6] Lawal, B.O. 2004. Comparative Education. Osogbo, Swift Publishers Nig Ltd.
[7] Marunic, G. & Glazar, V. 2014. Improvement And Assessment Of Spatial Ability In Engineerin Education. Engeneering Review, Vol.
34, Issue 2, 139-150.
[8] National Council of Teacher of Mathematics. (2006). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics (A Quest for Coherence, Reston VA: Autor ed.).
[9] National Research Council. (2006). Paying Attention to Spasial Reasoning (Support document for Paying Attention to Mathematics Education). (K.-1. N. Press., Ed.) Washington, DC.
[10] Ontario Ministry of Education. (2007). The Ontario Curriculum:
Grade 11 dan 12. (ON: Queen's Printer for Ontario ed.).
Toronto:http://www.edu.gov.on.ca/eng/curriculum/secondary/
math 112 currb.pdf.
[11] Polya. (2004). How to Solve It: A New Aspect of Mathematical Method. Princenton, New Jersay: Princenton University Press.
[12] Schultheis. & Carlson. 2013. Spatial Reasoning : The Oxford Handbook of Cognitive Psychology. (E. B. Reisberg, Ed.)
[13] Uttal, D. H., Meadow, N. G., Tripton, E. H., Alden, A. W., &
Newcombe, N. 2013. The Malleability of Spatial Skill: A Meta-Analisis of Training Studies. Psichological bulletin, 139 (2), 352-402. Doi: 10.1037/ A0028446.
[14] Wertheimer. 1923. Psikologi Gestalt (Gestalt Psychology). http://
Psikologi.or.id. Di Akses Tanggal 10 Januari 2017.
[15] [Wuersch, M. & Egenhofer, M. J. 2003. Perceptual Sketch Interpretation. Electronic Theses and Dissertations. Paper 576.
[16] [16] Zuraidah. 2015. Reproduksi Visual Spasial Siswa SMK dalam Mengkonstruksi Kubus (Visual Spatial Reproduction of Vocational Students in Constructing Cubes). Dissertation. State University of Malang.
[17] Risalah, Dewi; Nusantar, Toto; Sutawidjaja, Akbar; Susiswo. 2019.
Spatial Reasoning Based on the Tendency of Gestalt Law to Solve Geometry Problems. Universal Journal of Educational Research, Vol.7 / No.12, November 2019, e-ISSN: 2332-3213.