Spatial Strategies Used by Students With Visual Impairments to Solve Questions of Spatial Visualization

Abstract

Introduction: This study examines the spatial abilities of middle school students with visual impairments (i.e., blindness and low vision) in the context of spatial visualization. The study also aims to examine the strategies used by such students in solving questions requiring spatial ability. Methods: Participants comprised eight students with visual impairments attending the 8th grade of a school in Ankara, Turkey, which teaches students with visual impairments. The data collection tool is composed of eight questions under the guidance of the definition for spatial visualization. Question types belonging to the spatial visualization subcomponent were organized in four topics: 2D rotation, 3D rotation, paper folding, and cube folding. Results: It was observed that students with visual impairments used mental rotation and key feature strategies for 2D rotation questions. They used the key feature strategy for 3D rotation questions and the mental manipulation strategy for cube folding and paper folding questions. Discussion: In this study, it was identified that strategies used by students with visual impairments show similarities with spatial strategies defined in the literature as used by students without visual impairments. Of all the other types of questions, the most successful question of students with visual impairments is the paper folding question. Implications for practitioners: The results of this article can help teachers become aware of the kind of difficulties that students with visual impairments encounter when they try to solve questions that require spatial ability.

Keywords

spatial ability spatial strategy geometry spatial visualization students with visual impairments

Spatial ability is essential to meeting the fundamental needs in daily life. For example, while driving a car or following instructions for assembling furniture, this ability is in constant use (Rodan, Gimeno, Elosúa, Montoro, & Contreras 2019). Similarly, the ability to move independently in the spatial environment for people with visual impairments depends on the ability to form mental representations of their surroundings (Picard & Pry, 2009).

There are different beliefs about the spatial abilities of individuals with visual impairments (i.e., those who are blind or have low vision) in the literature (Andreou & Mccall, 2010; Cattaneo et al., 2008; Morrongiello, Timney, Humphrey, Anderson, & Skory, 1995; Noordzij, Zuidhoek, & Postma, 2006). One of these views is that the lack of vision experience negatively affects spatial ability. However, research evidence shows that this believe is not true, that blind individuals use different cognitive mechanisms compared to sighted individuals, and that they can perform as well as individuals with no visual impairments in some spatial tasks (Cattaneo et al., 2008; Morrongiello et al., 1995; Noordzij et al., 2006). For instance, in the study by Morrongiello et al. (1995), it was stated that vision experience was not required for spatial knowledge, and it was found that children with congenital blindness showed similar abilities compared to sighted individuals in some spatial tasks. Similarly, in the study of Noordzij et al. (2006), no difference was found between individuals who are blind or sighted in the ability to form spatial mental models.

In this study, the definition of spatial ability provided by McGee (1979), which is considered to have provided a general framework, was taken as the basis. According to McGee (1979), spatial ability is composed of the ability to mentally visualize 2D and 3D structures, to shift their places, rotate them, manipulate them, and reverse them. Given the inconsistency in defining spatial ability, various subcomponents of this ability have been identified. In this study, as a subcomponent of spatial ability, spatial visualization, which is a classification by McGee (1979) that has been employed prominently in a majority of the studies in the literature, was taken as the basis (Ekstrom, French, Harman, & Dermen, 1976; McGee, 1979). Spatial visualization is identified as the skill of forming 2D and 3D visual objects, and mentally opening, closing, rotating, and transforming (turning, bending, and reversing) them (McGee, 1979).

In this study, an answer to the following question is sought:

What are the strategies used by 8^th grade students with visual impairments in solving spatial visualization questions, and how do they use these strategies?

Methods

In phenomenological research, researchers define the meaning of shared experiences of a phenomenon for several individuals (Creswell, 2007). It is thought that phenomenological research is a suitable method in which to understand the spatial abilities of students with visual impairments and the strategies they develop while solving the spatial problems.

Participants

The participants were eight students with visual impairments attending the 8^th grade of a middle school located in the Altındağ District, one of the two middle schools for visually impaired students in Ankara Province. Four of these students had “total visual impairment” (i.e., blindness), while the other four had low vision. Turkey uses the visual impairment classifications of the Ministry of National Education’s Regulation for Schools of Special Education and Rehabilitation Centre, which are aligned with such standards used in Britain. Accordingly, an individual whose visual acuity is 20/200 or less after all possible corrections is considered an individual with total visual impairment (hereafter, blind), while an individual whose visual acuity is from 20/70 to 20/200 after all possible corrections and requiring specialized aids for education is considered as an individual with low vision (MoNE, 2008).

The criteria for student inclusion in the study were as follows:

visual impairment;

no additional impairment or disability other than visual impairment;

8^th grade student;

ability to read and write in Braille; and

volunteered for and demonstrated eagerness and motivation to participate in the study.

Since the aforementioned criteria were designated before the study, as a sampling method, criterion sampling was used.

Based on the degree of their visual impairment, students were coded as B or LV. The Ministry of National Education and Ethical Committee granted permission for this study. Students who participated in this study were given an informed consent form that was signed by their parents. All parents signed the form voluntarily.

The data collection tool and its development

The data collection tool comprised eight questions based on the definition of spatial visualization. Tests used by other researchers were evaluated in accordance with the spatial visualization component of spatial ability and the appropriateness of the objectives in middle school mathematics curriculum. Attention was paid to the selection of different question types that measure spatial visualization. Question types associated with the spatial visualization subcomponent were handled under four topics: 2D rotation (questions 1 and 6), 3D rotation (questions 4 and 8), paper folding (questions 3 and 7), and cube folding (questions 2 and 5). Both 2D rotation questions were taken from the test developed by Olkun and Altun (2003) with the title Test of Spatial Visualization in 2D Geometry. Since they involve the spatial visualization skill of mentally rotating an object given in its visual form, these two questions were considered as involving the spatial visualization subcomponent. Both paper folding questions were taken from the Paper Folding Test developed by Ekstrom et al. (1976) and adapted to Turkish by Delialioğlu (1996). Two questions about 3D rotation were taken from the Middle Grades Mathematics Project (MGMP) test that was adapted to Turkish by Turğut (2007). Two questions associated with cube folding were asked. The first was taken from Guay’s Visualization of Views Test developed by Eliot and Smith (1983). When selecting any question, the possibilities of writing it in Braille and reflecting the Turkish middle school curriculum were considered.

The eight questions were developed in two forms. One of the forms was drawn to be readable by sighted individuals, while the other form was embossed in Braille by the first researcher, to enable the students to read the questions, and the shapes were drawn with a roulette. A roulette is a tool designed to assist individuals with visual impairments in drawing lines. It contains a cylinder at one end to emboss the paper. Afterward, opinions from one professor, two assistant professors, two doctors working in the field of mathematics education, and one research assistant studying the subject were taken on the compatibility of the questions with the spatial visualization subcomponent. After the questions were once again embossed in Braille and the shapes were drawn, an educator working in the field of individuals with visual impairments and special education was asked by the first researcher to review the questionnaire in Braille and the tactile drawings and assess the comprehensibility of its wording and correct any misspellings.

Data collection process

Since the study required one-to-one interviews with the students, it was conducted in the library, as assigned by the school principal. During interviews, a video camera that was able to track the students’ movements was placed in the environment, at a spot where the camera did not capture the students’ faces. The students were informed that they would be recorded on camera, and that no one other than the researchers would be permitted to see the videos.

Before starting the interview questions, the students were told that their detailed description of the structure they formed in their minds would be essential. During the interview, without guiding their answers to the questions, if the students had difficulty in reading the text, the questions was read out by the researchers.

Data analysis

Before analyzing the data, video recordings and notes taken during interviews were organized for each student. Subsequently, interview records were transferred to a computer. Afterward, observation notes taken during interviews were attached to interview transcripts. At data analysis, the phenomenological method was used; it is one of the most frequently encountered types of analysis in this research technique. In this method, after the interview, the researcher analyzes the recorded analysis notes in accordance with the purpose of the research. First, the groups of data that are close to each other are categorized and, if necessary, themes of these categories are identified. After checking these themes with the available data, the final stage is reached. In the last stage, the researcher interprets the perceptions of the participants in their own words and creates a report (Smith and Eatough, 2007). The languages the students use when solving questions involving spatial ability and similarities and differences between their points of emphasis were identified. According to these similarities and differences, by taking strategies designated as spatial strategies in the literature into consideration (Eme & Marquer, 1999; Glück & Fitting, 2003; Kayhan, 2012; Schultz, 1991), spatial strategies used by the students with visual impairments were identified. These strategies were clustered under three topics: mental rotation, mental manipulation, and key feature. Mental rotation is the ability to rotate 2D and 3D objects in a rapid and accurate manner. Mental manipulation includes applying certain steps of a process, such as folding and unfolding, of the given shape. On the other hand, key feature involves identifying and manipulating a significant feature of an object (Kayhan, 2012).

Validity and reliability

The following procedures were implemented to assure validity and reliability (Merriam, 2009; Yıldırım & Şimşek, 2013).

Transferability

In this context, information such as the name of the institution where the study had been implemented, the number of participants, inclusion criteria for the participants, the method of data collection was provided in details and findings of the study were depicted in a detailed fashion, by citing direct quotations.

Credibility

The study was implemented at a school where the first researcher had been active for four years as a teacher. Therefore, since the researcher had a close contact with the students and the students were acquainted with the researcher, active participation of the students and their comfortable adaptation in the process were ensured.

Confirmability

In this context, the focus was on the students’ experiences and opinions, rather than the researcher’s own preferences. In the data analysis procedure, expressions of the students with visual impairments were reflected verbatim.

Consistency

Data of the study, methodology used in the study and progress of the study procedure, and the decisions made were explained in details and also, during the analysis stage, data were presented with comparing to each other.

Findings

2D rotation

The strategies used in association with the 2D rotation question (see Figure 1) and their frequencies are provided in Table 1.

Table 1.

Strategies used in the 2D rotation question.

Strategies	Q1				Q6
	Blind		Low vision		Blind		Low vision
	Wrong	Correct	Wrong	Correct	Wrong	Correct	Wrong	Correct
Key feature Comparing the relative positions	B1 and B3		LV1 and LV3	LV2	B3	B1	LV1 and LV3	LV2
Mental rotationRotating the piece		B2 and B4			B2	B4
Strategy not identified			LV4				LV4
Total	2	2	3	1	2	2	3	1

Note: B = blind; LV = low vision.

As observed in Table 1, the students usually used similar strategies in solving the 2D rotation question. These strategies included comparing the relative positions under the key feature and rotating the piece under the mental rotation. In the strategy of comparing the relative positions, the individual compares the patterns comprising pieces of the objects given and makes use of a key feature of the object. That is, he designates a significant feature of the object for use to solve the problem (Schultz, 1991). In contrast, the strategy of rotating the pieces involves dividing the rotated object into pieces on the basis of its structural characteristics, and afterward, imagining a rotation for each piece or for certain designated pieces (Eme and Marquer, 1999).

Figure 1 provides an example of a question that was asked of the students. An example of the solutions a student used to answer that question is provided in the following response from a student (LV1), who used the strategy of comparing the relative positions of the diagram.

I took this shape and rotated it clockwise. Now, the positions of the squares have changed. The shape isn’t supposed to change. In both options, the place where three squares are placed vertically is on the right. However, I took a look at the place where two squares were one under the other [shows the right side of the actual shape]. The shape shouldn’t change with the rotation. Therefore, it is the second shape.

As demonstrated in LV1's answer, while solving this question, the student indicated that the shape would not change during the rotation process and, designating the square in the middle as a point of reference, changed the places of the squares located vertically on the right and on the left. In his mind, he encoded the shape as three squares on the left, two squares on the right, and one square in the middle and asserted that the process of rotation is supposed to change their places but that the patterns will remain in their original form. He indicated that the two squares on the right side of the shape are supposed to be kept one under the other and should face downward. This pattern comprises two squares placed vertically on the right side of the shape. He also asserted that, based on the prerequisite that these two squares should face downward at the end of the rotation process, the second shape may be obtained after the rotation. One may argue that students using the strategy of comparing relative positions are unable to visualize the rotation process. Indeed, as observed in Table 1, most of the students who used the strategy of comparing the relative positions gave wrong answers to the question. These students encoded the pattern constituted by the pieces in the given shape in their minds and looked for the same encoded pattern in the rotated object, but failed.

In contrast, the students who use the strategy of rotating the piece had visualized moving and rotating the given object as required. When rotating the shapes in their minds, students rotated the given object in an imaginary way; that is, they mentally manipulated the object. While using the strategy of moving the object, they divided the object into pieces that they thought would rotate the object more easily. For the example question presented in Figure 1, they split the object into two squares, one under the other on the right side, one square in the middle, and three squares one under the other on the left side. One of the students (B2) expressed the measure of rotation in degrees and, by comparing the shape to the options in a gradual manner, had reached the correct solution. That student’s path of solution was as follows:

In the shape, there are three squares on the left, one square in the middle, and two squares on the right. If we rotate it 90 degrees, one square is kept in the middle. The shape on the right [points at the two squares placed one under the other] comes under and the shape on the left [points at the three squares placed one under the other] comes to the top. There is no shape inclined like this. If we rotate it 180 degrees, these three squares [points at the three squares on the left of the shape] will come to the right and the two squares [points at the two squares on the right side of the shape] will come to the left. Two squares are facing downwards and it is supposed to face upwards after rotation. Therefore, it is the option A.

Cube folding

The cube-folding question is presented in Figure 2. Strategies used by students in the cube-folding question and their frequencies are provided in Table 2.

Table 2.

Strategies used in the cube-folding question.

Strategy	Q2				Q5
	Blind		Low vision		Blind		Low vision
	Wrong	Correct	Wrong	Correct	Wrong	Correct	Wrong	Correct
Mental manipulation Applying the procedure in all steps	B3	B2, B4	LV1, LV2, and LV3		B2	B3 and B4		LV1, LV2, LV3, and LV4
Mental manipulation Applying the procedure in certain steps	B1		LV4			B1
Total	2	2	4	0	1	3	0	4

Note: B = blind; LV = low vision.

We observed that the students used the mental manipulation strategy when solving these problems. Students who applied this strategy to cube-folding question used various methods, including applying the procedure in all steps and applying the procedure in certain steps. Applying the procedure in all steps refers to implementing all steps of the folding process on each square. Applying the procedure in certain steps refers to implementation of the required process in a certain step (Kayhan, 2012).

The answer to the cube-folding question from a student (B4) who used the strategy of applying the mental manipulation procedure in all steps is given below:

This first shape forms a cube. I rotated this square and took it to this side. [Holding the single square on the top, folds it to the right and forms two faces of the cube.] I folded this upwards. [Brings the single square on the bottom to an angle of 90 degrees.] It closes down when I bring the square on the far right over it.

The student (B4) applied all the steps of the process to obtain the correct answer. At the end, as if he were forming a cube in his hands, he asserted where each face would be. Since the student reached the correct answer by implementing all steps, it may be argued that the student made use of the strategy of applying the procedure in all steps.

On the other hand, a student (B1) who used the strategy of applying the procedure in certain steps, rather than forming the entire cube, applied a number of processes that she deemed necessary and beneficial for obtaining the result:

I will first count how many squares there are. We have six squares in both options. If I close them to their sides, [Closes two squares in option A, one on the far bottom and one on the far top, to form front and back faces of the cube.] I can form a cube in option A. In option B, squares overlap. There is a gap left.

In the second question about cube folding, students were asked to fold given net into a cube and find out which number is on the opposite face. The students were asked to explain the front, back, right, left, top, and bottom of the cube in detail while solving the question in order to clearly understand how they formed the cube. In addition, they were asked to read the numbers on each faces. Students were more successful in question 5 than question 2. The reason for this may be that the second cube-folding question required a more complex mental process. To arrive at the correct answer to this question, it is not enough to form the cube, which face would be opposite of the other face will be found out. Because students with visual impairments cannot combine different elements and combine them with visual stimuli, they may have difficulty in coding and memorizing information (Demir & Şen, 2009). This difficulty can lead to problems in questions that require more mental skills.

Paper folding

Strategies used by students in the paper-folding question and their frequencies are provided in Table 3, and an example of a paper-folding question is provided in Figure 3.

Table 3.

Strategies used in the paper-folding question.

Strategy	Q3				Q7
	Blind		Low vision		Blind		Low vision
	Wrong	Correct	Wrong	Correct	Wrong	Correct	Wrong	Correct
Mental manipulation Applying the procedure in all steps		B1, B2, B3, and B4		LV2 and LV3		B1, B2, B3, and B4		LV2 and LV3
Mental manipulation Visualizing the procedure in its final form			LV4	LV1				LV1 and LV4
Total	0	4	1	3	0	4	0	4

Note: B = blind; LV = low vision.

The strategy of applying the procedure in all steps involves implementing all the processes of folding and unfolding (Kayhan, 2012), whereas the strategy of visualising the procedure in its final form involves the final consequence of implementing processes of folding and unfolding (Glück & Fitting, 2003).

A dialogue including an answer from a student (B2) who used the strategy of applying the procedure in all steps, along with questions from the researcher, follows:

Student B2: “If we think we have a paper in our hands and fold it in two, the puncture will first create a hole on the top left corner. Let’s look at the options. It can’t be A. We have to find the one with a hole on the top left corner. It may be B or it may be C. It can’t be D because there is no hole on the top left. I think it’s the second option.”

Researcher: “Why is it the second option?”

B2: “Now, if I fold it and puncture the paper, (holds the questionnaire and mimics folding the paper in two and puncturing it on the top left corner) the hole stays in the point I punctured (points at the top left corner of the paper). If I unfold it, there should be a two-sided hole. Frankly, I’m stuck between B and C.”

R: “What difference do B and C have?”

B2: “Here, it is formed in a crisscross fashion [points at option B]. And here, they are one under other [points at option C]. At a second glance, it is supposed to stay one under other. When I unfold the paper, the other hole comes below and the two holes are not transverse. Therefore, it is C.”

As demonstrated in the dialogue between B2 and the researcher, students who used the strategy of applying the procedure in all steps first folded the paper either mentally or by gestures with a held questionnaire, and later opened a hole at the point designated in the question; then, by unfolding the paper they showed where the hole was formed.

3D rotation

An example of a 3D-rotation question is presented in Figure 4, and the strategies used by students for the 3D-rotation question and their frequencies are provided in Table 4.

Table 4.

Strategies used in 3D rotation question.

Strategy	Q4				Q8
	Blind		Low vision		Blind		Low vision
	Wrong	Correct	Wrong	Correct	Wrong	Correct	Wrong	Correct
Key feature Comparing the relative positions	B1	B2, B3, and B4	LV2 and LV4	LV1 and LV3	B2	B1, B3, and B4	LV1, LV2, LV3, and LV4
Total	1	3	2	2	1	3	4	0

Note: B = blind; LV = low vision.

The answer from a student (LV1) who used the strategy of comparing relative positions for question 4 follows:

From another side of the building, the three squares here stay where they are [points at the three cubes standing on the forefront and resembling the letter L]. Here, option A has the same cubes. We can place the shape under this one [pointing at the cube in the middle of the shape, tells that it shall come under in option A]. The remaining two cubes correspond to the two cubes in option A [points at the two cubes in option A, which are placed one under another on the far left].

The student, when seeking an answer to this question, mentally encoded the three cubes in the forefront, identified them with the letter “L”, and looked in the options for this encoded structure. The analysis of the students’ answers revealed that all of them ignored the invisible cubes in both questions. Furthermore, all students, rather than thinking about how the structure may look from a different direction, had mentally encoded the structure given in the question and looked in the options for a structure resembling it. That is, they did not apply mental rotation. They identified a prominent characteristic of the shape in the question and looked in the options for this patterned on the assumption that the structure’s view from a different direction is also supposed to keep with the same pattern.

Discussion and conclusions

In this study, we identified that strategies used by students with visual impairments show similarities with spatial strategies defined in the literature as used by sighted students. The strategies used by students with visual impairments were classified under three main topics: mental rotation, mental manipulation, and key feature strategies.

Under the strategy of mental rotation, we observed that the students with visual impairments used the strategy of rotating the piece. Mental rotation strategy is a strategy identified in several earlier studies (Glück & Fitting, 2003; Schultz, 1991). Although this strategy resembles ones identified in the literature, it is noteworthy that, in mental rotation, all students with visual impairments split the shape into pieces rather than taking the shape as a whole. For instance, students who used the mental rotation strategy for the question type requiring 2D rotation had applied the rotation process by dividing the given objects into pieces, rather than imagining them in their entirety.

Of all the other question types, the one answered most accurately by the subjects of this study was the paper-folding question. Some students indicated that they were familiar with this type of question and have participated in similar activities in modeling classes. Modeling classes involve shaping formable materials such as clay, beeswax, and paper on the basis of practice and manual skills (Turani, 1975). The reason for the success of students in this question type may be their experience in such activities performed directly with concrete materials under guidance of a teacher in modeling classes.

Another striking result was that, although the students were aware of structural characteristics of a cube (such as the number of faces, corners, or edges), in questions where they were asked to count the cubes, they actually counted the cubes' faces. This condition may arise from the fact that although they are acquainted with certain concepts and definitions, they may experience difficulties in perceiving the questions given the form drawn in 3D. When teaching the concepts to students with visual impairments, concrete materials may be used, and it may be assumed that the students discover the characteristics of geometric concepts in the first instance on their own. Such concrete materials may include unit cubes or magnetic materials. Clements and Battista (1992) and Klingenberg (2012) argue that students’ spatial abilities can be improved by playing with and drawing 3D and 2D objects.

There are three major limitations of the current study. There are limitations regarding the number of participants in the study group, limitations regarding the question requiring spatial ability, and the limitation regarding providing concrete material to students with visual impairments. This research was conducted with only eight students with visual impairments. Future research may wish to repeat this study with more participants, and also to consider other components of students' spatial abilities. The content of the questions in the present study was limited to spatial visualization that involved 2D and 3D rotation, paper folding, and cube folding. However, there are other components of spatial abilities such as spatial perception, mental rotation, and the like. Researchers could focus on different question types in future studies regarding spatial perception to elicit students’ spatial abilities. In addition, by providing concrete materials, it may be possible to examine whether spatial strategies used by students with visual impairments can be altered in future studies.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

Andreou

Mccall

(2010). Using the voice of the child who is blind as a tool for exploring spatial perception. British Journal of Visual Impairment, 28(2), 113-129.

Cattaneo

Vecchi

Cornoldi

Mammarella

Bonino

Ricciardi

Pietrini

(2008). Imagery and spatial processes in blindness and visual impairment. Neuroscience and Biobehavioral Reviews, 32, 1346-1360.

Clements

D. H.

Battista

M. T.

(1992). Geometry and spatial reasoning. In Gruws

D. A.

(Ed.), Handbook of research on mathematics teaching and learning (p. 420–464). New York: Mac Milan.

Creswell

J. W.

(2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks: Sage.

Delialioğlu

Ö.

(1996). “Contribution of students’ logical thinking ability, mathematical skills and spatial ability on achievement in secondary school physics”, Master’s Thesis, METU, Ankara.

Demir

Şen

Ü.

(2009). “Görme engelli öğrencilerin çeşitli değişkenler açisindan öğrenme stilleri üzerine bir araştirma” [a study of learning styles of visually impaired students in accordance with certain variables]. Uluslararası Sosyal Araştırmalar Dergisi, 2(8), 154-161.

Ekstrom

R. B.

French

J. W.

Harman

H. H.

Dermen

(1976). Kit of factor referenced cognitive tests. Princeton, NJ: Educational Testing Service.

Eliot

Smith

I. M.

(1983). An international directory of spatial tests. Windsor, Berkshire: Nelson.

Eme

P.-E.

Marquer

(1999). Individual strategies in a spatial task and how they relate to aptitudes. European Journal of Psychology of Education, 14(1), 89-108.

10.

Glück

Fitting

(2003). Spatial strategy selection: interesting incremental information. International Journal of Testing, 3(3), 293-308.

11.

Kayhan

E. B.

(2012). Strategies and difficulties in solving spatial visualization problems: A case study with adults. Unpublished Doctoral Dissertation, METU, Ankara. Retrieved from http://etd.lib.metu.edu.tr/upload/12614344/index.pdf.

12.

Klingenberg

O. G.

(2012). Conceptual understanding of shape and space by braille-reading norwegian students in elementary school. Journal of Visual Impairment & Blindness, 106(8), 453-465.

13.

McGee

M. G

(1979). Human spatial abilities: Sources of sex differences. New York: Praeger.

14.

Merriam

S. B.

(2009). Qualitative research: A guide to design and implementation. San Fransisco: Wiley Publications.

15.

Ministry of National Education (MoNE) (2008). Özel eğitim ve rehabilitasyon merkezi görme engelli bireyler destek eğitim programı. Ankara: MEB.

16.

Morrongiello

B. A.

Timney

Humphrey

G. K.

Anderson

Skory

(1995). Spatial knowledge in blind and sighted children. Journal of Experimental Child Psychology, 59, 211-233.

17.

Noordzij

M. L.

Zuidhoek

Postma

(2006). The influence of visual experience on the ability to form spatial mental models based on route and survey descriptions. Cognition, 100, 321-342.

18.

Olkun

Altun

(2003). “İlköğretim öğrencilerinin bilgisayar deneyimleri ile uzamsal düşünme ve geometri başarilari arasindaki ilişki” [the relationship between computer experiences of elementary students and spatial thinking and geometry achievements]. The Turkish Online Journal of Educational Technology, 2(4), 86-91.

19.

Picard

Pry

(2009). Does knowledge of spatial configuration in adults with visual impairments improve with tactile exposure to a small-scale model of their urban environment? Journal of Visual Impairment & Blindness, 103(4), 199-209.

20.

Rodan

Gimeno

Elosúa

M. R.

Montoro

P. R.

Contreras

M. J.

(2019). Boys and girls gain in spatial, but not in mathematical ability after mental rotation training in primary education. Learning and Individual Differences, 70, 1-11.

21.

Schultz

(1991). The contribution of solution strategy to spatial performance. Canadian Journal of Psychology, 45(4), 474-491.

22.

Smith

J. A.

Eatough

(2007). Interpretative phenomenological analysis. Los Angeles: Sage Publications.

23.

Turani

(1975). Sanat terimleri sözlüğü. Ankara: Toplum Yayınları.

24.

Turğut

(2007). “İlköğretim II. kademede öğrencilerin uzamsal yeteneklerinin incelenmesi.” [Investigation of 6, 7 and 8 grade students’ spatial ability] Unpublished, Master Thesis, Dokuz Eylül University, İzmir.

25.

Yıldırım

ve Şimşek

(2013). Sosyal bilimlerde nitel araştırma yöntemleri. (9. Baskı). Ankara: Seçkin Yayıncılık.