SPATIAL VISUALIZATION

The following are definitions of spatial visualization:

According to Lowrie, Logan and Ramful (2016:408) spatial visualization is the ability to “manipulate or transform the image of spatial patterns into visual arrangements”.

Augustynaik, Murphy and Philips (2004) described spatial visualization as a vital skill for understanding and developing crucial mathematical skills and is an opportunity to better problem solving.

Lohman (2000) defined spatial visualization as an adeptness to comprehend imaginary movement or the aptitude to manipulate objects in the mind.

To place spatial visualization into the perspective of visualization, it can be described as mentally manipulating a pictorial stimulant to understand the visual information. Idris (1998) found in his study that spatial visualization is related to mathematics achievement and goes further to state that visualization does not only influence mathematics success but also improves

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the learners overall academic accomplishment on the whole. Rabab‟h and Veloo (2015) stated that the learner‟s low achievement in mathematics is of concern to the teachers. By having high spatial visualization ability motivates them to enhance their academic success.

Given the role played by visual spatial skills in visualization and the development of mathematics, it is significant to build on it early on in the learner‟s academic life as it will support mathematical development in later stages (Meyer et al, 2010). According to Kim and Cameron (2016:11) visual skills is basically overlooked in school settings and given its magnitude in school readiness, the teachers need to focus on developing these skills. A suggestion is made by Diamond and Lee (2001) that visual skill programs should be made part of the school curriculum such that the learners are able to engage in real world tasks.

Ozdemir and Yildiz (2015) examined the pre-service teacher‟s spatial skills through the SOLO model to raise awareness for their own visual skills. The SOLO taxonomy evaluated the pre- service teacher‟s mathematical understanding of concepts and their thinking skills. It consists of five levels, namely, prestructural, unistructural, multistructural, relational and extended abstract levels (Ozdemir et al, 2015:219). In the prestructural level finding the solution is not adequate. There are aspects in the problem which are a distraction. In the unistructral level the focus is on the problem. A part of the information is used and as a consequence the data in the problem cannot be related with previous situations thus resulting in an incoherent answer. In the multistructural level the multiple data is used to arrive at the answer but there are still inconsistencies in the answer. Within the relational level all the data in the problem is utilized to arrive at the solution and the association is seen with other data in the problem. In the extended level when a solution is arrived at, generalizations can be made thus creating new thinking styles (Ozdemir et al, 2015:219). In their study it was discovered that the pre-service teachers were within the multistructural and relational level – working with the problem and making associations with known data.

The Institute of Education Sciences (2012:26) made a strong recommendation that visualization be used in mathematics because it was found in their studies that “students with learning disabilities performed better when taught to use visual representations”. Visual spatial learners have a different brain structure and they learn differently from other learners. They learn visually thus visual representations assist these learners in organizing the data which is then analysed leading to a solution. As a result of these learners learning styles they need more than one representation to solve a problem. Due to its importance in mathematics, representations (included herein is multiple representations) “helps learners by employing their own thinking and learning habits” (Ozdemir and Reis, 2013:86). Multiple representations provide visual

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material for problem solving. It is helpful to these learners in the problem solving process in that it can make their solutions visible (Ozdemir and Reis, 2013:86). Spatial visualization and visual representations assists in organizing the given problem for better understanding thus paving the way for the solution.

Visuospatial skills are a vital foundation for the learners to learn mathematics (Uttal et al, 2013; Mix and Cheng, 2012). Even though visualization demands spatial skills, it can be used to improve spatial skills as visual spatial skills contribute to the development of the learner‟s mental representations as they use strategies to solve problems.

Visualization research has shown that the learner‟s spatial skills and prior knowledge are related to the use of external and internal representation. External visualization can refer to the use of diagrams, graphics and models in learning whilst internal visualization is used to portray mental construction of ideas. In order for the learners to externalize their thoughts prior knowledge is needed. This prior knowledge is a means of association of previously acquired knowledge. This is stored in the brain as visual images thus allowing the learners to create new visual pictures in order to learn. The learners who have dominant visual-spatial intelligence learn best through visualizing entities, events or by studying with images, drawings and colours (Yenilmez and Kakmaci, 2015). According to Dryden and Vos (2012:323) the learners should be encouraged to “visualize precisely”. They must first see the bigger picture and grasp the concepts for learning to occur. In this manner the learners will be able to apply their visuals to the problem and reinforce their learning.

Language is an important component to visual spatial learning. Language originates within an individual thus the learners need to verbalise it in order to acquire certain types of mathematical knowledge. As in English, the learners sound out the letters of the alphabet in phonic form to learn words. These words have to be constructed and translated into making meaning of mathematical concepts. The learners verbalize these words to develop their conceptual knowledge to communicate, example, learning to count using their fingers. Seeing their fingers as representation of numbers, an association is made between a word and the number of fingers seen visually. This type of counting skill will assist the learners to represent the numbers they are counting. Visual spatial learners will by association reproduce this imagery diagrammatically for a better conceptual understanding.

According to Lowrie et al (2016) diagrams are critical to success in mathematics. The learners think critically, decode their information and use the diagrams to represent their thoughts. In their imagining the learners think vividly and they organise ideas from within their world of

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experience. Thus one can state there is a link between spatial thinking and mathematical thinking.

Jitendra, Star, Dupuis and Rodriguez (2013) found in their study on Schema Based Instruction (SBI) that it has links with spatial visualization and problem solving skills. This was a four step strategy, namely, priming the mathematical structure of the problem. According to Jitendra et al (2013) this involved schema training in unravelling the relevant from the irrelevant information; using visual spatial representations; using pictorial and schematic illustrations which are an indication of an individual‟s idea and instructing through problem heuristics. Jitendra et al (2013:115-117) stated that the learners draw their representations or use strategies to represent and analyse the solutions to the problem. The teacher aids in modifying details in a step by step teaching process.