The learning principles usually not visually. The visual understood as an analytical and facilitate an idea. That is the visual is parallel to other representation. The visual ability is not only a tool, or a strategy, or a type of thinking, but also the chain of reasoning to achieve the formal analytic abilities. In this study, the visual ability examined, as a strategy or way of thinking to solve a problem. The question to be addressed is: How do students come to their mathematics identities based on visual imagery? The research conducted at classes of the preservice mathematics education students namely provides evidence for what is their identity relative to their experiences. The results conducted based on explorative studies for the visual abilities. The performance obtained during the teaching and learning, i.e., visualizing and answering analytically or visually, manipulating and answering analytically or visually or by formulas, and visualizing and the answering visually or analytically or based on the conditions. The performance linked to the visual representation and related to intuition underlies formal abilities. The visual perceptions disturbed by prior knowledge, and the level based on optical illusions, so the teaching and learning make a difference between potential and abilities. The analytical affects visual perception and the belief system, so difficult to construct knowledge. However, the level of thinking is different, i.e., not yet formal or new optical illusion. The visual model related to high-level thinking, which distinguished from the analytical thinking model. In the visual model, thinking activities based on the transformations and understood as the other operations in mathematics. The visual model also shows the analytic thinking and hierarchical. The visual and the analytical thinking integrated to develop a richer understanding of mathematical concepts. Through visual thinking, the mental processing was constructed and interpreted as mental objects and processed analytically. The next, exhibits the analytical, consist of the construction process from the visual, namely the reflective abstractions. The visual abilities not related to the duration of courses in the mathematics education department. The longer increases the analytic but in contrary to the visual. Through the learning of the visual abilities, the difficulties in solving the problems decrease, but resistant to the analytic show a specific performance. Visual learning reveals a hierarchical level of the thinking, so the best performance is the highest learning ability. When learning the visual abilities given, the performance increases.
This research is an experiment of categorizing visual abilities by representations of a solving problem through class experiment. The research is to investigate, explore, and enhance geometry thinking in solving mathematics problems presented visually. The tasks are cognitive strategies that rely on the visual representations and the genesis of the abilities with the assumption that the performance requires the manipulation of the visual representations. The model of the research developed from the students’ imagination of a visual problem or situations for accomplishing the solution and called binocular rivalry. The data are of interconnection for promoting visual abilities or senses, as the flexibility of thinking and the likelihood of having representations available in prior knowledge. The data analyzed by categorizing according to the visual abilities and by Control Chart of Attributes. The results are: 80% of the visual abilities are nonconforming index; the variation of visual representations is high in nonconforming index, but the depth struggle by the subjects and 70% select the general geometric figures that recognized. The conclusions are comprehensive, and the visual representations are nonconforming index, and the visual senses enhance in all categories. Keywords: Visual representation; Visual ability; Categorize visual skills; Geometry thinking; Cognitive strategy.
Abstract-The researcher presents data from teaching and learning series by a group of pre-service Mathematics education students from 2012 to 2014. The question addressed is: How do students of geometry come to think visually? The researcher gave students a written test to ascertain their visual levels and acquisition degree of spatial abilities. Some students volunteered to work in small groups, whose task was to determine the nature of the object by asking questions about it. The purpose of the instruction was to investigate information on students' visual thinking and geometry competencies in solving some geometric problems in class. The purpose of the group discussions was to elicit information on the students' visual perception and image formation in describing several geometric figures. Visual representations in the identification of the general view of geometric figures and to be manipulated figures. A common scheme used by students was identified and the identification consisted of describing and imagining simple geometric forms in terms of simpler geometric parts. All students were given a written test to ascertain their categories of spatial abilities. Whilst the visual pattern generally reflects the Geometric Thinking Models, an exploration at each levels compared to the written tests indicated that those levels are not hierarchical. Generally, visual perception correlates with a spatial, but the image formation seems to require a different sort of ability.
This research aims to explain the typical rationale design of mathematics education research for a teacher to become a specialist in teaching mathematics. The structure shows learning environment as a natural way to address the teachers in their primary role and as the approach for effectively improving mathematics teaching -which is a didactical situations-based teaching model, illustrating how the model can be applied in real life by drawing from processes inherent in mathematics in a concrete case, turning out from a genetic view of mathematics, and relates to the consequences for teacher education in demanding special mathematical courses for teachers. That is a method by which the students acquire knowledge and skills more than in the past and acquire themself, delivering subject matter to develop their abilities. The main question formulated: What are the basic but practical teaching methods that can scientifically support the development of students to the expected goals? The teachers get two instruments: providing opportunities and stimulating individual growth. The result is students with an excellent foundation to penetrate mathematically in all matters, and the phenomenon of numerical literacy will be enlightened in terms of skills. In this case, students are no longer tuned to receive knowledge passively but to acquire it actively. For this reason, the characteristic of teaching methods is not instruction and reception but organization and activity.
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