The Exploring of Visual Imagery: In their Relation to the Students’ Mathematical Identity

Abstract

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.

Enhancing Visual Abilities in Solving Mathematics Problems

“…The visualization is built between the enhancing of thinking and the thinking of representations. Reference ( [1], [11]) ensure that a perception of a drawing operations and concepts in mathematics lead to mental imagery.…”

“…The visual representation stayed on mental imagery [4], spatial properties, and considered picture ( [5], [1]). The representation is a quasi-pictorial, but an account of mental imagery [6], a computational model, and a neurological one [7], won the analogpropositional [4] because its notion used ambiguously and incoherently.…”

“…That is mental imagery when the students manipulate a visual in many representations, focused on the performance to achieve a transition from geometry to the next visual representation. So, the students learn more than just mathematical concepts and skills and involved at more than just a cognitive level [1]. Furthermore, [2] stated that "how a person learns a particular set of knowledge and skills and the situation in which a person learns, become a fundamental part S of what learned."…”

Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration

“…PMT2's justification relied heavily on visualizing the problem, which aided him in recalling specific axioms through intrapersonal communication based on his visual images. Rif'at (2018) argues that visualization in mathematical problem-solving is not only a thinking tool but also an interconnected sequence of reasoning that leads to the development of formal analytical abilities. PMT2's justification involved the use of the endorsed narrative "radius perpendicular to a chord bisects it at the midpoint."…”

Students’ empirical thinking in solving mathematics problems

“…This research is about the students' thinking (Rif'at, 2018), closing to mathematics gap, and exploring the solutions to performance from problems. The students use each representation to solve the issues presented visually or need to visualize them in making or arranging the solutions (Darmawan et al, 2020;Rif'at et al, 2019).…”