Introduction of online learning
Online learning consider that each stage of reasoning is incorporated into logical and mathematical justifications considered standard, and its validity and relevance appear to be autonomous. In the authors’ proposal, the interpretation of students’ solutions must consider a larger and more complex system, if the teacher’s intention is to instigate them or even explain why such forms of reasoning, correct or not, were produced.
In parallel, with regard to intuition, focused strictly on mathematics, this has been the subject of discussions in the field of mathematics education. management courses online We can say that intuition refers to a product of representations made from reality and, in this sense, has an auxiliary role in the students’ learning process, which can be considered by the teacher.
Types of online learning
Social Learning
online learning are synthesize a globalized and structured view of the basic ideas for solving a problem previously elaborated, thus depending on the other three types of intuition mentioned above.
It enables the generalization of the mathematical structure for the proposed problem and the replication of the solution model in similar situations. management courses online Foschini thoroughly examines the teaching and learning process by considering that, recurrently, the student faces obstacles in their learning, understanding, and problem solving at more advanced levels.
online study given the fact that, sometimes, their techniques and strategies of reasoning are driven by implicit and/or intuitive, sometimes inadequate, models. In this sense, the teacher supposedly has the task of investigating and recognizing such models.
Blended Learning
level reasoning describing it as a reasoning model not yet formulated, but related to the subject’s position in an action situation in TDS, we can see a similarity with the category Foschini’s affirmative intuition. This relationship can be seen when Foschini proposes that the subject has a preliminary view of the problem and a superficial view of its solution path, being able to observe and analyze, based on structures of inductive thought.
management courses online At this level of reasoning and intuitive category, the student has not yet taken any action to solve it but is in the process of predicting his hypotheses and then establishing a path that makes sense to him. The ND level reasoning proposed by Rousseau.
Synchronous Online Learning:
Given the above, we can infer a relationship between what Rousseau and Gibe propose about the different levels of mathematical reasoning in the development of TDS and what Foschini explains in his categorization of intuition. online study In this sense, we propose a correlation between.
This reasoning model can be related to the conjectural intuitions proposed by Foschini in which the student starts with analytical reasoning about each part of the problem. Thus, the student begins their deductions from a starting point, being able to associate, classify, and express themselves verbally, formulating ideas and establishing a path to the solution more explicitly.
Theme of online learning
online learning are perspective, we can understand that 3rd. level reasoning is defined by Rousseau and Gibe as a formal, global, and finished model, which is based on the sequential connection of inferences articulated cohesively (although such reasoning is not correct as a format presented in validation situations in the TDS. It is possible to relate 3 rd. level reasoning to what Foschini proposes as anticipatory intuition and/or conclusive intuition.
management courses online are depending on how this reasoning was produced by the student. We understand that both the levels of reasoning proposed by Rousseau and Gibe and the categories established by Foschini show that the learning trajectory of new reasoning occurs when it is promoted from a single particular means of solving a problem. online study problem to a universal means of solving all problems of a given type and is integrated as such with the subject’s knowledge.
Positive negative of online learning
The preliminary analysis of a study considers the general didactic theoretical framework regarding a given mathematical object, being composed of an investigation that considers the epistemological, historical, and didactic prism Almouloud & da Silva, The current teaching of a given mathematical object, its effects, conceptions, and obstacles faced by students must be considered, as well as an analysis of the field.
online learning where teaching achievements will be effectively developed In this preliminary analysis, we present a mathematical discussion about two specific ways of representing the parabola: from the point of view of quadratic functions and as a locus in analytical geometry. We also seek to present some particularities in their teaching and the possible gaps present in initial training regarding the topic.
Conclusion
online learning form is viable in solving situations in which the vertex coordinates are known. This format is little explored in mathematics classes at school, and many textbooks do not cover this topic. Lucian and Tirana state that the study of the parabola occurs through “teaching that prioritizes algebraic treatment and leaves the geometric interpretation of the represented mathematical object to be desired, which makes it difficult to deepen the concepts in focus”.
This makes us reflect on the importance of seeking different approaches to teaching this topic in the classroom. Furthermore, other research such as Borer and da Silva Tanti and Felts and Pull state that the teachers’ methodology in the Brazilian context brings with it some gaps, with traditional classes and little use of technological resources or practical applications.
Management courses online are Thus, students tend to develop the abstract thinking part little, presenting a narrow and reductive view of the parabola and the quadratic function itself. There is still a lack of a deeper discussion on the concept of quadratic function in de Sousa et al.
online study Pedagogical Research, the classroom, as well as the exploration of multiple representations of functions, considering the relationship between the concept and the image, and a consequent exploration of (intuitive) mathematical reasoning, as defended by Foschini.
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