# Behavioral Engagement Thesis

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Student engagement helps the students in getting involved in their own learning. It removes the element of the teacher as a supervisor and gives the students an option to use their own way of learning. In this way, a student is able to use his own method to learn about a certain subject. The student can also share his way of learning with others by telling them. This will lead to positive criticism of the methods of that student and the idea of involving a student in his studies brings about fruitful results. (Theilheimer, 1991)

Academic engagement pushes a student to take risks. A student will take different routes to solve a problem in order to find the fastest way out. This will lead him to undesired dead ends as well but if the student is truly interested and engaged in a certain subject, then his interest will push him to take risks which will eventually get him in the right place. (Magdol, n.d.)

According to Lynn Magdol 2009, Academic engagement helps a student is avoiding many risks which can be serious. Some of these risks are related to low confidence, poor self-control, alienation and other significant behavior problems. In this way, the student can avoid several problems if he is given a proper environment to engage in activities. (Magdol, n.d.)

Mathematical Justification

Mathematical justification refers to the act of supporting mathematical supports and ideas using facts and formulae. Mathematical justification is very crucial as it forms the base of mathematical learning and working. The whole study of mathematics is based on proofs and concrete calculations. If the students are not able to justify their steps and calculations, they will never master the subject of mathematics. (Holdan & Lias, 2009)

These justifications are also important to the teacher as well. The teacher, most of the times, is not interested in the answer but in the method via which the student arrived at that answer. Therefore, the mathematical justification of steps and formulae is an important part of mathematical studies. (Werndl, 2009) (Members of The National Council of Teachers of Mathematics, 2009)

As mentioned in the work of Charlotte Werndl 2009, mathematical reasoning has the following three steps which do not follow a definite order: (Werndl, 2009)

Conjecturing

Generalizing

Justification (Werndl, 2009)

In the first step, the student uses the given facts or assumptions in order to draw preliminary conclusions about the problem. These conclusions are preliminary, as mentioned earlier, and are not certified to be true. (Werndl, 2009)

In the second step, the student finds a relationship between this problem and the other problem he has solved. In this step, the student endeavors to find a common link between the two or more problems of the same kind so that they can be solved in a similar way. (Werndl, 2009)

In the third step, the student justifies the steps he has taken. Justification completes mathematical reasoning. If the student does not know the reason behind applying a certain formula, his reasoning will be useless. He may get the correct answer, but the method will be incorrect. (Werndl, 2009)

Mathematical reasoning helps the students in supporting their proofs. If a student claims a certain formula to be applicable in a certain scenario, he will need reasoning in order to prove it to others. If mathematical reasoning is not given, the claim will just be considered as a guess. In addition to that, Martin et al., also mentions the mathematical reasoning as a basis of sense making in mathematics. If a student is able to provide correct mathematical reasoning, it means that he has understood the concept clearly. (Members of The National Council of Teachers of Mathematics, 2009)

The connection between mathematical reasoning and student engagement is quite obvious. It is a very simple notion that a student who is engaged a lot in studies and school activities will be able to make good justifications as he will take interest in understanding the concepts and formulae clearly. In addition, the student will be better at communicating the justification as he will develop a handsome level of confidence. Hence, academic engagement benefits a mathematics' student in making and communicating his justifications better. (Members of The National Council of Teachers of Mathematics, 2009)

Facilitation of Student Engagement

The role of the teacher is instrumental in facilitating the student engagement. The teacher is the one who triggers the thoughts of the students and thus he can control the thoughts better. The following factors affect the student engagement level in a class and the teacher can manage them to get better results:

Teachable Moments

Teachable moments, as defined in the research of Beverly Scholz 2010, are time periods where the process of learning is the easiest. During teachable moments, the students can learn the maximum in a small amount of time. For instance, students easily understand a chemical reaction in a chemistry lab which they were unable to understand in the classroom. (Scholz, 2010)

These teachable moments should therefore be used and managed with immense care. The teacher should try to make the students grasp the most by giving detailed answers to their questions. As the teachable moments are time periods in which the level of interest of a student is at its peak, the students rarely forget the things they learn during these moments. (Scholz, 2010)

As a result, the students have sufficient knowledge to indulge into questions and answers with the teacher and other students. This will increase the level of participation in the classroom activities and hence, the level of student engagement. Moreover, the reputation of the student will improve in the eyes of the teacher and the students and his confident level will also improve. (Scholz, 2010)

Exploration vs. Instruction

According to Adelson 2004, instruction is a direct guideline about how to do a certain thing. It is a teaching style in which the teacher gives the students methods to solve their problems and getting answers. (Adelson, 2004)

Although it seems to limit the potential of the students, Adelson quotes Klahr saying that direct instruction is more organized and disciplined and can get the students out of certain complex situation more easily and efficiently than exploration. Klahr supports his point by saying that most of the things we know about science were taught to us and we did not discover them. (Adelson, 2004)

Exploration, on the other hand, is defined as a method in which the students are given situations and tools to deal with those situations. In this method, the students do not get a way out from the teacher, they find their own way out. In this way, the potential of the students is harnessed. (Adelson, 2004)

Exploration learning is slower than instruction-based learning but this method gives full knowledge to the students. In addition to that, exploration does not limit the learning ability of the student. Moreover, exploration gives way to further studies which increases the innovative ideas as well. (Adelson, 2004).

Active and Passive Learning

Michel et al., 2009, defines active learning as a broad term encompassing several styles of teaching in which the students participate in the teaching process as well. He further states that active learning refers to all the teaching methods in which the students do a task and think about that task at the same time. Some characteristics of active learning are momentary pauses during the lectures for writing and discussing purposes. (Michel, Cater & Varela, 2009)

Michel et al., 2009, also mentions the prerequisites of active learning. The first prerequisite is the atmosphere of the classroom which should be friendly and relaxed. If the teacher creates a strict environment, the students will not actively participate in the discussions and other activities. (Michel, Cater & Varela, 2009)

In addition to the atmosphere, planning is also an important requirement of active learning. The pauses and discussions should be planned in a way that they bring about the greatest benefit to the class. Moreover, the teacher should also implement the plan made or else the main purpose of the active learning method will be lost. (Michel, Cater & Varela, 2009)

Lastly, continuous improvement is also necessary for active learning. Continuous learning means discussing the class plans and methods with the students and getting their recommendation in order to improve the system. (Michel, Cater & Varela, 2009)

Passive learning, as defined by Michel et al., 2009, is the teaching method in which the teachers enter the class, deliver a tedious lecture and leave. In this method, the students are not given time either to note the lecture or to discuss it. In addition, the syllabus and the class schedule is also decided by the teacher and handed over to the students to follow. This makes it a rather stringent method of teaching. (Michel, Cater & Varela, 2009)

The biggest disadvantage of passive learning is that the students have trouble in understanding and remembering information imparted by the teacher. Michel et al.,…
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