Number theory Number theory is traditionally concerned with the properties of integers. More recently, it has come to be concerned with wider classes of problems that have arisen naturally from the study of integers. It can be divided into elementary number theory where the integers are studied without the aid of techniques from other mathematical fields ; analytic number theory where calculus and complex analysis are used as tools ; algebraic number theory which studies the algebraic numbers - the roots of polynomials with integer coefficients ; geometric number theory ; combinatorial number theory ; transcendental number theory ; and computational number theory.
Intrinsic Motivation Intrinsic motivation is an energizing of behavior that comes from within an individual, out of will and interest for the activity at hand. No external rewards are required to incite the intrinsically motivated person into action. The reward is the behavior itself. However, it is certainly not the case that every real world behavior stems from an intrinsic energy.
Schools are of particular interest when it comes to intrinsic versus extrinsic motivation, particularly because of the different outcomes that researchers have shown to result from intrinsic motivation: Why do some students pursue academic learning for its own sake while others are motivated by external factors?
Over the years, several theorists have offered insights into the phenomenon through their conceptions of intrinsic motivation.
SDT states that humans have three innate psychological needs: Intrinsic motivation develops out of the support of these needs. The authors go on to say that when people feel competent, autonomous and self-determined, they will freely seek what interests them.
Under what conditions, then, would a person freely seek to engage in academic endeavors? According to the authors, intrinsically motivated learning can only occur when an individual feels freedom to make choices in the process, when the activity is challenging, and when the challenge can be conquered.
Whether these conditions are met depends on the person as well as the environment. After all, different circumstances afford different perceptions.
The authors stipulate that individuals can perceive specific events as informational preserving a sense of competence and freedomcontrolling conveying a pressure to think, feel or behave a certain wayor amotivating conveying personal incompetence and a sense that particular outcomes are impossible to achieve.
Further, the environment in general can contain any mix of elements that could be defined as autonomy supportive, controlling or amotivating. For example, a teacher may allow her students to choose the books they read for reports autonomy supportiveyet remind them that they will be evaluated and should strive for high marks controlling.
After the assignments are turned in, she could opt to grade on a curve, opening up the possibility of equal student efforts leading to differential outcomes amotivating.
Deci and Ryan do acknowledge that even when a school environment supports autonomy and competence, if a person is simply not interested in a particular learning activity, he will not be intrinsically motivated for engagement Rather, he will be motivated by external factors like grades.
However, the authors do stipulate that external motivations can be internalized.
Despite his lack of interest, a person can still be self-determined if he can integrate the activity into his sense of self. For example, a student may find balancing chemical equations uninteresting and therefore not be intrinsically motivated to complete homework problems. However, if he can come to understand how such an activity can be valuable and important as a means of personal growth and skill enhancement i.
Through this process, the student can now approach the activity with a sense of will rather than pressure. In summary, according to Self-Determination Theory, intrinsic motivation is dependent on the interaction between different individual perceptions of the environment and different perceptions of the self.
Because of the pervasive use of external incentives, both to incite achievement of certain standards and simply to promote task completion, research findings in this area are particularly critical for instructional practice. In Intrinsic Motivation Deci presented a variety of reward studies with variable results.
In a similar study with children, when rewards were expected, intrinsic motivation decreased Lepper et al. In a more recent study by Ryan, Mims and Koestner an attempt was made to cover multiple comparisons in a single investigation.
College student participants were divided among three experimental groups: The remaining participants were placed in three comparison groups: Results showed lower intrinsic motivation for the activity in the performance-contingent reward groups relative to their respective feedback comparison groups.
Results also demonstrated that the informational reward group and informational feedback comparison group had higher levels of intrinsic motivation than their control oriented counterparts and the task-contingent no feedback reward group.
A final point noted by the authors is that the no reward, no feedback group showed higher intrinsic motivation than the task contingent group and the control oriented performance-contingent reward group, but less than the two informational oriented groups.
Deci explains these variable findings through the notion that rewards, like other aspects of the classroom environment, convey both messages of competence information as well as elements of control.
The outcome of a reward on intrinsic motivation depends on which message is more salient to the recipient. The type of reward and the mode of delivery can influence saliency.
If a person feels pressured, incompetent or as though she is engaging in a behavior not for her own reasons, but for something external i. If, however, the element of control is very low in the reward delivery and the competence feedback of the reward is high, intrinsic motivation may increase as a result.
Deci, of course is just one of the many contributors to the body of rewards research.Analysis of Education Informaton Systems In the Context of Systemic Reform Christopher A. Thorn, Jeffery Watson, & Susan Zeyher ANALYSIS OF EDUCATION INFORMATION SYSTEMS IN THE CONTEXT OF SYSTEMIC REFORM education system has to attend to and incorporate all of the vital needs and content areas of a .
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10 3 17 4 14 Intrinsic and extrinsic brain regions in the posterior cortex 18 6 2 1 With respect to the posterior cortex, our analysis showed 5 two key regions involving the intrinsic system: the lateral 8 temporal (fBA 5) and the temporo-parietal (fBA 10) 7 cortex.