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Bharath Sriraman 《Interchange》2006,37(1-2):151-178
This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use
of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly
diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom discourse that conveys the
Lakatosian (thought-experimental) view of mathematics as that of continual conjecture-proof-refutation which involves rich
mathematizing experiences. I present a pathway towards this pedagogical goal by presenting student insights into an unusual
counting problem and by using these outcomes to construct ideal mathematical possibilities (content and process) for discourse.
In particular, I re-construct the quasi-empirical approaches of six!4-year old students’ attempts to solve this unusual counting
problem and present the possibilities for mathematizing during classroom discourse in the imaginative spirit of Imre Lakatos.
The pedagogical implications for the teaching and learning of mathematics in the secondary classroom and in mathematics teacher
education are discussed. 相似文献
2.
Bharath Sriraman 《Roeper Review》2017,39(3):206-209
Sternberg (2017) summarizes the history of identification of giftedness in the 20th century and presents a case for the shortcomings of measures such as IQ for problem-solving skills required in the 21st century. The Active Concerned Citizenship and Ethical Leadership (ACCEL) model is proposed to replace the outdated construct of IQ, particularly for the field of gifted education. In this commentary, the mathematical dimensions of ACCEL are teased out in contrast to its presence in psychometric testing. Further, what is considered relevant in mathematics for learners today is addressed in relation to the skills outlined in the ACCEL model. 相似文献
3.
The tendency to generalize from specific experiences leading to new, more abstract concepts is a natural aspect of human thought.
Generalizations are the end result of an inductive process that begins with the identification of similarities in seemingly
disparate situations. It is the existence of such generalizations that makes it possible for us to understand each other and
the world around us. It is pedagogically weak to present generalizations to students and expect them to know how and when
to apply them. On the other hand if students experience the inductive process in classrooms and discover generalizations,
they are likely to remember and use this process when tackling other problems. The authors illustrate the pedagogical value
of such an approach and the interdisciplinary nature of the inductive process by reflecting on teaching practices in English
literature and mathematics in a high school classroom. In particular the authors reflect on how the inductive process was
applied to four short stories and four problem-solving situations, which resulted in high school students arriving at generalizations
that characterized the stories and the problems. A conceptual model that illustrates how inductive processes facilitate generalizations
in the classroom is presented. 相似文献
4.
In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in mathematics by analyzing their problem-posing abilities in geometric scenarios. The participants in this study were from one location in the USA and two locations in China. All participants were enrolled in advanced mathematical courses in the local high school. Differences in the problems posed by the three groups are discussed in terms of quality (novelty/elaboration) as well as quantity (fluency). The analysis of the data indicated that even mathematically advanced high school students had trouble posing good quality and/or novel mathematical problems. We discuss our findings in terms of the culture and curricula of the respective school systems and suggest implications for future directions in problem-posing research within mathematics education. 相似文献
5.
In modern science, the synthesis of “nature/mind” in observation, experiment, and explanation, especially in physics and biology increasingly reveal a non-linear totality in which subject, object, and situation have become inseparable. This raises the interesting ontological question of the true nature of reality? Western science as seen in its evolution from Socratic Greece has tried to understand the world by objectifying it, resulting in dualistic dilemmas. Indian science, as seen in its evolution from the Vedic times (1500–500 bc) has tried to understand the world by subjectifying our consciousness of reality. Within the Hindu tradition, the Advaita-Vedanta school of philosophy offers possibilities for resolving not only the Cartesian dilemma but also a solution to the nature of difference in a non-dualistic totality. We also present the Advaita-Vedanta principle of superimposition as a useful approach to modern physical and social science, which have been increasingly forced to reject the absolute reductionism and dualism of classical differences between subject and object. 相似文献
6.
Bharath Sriraman 《Interchange》2017,48(2):117-128
The aim of this article is to provide the reader, or anyone interested in creativity, a glimpse into the findings of existing psychological and psychiatric literature on manic depression, its occurrence in creative individuals, ways in which it manifests and affects their functioning and creative output (positively and negatively), and the lessons one can draw from these individuals attempts to creatively associate and even reconcile opposite positions. The literature from educational philosophy, psychology and psychiatry is used as a lens to examine mythological, biographical and autobiographical accounts of the lives of creative individuals, particularly frames or episodes of their mind. The construct of “happiness” is deconstructed with didactical implications for education. 相似文献
7.
While chemistry provides the framework for understanding the structure and function of biomolecules, the immune system provides
a highly evolved natural process to generate one class of complex biomolecules-the antibodies. A combination of the two could
be exploited to generate new classes of molecules with novel functions. Indeed, one example of this productive interplay is
the generation of catalytic antibodies or abzymes. A catalytic antibody is a sort of natural artificial enzyme — it is a natural
protein synthesized by the usual biological processes and is intended to catalyze a reaction for which no real enzyme is available.
The essential idea is to raise antibodies to a molecule considered to mimic the transition state intermediate of a reaction
that is to be catalyzed i.e., a molecule resembling a strained structure intermediate between the substrate and product, believed
to occur in the reaction pathway. The hope is that some of the antibodies produced will happen to possess groups capable of
promoting the reaction. 相似文献
8.
Interchange - An allegorical thought experiment occurring in a pseudo Huxleyean world in the future is conducted, in which “Euclidean” geometry has been forgotten and can only be... 相似文献
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