Related papers: Fractions in elementary education
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
For many structured learning tasks, the data annotation process is complex and costly. Existing annotation schemes usually aim at acquiring completely annotated structures, under the common perception that partial structures are of low…
A simple estimate in terms of currency units shows that a meaningful educational reform process can be launched and sustained over many generations of teachers with support of parents of students. In the estimate, the steady inflow of…
The rapid advances in technology over the last decade have significantly altered the nature of engineering knowledge and skills required in the modern industries. In response to the changing professional requirements, engineering…
A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…
Underlying complex systems, there is a rich web of interconnected components that determine the relational properties of the system. Yet, traditional methods used in education sciences often disregard the underlying complexity of the…
In many longitudinal settings, economic theory does not guide practitioners on the type of restrictions that must be imposed to solve the rotational indeterminacy of factor-augmented linear models. We study this problem and offer several…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.
Papert's (1980) work with Turtle Geometry offered an early and provocative vision of how digital technologies could be used with young learners. Since then, research on digital technology use has focused on the middle and high school…
Experiments used in current continual learning research do not faithfully assess fundamental challenges of learning continually. Instead of assessing performance on challenging and representative experiment designs, recent research has…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
Irrational numbers are introduced usually already introduced in lower secondary level schools. But typically, maybe with the exception of $\sqrt{2}$, no mathematical proof of irrationality is provided. In particular it is not proven that…
The current conventional approach in teaching STEM seems inadequate; it is failing both the students and the work-force demands in several aspects. Perhaps it is succeeding in equipping students with information and facts but surely falls…
One of the capabilities which 21st-century skill compulsory a person is critical thinking and problem-solving skill that becomes top positions rank. Focus on problem-solving skills can be taught to a child, especially begun in elementary…
A summary of an experimental course on fractals is given that was held for young learners at age 12. The course was a part of Epsilon camp, a program designed for very gifted students who have already demonstrated high interest in studying…
The physics community explores and explains the physical world through a blend of theoretical and experimental studies. The future of physics as a discipline depends on training of students in both the theoretical and experimental aspects…
Very little is known about how the nature of expertise in introductory and advanced courses compares in knowledge-rich domains such as physics. We develop a framework to compare the similarities and differences between learning and patterns…
Recent empirical work has shown that human children are adept at learning and reasoning with probabilities. Here, we model a recent experiment investigating the development of school-age children's non-symbolic probability reasoning ability…