The Development of Mathematical Induction as a Proof Scheme : A Model for DNR - Based
نویسنده
چکیده
Students’ conceptions of mathematical induction in a standard teaching approach were found to be largely manifestations of deficient proof schemes, such as the authoritative and the symbolic non-quantitative proof schemes. On the other hand, when a fundamentally different instructional treatment of mathematical induction was implemented in an elementary number theory course taught to prospective secondary teachers, students’ conception of mathematical induction developed as a transformational proof scheme—a mathematically mature way of thinking. The alternative instructional treatment was guided by a system of learning-teaching principles, called the DNR system, which was developed and in turn implemented in a sequence of teaching experiments on the concept of mathematical proof.
منابع مشابه
Computationally secure multiple secret sharing: models, schemes, and formal security analysis
A multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants. in such a way a multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants, such that any authorized subset of participants can reconstruct the secrets. Up to now, existing MSSs either require too long shares for participants to be perfect secur...
متن کاملMathematical Proof for the Minimized Stray Fields in Transformers Using Auxiliary Windings Based on State Equations for Evaluation of FEM Results
Stray magnetic field is one of the main issues in design of transformers, since it causes non-ideal behavior of transformers. One of the techniques is usually adopted to mitigate the unwanted stray magnetic field is the use of auxiliary windings creating a magnetic field opposite to the incident one giving rise to the reduction of the total magnetic fields. This paper presents a new mathematica...
متن کاملA new security proof for FMNV continuous non-malleable encoding scheme
A non-malleable code is a variant of an encoding scheme which is resilient to tampering attacks. The main idea behind non-malleable coding is that the adversary should not be able to obtain any valuable information about the message. Non-malleable codes are used in tamper-resilient cryptography and protecting memories against tampering attacks. Many different types of non-malleability have alre...
متن کاملNeuron Mathematical Model Representation of Neural Tensor Network for RDF Knowledge Base Completion
In this paper, a state-of-the-art neuron mathematical model of neural tensor network (NTN) is proposed to RDF knowledge base completion problem. One of the difficulties with the parameter of the network is that representation of its neuron mathematical model is not possible. For this reason, a new representation of this network is suggested that solves this difficulty. In the representation, th...
متن کاملOn the development of a sliding mode observer-based fault diagnosis scheme for a wind turbine benchmark model
This paper addresses the design of an observer-based fault diagnosis scheme, which is applied to some of the sensors and actuators of a wind turbine benchmark model. The methodology is based on a modified sliding mode observer (SMO) that allows accurate reconstruction of multiple sensor or actuator faults occurring simultaneously. The faults are reconstructed using the equivalent output err...
متن کامل