Sharing Teaching Ideas: Calculator Cryptography

2003 ◽  
Vol 96 (3) ◽  
pp. 210-212
Author(s):  
Matthew Hall
Keyword(s):  
Mathematics Teachers ◽  
Real World ◽  
Mathematical Ideas ◽  
Use Of Technology ◽  
Real World Applications ◽  
Teaching Ideas

Allowing students to participate in real-world applications of mathematics enables them to advance their own understanding of mathematical topics. Furthermore, most mathematics teachers would agree with NCTM's statement that “students' engagement with, and ownership of, abstract mathematical ideas can be fostered through technology” (NCTM 2000, p. 25). However, finding real applications becomes increasingly difficult as students progress into higher forms of mathematics like algebra. One topic that I have found particularly effective in demonstrating the importance of algebra and the use of technology is cryptography, or the encoding and decoding of messages.

Implementing the “Curriculum and Evaluation Standards”: Ladders and Saws

1993 ◽  
Vol 86 (6) ◽  
pp. 510-513
Author(s):  
Debra Tvrdik ◽  
Dave Blum
Keyword(s):  
Real World ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
School Year ◽  
Real World Applications ◽  
Geometry Class

How many of our students begin the school year apprehensive and fearful of their geometry class? They enter the room having heard all sorts of horror stories about the dreaded two-column proof and all those theorems. Too often, geometry is taught mechanically with an emphasis on recalling facts. The NCTM's Curriculum and Evaluation Standards (1989) calls for a move away from geometry as a tour through a collection of predetermined Euclidean theorems and their proofs. Instead, they advocate greater attention to approaches using coordinates and transformations, to real-world applications and modeling, and to investigations leading to student-generated theorems and conjectures, with supporting arguments expressed orally or in paragraph form. As teachers, we search for activities that will involve our students in the study of geometry and help them to understand the “whys” behind the facts. The following activity employs several strategies to enable students to make conjectures, construct mathematical ideas, and use mathematics as a tool to communicate with others.

Sharing Teaching Ideas: Mathematical Connection-a Baseball Opportunity

2000 ◽  
Vol 93 (7) ◽  
pp. 552-553
Keyword(s):  
Mathematics Teachers ◽  
Real World ◽  
Teaching Ideas ◽  
Mathematical Connection

Like most mathematics teachers, I am always seeking connections to real-world situations.

Technology, Linear Equations, and Buying a Car

1992 ◽  
Vol 85 (7) ◽  
pp. 562-567
Author(s):  
James T. Sandefur
Keyword(s):  
Secondary School ◽  
Mathematics Teachers ◽  
Linear Equations ◽  
Discrete Mathematics ◽  
Mathematical Concepts ◽  
School Year ◽  
Use Of Technology ◽  
Real World Applications ◽  
Summer Workshop

We ran an NSF Teacher Enhancement summer workshop on modeling with discrete mathematics at Georgetown University for three summers ending in 1991. Each summer we worked with forty secondary school mathematics teachers in the Washington, D.C., area, with a school-year follow-up consisting of classroom visits and monthly seminars. One objective of this workshop was to work with teachers in developing real-world applications that are relevant to students but that contain important mathematical concepts. The use of technology broadens the range of applications that can be used.

scholarly journals Electronic Phenomena of Transition Metal Oxides

Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 256
Author(s):  
Christian Rodenbücher ◽  
Kristof Szot
Keyword(s):  
Solid State ◽  
Transition Metal ◽  
Metal Oxides ◽  
Real World ◽  
Transition Metal Oxides ◽  
Major Research ◽  
Research Fields ◽  
Real World Applications

Transition metal oxides with ABO3 or BO2 structures have become one of the major research fields in solid state science, as they exhibit an impressive variety of unusual and exotic phenomena with potential for their exploitation in real-world applications [...]

scholarly journals Applications of Distributed-Order Fractional Operators: A Review

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 110
Author(s):  
Wei Ding ◽  
Sansit Patnaik ◽  
Sai Sidhardh ◽  
Fabio Semperlotti
Keyword(s):  
Fractional Calculus ◽  
Real World ◽  
Transport Processes ◽  
Model Systems ◽  
Variable Order ◽  
Fractional Operators ◽  
Research Activity ◽  
Road Map ◽  
Real World Applications ◽  
Distributed Order

Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

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