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Elizabeth Durkin

Tiered instruction: rationale, and characteristics of a tiered lesson - 0 views

  • Whether we isolate high achieving students into accelerated courses, learning disabled students into special education classes, students who have fallen behind into remedial classes, or English language learners into a stream of their own, we frequently do so at a cost to both the students themselves and to the mainstream population from which they’ve been separated. If we embrace full inclusion without applying effective differentiation strategies, we fail as well.  Diverse classrooms where every learner makes significant progress are possible in part through tiered instruction and assessment.
  • Students at the beginning end of the readiness continuum will have learned the most. Students who were initially in closer proximity to the learning target will have grown less. It’s possible, if not likely, that some highly advanced students may be proficient while having experienced no growth at all. We will deserve credit for helping struggling students develop proficiency and will deserve  blame for setting a limit on what our advanced students were able to learn.
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    Why use this instruction model for middle school mathematics? How does a tiered lesson look? Strategies for managing a tiered classroom.
Elizabeth Durkin

30umX.jpg (JPEG Image, 500x313 pixels) - 0 views

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    Trig joke
Elizabeth Durkin

Math demos: Domain and range - 0 views

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    Interactive demo of domain and range from graph
Elizabeth Durkin

Mathematical Advances Strengthen IT Security - 1 views

  • Elliptic curves are equations with two variables, say x and y, including terms where both x and y are raised to powers of two or more (in the form y2 = x3 + ax + b)
  • recent workshop organised by the European Science Foundation (ESF), which set the stage for development of a programme of European-wide research on the field.
  • google_hints = "Math Puzzles; Hacking; Encryption; Information Technology; Mathematics; Computer Programming"; google_ad_channel = "9363733909+4685929003+5855393847+0524954116+7497946760+8476969570"; Science News Share   Blog   Cite Print   Bookmark   Email Mathematical Advances Strengthen IT Security ScienceDaily (May 12, 2009) — Rapidly rising cyber crime and the growing prospect of the Internet being used as a medium for terrorist attacks pose a major challenge for IT security. Cryptography is central to this challenge, since it underpins privacy, confidentiality, and identity, which together provide the fabric for e-commerce and secure communications.
  • ...11 more annotations...
  • Information Technology Mathematics Computer Programming Reference Cryptography Security engineering Algebraic geometry Cyber security standards Cryptography since the beginning of the Internet has been based extensively on the RSA public key system, used for digital signatures and the exchange of private keys that in turn encrypt message content. The
  • See Also: Computers & Math Math Puzzles Hacking Encryption
  • RSA cryptosystem, introduced by Rivest, Shamir, and Adlement in 1977, relies for its security on the difficulty of working out the factors dividing large integers (whole numbers).
  • protection it provides has been eroded
  • Elliptic curves are equations with two variables, say x and y, including terms where both x and y are raised to powers of two or more (in the form y2 = x3 + ax + b).
  • Fermat’s Last Theorem,
    • Elizabeth Durkin
       
      Students can relate to this early on in the article.
  • ecent workshop organised by the European Science Foundation (ESF), which set the stage for development of a programme of European-wide research on the field.
  • Indeed it so happened that elliptic curves started to be applied to both number factorisation and cryptography at about the same time, in the late 1980s. At first the application to factorisation advanced much more quickly, while the technical difficulty involved held back elliptic curve cryptography. But the very success of elliptic curve factorisation started to undermine the security of RSA, since this relies on the difficulty of factorising the product of two prime numbers. This in turn has stimulated development of elliptic curve cryptography in more recent years, said Kohel. So having first undermined the prevailing RSA method of cryptography, the sophisticated mathematics of elliptic curves has itself come to the rescue.
  • Indeed keys 160 bits long provide ECC with the same level of security as 1024 bit keys for RSA.
  • In effect then ECC will make it easier to stay a step ahead of the hackers without undue load on computers
    • Elizabeth Durkin
       
      This is all very current. Good for kids to see.
  • he ESF workshop was highly successful in bringing together mathematicians and computer specialists whose combined expertise is required to implement complex cryptographic algorithms.
    • Elizabeth Durkin
       
      Good to get the history of the cryptography. Quite confusing though if you don't understand it.
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    Great links between math and cryptography, elliptical relations, current research.
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    Great link to advanced algebra
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    This article shows how algebra is used in current internet cryptography.
Elizabeth Durkin

Quadratic functions - 1 views

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    Quadratic tutorials with practice problems and instant answers.
Elizabeth Durkin

Log tables - 0 views

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    How log values were obtained in the "olden days". Through use of a table of values. Includes a dynamic tutorial on how to use the log tables.
Elizabeth Durkin

The log memory game - 0 views

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    Identify pairs of log expressions that are equal to each other. Like Memory card game.
Elizabeth Durkin

Logger - 0 views

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    Game like "frogger" where laws of logs are used to advance.
Elizabeth Durkin

Graph of cosine function - 0 views

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    Use this interactive demo to understand how the graph of y = cos x is produced.
Elizabeth Durkin

Graph of sine function - 0 views

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    Use this interactive applet to understand how the graph of y = sin x comes about.
Elizabeth Durkin

Six trig functions - 0 views

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    Get a better sense of the definitions of all 6 trig with this interactive demo
Elizabeth Durkin

Tan box - 0 views

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    Use this interactive demo to get a better idea of the definition and properties of tan
Elizabeth Durkin

Sine box - 0 views

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    Use this interactive demo to have a better understanding of the definition of sine.
Elizabeth Durkin

Cosine box - 0 views

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    Use this applet to have a better understanding of the definition of cosine.
Elizabeth Durkin

Trigonometry - 4 views

All things related to the trig units we do.

trig 10+

started by Elizabeth Durkin on 27 May 11 no follow-up yet
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