Using Music to Teach Computation and Mathematics in Secondary

1

• Using Music to Teach Computation and Mathematics
  in Secondary
• Education
• John Peterson
• Paul (who me, travel?) Hudak
• Yale University

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Good Morning Class!

• Lets learn about programming!
• Please get out your computers .

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All About Computation!
Programming is fun! Lets do something exciting
Great!
4
All About Computation!
OK - heres a really amazing function. Its
called factorial
Huh?
5
All About Computation!
factorial 0 1 factorial x x factorial
(x-1)
Big deal
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All About Computation!
OK - I know. Ill show you how to sort a list!
Zzzz
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Generating Interest

• So how do we get students interested in
  computation?
• Be concrete! Constantly produce artifacts that
  motivate students to keep going
• Keep it simple avoid unnecessary detail
• Cool domains such as music, robots, or
  pictures
• Exploit creativity allow students to build
  interesting artifacts and share them with others
• Tools that are powerful yet appropriate

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What Weve Done

• Paul Hudak has developed Haskore, a system for
  describing music using functions. Haskore is a
  Haskell library.
• Ive taken Haskore on the road to high school
  students. Students were very interested in music
  as a way to express patterns.
• Paul has looked at the algebraic properties of
  music and a formal semantics of music
  performance.

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About Haskore

• type Pitch (PitchClass, Octave)
• data PitchClass Cf C Cs Df D Ds Ef
  E Es Ff F Fs
• Gf G Gs Af A As
  Bf B Bs
• type Octave Int
• data Music
• Note Pitch Dur -- a note
  \ atomic
• Rest Dur -- a rest
  / objects
• Music Music --
  sequential composition
• Music Music --
  parallel composition
• Tempo Int Int Music -- scale the
  tempo
• Trans Int Music --
  transposition
• Instr IName Music --
  instrument label
• type Dur Float -- in
  whole notes
• type IName String
• type PName String

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Teaching Computation

• Vocabulary pitch and duration, sequential and
  parallel composition
• Naming reusing elements of music
• Music transformation tempo scaling,
  transposition
• Functional abstraction
• Recursion and iteration
• Higher order functions

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An Example
A function to recursively apply transformations f
(to elements in a sequence) and g (to accumulated
phrases) rep (Music -gt Music) -gt (Music -gt
Music) -gt Int -gt Music -gt Music rep f g 0 m
Rest 0 rep f g n m m g (rep f g (n-1) (f
m)) An example using "rep" three times,
recursively, to create a "cascade" of
sounds. run rep (Trans 5) (delay
tn) 8 (c 4 tn) cascade rep (Trans 4) (delay
en) 8 run cascades rep id (delay sn) 2
cascade waterfall cascades revM cascades
Good music in just 6 lines!
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The Algebra of Music

• Using simple equational reasoning, many useful
  axioms
• are easily proven
• Tempo-scaling is multiplicative.
• Transposition is additive.
• Parallel composition is commutative.
• Tempo-scaling and transposition are
  distributive over both sequential and parallel
  composition.
• Sequential and parallel composition are
  associative.
• Rest 0 is a unit for Tempo and Trans, and a zero
  for sequential and parallel composition.

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Evaluation

• Does an arts style of instruction work in a
  technical domain?
• Can we reach students that are not otherwise
  motivated to study computing?
• Does computing have a measurable impact on other
  learning domains?
• Is this a good way to teach standard music
  education?

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Where to from here

• Use the principles to Haskore to build a
  student-friendly algorithmic music system
• Explore music as a teaching context for computing
  principles using Haskore
• Integrate computing into a music education
  curriculum
• Investigate music as a way of exploring
  algebraic reasoning

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To All You Haskell Instructors

• Haskore is a great tool for teaching.
• Its simple, easy to install, and opens up a new
  domain for students.

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Examples
Eric
Abe
Little
Davis