Multiple intelligences approach to Number Systems

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An example of how number systems can be taught while incorporating Gardner's theory of multiple intelligences

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Multiple intelligences approach to Number Systems

  1. 1. Multiple Intelligences Approach to Teaching Number Systems
  2. 2. MI Theory: <ul><li>First described by Howard Gardner (1983) </li></ul><ul><li>Intelligence has to do with: </li></ul><ul><ul><li>Capacity for solving problems </li></ul></ul><ul><ul><li>Fashioning products in context-rich settings </li></ul></ul>
  3. 3. MI Theory <ul><li>Intelligence theory (about how we are ‘smart’) </li></ul><ul><li>not – </li></ul><ul><li>learning theory (about how we get ‘smart’) </li></ul><ul><li>The multiple intelligences are… </li></ul>
  4. 4. 8 Intelligences (+ 1): <ul><ul><li>Linguistic (words) </li></ul></ul><ul><ul><li>Logical-Mathematical (numbers, logic) </li></ul></ul><ul><ul><li>Spatial (pictures, charts, 3D) </li></ul></ul><ul><ul><li>Musical (music, song, sound) </li></ul></ul><ul><ul><li>Bodily-Kinesthetic (physical activity) </li></ul></ul><ul><ul><li>Interpersonal (social) </li></ul></ul><ul><ul><li>Intrapersonal (self, philosophy) </li></ul></ul><ul><ul><li>Naturalistic (living vs non-living) </li></ul></ul><ul><ul><li>Existential (why are we here?) </li></ul></ul>
  5. 5. Criteria for inclusion (as MI):
  6. 6. Criteria for inclusion: <ul><ul><li>Ability to isolate (brain damage; savants; prodigies; testing; experimentation) </li></ul></ul><ul><ul><li>Definable set of “end-state” performances; operations (‘works’, events, rituals, etc.) </li></ul></ul><ul><ul><li>Susceptible to encoding (supported by symbol system – which intelligence is Braille?) </li></ul></ul>
  7. 7. Key points:
  8. 8. Key points: <ul><li>Everyone has all of them </li></ul><ul><li>We have favorites </li></ul><ul><li>Most can develop the rest </li></ul><ul><li>They often work together </li></ul><ul><li>Many ways to be intelligent within each category </li></ul>
  9. 9. How can we use this?
  10. 10. How can we use this? <ul><li>If students aren't “getting it”, we may try a different approach (rather than pronouncing the student ‘not smart enough’) </li></ul>
  11. 11. How can we use this? <ul><li>If students aren't “getting it”, we may try a different approach </li></ul><ul><li>A means to a fresh approach to the same old stuff </li></ul>
  12. 12. How can we use this? <ul><li>If students aren't “getting it”, we may try a different approach </li></ul><ul><li>A means to a fresh approach to the same old stuff </li></ul><ul><li>Opens possibility for other ways for students to demonstrate mastery (legitimacy of different approaches) </li></ul>
  13. 13. Anatomy of a Lesson
  14. 14. Anatomy of a Lesson <ul><li>Attention </li></ul>
  15. 15. Anatomy of a Lesson <ul><li>Attention </li></ul><ul><li>Activity </li></ul>
  16. 16. Anatomy of a Lesson <ul><li>Attention </li></ul><ul><li>Activity </li></ul><ul><li>Assessment </li></ul>
  17. 17. Assertions:
  18. 18. Assertions: <ul><li>All learners can learn to some extent with each (or almost any) approach. </li></ul>
  19. 19. Assertions: <ul><li>All learners can learn to some extent with each (or almost any) approach. </li></ul><ul><li>It is not possible to fully &quot;understand&quot; something (depth) without involving more than one &quot;intelligence&quot;. </li></ul>
  20. 20. Assertions: <ul><li>All learners can learn to some extent with each (or almost any) approach. </li></ul><ul><li>It is not possible to fully &quot;understand&quot; something (depth) without involving more than one &quot;intelligence&quot;. </li></ul><ul><li>Thorough assessment (of understanding) is not possible if it is based on a single intelligence. </li></ul>
  21. 21. Assertions: <ul><li>All learners can learn to some extent with each (or almost any) approach. </li></ul><ul><li>It is not possible to fully &quot;understand&quot; something (depth) without involving more than one &quot;intelligence&quot;. </li></ul><ul><li>Thorough assessment (of understanding) is not possible if it is based on a single intelligence. </li></ul><ul><li>Most lessons are not &quot;pure&quot; in that they already address more than one intelligence. </li></ul>
  22. 22. Assertions: <ul><li>All learners can learn to some extent with each (or almost any) approach. </li></ul><ul><li>It is not possible to fully &quot;understand&quot; something (depth) without involving more than one &quot;intelligence&quot;. </li></ul><ul><li>Thorough assessment (of understanding) is not possible if it is based on a single intelligence. </li></ul><ul><li>Most lessons are not &quot;pure&quot; in that they already address more than one intelligence. </li></ul><ul><li>Many aspects of a lesson are also not pure : attention-getting can help learning; activities can gain attention or be used to assess; people can learn from assessments. </li></ul>
  23. 23. Concept for this Lesson: Number Systems defined: <ul><li>Common elements of number bases like decimal, binary, octal, and hexadecimal </li></ul><ul><li>A way of symbolizing quantity </li></ul>
  24. 24. Concept: Number Systems <ul><li>Why learn this? </li></ul>
  25. 25. Concept: Number Systems <ul><li>Why learn this? </li></ul><ul><ul><li>fundamental data form in CS is binary strings; everything else built on this </li></ul></ul><ul><ul><li>helps to understand many other concepts related to numbers </li></ul></ul><ul><ul><li>number systems are higher-level concept from binary or octal == if you get this, then binary, octal, hex, ... follows </li></ul></ul><ul><ul><li>an example of abstraction / symbolism </li></ul></ul><ul><ul><li>‘ cause we said so… </li></ul></ul>
  26. 26. Concept: Number Systems <ul><li>Target audience: Beginning CS </li></ul><ul><li>How will understanding be demonstrated? </li></ul>
  27. 27. Concept: Number Systems <ul><li>Understanding Demonstrated By: </li></ul><ul><ul><li>ability to convert numbers between arbitrary bases [to & from base 10] </li></ul></ul><ul><ul><li>be able to explain an arbitrary base (such as base 5 or base 13) without having been shown that base </li></ul></ul><ul><ul><li>show / tell / demonstrate conversion of specific numbers from base X to base Y </li></ul></ul><ul><ul><li>be able to count in an arbitrary base </li></ul></ul><ul><ul><li>be able to perform simple arithmetic in an arbitrary base </li></ul></ul>
  28. 28. Getting Attention: Openers...
  29. 29. Getting Attention: Openers... (hooks) <ul><li>Linguistic &quot;Aliens have landed and are starting to ask questions. They want to know about this METRIC thing.&quot; </li></ul><ul><li>Logical-Mathematical &quot;Why do we count using base 10?&quot; </li></ul><ul><li>Logical-Mathematical, Interpersonal &quot;What do you suppose would be different in the world if we only had 8 fingers?&quot; </li></ul><ul><li>Spatial &quot;By the time we are done today, you'll know how to count to 1000 on your fingers.&quot; </li></ul>
  30. 30. Getting Attention: <ul><li>Musical Play Tom Lehrer's &quot;New Math&quot; </li></ul><ul><li>Intrapersonal Explain to class why learning about number systems is useful. </li></ul><ul><li>Bodily-Kinesthetic Get the class to fold a piece of paper in half, then in half again, then in half again,... till they can't any more. </li></ul><ul><li>Naturalistic Explain the &quot;6 Degrees of Separation&quot; Theory. </li></ul>
  31. 31. Activities:
  32. 32. Explain general form of number systems (# symbols, powers of X, how to count) <ul><li>Linguistic, Spatial, Logical-Mathematical </li></ul><ul><li>Do base 10, then base 8, then base 2, then base 16 </li></ul><ul><li>General Rules: </li></ul><ul><ul><li>x 0 = 1;    x 1 = x;     x 2 = x * x;      x -1 = 1/x;    x -2 = 1/ (x*x); </li></ul></ul><ul><ul><li>leading zeros are not significant, and unless they appear to the right of a decimal place have no effect on the value of the number </li></ul></ul><ul><ul><li>when adding and subtracting the decimal points of real numbers must be vertically aligned </li></ul></ul><ul><ul><li>when dividing two real numbers they must both be adjusted (multiplied by their base) until the divisor is an integer </li></ul></ul><ul><ul><li>for real number addition and subtraction the exponents must be the same </li></ul></ul><ul><ul><li>for real number multiplication one must multiply the mantissas and add the exponents </li></ul></ul><ul><ul><li>for real number division one must divide the mantissas and subtract the exponents </li></ul></ul>
  33. 33. Explain how numbers are built <ul><li>Logical-Mathematical, Linguistic </li></ul><ul><ul><li>represented by 10 distinct symbols: 0,1,2,3,4,5,6,7,8,9 </li></ul></ul><ul><ul><li>based on powers of 10 </li></ul></ul><ul><ul><li>each place to the left of a digit in a string increases by a power of 10; each place </li></ul></ul><ul><ul><li>to the right of a digit in a string decreases by a power of 10 </li></ul></ul><ul><ul><li>Example: 4769210 in expanded notation looks like: </li></ul></ul><ul><ul><li>= 4 * 10 4 + 7 * 10 3 + 6 * 10 2 + 9 * 10 1 + 2 * 10 0 </li></ul></ul><ul><ul><li>= 4 * 10000 + 7 * 1000 + 6 * 100 * 9 * 10 + 2 * 1 </li></ul></ul>
  34. 34. The Odometer Analogy-1 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 6 7 8 9 0 1 3 4 5 6 7 8 6 7 8 9 0 1 1000's 100's 10's 1's
  35. 35. The Odometer Analogy-2 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 6 7 8 9 0 1 3 4 5 6 7 8 7 8 9 0 1 2 1000's 100's 10's 1's
  36. 36. The Odometer Analogy-3 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 3 4 5 6 7 8 7 8 9 0 1 2 1000's 100's 10's 1's
  37. 37. The Odometer Analogy-4 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 7 8 9 0 1 2 1000's 100's 10's 1's
  38. 38. The Odometer Analogy-5 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 8 9 0 1 2 3 1000's 100's 10's 1's
  39. 39. The Odometer Analogy-6 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 9 0 1 2 3 4 1000's 100's 10's 1's
  40. 40. The Odometer Analogy-7 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 0 1 2 3 4 5 1000's 100's 10's 1's
  41. 41. The Odometer Analogy-8 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 1 2 3 4 5 6 1000's 100's 10's 1's
  42. 42. The Odometer Analogy-9 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 2 3 4 5 6 7 1000's 100's 10's 1's
  43. 43. The Odometer Analogy-10 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 3 4 5 6 7 8 1000's 100's 10's 1's
  44. 44. The Odometer Analogy-11 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 4 5 6 7 8 9 1000's 100's 10's 1's
  45. 45. The Odometer Analogy-12 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 5 6 7 8 9 0 1000's 100's 10's 1's
  46. 46. The Odometer Analogy-13 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 7 8 9 0 1 2 4 5 6 7 8 9 6 7 8 9 0 1 1000's 100's 10's 1's
  47. 47. The Odometer Analogy-14 <ul><li>Spatial </li></ul><ul><li>Bodily-Kinesthetic </li></ul>0 1 2 3 4 5 8 9 0 1 2 3 4 5 6 7 8 9 7 8 9 0 1 2 1000's 100's 10's 1's
  48. 48. The Base 8 Odometer <ul><li>Same deal – smaller wheel </li></ul>512's 64's 8's 1's 1 2 3 4 5 7 0 1 2 3 5 6 7 0 1 6 7 0 1 2
  49. 49. Look at how we count (then do the same in other bases). <ul><li>Logical-Mathematical </li></ul><ul><li>Linguistic </li></ul><ul><li>Spatial (patterns) </li></ul>1000 999 109 ... ... 302 102 301 101 300 100 299 99 ... .. 202 12 201 11 200 10 199 9 ... .. 112 2 111 1 110 0
  50. 50. Look at how we count in different bases. <ul><li>Logical-Mathematical </li></ul><ul><li>Linguistic </li></ul><ul><li>Spatial (patterns) </li></ul>10 20 10000 16 F 17 1111 15 E 16 1110 14 D 15 1101 13 C 14 1100 12 B 13 1011 11 A 12 1010 10 9 11 1001 9 8 10 1000 8 7 07 0111 7 6 06 0110 6 5 05 0101 5 4 04 0100 4 3 03 0011 3 2 02 0010 2 1 01 0001 1 0 00 0000 0
  51. 51. Show how to convert numbers from some base to base 10. <ul><li>Logical-Mathematical </li></ul><ul><li>Example: 10111001 2 in expanded notation looks like: </li></ul><ul><li>= 1 * 2 7 + 0 * 2 6 + 1 * 2 5 + 1 * 2 4 + 1 * 2 3 + 0 * 2 2 + 0 * 2 1 + 1 * 2 0 </li></ul><ul><li>= 1 * 128 + 0 * 64 + 1 * 32 + 1 * 16 + 1 * 8 + 0 * 4 + 0 * 2 + 1 * 1 </li></ul><ul><li>= 128 + 32 + 16 + 8 + 1 </li></ul><ul><li>= 185 </li></ul>
  52. 52. Show how to convert numbers from base 10 to others. <ul><li>Logical-Mathematical </li></ul>Division Quotient Remainder Binary Number 2671 / 2 1335 1 1 1335 / 2 667 1 11 667 / 2 333 1 111 333 / 2 166 1 1111 166 / 2 83 0 0 1111 83 / 2 41 1 10 1111 41 / 2 20 1 110 1111 20 / 2 10 0 0110 1111 10 / 2 5 0 0 0110 1111 5 / 2 2 1 10 0110 1111 2 / 2 1 0 010 0110 1111 1 / 2 0 1 1010 0110 1111
  53. 53. Relate octal numbers to the musical scale. <ul><li>Musical </li></ul><ul><li>Spatial (patterns) </li></ul>
  54. 54. Show how to count in binary on your fingers. [Beware of ‘4’!] <ul><li>Bodily-Kinesthetic </li></ul><ul><li>Spatial </li></ul>
  55. 55. Use an Abacus <ul><li>Bodily-Kinesthetic </li></ul><ul><li>Spatial </li></ul><ul><li>Intrapersonal (leave them to play with it) </li></ul>
  56. 56. Act It Out (each person gets a wheel, list, or flip-book of numbers; have them count; when one gets to '9' they get to poke the next guy). <ul><li>Bodily-Kinesthetic </li></ul><ul><li>Interpersonal </li></ul>9 9 9 2
  57. 57. Multiplying like Bunnies (Relate to generations of bunnies, each having 'N' babies. 'N' can be 2, 8, 10). <ul><li>Naturalistic </li></ul><ul><li>Spatial (patterns) </li></ul>
  58. 58. Assessment: Musical <ul><li>Propose a numerical code (octal mapping) for musical notes. Encode a simple song - try reading it using the numerical code. </li></ul>
  59. 59. Assessment: Logical-Mathematical , Linguistic <ul><li>Explain base 'X' [using symbols, powers] </li></ul><ul><li>Explain base '5', or '13' </li></ul><ul><li>worksheets: fill in the blanks... </li></ul>647 FF 11010 32 Base 16 Base 8 Base 2 Base 10
  60. 60. Assessment: Logical-Mathematical <ul><li>What's the next number in base 'X'? </li></ul><ul><li>Simple Additions in various bases </li></ul><ul><li>Naturalistic </li></ul><ul><li>Find examples in nature (asexual reproduction; propagation) </li></ul>
  61. 61. Assessment: Bodily-Kinesthetic, Spatial, Interpersonal <ul><li>Show me n in binary using your hands. </li></ul><ul><li>Get people to be &quot;bits&quot; - standing = 1; sitting = 0 - do counting or arithmetic using people </li></ul>
  62. 62. Thanks!

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