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Research & Exploration in the Classroom: Increasing Investment in Science and Engineering Education for a Competitive Kn

This research explores the importance of investing in science and engineering education, aiming to increase the number of graduates in these fields and promote a competitive knowledge economy. It focuses on the impact of research and exploration in the classroom, emphasizing the need for active student engagement, improved research skills, problem-solving abilities, and increased student achievement.

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Research & Exploration in the Classroom: Increasing Investment in Science and Engineering Education for a Competitive Kn

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  1. Research & Exploration in the classroom Koen Stulens Hasselt University

  2. Lissabon Declaration (2000) Increase Investment in Research + 15 % graduates in Science and Engineering European Competitive Knowledge Economy Gross Domestic Product 2000 1,9 % 2010 3 % + 700 K Researchers

  3. Annual mean decrease/increase of graduates Flanders Netherlands France Germany

  4. Researchers Generation Students Generation Students in Flanders Mathematics, Physics, Biology, Chemistry, Computer Science = 2,7

  5. Technology

  6. Technology

  7. Technology

  8. Technology Less Math? More Math! Different Approaches Gain a better insight in Math More Active Student Engagement Improve Research Skills Problem Solving Skills Reasoning Skills Improve Student Achievement

  9. Research & Exploration in the classroom Successive Integers Armando M. Martínez Cruz

  10. Successive Integers Choose four successive integers a, b, c and d. a=1, b=2, c=3, d=4 Make the sum a + b2 + c3. a + b2 + c3 = 1 + 4 + 27 = 32 Divide the sum by d. (a + b2 + c3) / d = 32 / 4 = 8 Conclusion? Divisible! Numerical Exploration

  11. Symbolical Generalization Successive Integers Choose four succussive integers a, b, c and d. a=1, b=2, c=3, d=4 Make the sum a + b2 + c3. a + b2 + c3 = 1 + 4 + 27 = 32 Divide the sum by d. (a + b2 + c3) / d = 32 / 4 = 8 Conclusion? Divisible! Symbolical Generalization

  12. Graphical Exploration Successive Integers Symbolical Generalization

  13. Successive Integers Graphical Exploration Conjecture And See

  14. Conjecture AndSee Plot a cubic function with three zeros a, b and c. Plot the tangent line in the midpoint between a and b. Conclusion?

  15. Research & Exploration in the classroom Optimization

  16. Optimization Classical Box Problem Geometrical exploration Numerical representation Graphical representation

  17. Optimization Classical Box Problem GRAPHICAL EXPLORATION &MODELLING

  18. V RESUD x x Optimization Classical Box Problem STATISTICAL EXPLORATION

  19. Optimization Classical Box Problem SYMBOLICAL EXPLORATION

  20. Optimization Angle of View

  21. Optimization Angle of View

  22. Optimization A numerical solution

  23. Research & Exploration in the classroom Code Theory

  24. 25 0 1 2 a b c d e f g h i j k l m n o p q r s t u v w x y z                           a b c d e f g h i j k l m n o p q r s t u v w x y z w i s k u n d e w w i i s s k k u u n n d d e e                         x y z 22 8 18 10 20 13 3 4 z z l l v v n n x x q q g g h h            23 24 25         25 11 21 13 23 16 6 7 + 3    26 27 28 0 1 2 Caesar code 100-44 BC BUT + 3 + 23 + ? - 3

  25. Modulo 9 + 5 = 2 9 + 5 = 14 9 + 5 =2 9 + 1 =10 9 + 2 =11 9 + 3 =12 9 + 4 =1 9 + 5 =2 + 2 + 1 + 4 + 3 + 5

  26. inString(Str1,Str2)-1-KA 26N prgmMOD (A modulo N  A) sub(Str1,A+1,1)Str2 Caesar code & TI-84 Plus DefinitionCharacters "ABCDEFGHIJKLMNOPQRSTUVWXYZ"Str1 Disp "MESSAGE" Input Str2 Disp "KEY" Input K Input Character & Key MStr2 20K inString(Str1,Str2)-1+KA 26N prgmMOD (A modulo N  A) sub(Str1,A+1,1)Str2 -14 Coding Decoding 32A 12 6A GStr2 M Output Code G Disp Str2

  27. Caesar code & TI-84 Plus Definition Characters "ABCDEFGHIJKLMNOPQRSTUVWXYZ"Str1 Disp "MESSAGE" Input Str2 Disp "KEY" Input K InputMessage& Key WISStr2 20K " "Str0 For(θ,1,length(Str2)) θ = 2 θ = 1 θ = 3 sub(Str2,θ,1)Str3 SStr3 IStr3 WStr3 inString(Str1,Str2)-1+KA 26N prgmMOD (A modulo N  A) sub(Str1,A+1,1)Str2 42A 28A 38A inString(Str1,Str3)-1+KA 26N prgmMOD (A modulo N  A) Str0+sub(Str1,A+1,1)Str0 Coding 2A 16A 12A Str0 + Q Str0 + M Str0 + C End sub(Str0,2,length(Str0)-1)Str0 Output Code Disp Str0 Disp Str2 QCM QC Q

  28. Str0

  29. PublicFunc SecretFunc M PublicFuncX X Y SecretFuncX M Public Key Systems C Condition SecretFuncX(PublicFuncX(M))=M

  30. PublicFunc SecretFunc M X Y M 1978 -Rivest,Shamir &Adleman RSA code C PublicFuncX Mdmod n Cemod n SecretFuncX Public  d= 7 en n = 55 Secret e= 23 en n = 55 ? ?

  31. Euler’s theorem If gcd(a,n) = 1 than aφ(n) ≡ 1 mod n RSA code Two Primes p = 5 & q = 11  n = pq = 55 en φ(n) = 40 Secret Key Determine e :1 < e< φ(n) = 40 and gcd(e,φ(n)) = 1 e= 23 & n = 55 Public key Determine d :1 < d< φ(n) = 40 and e.d = 1 mod φ(n) eφ(φ(n))≡ 1 mod φ(n) e.eφ(φ(n)) - 1≡ 1 mod φ(n) eφ(φ(n)) - 1= 2315 and 2315≡ 7 mod φ(n) d= 7 en n = 55

  32. RSA code M Public  d= 7 en n = 55 PublicFunc(x) = xdmod n e.d = 1 mod φ(n) Md SecretFunc(x) = xemod n Secret e= 23 en n = 55 (Md )e (Md )e ≡ Mde ≡ M1 + kφ(n) ≡ M.(Mφ(n))k ≡ M mod n

  33. RSA code

  34. Research & Exploration in the classroom Boyle’s Law

  35. Boyle’s Law Volume versus Pressure

  36. Research & Exploration in the classroom THE END

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