1. Wolfram Alpha is here. How will we change? musings of Maria H. Andersen Muskegon Community College read more at www.TeachingCollegeMath.com

2. 1.What does Diffusion of Innovation Theory tell us about the likely adoption rate of Wolfram Alpha? Reference: Rogers, E. Diffusion of Innovations, 5 th edition, 2003.

3. For the purpose of understanding past and present innovations and their diffusion rates, I compare the attributes of CAS technology with those of Wolfram Alpha (W|A).

4. Relative Advantage The degree to which an innovation is perceived as being better than the idea it supersedes (strongest predictor of adoption) Cost Definite Learning Curve CAS Technology Free Similar to search engines Wolfram|Alpha

5. Complexity The degree to which an innovation is perceived as relatively difficult to understand and use You had to know exactly how to ask for what you wanted. CAS Technology The less specific the request, the more info you get. Wolfram|Alpha

6. Trialability The degree to which an innovation may be experimented with on a limited basis Had to obtain software or calculators to trial it. CAS Technology Available everywhere where there’s Internet. Wolfram|Alpha

7. Compatibility The degree to which an innovation is perceived as consistent with the existing values, past experiences, and needs of potential adopters Reform Wars show community is already split. CAS Technology Quick adoption by instructors who had beliefs consistent with CAS but were unable to implement because of logistics. Wolfram|Alpha

8. Observability The degree to which the results of an innovation are visible to others Required F2F contact for spread. CAS Technology Requires URL for spread. Wolfram|Alpha

9. Type of innovation-decision The more people involved in making an innovation decision, the slower the rate. If it is easy for an individual to adopt the innovation, it is more likely to happen. Costs required outside buy-in. CAS Technology Instructors could just adopt. Wolfram|Alpha

10. Nature of Communication How does knowledge of the innovation spread? Instructor-to-instructor Conferences Papers Interpersonal channels CAS Technology Student-to-student (social networks) Student-to-instructor (use in courses) Instructor-to-instructor Wolfram|Alpha

11. Nature of Social System The more interconnected the system, the faster the adoption rate. Network of instructors was not well-connected. CAS Technology Network of instructors is more well-connected. Students are extremely well-connected. Wolfram|Alpha

12. Promotion Efforts When the opinion leaders adopt, the adoption rate amongst the general population is faster. Once a critical mass of 15-20% is reached, the innovation will spread with little promotional effort. Has not yet reached critical mass (around 10%) CAS Technology ??? Wolfram|Alpha

13. 2. How have other changes spread through the higher ed math community? How might this one look?

14. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School The Higher Ed Math “Pyramid” Model.

15. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Graphing Calculators

16. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Graphing Calculators (strong push into higher ed from high schools as well as some adopters from within higher ed)

17. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Graphing Calculators (gradual and slow diffusion over approximately 15 years)

18. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Graphing Calculators (like it or not, all schools eventually had to consider the impacts)

19. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Graphing Calculators (CBMS data tells us GC have a high rate of adoption today)

20. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Calculus Reform (origin inside of higher ed)

21. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Calculus Reform (math reform wars cause two tracks of calculus to form)

22. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Diffusion of Calculus Reform (even today many schools have two calculus tracks)

23. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Today, adoption of reform Techniques in many textbooks Has brought the system closer to equilibrium again.

24. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Now we consider W|A … If adoption is only made at the top of the math pyramid,

25. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School If adoption is only made at the top of the math pyramid …

26. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School … the system can withstand a little bit of disruption.

27. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School But what if the change is sudden and spread throughout the all the levels of the system? ?

28. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Sudden, random changes Throughout the system.

29. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School This could cause significant disruption.

30. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School What if we at least aim for similar changes (vs. random)?

31. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School While a radical change could still be a problem…

32. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School A well-planned global change could be less disruptive.

33. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School The perspective of one, individual college or instructor, if they are thinking about the system.

34. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School If you are thinking about the whole system, the change is restricted to some extent.

35. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School You want to avoid changing like this …

36. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School But you might be able to get away with this as long as you have good company and the whole system is adapting in the same way.

37. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Ideally, we would all change together, which might look like this.

38. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Or this.

39. Algebra Precalculus Calculus Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School New course in rigorous algebra and trigonometry New course in rigorous calculus Or even this.

40. With the inclusion of more interesting topics at the undergraduate levels.

41. Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 4-yr school 2-yr school High School Aiming for well-planned similar change would be a good goal if W|A ends up having a fast diffusion rate.

42. 3. How do we bring about a well-planned similar change in thousands of math courses all over the country?

43. Someone (a group, a professional organization, an NSF committee) has to provide a goal for faculty to aim for if they decide to incorporate W|A into their courses. What stays in? What is eliminated? What can we do now that we couldn’t do before?

44. Okay, but we have YEARS to think about this.

45. No, I don’t think so. While instructors have always been slow to adopt new tools, students have always embraced them.

46. There is no cost or complexity barrier to diffusion, which points to students adopting W|A quickly.

47. If all of your students are using it, you have no choice but to at least consider how it impacts the courses you teach and the way you teach them.

48. 4. What can YOU do right now?

49. For now, start the conversation… With your colleagues In your department With your transfer institutions Within your professional organizations.