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##### Wolfram Alpha is here. How will we change?

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**Wolfram Alpha is here.How will we change?**musings of Maria H. Andersen Muskegon Community College read more at www.TeachingCollegeMath.com**What does Diffusion of Innovation Theory tell us about the**likely adoption rate of Wolfram Alpha? Reference: Rogers, E. Diffusion of Innovations, 5th edition, 2003.**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).**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 Free Similar to search engines CAS Technology Wolfram|Alpha**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. The less specific the request, the more info you get. CAS Technology Wolfram|Alpha**Trialability**The degree to which an innovation may be experimented with on a limited basis Had to obtain software or calculators to trial it. Available everywhere where there’s Internet. CAS Technology Wolfram|Alpha**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. Quick adoption by instructors who had beliefs consistent with CAS but were unable to implement because of logistics. CAS Technology Wolfram|Alpha**Observability**The degree to which the results of an innovation are visible to others Required F2F contact for spread. Requires URL for spread. CAS Technology Wolfram|Alpha**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. Instructors could just adopt. CAS Technology Wolfram|Alpha**Nature of Communication**How does knowledge of the innovation spread? Instructor-to-instructor Conferences Papers Interpersonal channels Student-to-student (social networks) Student-to-instructor (use in courses) Instructor-to-instructor CAS Technology Wolfram|Alpha**Nature of Social System**The more interconnected the system, the faster the adoption rate. Network of instructors was not well-connected. Network of instructors is more well-connected. Students are extremely well-connected. CAS Technology Wolfram|Alpha**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**2. How have other changes spread through the higher ed**math community? How might this one look?**Grad school**The Higher Ed Math “Pyramid” Model. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Graphing Calculators 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Graphing Calculators (strong push into higher ed from high schools as well as some adopters from within higher ed) 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Graphing Calculators (gradual and slow diffusion over approximately 15 years) 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Graphing Calculators (like it or not, all schools eventually had to consider the impacts) 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Graphing Calculators (CBMS data tells us GC have a high rate of adoption today) 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Calculus Reform (origin inside of higher ed) 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Calculus Reform (math reform wars cause two tracks of calculus to form) 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Diffusion of Calculus Reform (even today many schools have two calculus tracks) 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Today, adoption of reform Techniques in many textbooks Has brought the system closer to equilibrium again. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Now we consider W|A … If adoption is only made at the top of the math pyramid, 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**If adoption is only made at the top of the math pyramid … 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**… the system can withstand a little bit of disruption. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**But what if the change is sudden and spread throughout the all the levels of the system? 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq ? Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Sudden, random changes Throughout the system. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**This could cause significant disruption. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**What if we at least aim for similar changes (vs. random)? 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**While a radical change could still be a problem… 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**A well-planned global change could be less disruptive. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**The perspective of one, individual college or instructor, if they are thinking about the system. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**If you are thinking about the whole system, the change is restricted to some extent. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**You want to avoid changing like this … 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad 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. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Ideally, we would all change together, which might look like this. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Or this. 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**Grad school**Or even this. 4-yr school 2-yr school High School New course in rigorous calculus New course in rigorous algebra and trigonometry Grad school Sr. math major Jr. math major Calc III – DiffEq Calculus Precalculus Algebra**With the inclusion of more**interesting topics at the undergraduate levels.**Aiming for well-planned**similar change would be a good goal if W|A ends up having a fast diffusion rate. Grad school 4-yr school 2-yr school High School Grad school Sr. math major Jr. math major Calc III – DiffEq Calc II – LinAlg Calc I Trig Coll. Alg. Int. Alg. Elem. Alg.**3. How do we bring about a well-planned similar change in**thousands of math courses all over the country?**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?**No, I don’t think so.**While instructors have always been slow to adopt new tools, students have always embraced them.**There is no cost or complexity barrier to diffusion, which**points to students adopting W|A quickly.**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.**For now, start the conversation…**• With your colleagues • In your department • With your transfer institutions • Within your professional organizations.