W|A: Recalculating Teaching and Learning

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Slide 2: 

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.

Slide 3: 

For the purpose of understanding past and present innovations and their diffusion rates, let’s compare CAS technology with Wolfram Alpha (W|A).

Relative Advantage : 

Relative Advantage The degree to which an innovation is perceived as being better than the idea it supersedes (strongest predictor of adoption) Complexity The degree to which an innovation is perceived as relatively difficult to understand and use

Trialability : 

Trialability The degree to which an innovation may be experimented with on a limited basis Observability The degree to which the results of an innovation are visible to others

Nature of Communication : 

Nature of Communication How does knowledge of the innovation spread? Nature of Social System The more interconnected the system, the faster the adoption rate.

Compatibility : 

Compatibility The degree to which an innovation is perceived as consistent with the existing values, past experiences, and needs of potential adopters. 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.

Slide 14: 

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

Slide 15: 

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

Slide 16: 

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

Slide 17: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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)

Slide 18: 

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

Slide 19: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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)

Slide 20: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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)

Slide 21: 

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

Slide 22: 

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

Slide 23: 

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

Slide 24: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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.

Slide 25: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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,

Slide 26: 

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

Slide 27: 

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

Slide 28: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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? ?

Slide 29: 

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

Slide 30: 

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

Slide 31: 

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

Slide 32: 

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

Slide 33: 

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

Slide 34: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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.

Slide 35: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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.

Slide 36: 

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

Slide 37: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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.

Slide 38: 

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

Slide 39: 

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

Slide 40: 

Algebra Precalculus Calculus Calc III – DiffEq Sr. math major Jr. math major Grad school 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.

Slide 41: 

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

Slide 42: 

Elem. Alg. Int. Alg. Coll. Alg. Trig Calc I Calc II – LinAlg Calc III – DiffEq Sr. math major Jr. math major Grad school 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.

Slide 43: 

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

Slide 44: 

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?

Slide 45: 

Okay, but we have YEARSto think about this.

Slide 46: 

No, I don’t think so. While instructors have been slow to adopt new web tools, students have always embraced them (even invented them).

Slide 47: 

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

Slide 48: 

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.

Slide 49: 

4. What can YOU do right now?

Slide 50: 

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

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