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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