Wolfram Alpha is here.How will we change? : Wolfram Alpha is here.How will we change? musings of Maria H. Andersen
Muskegon Community College
read more at
www.TeachingCollegeMath.com
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, I compare the attributes of CAS technology with those of 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) Cost
Definite Learning Curve CAS Technology Free
Similar to search engines Wolfram|Alpha
Complexity : 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
Trialability : 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
Compatibility : 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
Observability : 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
Type of innovation-decision : 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
Nature of Communication : 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
Nature of Social System : 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
Promotion Efforts : 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
Slide 13: 2. How have other changes spread through the higher ed math community? How might this one look?
Slide 14: 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 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 Diffusion of Graphing Calculators
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
(strong push into higher ed from
high schools as well as some
adopters from within higher ed)
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
(gradual and slow diffusion
over approximately 15 years)
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
(like it or not, all schools eventually
had to consider the impacts)
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
(CBMS data tells us GC have a
high rate of adoption today)
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 Calculus Reform
(origin inside of higher ed)
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
(math reform wars cause two
tracks of calculus to form)
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
(even today many schools have
two calculus tracks)
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 Today, adoption of reform
Techniques in many textbooks
Has brought the system closer to
equilibrium again.
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 Now we consider W|A …
If adoption is only made at the
top of the math pyramid,
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 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 … the system can withstand
a little bit of disruption.
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 But what if the change is sudden
and spread throughout the all
the levels of the system? ?
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 Sudden, random changes
Throughout 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 This could cause significant
disruption.
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 What if we at least aim for
similar changes (vs. random)?
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 While a radical change could
still be a problem…
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 A well-planned global change
could be less disruptive.
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 The perspective of one,
individual college or instructor,
if they are thinking about
the system.
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 If you are thinking about the
whole system, the change
is restricted to some extent.
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 You want to avoid changing
like this …
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 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 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 Ideally, we would all change
together, which might look
like this.
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 Or this.
Slide 39: 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 40: With the inclusion of more
interesting topics at the
undergraduate levels.
Slide 41: 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 42: 3. How do we bring about a well-planned similar change in thousands of math courses all over the country?
Slide 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?
Slide 44: Okay, but we have YEARSto think about this.
Slide 45: No, I don’t think so.
While instructors have always been slow to adopt new tools, students have always embraced them.
Slide 46: There is no cost or complexity barrier to diffusion, which points to students adopting W|A quickly.
Slide 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.
Slide 48: 4. What can YOU do right now?
Slide 49: For now, start the conversation…
With your colleagues
In your department
With your transfer institutions
Within your professional organizations.