Wolfram Alpha is here. How will we change?
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Transcript of 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
1. 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)
CostDefinite Learning Curve
CAS Technology
FreeSimilar to search engines
Wolfram|Alpha
Complexity
The degree to which an innovation is perceived as relatively difficult to understand and use
You had to know exactlyhow to ask for what
you wanted.
CAS Technology
The less specific the request, the more info you get.
Wolfram|Alpha
Trialability
The degree to which an innovation may be experimented with on a limited basis
Had to obtain software orcalculators to trial it.
CAS Technology
Available everywherewhere there’s Internet.
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.
CAS TechnologyQuick adoption by instructors
who had beliefs consistentwith CAS but were unable to
implement because oflogistics.
Wolfram|Alpha
Observability
The degree to which the results of an innovation are visible to others
Required F2Fcontact for spread.
CAS Technology
Requires URL for spread.
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.
CAS Technology
Instructors could just adopt.
Wolfram|Alpha
Nature of Communication
How does knowledge of the innovation spread?
Instructor-to-instructorConferences
PapersInterpersonal channels
CAS TechnologyStudent-to-student(social networks)
Student-to-instructor(use in courses)
Instructor-to-instructor
Wolfram|Alpha
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 ismore well-connected.
Students are extremelywell-connected.
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 criticalmass (around 10%)
CAS Technology
???
Wolfram|Alpha
2. How have other changes spread through the higher ed math community? How might this one look?
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
The Higher Ed Math “Pyramid” Model.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Graphing Calculators
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Graphing Calculators(strong push into higher ed from high schools as well as some adopters from within higher ed)
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Graphing Calculators(gradual and slow diffusion over approximately 15 years)
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Graphing Calculators(like it or not, all schools eventuallyhad to consider the impacts)
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Graphing Calculators(CBMS data tells us GC have ahigh rate of adoption today)
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Calculus Reform(origin inside of higher ed)
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Calculus Reform(math reform wars cause two tracks of calculus to form)
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Diffusion of Calculus Reform(even today many schools havetwo calculus tracks)
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Today, adoption of reform Techniques in many textbooks Has brought the system closer to equilibrium again.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Now we consider W|A …If adoption is only made at thetop of the math pyramid,
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
If adoption is only made at thetop of the math pyramid …
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
… the system can withstand a little bit of disruption.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
But what if the change is suddenand spread throughout the allthe levels of the system?
?
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Sudden, random changes Throughout the system.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
This could cause significantdisruption.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
What if we at least aim for similar changes (vs. random)?
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
While a radical change couldstill be a problem…
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
A well-planned global change could be less disruptive.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
The perspective of one, individual college or instructor,if they are thinking aboutthe system.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
If you are thinking about thewhole system, the changeis restricted to some extent.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
You want to avoid changing like this …
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
But you might be able toget away with this as long asyou have good company and the whole system is adapting in the same way.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Ideally, we would all change together, which might looklike this.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Or this.
Algebra
Precalculus
Calculus
Calc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
New course inrigorous algebraand trigonometry
New course inrigorous calculus
Or even this.
With the inclusion of more interesting topics at the undergraduate levels.
Elem. Alg.
Int. Alg.Coll. Alg.
TrigCalc I
Calc II – LinAlgCalc III – DiffEq
Sr. math majorJr. math major
Grad school
Grad school
4-yr school2-yr schoolHigh School
Aiming for well-planned similar change would be a good goal if W|A ends up having a fast diffusion rate.
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?
Okay, but we have YEARS
to think about this.
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.
4. What can YOU do right now?
For now, start the conversation…
• With your colleagues
• In your department
• With your transfer institutions
• Within your professional organizations.