Wolfram Alpha is here. How will we change? musings of Maria H. Andersen Muskegon Community College...

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



Grad school

Grad school


Diffusion of Graphing Calculators

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad 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



Grad school

Grad school


Diffusion of Graphing Calculators(gradual and slow diffusion over approximately 15 years)

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


Diffusion of Graphing Calculators(like it or not, all schools eventuallyhad to consider the impacts)

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


Diffusion of Graphing Calculators(CBMS data tells us GC have ahigh rate of adoption today)

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


Diffusion of Calculus Reform(origin inside of higher ed)

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


Diffusion of Calculus Reform(math reform wars cause two tracks of calculus to form)

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


Diffusion of Calculus Reform(even today many schools havetwo calculus tracks)

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad 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



Grad school

Grad 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



Grad school

Grad school


If adoption is only made at thetop of the math pyramid …

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


… the system can withstand a little bit of disruption.

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


But what if the change is suddenand spread throughout the allthe levels of the system?

?

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


Sudden, random changes Throughout the system.

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


This could cause significantdisruption.

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


What if we at least aim for similar changes (vs. random)?

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


While a radical change couldstill be a problem…

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


A well-planned global change could be less disruptive.

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


The perspective of one, individual college or instructor,if they are thinking aboutthe system.

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


If you are thinking about thewhole system, the changeis restricted to some extent.

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


You want to avoid changing like this …

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad 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



Grad school

Grad school


Ideally, we would all change together, which might looklike this.

Elem. Alg.

Int. Alg.Coll. Alg.

TrigCalc I



Grad school

Grad school


Or this.

Algebra

Precalculus

Calculus

Calc III – DiffEq


Grad school

Grad 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



Grad school

Grad 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.

Wolfram Alpha is here. How will we change? musings of Maria H. Andersen Muskegon Community College...

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