I’ve had almost two weeks to think about the impact of Wolfram|Alpha (abbreviated as W|A, and now pronounced by me as “Walpha”), and I’m ready to share some of my thoughts with you.

After spending hundreds of hours* *reading more than 200 papers on innovation in math instructional practices, change in higher education, and diffusion of innovation theory, it is strange to suddenly find myself observing the possibility of a sudden shift in math education caused by a new innovation. I liken it to being a vulcanologist who has, up until this point, been observing a dormant volcano and then quite unexpectedly, it begins rumbling.

Please keep in mind that these are **my own** predictions and thoughts, for better or for worse.

1. The adoption rate of W|A amongst **students** in higher education will be extremely fast.

I’ve examined the attributes and variables that affect the diffusion of innovations, and found that every single one points to a fast adoption amongst students. Because W|A is free and similar to other technologies they know how to use (designed like a search engine), it has *relative advantage* over other CAS technologies. With prior CAS technologies, you had to know exactly what series of steps or commands to write in order to extract the outcome you desired, but with W|A, the less you ask for, the more you get out. W|A just assumes you want all relevant information it can generate. W|A is easily *trialable* – anyone with Internet access can try it. Not only that, but *observability* is also high – simply use a hyperlink to share what you’re doing in W|A with others. Compound this ease of observability with the incredible connectedness of the student population in the U.S. (Facebook, MySpace, etc.), and you can see why I don’t think it will take long for W|A to spread to the undergraduate population of math students.

Most students take their math classes for one reason: they are required to for their degree. W|A will provide solutions to problems, relevant mathematical information, and in many cases, steps for how the solution was obtained. Thus, for the reason that it appears to be a means to an end (getting through that math course with the least pain possible), using W|A to help complete assignments for math courses will be extremely *compatible* with the belief systems of these students.

2. There will be a sizable group of math instructors that **immediately** shifts to using Wolfram Alpha in instruction, and thus, begins to shift the curriculum in those classes away from computational mathematics.

I’ve already outlined many reasons why students will be fast adopters, and for the most part, these are the same reasons that instructors will be fast adopters (high *relative advantage*, low *complexity*, good *trialability* and *observability*). The main difference between the student and instructor populations will be the *compatibility* between their beliefs systems and the innovation. This is the only attribute where the adoption rate of W|A might be slowed. For example, Computer Algebra System (CAS) technology (TI-89 calculators, Maple, Mathematica, etc.) has been around for at least 10 years, and yet CAS is **not** widely adopted in math courses (see the latest CBMS Statistical Report).

That’s not to say that math instructor beliefs aren’t compatible with the use of CAS Technologies. I suspect that many, like myself, simply found that *implementation* of CAS in the classroom was too difficult. In my case, I questioned how could I ask my students, who already had a non CAS-calculator in-hand from high school, to pay for extra software or another calculator to adopt the curriculum to CAS-inclusion. To teach using software (before students all began buying laptops), we would require computer labs and site licensing, and this was not in the budget for many of us. Whether it was calculators or software, either decision would require students to spend more money, and thus, these were decisions that would likely have required department buy-in.

What does this mean for the adoption of W|A today? Instructors who already teach with CAS technologies will easily make the shift to using W|A. Instructors who liked the *idea* of teaching with CAS, but were unable to implement for logistical reasons, will quickly also quickly make the shift to using W|A (you may think I’m full of it here, but I already know of several who have **already** changed their courses). The real beauty of W|A being free is that individual instructors, under the umbrella of academic freedom, do not have to ask their departments or colleagues for buy-in. Shoud they? **Yes. ** And if they are under some kind of contract to teach in a prescribed manner given by the department, then they should **definitely** ask. But for the majority of us, if we just decided to change our courses tomorrow, very little could be done to stop it.

For my complete analysis of the rate of diffusion of W|A, you can download the 2-page analysis or view the slides that compare CAS and W|A.

3. There will be a sizable group of math instructors that attempt to either ignore W|A or put up an active resistance to it.

While some instructors will actively ignore the existence of W|A (look at the theory of cognitive dissonance), some will just passively miss it for a while (you know, by ignoring that email that they get sent that warns them to take a look at what W|A does).

However, given that there are still pockets of instructors and departments in the U.S. where graphing calculators are still not allowed, some instructors will likely react with resistance (i.e. we still don’t change anything) or possibly even with the charge that using W|A is cheating. For these instructors, compatibility of beliefs is not there.

4. We **can** change if we do so by focusing on **areas of agreement** instead of disagreement.

Mathematicians in higher education have been divided over reform teaching for 20 years now. Much like some of the political hot potatoes of our time (which shall go unnamed here for fear of blog spammers), it is unlikely that the two camps of traditionalists and reformists will ever sway followers from the opposite side. However, we can hope to agree on a middle ground. I think we would all agree that we want to make sure that math instruction focuses on learning* concepts*. I think we would all agree that *some* understanding of algebraic manipulation is important to lay the foundational structure upon which the rest of mathematical understanding is laid. I think we would all agree that there is *some* set of fundamental skills that must be learned extremely well in order to progress to higher levels of mathematics. Finally, I think we would all unanimously agree that we wish we had more time in our classes to be flexible in what we teach – to bring in interesting mathematical examples from the world around us even if the math doesn’t directly relate to the topic of the day’s lesson.

Perhaps this is the time for us to reach out and embrace a tool that might allow us to jettison some of the computational knowledge from the curriculum, and give math instructors greater flexibility in supplemental topics in the classroom. Just like each English instructor has their own favorite books to teach with, math instructors have their own favorite topics they wish they could share with students: fractals, trend analysis, network theory, number theory, modern algebra … maybe these finally get a turn at the table.

One more thing. You (my readers) have to understand how scary this whole thing might be for some math instructors. I still think that anyone who is not a *little *scared by the changes that W|A brings hasn’t thought about it enough yet. I’ve always been an instructor that lived for change, and I’ve been uneasy since W|A launched on May 15. I have no doubt that I **can** change my courses to adapt to the new environment, and I know that in the end, the changes will be good ones – but the thought of changing so much across the board in all my courses is a daunting one.

We math folks were attracted to mathematics for its beauty, its power, and its logic. In the classroom, we have always been the beneficiaries of its non-changing nature. Algebra is algebra and calculus is calculus. In all the languages of the world, algebra and calculus have been fundamentally the same for hundreds of years. You can walk into any colleague’s class and cover for them as long as they tell you which topic to launch into. This has been a fairly easy world for us to inhabit and teach in up to now. So now, things change. And probably, they change quickly.

5. We all need to keep the system in mind.

None of us teaches in a vacuum. You cannot make major changes to your course without at least *considering* the impact that it will have when those students move to the next course, the next instructor, or the next college. Make sure that your course changes still provide sufficient “math backbone” to span students successfully to the next level of mathematics. For more on this, view the slides starting on slide #13.

Personally, I do plan to change my courses to incorporate W|A in the fall, and let me tell you that I’m grateful to have another couple of months to think about exactly how to do it. To those of you who are already using W|A this summer – you are the pioneers! Please blog, write, comment, or email about how it is going and advice for making it work.

Note: Derek has also put up a WalphaWiki where we can all begin to document how W|A handles traditional math topics and the impacts this will have on our courses.

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Showed Walpha to high school math dept. heads – I could tell they loved it, but no one said so out loud Possibly stunned silence there. As you point out, students will be on Walpha right away. I’d love to see Walpha on a browser (e.g. smart phone) in class, right beside a graphing calculator and Geometer’s Sketchpad. Where students don’t have a browser in math class, teachers will need to think about how students are doing school work at home. (added by Mobile using Mippin)

I have shown both my High School Geometry classes and my College Algebra classes. I need to rethink quite a few things. I originally showed this to my HS class as another tool to help them solve geometric optimization problems. They had been struggling with finding appropriate window settings on their TI-NspireCAS, and I felt that W|A would eliminate that (window settings was not the point anyway). Well, the way I showed my students to use W|A required my students to use parentheses correctly. A whole NEW problem.

Someone posted this link to an Asimov story about “liberation from the machine” and I thought it was appropriate to share here: http://www.cs.utexas.edu/users/vl/notes/asimov.html

“I think we would all agree that some understanding of algebraic manipulation is important to lay the foundational structure upon which the rest of mathematical understanding is laid.”

Coming from a middle position (hence, not really comfortable in either group of the Math Wars), I’m not sure of this conditionalized statement. I don’t think a person with the computational perspective of mathematics would settle for ‘some'; to some this is what mathematics is and to settle for less would not be teaching mathematics.

I’m wondering if there needs to be a concern from a mathematics educators who views mathematics as the ability to work symbolically. So, couldn’t one say, ‘what should I worry about? My students can’t use their computer on my tests, so they’ll have to learn the math eventually without the crutch.’

Seems like it comes down to one group having a no-cost resource that can be integrated into their teaching and one group standing their ground for what they believe mathematics to be. Seems to me that we’ll continue to hear same-ol’ conversations in the teacher’s lounge about how the students are not prepared and how so-and-so instructor’s students just don’t do well in the next class.

Maria,

Thank you for taking the lead on this. Your commentary was very interesting to read. This certainly will change the way teachers can teach. I am reminded of when graphing calculators came out and many, many faculty did not realize the capability of those “new electronic devices.” I tried to educate faculty at Terra so that they would understand what students could easily do on the calculator. Now we need to educate faculty on what students can easily do with their blackberry.

I wrote a post about WAlpha recently. My conclusion is that just as we still (or should still) teach computation even though hand-held calcs are ubiquitous, we should still teach algebraic computation even though we have increasing CAS capabilities.

Why? Critical thinking – students can’t think critically about something they don’t understand.

http://richbeveridge.wordpress.com/2009/05/18/wolfram-alpha-is-up-and-running/

there is now SAGE: http://www.sagemath.org/ you can use use it from the web, free and adaptable to different math levels. YOu can even do your own math labs. It is open source. Never a CAS was so accesible like now.

i remember when many thought that pocket calculator gonna harm the young minds and now we have W|A… anyway around 80% or 95% of all students are lazzy… maybe with the patience of W|A this rate diminish… greets to Maria

Greeting Maria!

Kudos Maria for breaking through to the Chronicle this morning. Kudos too for this blog getting it right, again. I was going to write and ask how “Walpha” differs from the online tools like Cramster and Course Hero (see NY Times article, May 18). Now I see! Now I also see why you are thinking of ways to use in class. Walpha is soooooo cool. My goodness. It’s going to be very exciting to see all the ways people DO teach with Walpha. Thanks for keeping us on the cutting edge. I’ve not yet taken the time to learn my TI-nspire … now I have 2 immediate tasks

“Most students take their math classes for one reason: they are required to for their degree.”

This is true, but why are those math classes required for their degree? That is the question you need to know the answer to. When one answer is that the professional engineering exams do not allow graphing calculators (you are not even allowed to possess a cell phone inside the testing site) but do supply a 200 page book that (among many other things) contains key facts from calculus and trig while only giving you 2 minutes to answer each engineering problem, the question about what to know and what to look up should become clearer to you.

When students often “minimize pain” by minimizing learning, success in other classes can suffer. Wolfram argues (correctly) that his CAS, like graphing calculators, allows students “to intuitively determine how functions work” – yet my experience is that student understanding of how functions work has not improved with the use of graphing calculators. This might be because “can do” and “actually do” are not the same thing, particularly if a student’s goal is to minimize effort.

When another answer is that the professional expectations are that you will use a specific CAS at work (and on a computer with a lock-down browser during an exam that requires its use), the implications for teaching very challenging word problems rather than algebraic manipulations might also come into focus.

Those are two typical “outcomes” expectations of the faculty that consume the product of your college classroom. Talk to your nearby engineering or physics faculty and you can learn about others.

PS – What students can easily do with their Blackberry or iPhone is have someone else take a test for them, by sending a photo of the page and getting an answer back. If you allow that, be sure that less wealthy students are allowed to bring a friend to the exam.

I find it curious that Ms. Anderson says she has been opposed to using any kind of CAS before because she did not want students “to pay for extra software”, yet apparently she had no problem requiring her students to spend $100+ on graphing calculators! As the Chronicle article mentions, W|A basically renders those clunky devices completely obsolete (though they were obsolete many years ago). And as someone else here mentioned, there have been free software alternatives for a while. In addition to Sage, there is also Maxima and REDUCE, for example. Can we now finally put an end to requiring students to buy outdated graphing calculators? (and almost always a specific model, no less!) No one uses those devices outside of academia; a basic $10 scientific calculator is good enough, and one of the freely available CAS software programs can handle the rest. Math departments have been behind the times for a while, and nothing illustrates this more than requiring students to buy graphing calculators (which have their own learning curve, just like any CAS) that became irrelevant at least 8 years ago and were never necessary in the first place, in my opinion.

About 90% of my students already have a non-CAS graphing calculator before they come to my class (they were required to purchase one in high school), which is the main reason we use this technology. Purchasing software or a CAS calculator would be additional cost on top of the calculator they already have. I would love to use software in class instead of graphing calculators. If you’d like to fund a computer lab for our math department, we can make that happen.

Also, I have no great love for graphing calculators (see post: http://teachingcollegemath.com/?p=236).

Hello –

I am an inspiring high school math teacher an am excited about the possibilities of W|A in my future classroom. I see how the program can really help students visualize the language of math.

However, I do have concerns about the need for students to practice math. Concepts are a good start, but all the research I am reading now emphasizes the need for some skills to be practiced to be mastered and truly understood. I hope to provide practicing opportunities in a rich, real-world context, but it still needs to get done.

How do we motivate our students to do this chore _and_ use W|A to help them get the concepts? Any ideas?

Joan

you like walpha better than wolfa? walpha sounds too childish to me…

I’m studing e-learning, in the process of career change to teaching secondary maths. Walpha looks like a fabulous tool. Has anyone heard of academic research about Walpha? Conference papers? My searches are only coming up with newspaper articles, blogs etc.

Well, Wolfram Alpha is not even a year old yet, and academic journals can take 1-2 years to publish an article – so I’m not surprised that you haven’t found any research yet. You probably won’t see any published research until 2012 or so.

I’m not completely sure about point two. I don’t know how prepared college math instructors are for adopting new technologies. I know many of them who not completely sure what CAS is, so…

Well, the first CAS was built in 1988 (Derive) and there have been many iterations of CAS: maple, mathematica, scientific notebook, mathcad, sage, matlab, … TI-92 calculators were the first to use CAS in 1995. So … CAS has been used for 20 years. I don’t mean to sound crass, but I’m trying to find a valid reason how a math instructor could have missed encountering CAS in the last 22 years. They might not know it by the name CAS, but surely they know of the technology … and if not … well, they are not likely to learn about Wolfram Alpha either I think.