On May 27, Maria Andersen and Derek Bruff organized an online discussion among several math educators on the possible impact of Walpha on undergraduate mathematics education. Below you'll find a summary of that discussion.
Update: Maria Anderson has posted a very thoughtful analysis of the potential impact of Walpha on undergraduate math education on her blog.
What can Walpha do?
See Derek’s PowerPoint slides, as well as examples on Walpha site. There aren’t many problems in a typical undergraduate, non-major math textbook that Walpha can’t solve or help with solving. Walpha doesn’t provide the programming ability that Mathematica does. However, few of the problems typically assigned to students in undergraduate courses (at least those before Calculus II) require that level of programming.
The Walpha interface is similar in feel to Google, but the syntax is different. Walpha takes a “less is more” approach: The less you specify in your query, the more information it provides. This takes some getting used to, since it’s a different approach than the one Google uses (where using more search terms helps to refine a search) or Mathematica (where one needs precision in one’s queries).
It's worth noting that Walpha works on iPhones and other Web-enabled devices.
How might students react?
In one class, a few students were excited. Most were not. Perhaps some students take these kinds of technologies for granted? Might this widen the disconnect between faculty use of technology and student use of technology?
Students using Walpha in a few courses this summer are likely to spread the word about it to their peers using face-to-face and online social networks. This might create a demand from many students for use of Walpha this fall. Certainly by the spring semester, word about Walpha will have spread among students. Student demand might provoke change to teaching practices and curricula.
Why make use of Walpha?
Walpha doesn’t require department or campus resources other than ones that provide students with access to computers. And, in fact, many students own laptops or smart phones that provide Internet access, further reducing the need for department or campus resources. Calculators and computer algebra systems, in contrast, require more resources.
Some would argue we have a responsibility to teach students how to make use of computational tools, as well as show them the limitations of technological tools like Walpha. Here are a couple of (somewhat snarky) quotes that were shared:
- “Anything a computer can do, I don’t call mathematics. I call it an algorithm.”
- “What separates us from animals is our use of tools.”
- “Too many classrooms are like airplane flights: Please power off your electronic devices and stow them for the duration of the flight.”
How might Walpha affect learning goals?
When does teaching procedures enhance conceptual understanding? When does it get in the way? When students get to the point that they understanding a topic conceptually, do we then stop teaching further layers of algorithms?
Mathematicians don’t feel bad using a calculator to multiply three-digit numbers because they know they could do it by hand if they really needed to. Can we apply the same logic to use of Walpha? Students can use the tool as long as they have demonstrated they can do the computations by hand? However, proficiency with computations doesn’t necessarily imply conceptual understanding.
On the other hand, most mathematicians don’t know how to find square roots by hand. So there are some procedures that do become obsolete over time.
Walpha can reduce time spent on procedures, making more time available for teaching concepts and applications. (See Maria's slides for a possible vision of how this might change the curriculum.)
Does it change the idea of procedural knowledge? Perhaps procedural knowledge now means knowing when and why to use a procedure, but not necessarily how to implement the procedure. For instance, AP calculus exams now require students to set up computations but not to complete them to earn full credit.
Might this lead to more math majors? Without messy computations to deal with, students might be more attracted to mathematics.
What about “client” disciplines like physics, biology, engineering, and business? What are their reactions to Walpha? What changes in learning goals would they want math educators to make?
How might Walpha affect curricula?
Some faculty who already avoid technology in their teaching don’t think it will make any difference. These faculty are likely to work around Walpha. Many faculty see themselves as responsible for the courses they teach but not necessarily for how their courses fit within curricula. Academic freedom for these faculty can mean freedom to do as they choose in their own courses without particular regard for the impact of their decisions on faculty teaching other courses. This complicates decisions about how to use or not use Walpha in courses and curricula. (See Maria's slides for more on possible ripple effects of individual instructors decisions regarding Walpha.)
If students in one course use Walpha regularly but understand concepts and applications sufficiently well, will they be equipped to move on to subsequent courses where Walpha use is discouraged or forbidden? Some would argue yes given current experiences using calculators and computer algebra systems.
Where do we go next with this discussion?
Continue contributing examples of how Walpha handles typical problems in math courses to the Walpha Wiki. Examples of problems that are made somehow better by Walpha and examples of misleading answers provided by Walpha would be particularly useful.
Start local discussions within departments. Potentially include client / partner disciplines like physics, economics, engineering, and so on.
Start larger discussions at upcoming mathematics conferences like MathFest and the Joint Mathematics Meetings.
Check back on Walpha Wiki for future online discussions.