Monthly Archives: April 2011

Wolfram|Alpha Queries

This is my response to this post by Mr. Morford concerning his view of Wolfram|Alpha.

In my Finite Math class this semester, I have been using Wolfram|Alpha a lot.  The other day one of my students wanted to use Wolfram|Alpha to reproduce one of the feasible regions, when all she knew were the corner points.  I told my student to do it directly.  Our first query was 'shape with corner points at (1,3) (4,5) (8,6) and (3,1)'.  Wolfram|Alpha didn't take very well to that.

After a few trials, I put in the query:  'polygon with vertices at (1,3) (4,5) (8,6) and (3,1)' and poof, Wolfram|Alpha gave me the required feasible region.  My student immediately commented that there's almost no way without my guidance that she would have ever thought to use the words polygon and vertices.  But she did tell me that she now recognizes the importance of knowing what things are called and the vocabulary that goes along with mathematics.

I think that this part of the roadblock to some students learning mathematics — that they simply don't know what things are called because they have somehow been taught that mathematics is simply about getting the right answer, and if you can't get the right answer on the first try, then you simply just don't know how to do math at all and you never will know how to do math.  Because math is difficult.
But take this first example of Wolfram|Alpha, our first query wasn't correct, so we tried until we got a query that did work.  We didn't give up on one try.  My student didn't say to me, 'Oh well, we couldn't get Wolfram|Alpha to do this on the first try, so Wolfram|Alpha must be hard to use, and we will never know how to use Wolfram|Alpha."  No, instead I saw the same phenomena that I see with many of my students — once they see that Wolfram|Alpha, or any other computer-based tool can do a math problem, they are willing to figure out how to get that tool to do that math problem so that they don't have to do it.

However, if we look at this from a different perspective, this may actually be a good thing.  First of all, in the long run, the students are still doing the math.  The students are getting an answer.  And if Wolfram|Alpha is doing the computation, then we have more time to focus on the critical thinking.  And second of all, isn't the whole trial and error step of how to get Wolfram|Alpha to read my query part of the critical thinking process that the students would have missed had they not used Wolfram|Alpha?  If I see a student trying different queries until he or she figures out what is an appropriate query, that makes me happy.  That idea of investigating as a part of the learning process is something that I think that is missed with traditional, non-computer learning.

Think about it this way.  In a traditional classroom, if a student who is solving an equation tells me that they cannot figure out the next step, I generally will ask the student what they think the next step will be.  Now, with Wolfram|Alpha, I can say, 'Enter the equation as a query in Wolfram|Alpha," and now you tell me what the next step is.  Then I ask the student to enter another, and another, and yet another.  And eventually through investigating how different equations are solved, the student starts to get a better sense of what it is that you are allowed to do when solving an equation, and what it is that you are not allowed to do when solving an equation.

Just a thought, whether the problem is difficult, or easier, I see plenty of open opportunities for students to use Wolfram|Alpha as a tool for investigative learning.  But I definitely do believe that the students still need the instructor's guidance to lead their investigations and their critical thinking.

Statistics Resources from Across the Web

I’m preparing to teach statistics this summer, so statistics resources are on my radar right now.  Here are some that have been fed to me recently:

1.  Prezi on ‘Beyond Tables’ – Awesome Prezi on ditching the tables and integrating applets such as those over at Surf Stat.  

2.  YouTube Video – “Benford’s Law — How Mathematics Can Detect Fraud!”  – I wanted to teach Benford’s Law better the last time I taught statistics, but I didn’t know how.  This will help.

3.  10 Jaw-Droppingly Awesome Infographics on Education — If you didn’t see my spiel on Infographics from the last time I taught statistics, I would definitely plan using this assignment again in the future.  This is just one more example of why — Infographics are just so awesome!

4.  Chi-Square Goodness of Fit Resources — Some highlights of a recent web search I did on the topic.

New Game for Evaluating Functions

Here’s the new game I created for evaluating functions.  I haven’t played it with any students yet, but it has gotten a couple of test runs, and seems to be a hit among the instructors that have seen it.  If you play it, I would love to hear your feedback.  Enjoy!

Factoring the Difference of Two Perfect Squares

These videos are on Section 6.5.  Please watch the videos over the weekend and come prepared with the completed handout on Monday.  We will have further discussion in class.



View on screencast.com »

Factoring_Demos.pdf
Download this file

Using Virtual Tools to Solve Real-World Problems

I recently saw this video come up in my Twitter Feed.  It is about a group of teenagers who are working on a project for Abbott Labs, and the story of their teacher who realizes that after working on this Real-World Problem, that the students will never be able to learn the same way ever again.  Meaning, in the traditional sense, without the technology and virtual tools.  I understand where the teacher is coming from.  But as an educator, I don’t think it should take a project from Abbott Labs for us to realize this.  We need to realize this now.  We need to revolutionize learning for our students now.  We need to take action before its too late.