Discovery Learning – Rational Expressions

This week I tried something a little different in my Elementary Algebra class for simplifying rational expressions. Typically I walk through an example of simplifying a numerical fraction to lowest terms and try to extract the key ideas and apply them to rational expressions containing variables. Based on some things I had seen/heard at AMATYC, particularly about how WolframAlpha (W|A) will impact the way we teach, I decided to try a new approach.

At the top of the board I wrote

At the bottom of the board I wrote

Then I said to my class “The correct result for this problem is at the bottom of the board. How do we get it?”, and I gave them a moment to think about it. I could see the wheels spinning.

• “How does turn into ?”
• “How does turn into ?”

And then it happened – someone said we need to factor the numerator and denominator. So many times I have taught this and told my students “This is how you do it.” It seemed that the process was more accessible to my students because it came from one of them instead of coming top down from the instructor.

After walking through a few examples, I introduced multiplication of rational expressions and later division of rational expressions in the same way. It might have been the easiest day I have ever had teaching these topics. This will definitely not be the last time I use this approach!

Summary

The idea is to give your students a problem and an answer, and see if they can find the path to get there. Do you use this approach in your classroom? Have you used WolframAlpha in a similar way? Please share any experience or opinions by commenting on this blog, or you can reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Wednesday I post an article related to General Teaching on my blog. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com

Math Study Skills – Sharing Class Notes

Today’s study skill blog is a spin-off of an idea that was discussed in my AMATYC workshop. It came from a group of 4 participants from Valencia CC (FL), Johnson & Wales (NC), Collin College (TX), and St. Charles CC (MO).

The suggestion was to use LiveScribe in class to “PenCast” notes. LiveScribe is a pen that captures notes as you take them in a fashion that can easily be uploaded to the web. Not only does it capture notes – it also captures audio as well. (For more information, check out their website LiveScribe.com.

The instructor selects a student that takes good notes, and asks that student to be the note taker for the day. The instructor then gives the student the LiveScribe pen and the special note paper, and the student takes notes as they normally would. At the end of class, the instructor gets the LiveScribe pen back from the student and uploads the notes and classroom audio to their web page.

This allows other students to view the notes with the real-time classroom audio for a review of what happened in class. It also allows students to spend more time concentrating on the lecture itself, rather than blindly copying down notes. This gives a student a chance to think and reflect during class, and to focus on truly understanding. 

I recently had a discussion with a colleague who lamented that his students spent so much of their mental energy in just copying what was on the board that he has considered a 15-minute “no pencil zone” in his class. This would help students to think and increase understanding. I think that this LiveScribe strategy could be just as effective.

My Spin

This idea can be used (without the classroom audio) without the LiveScribe pen. I can select a student as a note taker, collect the student’s notes, scan them, and post a pdf file. (You could also print them out for the class, although I’d rather post them online.)

This approach of a class note taker can have a positive impact on other students and their note taking. By seeing a set of high quality notes, students can learn better note taking skills. They can also use the online notes to supplement their own notes. Finally, this will help students to focus on the math during class, not on just copying everything down.

Summary

Do you have any experience with using the LiveScribe pen? Have you ever used a class note taker? Please share by leaving a comment, or reaching me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Tuesday I post an article related to Math Study Skills on my blog. If there’s a particular study skill you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.