How does technology change the way we teach and learn mathematics?

I don't think technology necessarily has an impact on the way we teach and learn math. There are poor ways to use technology and excellent ways.

But I can do some things more or better with technology than I can without it:

• More play (constructivism): Can play with ideas like the slope of a line, the parameter "a" in a parabola. Pencil and paper are slow. In a class period, a 7th grade student can only reasonably make about 5 graphs (and they would most likely complain about doing that many). With technology, they could make dozens and be able to see how changing parameters affects a line.
  
• More conceptual: Like bullet point #1. Students develop better intuition through play.
  
• More hands-on/real-world application: Students can easily measure real life objects and/or events through capturing video or photos and work with these real-life measurements. Data can be analyzed faster and more transparently. Example: Students can film someone on a swing (pumping at a constant rate), overlay a meter stick on say iMovie, share the movie with others, then at stations watch the movie and create a graph of height versus time. Hopefully they will see a beautiful sinusoidal curve!
  
• More organic sharing of products (of work): Kids can make final products like a voice thread or digital story and post online for kids to view and comment. There's no need for everyone to sit and listen to everyone's poster or Powerpoint presentation and then get bored after the third one.
  
• Less paper (but more energy use and toxic ewaste)

Day 4

What did I learn?
I love the example of students turning in a photo of a normal distribution. I've heard of doing this with parabolas. I teach algebra 1a and I'm wondering how this assignment can be meaningful with linear patterns. Lines abound, of course, but many are not that interesting from a math stand point.

What do I want to know more about?
I still want to know how to use photos and video to measure and graph and model motion. I'm emailing Dan Meyer (of the blog dy/dan) to see if he will share how he did it.

How do you use Sketchpad with students in way that is more open ended rather than cookbook style?

How can I connect this stuff to the classroom?
My biggest take away here was using digital story or movie software for kids to create math stories. This is something I want to think more about (for example: which unit, when, requirements, etc.) My first though was to do graph stories.

What did I learn?
I didn't know how box and whisker plots worked until today. Fathom was completely new and completely fabulous.

What do I want to know more about?
Same as yesterday. I'm interested in visual and audio media. Plus I'm interested in how technology can be used for more creative assessments (Fathom looks rich for opportunities).

How can I connect this stuff to the classroom?

Algebalance
This could be a useful addition to my algebra class. We use algebra tiles to learn how to solve equations. I talk about how it's important to keep the sides balanced, and some kids get this idea, but the idea is lost on a few. This activity would be useful to illustrate the idea that you must do the same thing to both sides to keep it balanced (or take away or add a zero). It would be great if you could create pages with set equations for kids to practice with. You could put kids in pairs. Each creates a balanced pan and then switch to solve their friend's equation.

More Slope Games
My two favorites here are matching and archery. Archery is a lot like guess the slope but way more fun. Also, it's not competitive (between students) so it's less likely to turn off students who shy away from competition or failing.

Parabolas in Factored Form
Don't like this ap. Confusing layout, don't like the fact that r1 and r2 are in parentheses (the unnecessary notation will confuse and distract some students from the key points here), and too hard to use.

Box and Whisker
The dynamic nature of this activity allows kids to play around with the concept and come up with their own understanding of what a box-and-whisker plot represents.

Fathom
The connections to statistics are obvious. i teach algebra and so i'm thinking about how to connect fathom to algebra. i would have students do something like what we did today: find data with two continuous, quantitative variables, scatter-plot the data and find the best fit line and then tell a story about the data. i would probably do this in pairs.

okay my arm feels like it's going to fall off, so i'm signing off.

Day 1

1. Describe something you learned
2. Questions you have or something you would like to learn more about
3. Describe connections to classroom practice

I learned some stuff about how to use Geometer's Sketchpad. I've used it, like, once before. I certainly didn't remember anything. I feel more confident and excited about using it in the future. I would have liked to do more advanced stuff with Geometer's Sketchpad. Like how do you use GS for algebra or calculus. I also would have liked to spend some time thinking about how to make these activities more inquiry based. These activities were so structured and did not harness the natural curiousity of students. For example, the quadrilaterals and triangles activities could have been way more open ended, asking for students to make some generalization about angle or side relationships without asking for all the side or angle measures first.

I would also like to learn more about how to use video for math. I'm thinking about a couple of lessons I read about on dy/dan's blog. One overlaid a ruler over a photo. Another overlaid a graph on top of video. I think that stuff is cool, and I'd like to learn more about it. Because I'm kind of a technophobe, I'm not the biggest risk-taker with technology and appreciate a little hand-holding.