After the AP test, we were required to do two or three little projects just so we didn't completely waste the last month of school. This text that she showed us was an example of one of the options we could choose from for our project. It was a three dimensional model of what an integral represented and that picture has stuck with me for a long time and helped me a ton once I got to multidimensional calculus. When it comes to math, a picture is worth more than a hundred symbols.
Another mathematical text I remember my mom using as she home-schooled me was a base 10 abacus and it really helped me understand why you "borrow" and "carry" when you subtract and add. She also had us create our own base 10 manipulatives with beads. I remember thinking that was really fun.
I think the most unique mathematical texts I have encountered have been introduced to me in college. I have discovered lots of amazing applets that could be used to teach mathematics more effectively and also a couple of cool videos and texts that I could use to supplement the textbook text.
One of my favorite things I have discovered is GeoGebra, an applet creation software. This software allows you to create your own applets and upload them to your website as an html page. I was so excited about it that I couldn't stop saying, "This is SO COOL!!!" when my teacher was explaining the features of the program.
I think I will use this software A LOT as a teacher because I really do think that a picture is often worth a hundred symbols in math and I can create applets that will help students visualize math. I know from my own experience that personally discovering a piece of mathematics makes it stick a lot better. I know I could design applets that would lead students to discover mathematics for themselves instead of just listening to me tell them the way it is.
You might be wondering exactly how an applet can be a text. Consider the fact that you can interact with it and draw conclusions from the interactions you have. I think in many ways, this makes it an even more powerful text than a textbook that doesn't give you feedback or allow you to explore your questions.
As a final note, I want to include an applet that I made using GeoGebra to introduce students to a unit on the transformation of the sine function. (Note: You need the most recent version of Java for it to work) Enjoy!
Sine FunctionJaylee Willis, 3 October 2013, Created with GeoGebra |
I love how you say that "a picture is worth more than a hundred symbols!" I specifically remember having trouble learning positive and negative numbers until my teacher gave the example of a perfectly flat sandbox. A positive number represented that many scoops of sand added on top and a negative number represented that number of scoops taken out of the box. I didn't get it until I had a picture, even though it was a mental one. I'm also glad to hear that there are other math texts out there and that you'll be using them. The math book was always my least favorite book. It was heavy, and had more numbers than letters (at least at first). I think using other texts will really benefit your students, I know it would have benefited me :)
ReplyDeleteUnfortunately I was not able to see the app because the computer that I am did not allow it but I think that this is great! Apps are such a good way to demonstrate how different mathematical equations and functions are influenced by their different parts. I imagine (because I didn't actually see the app) that this app about the sine function will show how the period and the amplitude affect the sine function. This was something that I kind of understood from my textbook but I know that seeing the graphic representation on an app would have helped me a lot. I would definitely consider apps to be a critical part of reading in mathematics.
ReplyDeleteHi Jaylee..I previously posted a comment to this board, but it didn't stick, so I wanted to post again just in case. In essence, what I wrote was that I completely agreed with you that many texts in mathematics will be visual. More and more high-interest, interactive graphics are coming out, which have the potential to interest students in math and teach them how fun quantitative displays of data can be. I liked your geogebra text as well...you could use it as a teacher model prior to asking students to make their own student versions. :) Thanks for your posting!
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