When I first watched the instructor talk about technology in the hands of students versus in the hands of teacher, I suddenly imagined a classroom full of students with open laptops working on a geometry problem together. I realized that even though technology is great to demonstrate, the students would get a more beneficial (and intriguing) experience if they could discover things for themselves. I remember the feeling of playing around with dynamic figures and devising my own conjectures. I couldn't wait to see if I was right or not, so I tried to prove them right away. I want to instill this feeling in my students. The instructor also talked a little about equity. I agree that the aid of technology helps level the playing field. It equalizes opportunities for all students.

In the reading, there was a focus on teaching strategies that should be used to implement technology in the classroom. The main focus was that technology should extend math and enhance learning. It should promote higher-order outcomes, such as reflection, reasoning, problem posing, problem solving, and decision making

(NCTM, 2005, p. 1). I want my students to be able to be able to develop these processes without worrying about technical difficulties or syntax errors. I want to be able to teach students how to use technology to help them, not do math for them. Technology should also be a tool or aid for students, not their brain. One really interesting argument against the use of technology is that it does the work for the students.

One really good example is prime factorization (Fundamental Theorem of Arithmetic). If the CAS can do it for the students, do they really need to know how to do it? Some might say no, but I think the students should at least *learn* how to do it first, and then use the calculator for more complex problems. That way, it's no magic trick. Once the students learn how to do something, they can use the CAS to do it for them afterward so they can focus their energy on the bigger picture, e.g., when should prime factorization be used? This example illustrates the white box-black box

strategy. First teach the students how to do it by hand, and then allow the technology to do it for them. (For those computer science folks who know what “information hiding” is, this is a really interesting subject to talk about.)

References

- Ball, L. & Stacey, K. (). Teaching strategies for developing judicious technology use. In W. J. Masalski & P. C. Elliott (Eds.), Technology-supported mathematics learning environments (pp. 3–15). Reston, VA: NCTM.
- The National Council of Teachers of Mathematics. (). The use of technology in the learning and teaching of mathematics. In W. J. Masalski & P. C. Elliott (Eds.),Technology-supported mathematics learning environments (pp. 1–2). Reston, VA: NCTM.
- Technology in mathematics education [video file]. (). Retrieved from http://www.youtube.com/watch?v=W58ReRyNYp8.

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