A great question has been raised about the handling of mathematical notation when using the tools described in this blog. How do we get square root symbols, division symbols, exponents, and other mathematical symbols that are not on the computer's keyboard in a blog entry?
Mathematics teachers have many tools at their disposal--manipulatives, calculators, textbooks, etc. However, it is impossible to use any one tool ALL OF THE TIME, for every lesson. I love manipulatives, but there are just some concepts that can't be taught with them. Likewise for technology. When all you want students to do is calculate the answer to an algebra problem, why have them do it in a blog?
My argument is that technology is best used to teach and assess reasoning, communication skills, problem-solving, and the ability to make connections among mathematical concepts and to the real world. I often choose to assess these through writing. Blogs, discussion forums, and wikis are mediums meant for writing.
Why use technology at all? Aren't students already doing a fine job writing with a pencil and a sheet of paper? Sure they are. But--and I know this from experience--technology is a HUGE motivator for students. Most of my students are bored, unmotivated, and generally uninterested in most of the assignments I give--and I am definitely a non-traditional teacher. But tell them they are going to do these same assignments on a laptop and suddenly they are excited, motivated, and extremely interested.
When I want a student to define a concept, defend an answer, or make a connection to the real world, with little notation, technology is the answer for me. Not convinced? Read the about page on my Web site.