Technology in the math class

Although I have not had many opportunities to teach the level of math that I enjoy, math remains one of my strongest interests. In my own math learning experience, it has been so much about numbers, letters and words. The MET program, and in particular, ETEC 533: Technology in the Mathematics and Science Classroom, has opened my eyes to a world of ways to use technology in the math class, including hand-held calculators and computerized virtual math manipulatives. The old saying "a picture is worth a thousand words" is very applicable to math, and the effect is even more powerful when the learner is able to generate the picture for herself and then manipulate the input variables to see what effect it has on the resulting picture.

Re-reflection for Technology in the Mathematics and Science Classroom efolio

The efolio is a description of and reflection about many of the technologies that we explored during ETEC 533. These include Technology-Enhanced Learning Experiences (TELEs), the Jasper Series, the WISE project, World Watcher, Wise Web, Illuminations, embodied learning and dynamic visualization software, among others. At the end of the course I also wrote a reflective piece about my experiences with the technology and how they enabled me to grow as a teacher.

Looking back

Technically speaking, my vision of what constitutes a good website has changed throughout the MET program. I have created websites for many of the courses, and each time I have challenged myself to learn more about web page development. At one point in my undergradute education, I considered (very briefly!) becoming a computer programmer. Web page development appeals to my logical and detail-oriented nature, and each time I have enjoyed learning more about html and Cascading Style Sheets (CSS). At the time that I developed the ETEC 533 ePortfolio, I was proud of the way it loooked. I spent a lot of time looking for the right combination of background and font colours. Since learning more about CSS, I now search for one look that will be the base for the whole site to help pull it together into a cohesive unit. I try to use more white space, including blocks on the sides and extra space between lines of text for easier reading. I use a sans serif typeface as the lack of "little feet" makes the text clearer. Visually, I want to make my sight easy to look at and easy to read.

Pedagogically, ETEC 533 Technology in the Mathematics and Science Classroom really opened my eyes to a wide spectrum of technology tools available for math. It also showed me new ways of using old tools, like a simple hand-held calculator. 

At the beginning of the course I wrote about my assumptions regarding the use of technology:

The technology would be used to "play" with the theories that are presented, in order to let the students see what effect changing numbers and variables has on the structure or visual output of the formulae. I believe that this is a good use of technology, because I feel that we should not use technology just for the sake of using it. I believe that technology is strongest when it is used as a tool to support the students in learning the theory, in that it helps motivate and engage students and speaks to different learning styles. I think that in math, especially at the higher levels, it can be hard for kinaesthetic learners because it may be hard to find manipulatives. Using technology allows them to be more "hands on". It can also support visual learners who need to look at models or diagrams rather than numbers or words.

A few weeks further into the course, my vision for the use of technology in the math class was broadened by a classmate:

Blake Buemann mentioned another use of technology in the lower levels that I also consider to be a good use of technology - using a calculator to perform many calculations to develop the idea of pi (Buemann, 2005). I think that technology can be used to help children develop abstract concepts. Rather than just telling them about pi and expecting it to be understandable, having them do an exercise through which the concept becomes clear will hopefully allow them to remember it better.

After teaching a few more math classes, my view of how technology can be used has widened. Not only can technology be used after the theory is presented in order to allow students to visualize the impact of changing numbers and variables, but it can also assist learners in building concepts from the ground up, and can act as a powerful tool in discovery learning. After one of my adult students learned to use a graphing calculator, I noted this in my math efolio:

However, the "Aha" moment came for me when, after producing several graphs, the student made and confirmed a discovery about assymptotes. He started to see a connection between the equation of the assymptote and the denominator of the rational expression. I'm not sure that he would have learned on his own by hand drawing the graphs. Because it takes so long to draw each graph, by the time he would get to the next graph, any patterns that he might see would be obscured.

At the end of ETEC 533 I reflected on all that I had learned. It is interesting to see the themes of constructivism, discovery learning, authentic learning and cognitive apprenticeship (among others) that arose during many of my MET courses, not only in the classes devoted to these theories and techniques, but also showing up in places where they weren't expected. At the end of this course, which was designed to examine the use of technology in math and science classes, I wrote:

I have been struck by my growth as an educator and my newfound awareness of different styles of teaching and learning. I now have new interests in discovery-based learning, authentic learning, and cognitive apprenticeship, among many of the other tantalizing issues that we have studied during the course. It has certainly raised my level of awareness of the different ways that teachers can teach and students can learn. 

Looking forward

As I continue to refine my vision for learning, I want to keep in mind my thoughts at the end of ETEC 533:

... [Technology] can help motivate and engage learners; assist with record keeping and mundane calculations; provide a simulated environment that allows students to investigate concepts without fear of danger or without having to travel; and it can do it over and over many times so that students can use discovery learning to understand concepts rather than getting caught up in the process of production.

Although I am often truly amazed and impressed by how technology can impact learning, I have to keep reminding myself to pursue opportunities for students to do other activities besides regular book work. Having been educated and trained as a teacher using a transmissive lecture-style format, my first inclination when planning for classes is to revert back to that style of teaching as well. I always want to rely on my ability to explain concepts to students, even when I know that some students don't always respond to spoken explanation with written text. To this end, I must be vigilant in searching out technology that can be used in different situations before the situations occur. This way I can build up a personal library of technology tools that can be used to support learning.

References

Buemann, B. (2005). Re: Jill's Analysis of Interview 2.. Message 1308, ETEC 533 MA-L2-Interview (Jeff) Discussion Forum.