Chapter 7
Perhaps a matter of imagination
TPCK in mathematics education
Kim Fuller
3/23/09
Imagination, mathematics and technology… A wicked problem?
Albert Einstein touted that imagination is more important that knowledge. He believed imagination embraced the world and all there is to understand. He approached learning and teaching mathematics with independent thinking, questioning and connecting mathematics to the real world. Sounds like the introduction written at the beginning of the math program I use with my students. His philosophy is certainly something teachers strive to do in their classrooms everyday. But it can be very challenging especially in the area of mathematics.
How do we define mathematics? According to Steen (1988), mathematics involves observing, representing and investigating patterns and relationships in social and physical phenomena and between mathematical objects themselves. Mathematics is often defined as the science of space and number… [but] a more apt definition is that mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination. Mathematical theories explain the relations among patterns… Applications of mathematics use these patterns to “explain and predict natural phenomena…
Then there is the question of how to use technology to enhance mathematic instruction and learning. It was interesting to think about using technology as a politically charged concept. Do we allow students to use calculators? Are they really learning if they use processing programs while taking an algebra course? And what about fractals? These are complicated geometric patterns that are more easily investigated by using computers and lead to understanding many real world phenomena such as weather patterns, plant growth and even functions of the human body.
Mathematics is a huge content area and most teachers at the middle and high school levels will specialize in one or two areas. This allow teachers to become experts in those areas so content is already strong in terms of the TPCK model. Elementary teachers are more challenged in that they teach all subjects and can get spread thin in terms of learning all the content areas equally. And currently there is such a push in the area of literacy that math seems to be on the “back burner”. Teachers who see math instruction as being just as important as literacy instruction need to be self- motivated to seek out solid strategies and technologies. NCTM is a good resource and has provided excellent recommendations for elementary math instruction. Cover less, but cover it more efficiently and in more depth. HOORAY!
NCTM also stated that the use of technology allows students to work within interesting problems and can facilitate student achievement in higher-order learning outcomes such as reflection, reasoning, problem posing and solving and decision-making.
TPCK
As technology becomes an integral part of our society it is perceived that technology is a critical tool for teaching mathematics. Pre-service teachers are encouraged to be open and experiment with how to apply technology in their math instruction. Technology is integrated seamlessly into the content area and pedagogy. Along with instruction technology is used to track student progress and a vast array of data collection. Its use is broad and includes communication among students, teachers, parents and community. There are ample opportunities for professional development and restructuring. The use of technology is always evolving.
Elementary-
This site provides virtual manipulatives for a variety of math concepts.
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
This is an organization site where teachers can select appropriate site for their students and add them into their portaportal. This site makes it very easy for young children to access specific sites with just one click.
http://www.portaportal.com/
Middle School-
This site shows students work using technology.
http://169.244.34.69/~sirish/Math/Properties.html
High School-
This site in very comprehensive and provides many math links.
http://www.nwmissouri.edu/library/courses/education2/elementary.html
This site provides activities for applied mathematics.
http://www.c3.lanl.gov/mega-math/
You are so right about having the right balance between content, pedagogy and technology. If you are going to live in the center of TPACK, there needs to be balance.
ReplyDeleteI agree with you. They need to learn the basic first and once they have the concept, rather then continuing the drill and kill on paper, using the interactive games for them to practice. They can practice with their parents at home once you show them.
The top ten math website are also great for parent to use in the summer time with their kids. Illuminations site was my favorite because this is where students can experience the math in the real world and it makes them think deeply.
Checkout these sites when you have time.
http://www.uen.org/k-2interactives/math.shtml Utah Education Network connects math with real life problems.
http://mathforum.org/teachers/elem/k-2/ The Math Forum provides much resource that will make math come alive for you students.
http://edtech.kennesaw.edu/web/math-k-2.html Online Activities
It’s about trying one tool at a time. Think back when you started teaching, that’s what we all went through. If a strategy didn’t work, we tried something else. This just adds more tools and creates strategies that enhance the learning process for students. TPACK is a wick problem but over time can create incredible opportunities for both the teacher and students that are rewarding.