## Making Math Visual and Interactive

*August 4, 2009 at 6:28 am* *
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Henri Picciotto is the Math department chair at Urban and started working with computers back on 1977. He reminisced about the commodore computer (wow, I remember those). The transition for the math department to the 1: 1 was natural. After all, they have been using 1:1 devices for many years- calculators. Before calculators, students would be shown a pattern and need to construct it by hand. Now, they are shown a pattern and they must construct a formula that will produce the pattern on their calculator. Since math teachers and students have been doing this for years, the transition to laptops was relatively smooth. With the advent of the calculator, “speed and accuracy in computation are no longer legitimate goals of math education.” New higher order thinking activities are possible and needed. While there is still a need of basic skills, one might challenge what constitutes a basic skill today. If you have any doubt, Henri shared Wolfram’s Alpha- check out www.wolframalpha.com. Enter an equation and see what happens.

So where does the computer fit into a math class? Henri believes it is there to visually support what has always been done. Programs like Cabri II and Geometers Sketchpad can help students visualize abstract math concepts and demonstrate their understanding of concepts. Interactive white boards (Smartboards) can be used to allow students to physically manipulate objects to build understanding and demonstrate the construction or meaning of a formula. While this can be done at the desk with various types of blocks, the solutions on the IWB can be archived and shared with others as there is no single solution to any of these problems. Both the software tools and IWB allow for the teacher to capture the students understanding. While there are many solutions, some are more “elegant” than others which can also provide insight to the students depth of understanding related to the concepts being covered.

Implications for learning with manipulatives include:

- The ability to capture understanding, generate reflection and discussion
- Complements and supports what is already being done
- The ability to visualize data

Moveing from manipulatives to visualization tools, we first looked at the ability to compare two data sets and explore their relationships. This can be done with simple temperature data on two scales- Fahrenheit and Celsius. These tools work well for explorations in Geometry as well. Using Cabri, we saw how a student could “discover” the relationships between angle of attack and rebound such as in a soccer match. How do you maximize the angle of a triangle as you move one point along a straight line? What relationships can you discover? Students can explore with the digital tool and get instant results. The same can be accomplished in a 3D environment as well. Cabri 3D allows for similar manipulations of geometric objects within the 3D environment so that all relationships can be explored. For example, how is volume of a pyramid related to the direction in which you move various points of the pyramid? What happens if you move outside the existing plane? These tools provide immediate feedback to the students explorations allowing them to discover the relationship for themselves. In another example, a student was able to take smoking data available from the web and use Fathom to discover relationships and trends.

Now, what about computer programming you ask? Well, Henri believes that all should have some understanding of programming. This provides another way to capture a student’s understanding of the mathematics. Using Scratch from MIT, students can tell a story with their math. Programming allows students to use the understanding and to demonstrate it to the world. Urban also makes use of ALICE, another programming language to develop and capture students understandings in mathematics.

So what are the implications for students learning math in a computer rich environment?

- Students are more motivated
- There is a lower threshold for access to information and concepts
- You can raise the ceiling by creating challenges for the students
- Students develop a deeper understanding of the mathematics

And implications for the teacher you ask?…

- Deepens understanding of Math as well
- The Teacher must learn the software
- Curriculum evolves- same courses but there is a different approach

Finally, remember that you can’t mandate this change. The teachers must “want” to explore these techniques and tools. They need to experience the reason why they can enhance their courses through the use of technology. Mandating the use of technology in the math department is almost certain failure. Explore the possibilities available to you. Scratch was designed for kindergartners but works well with 10^{th} graders. Consider your school culture and listen to your students. They will help you to learn about the new tools and the ways technology can help them learn.

Resources

Henri Picciotto Site: www.matheducationpage.org (Rich math resource)

Scratch: http://scratch.mit.edu/

Fathom: http://www.keypress.com/x5656.xml

Alice: http://www.alice.org/

Teacher Community for Scratch: http://scratched.media.mit.edu/

Diigo group for virtual manipulatives online: http://groups.diigo.com/groups/virtualmanipulatives

Leadership Resource:

Godin, S., Tribes: http://www.amazon.com/Tribes-We-Need-You-Lead/dp/1591842336

Seth Godin’s Blog: http://sethgodin.typepad.com/seths_blog/

I share the two Godin sites above because he writes about change on his blog and in Tribes. Here you can learn more about leading for change rather than managing status quo.

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