Mathematizing: Seeing Numbers, Supporting Science
Mark Roddy, PhD - Seattle University
College of Education - Master in Teaching Program
Mark Roddy, PhD - Seattle University
College of Education - Master in Teaching Program
"mathematizing" It's a word I am using to refer to the process of seeing and coming to understand aspects of the world through the abstraction of numerical representation. I am a teacher educator and the purpose of this little site is to provide teachers with some aids for mathematizing in science and mathematics classrooms.
The National Council of Teachers of Mathematics recently (summer 2021) published my work in a site called "Math Sightings." There you will find eight lesson plans and eight associated "stories," all of which are examples of this approach to math pedagogy.
The precursors to this work were some "Northwest Math Sightings" written for the WSMC publication, Washington Mathematics. These articles are all about seeing mathematics in our surroundings here in the upper-left corner of the United States.
Click on a title to access the article:
• Tidal Math,
• Tree Ring Math,
• Sun Sine Math,
• Cooling Math,
• Seeing the Light,
• Bracken Fern Math.
The precursors to this work were some "Northwest Math Sightings" written for the WSMC publication, Washington Mathematics. These articles are all about seeing mathematics in our surroundings here in the upper-left corner of the United States.
Click on a title to access the article:
• Tidal Math,
• Tree Ring Math,
• Sun Sine Math,
• Cooling Math,
• Seeing the Light,
• Bracken Fern Math.
Mathematizing with Grow Beasts
I have done a great deal of work with Grow Beasts as a way to engender active learning in math and science. You plunk them into a bowl of water and over the course of a few days they grow and grow and grow. What if you put them in root beer? They still grow ... or do they? How about salt water? Weak coffee? Predict, measure, record, graph, model. These little toys give you and your students, a great tool for scientific investigation and mathematizing. (Consider also their cousins, Grow Spheres.)
Click Here for my Grow Beast site.
And here are some ideas for a simple Grow Beast project.
I have done a great deal of work with Grow Beasts as a way to engender active learning in math and science. You plunk them into a bowl of water and over the course of a few days they grow and grow and grow. What if you put them in root beer? They still grow ... or do they? How about salt water? Weak coffee? Predict, measure, record, graph, model. These little toys give you and your students, a great tool for scientific investigation and mathematizing. (Consider also their cousins, Grow Spheres.)
Click Here for my Grow Beast site.
And here are some ideas for a simple Grow Beast project.
Here are a few web sites and applications that will supply various numerical representations of our world - great for mathematizing.
Google Earth - so many numerical and graphic representations of real time phenomena here, and so much potential for students to create and investigate according to their own interests! For example, go to the weather layer. Turn on the clouds. Turn on the "Conditions and Forecasts." Now, what happens to the temperatures in Fargo when a cold front goes through? How about in Sydney, Australia? (See also - Google Earth for Educators: http://sitescontent.google.com/google-earth-for-educators/)
PhET - dozens and dozens and more dozens of interactive science simulations from the University of Colorado at Boulder.
- Want to play around with the ideal gas law and see numerical representations of the consequences of that desire? Try this: Gas Properties
- What happens to the current in a simple circuit when you add a couple batteries and a resistor and a paperclip? Find out using the Circuit Construction Kit.
- What happens when you drop a 5 kg chunk of bricks into water? oil? What about the same mass of wood? Try the Buoyancy Playground.
There are so many more.... (Consider also - PhET "Teacher Ideas and Activities: http://phet.colorado.edu/en/for-teachers )
- Want to play around with the ideal gas law and see numerical representations of the consequences of that desire? Try this: Gas Properties
- What happens to the current in a simple circuit when you add a couple batteries and a resistor and a paperclip? Find out using the Circuit Construction Kit.
- What happens when you drop a 5 kg chunk of bricks into water? oil? What about the same mass of wood? Try the Buoyancy Playground.
There are so many more.... (Consider also - PhET "Teacher Ideas and Activities: http://phet.colorado.edu/en/for-teachers )
"Sheep Dash" Here's a fun thing you can do to gather data in cooperation with a restless flock of British sheep.
Tranquilize five sheep. Record your average and try five more. Did you get better? Five more? Try it with your left hand. Try it with the volume turned down. Does it make a difference? How much? Here's a handout describing how to use a spreadsheet to do some additional analysis:
BBC Sheep Sleep Hand out.pdf
Tranquilize five sheep. Record your average and try five more. Did you get better? Five more? Try it with your left hand. Try it with the volume turned down. Does it make a difference? How much? Here's a handout describing how to use a spreadsheet to do some additional analysis:
BBC Sheep Sleep Hand out.pdf
Want more weather data?
• Concentrating on the NW: Gray Skies
• Concentrating on everywhere else: WeatherSpark
• Concentrating on the NW: Gray Skies
• Concentrating on everywhere else: WeatherSpark
• Google's Ngram Viewer Specify sets of n words (up to four words in a set) like "know nothings," "greenpeace," or "mutual funds," and examine the frequency with which they appear in books that Google has scanned - and how that frequency has changed over time.
• Wolfram Alpha has become quite an extraordinary site for quantifying, analyzing, and representing life. Give it a try: https://www.wolframalpha.com/
(Try entering your name...)
(Try entering your name...)
• 101 Questions I think of this as Dan Meyer's crowd-sourced mathematizing site! Yay!
Here is the handout from my 2019 NCTM presentation at the regional conference in Salt Lake City. "Some Choice Math Activities HO.pdf"
some_choice_math_activities_ho.pdf |