Posted in Math videos

A 21st century skill: reading and writing codes

In Should We Do Away with Calculation, Conrad Wolfram says that if you want to know if students understands a computational procedure, ask them to do a program, let them code it.Here is another video which calls students to learn coding. The video titled What Schools Don’t Teach featuring Bill Gates, Mark Zuckerburg, and other software developer giants speaking, urges kids to learn how to write codes. Reading and writing codes should now indeed be part of our curriculum. And for the arts inclined? Well to borrow from WordPress: ‘Code is poetry’.

What schools don’t teach video promotes code.org, a nonprofit foundation created to help computer programming education grow.

To drive the point, see the graph below from code.org.

computer programming

Posted in Math videos, Mathematics education

Should we do away with calculation?

We don’t need to spend much time with calculation. Technology can do that for us. We can use the extra time saved for engaging in ‘higher-level’ thinking. Mr. Conrad Wolfram in his TEd Education Talk makes a lot of sense in this video. But, I have my reservations but not because I’m for teaching a lot of calculations.

We also said the same during the era of calculator. Did it improve the math education of our youth? So, what makes us think it will happen in the age of Mathematica, GeoGebra, Sketchpad? There is something in our math classes or math education that’s stuck in the middle ages, that’s not keeping with time. Unless we find and address this, no amount of technology can help us.

Posted in Algebra

Guest Post: Mega Math Challenge

Only a few days remain to register for Moody’s Mega Math Challenge

math challengeSo what’s the best way to teach mathematics to the fast-paced, multi-tasking young people of the information age? Crunching numbers with pencil and paper and poring over the pages of conventional textbooks just doesn’t cut it with this tech-savvy generation, so used to instant gratification!

Today’s math teachers, for their part, are finding new ways to make the subject relevant and engaging for their pupils, ultimately helping them use mathematics to solve everyday problems. There are many ways to stimulate the children of the digital revolution but perhaps none capture the spirit of applied mathematics like Moody’s Mega Math (M3) Challenge (http://m3challenge.siam.org/about/), which allows students to do rather than just read, memorize, or calculate.

The M3 Challenge is a free applied math competition for high school students that connects textbook and classroom learning to the “real world” by simulating the genuine and practical issues we face as a society and in our daily lives. Teachers who coach M3 Challenge participants realize the contest’s potential to educate students in math modeling. And while teacher involvement is critical – they register and prepare teams of juniors and seniors – the responsibility of developing a viable solution paper by the end of Challenge day (and possibly winning a share of the $115,000 in total scholarships) falls squarely on the shoulders of the thousands of students who participate each year.

Challenge Champion

“You have to let the kids do their thing. I try not to direct, I try not to drive,” Ellen Leblanc, an experienced coach from New Jersey’s High Technology High School, shared. “Initially, and prior to the Challenge weekend, the students and I do a little bit of brainstorming: what could the Challenge problem be this year? If the question were “X,” how would you approach it and what is important? Beyond that, you have to leave it up to the students,” she said.

With so much technology at their fingertips, high schoolers in 2013 are used to doing more than just reading and answering textbook problems. Some have the benefit of being offered math modeling classes at their high school, some experience technology-based lessons in their classrooms, and others use the skills in their math toolboxes for extracurricular activities.

“This is really the only competition in the nation where kids come together and have this day-long charrette in a high-performance work team that is so similar to what we do in industry. To have that experience as a high school junior or senior really opens their eyes to what a career in a math-related field can be like. It is incredibly influential,” explained Mary Redford, team coach from Nashoba Regional High School in Massachusetts.

Registration must be completed by each team’s teacher-coach by Feb 22 at 6:00 p.m. EST. It is both quick and easy and there are no fees whatsoever. Register now at http://m3challenge.siam.org/participate/.

Posted in Algebra, Calculus

8 Different Ways to Think of the Derivative

In his paper The Transition to Formal Thinking in Mathematics, David Tall presents W.P. Thurston’s seven different ways to think of the derivative:

  1. Infinitesimal: the ratio of the infinitesimal change in the value of a function to the infinitesimal change in a function.
  2. Symbolic: the derivative of x^n is nx^n?1, the derivative of sin(x) is cos(x), the derivative of f ? g is f ? ? g ? g? , etc.
  3. Logical: f ?(x) = d if and only if for every ? there is a ? such that when 0 <|?x|< ? , then slope
  4. Geometric: the derivative is the slope of a line tangent to the graph of the function, if the graph has a tangent.
  5. Rate: the instantaneous speed of f (t) , when t is time.
  6. Approximation: The derivative of a function is the best linear approximation to the function near a point.
  7. Microscopic: The derivative of a function is the limit of what you get by looking at it under a microscope of higher and higher power. (Thurston, 1994.)

David Tall argued that the list excluded the global concept of local straightness so he added added the eighth that he believes that other 7 can be built.

8. Embodied: the (changing) slope of the graph itself.

In the same paper, David Tall presents a learning framework for derivative based on his Three Worlds of Mathematics Framework.

understanding derivative