Idealism and Reality in Mathematics Technology

So, you're making your technology pitch to the school. You've just been to the conference and still feel the warm buzz of The Future, and you want the teachers to embrace the blogs, the wikis, the collaboration with schools in different cities, different states, different continents.


\n\n

Then you meet resistance.

\n\n

You up your game: you set up workshops, seminars, buy new software, buy new hardware, try to convert a few followers hoping entire departments will follow.

\n\n

Maybe you grab the English department and suddenly have every student in school with their own blog. Perhaps the technology people are putting student-produced videos on YouTube. You hear the foreign language folks are using Skype to call Mexico and work with a network of 5 classes.

\n\n

(Ok, ok, idealism here. But these things are at least possible.)

\n\n

But hit the math department –

And all I'm saying is, look, I've got some math to teach over here. And until I can count on two fingers the number of math teachers who are building a meaningful practice out of tech, until this stuff begins to approximate the importance of a cash register to a grocery store checker . . .

which is the good reaction. (Quote from Dan Meyer.)

\n\n

A lot of technology-coordination-types seem puzzled by this – why should math be any different from other subjects when adopting modern tech? – but it is, and there are (at least) three major reasons why.

\n\n

The difficulty in working with equations on a computer

\n\n

Sure, high school math teachers do statistics, and graphs, and even the occasional art project, but the meat of the content is working with equations. Even something easy to type like

\n\n

Solve for x: 2+x = 3

\n\n

can be a bear to demonstrate the steps on, and maybe could be done with fixed fonts and a fiddle like

\n\n

2+x=3
-2  -2
  x=1

\n\n

but this is a post-understanding sort of kludge, and it's not simply possible to work with things as easily as paper.

\n\n

Students 3.0

\n\n

The first graphing calculator was introduced in 1985, and it's been a battle ever since.

\n\n

One camp is fundamentally opposed to the notion of using graphing calculators, while the others think graphing calculators should be used at every level. This is still ongoing even though the AP Calculus tests require a graphing calculator and college expects students to arrive with the skills. (At one university I know of, they give incoming students a list of calculator tasks and say "if you don't know how to do these, figure it out, because we're not going to teach you.")

\n\n

Because the acceptance of graphing calculators is nearly a prerequisite for many modern math apps, arguments get stalled at the door. In other words, upgrading to wikis and the like is version 3.0, and 2.0 is still in beta.

\n\n

Sometimes there really is only one right answer

\n\n

With disciplines where multiple viewpoints are all equally valid, it's easy to have a collaborative discussion where every contribution is valued and important. When solving a problem with only one right answer, snarls can hit. Maybe one student dominates the discussion, or things shut down too early, or everyone is stuck in a way that requires massive teacher intervention. These issues often aren't discussed, and the edict to focus on process rather than solution gets messy in practice. (Although it's a start, and even if there's only one solution there may be multiple ways to get there.)

\n\n

How this week will roll

\n\n

I'm going to switch between general assessments of what's going on and specific examples. I'm going to make a wish list for what I'd like to see in modern technology, because my sentiments match closely with the quote above.

\n\n

I'm going to need your help. Some things I'm wanting really don't exist, but I'm hoping there's hidden gems out there I haven't come across yet. If nothing else, maybe a developer will take notice and fill the gaps.

\n\n

Jason Dyer, Guest Blogger

\n

Plants have awareness and intelligence, argue scientists

Research in plant neurobiology shows that plants have senses, intelligence and emotions.

Getty Images
Surprising Science
  • The field of plant neurobiology studies the complex behavior of plants.
  • Plants were found to have 15-20 senses, including many like humans.
  • Some argue that plants may have awareness and intelligence, while detractors persist.
Keep reading Show less

Vaping changes blood vessels after one use, even without nicotine

E-cigarettes may be safer than traditional cigarettes, but they come with their own risks.


John Keeble
/GETTY
Surprising Science
  • A new study used an MRI machine to examine how vaping e-cigarettes affects users' cardiovascular systems immediately after inhalation.
  • The results showed that vaping causes impaired circulation, stiffer arteries and less oxygen in their blood.
  • The new study adds to a growing body of research showing that e-cigarettes – while likely safer than traditional cigarettes – are far from harmless.
Keep reading Show less

Space is dead: A challenge to the standard model of quantum mechanics

Since the idea of locality is dead, space itself may not be an aloof vacuum: Something welds things together, even at great distances.

Videos
  • Realists believe that there is an exactly understandable way the world is — one that describes processes independent of our intervention. Anti-realists, however, believe realism is too ambitious — too hard. They believe we pragmatically describe our interactions with nature — not truths that are independent of us.
  • In nature, properties of Particle B may be depend on what we choose to measure or manipulate with Particle A, even at great distances.
  • In quantum mechanics, there is no explanation for this. "It just comes out that way," says Smolin. Realists struggle with this because it would imply certain things can travel faster than light, which still seems improbable.
Keep reading Show less