Learning at Scale Slides from ICTCM

Mar 11, 2017 by

Learning at Scale: Using Research To Improve Learning Practices and Technology for Teaching Math

In the last 5 years, there has been a rise in what we might call “large-scale digital learning experiments.”  These take the form of centralized courses, vendor-created courseware, online homework systems, MOOCs, and free-range learning platforms. If we mine the research, successes, and failures coming out of these experiments, what can we discover about designing better digital learning experiences and technology for the learning of mathematics?

 

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Celebrate the Errors in Math Practice

Jan 11, 2017 by

Dear math students,

As you work through your mathematics practice, I’m going to challenge you to embrace making errors in an entirely new way. 

Many students believe that every problem in math homework should be perfectly constructed with no errors. It might look something like this:

A nicely ordered problem solution with no mistakes.

 

But when it’s time to study after the initial problem run-through, what does this perfectly constructed problem say? Does it coach you on remembering how you struggled? Does it remind you where you made an error? No.

When you make an error as you’re working a problem, please don’t erase it from the face of the earth. Certainly you should learn from the struggle and complete a correct solution, but record your deviations from the straightforward solution path in another color. Leave yourself notes (also in a different color) to remind you what you should have paid more attention to the first time around. Maybe that would look something like this:

Worked problem with highlights and notes to self

 

 

Sometimes you’re going to recognize but you don’t have the right answer but you’re not going to be sure what’s gone wrong. You should always try first to figure it out yourself first. This process of error analysis in a variety of different situations is key to developing problem solving skills in mathematics. Without exploration of the problem space (which happens with error analysis), your brain is just recording rote procedures without the ability to transfer those procedures to new kinds of problems. It will, essentially, stunt your mathematical growth.

Now, I don’t want you to get to the point of tears or breaking your keyboard out of anger. If you get near that stage please just ask a question (email, discussions, chat-a-friend, etc), leave a sticky note on the page as a reminder to go back, and move on to the next problem or section of problems. Just switching to a slightly different problem can not only get you unstuck, but sometimes give you insights into the “stuck” problem. 

When you figure out how to do the problem you were stuck on, make sure to go find that flagged problem (remember the sticky note?) and annotate your corrections.

Worked math problem with cross-outs and restarts and notes to self.

 

Now you might be thinking “why do all these error corrections and problem annotating in another color?” When it comes time to study for your major assessments, you will be able to see the places where you stumbled the first time you tried the problem. These “notes to self” are the places where you’re most likely to make the same mistake again. They benchmark places to remember to be careful and show you problem types to repeat practice before an exam.

Celebrate your errors.

Embrace the messiness.

Learn from your mistakes.

Study from your struggle points.

And be great at mathematics!

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WolframAlpha Facebook Report

Apr 12, 2013 by

This is a delightful exercise that everyone seems to love. WolframAlpha will provide you with an extremely detailed analysis of your own Facebook data including visualizations, world clouds, graphs, and more.

Graph of Facebook Activity over time

 

 

 

Here’s how:

  1. Go to WolframAlpha.com.
  2. Type “Facebook Report” and execute the search.
  3. Allow WolframAlpha to have access to your Facebook account by clicking on “Analyze my Facebook Data” and following the directions.
  4. Wait while the data is analyzed.

Note: Sometimes the report seems to stall after 100% of the data is analyzed. If this happens, simply repeat steps 1-3. The second time, the report seems to load just fine.

Enjoy!

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Data Sleuthing

Apr 4, 2013 by

Khan Academy Idaho is a grant-funded initiative to help K-12 teachers in Idaho integrate digital devices and the Khan Academy program into their math classrooms. Yesterday I gave a keynote there called “Between a Rock and a Hard Place” about (1) the challenges facing math educators and (2) Data Sleuthing, a way to encourage math curiosity and data literacy in students.

Resources from this presentation:

Homework from the Presentation

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Level Up: Video Games for Learning Algebra

Nov 13, 2012 by

Last week I gave a presentation at AMATYC about video games for learning algebra. As usual, Mat Moore did a fantastic illustration for the prezi.

It was staged in five levels:

  • Level 1: Why use games?
  • Level 2: What is a game? (manipulatives, puzzles, and games)
  • Level 3: Become a Math Game Critic
  • Level 4: Play GOOD Games
  • Level 5: Good Algebra Video Games?

You can click through the Prezi below.

 

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