Recorded Webinar: Teaching Math in 2020

Just realized I never shared this webinar video from 2014 (you know, back when 2020 still seemed pretty far away).

What Does Teaching Math look like in 2020?

With every new iteration of technology, we create a generation of students whose primary media “language” for learning and interacting with the world is different than the one before it. In the last 5 years, technologies like free online videos, personalized learning software, and mobile devices, have been chipping away at the corners of education and traditional teaching. Technology-enhanced learning is here to stay, and it will alter the face of education, like it or not. This webinar is your guide to navigating and thriving in this new world.

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Strategies for Escaping the Echo Chamber

After the 2016 U.S. election ended, we all got a rude awakening to just how bad the echo chambers and filter bubbles have gotten. Our social networks are streams of one-sided news stories. News outlets are increasingly biased. Viral fake news spreads like wildfire and the implications are scary.

In light of recent events, I decided to make a conscious effort to escape from the echo chambers and redesign my consumption of news to try to get a better sense for what is a reflection of true reality and what is not.

filter-bubbles-and-truth

In case you find yourself in the same situation and would like to try to escape your echo chamber, here are some of my strategies:

1. De-newsed Facebook: One by one, I removed every single news source I encountered from Facebook using the “Hide” feature in the upper right hand corner of shared posts. This means I removed news sources I considered biased as well as those I consider legit. I will no longer allow Facebook to decide what news I see and what news I do not see. I just don’t want to see any news on Facebook. Period. On the bright side, Facebook has returned to a state where I actually do see pictures of friends, rants about “new math” and cute cat photos – which is a nice haven from what it had become. This removed my largest echo chamber source of news.

In case you don’t know how to turn off feeds from sites in Facebook, here’s what that looks like:

hide-in-facebook

2. One reliable news source: I read a single reliable news source each morning (for me that is the New York Times. In particular, I read using the “Today’s Paper” app, which delivers the paper in a very similar fashion to the printed version, without ads. This is important because if you just visit a news site, you still fall victim to following only the stories you’re likely to click on instead of seeing a list of all the stories of the day. While the NY Times might not be your choice for most unbiased news, I figure this is balanced by living in conservative Utah. Don’t judge. Also see #3.

3. Highly-biased contrast bumpers: After reading my daily dose of news, I  go to Blue Feed Red Feed, a project from the Washington Post. This provides the most extreme liberal and conservative “viral” posts on a variety of topics. While seeing some of these stories makes me a bit ill, I find it better than seeing delivery from friends and family on Facebook (with additional commentary from them that makes me even more ill). What I’m starting to find is that often both “sides” often tell an incomplete story, the part of the story that makes them look good or the other side look bad. One day last week, the blue feed had stories like “Trump has only lobbyists in his cabinet” and the red feed provided stories like “Trump fires all lobbyists from his cabinet.” Reality was somewhere between those two stories – Trump did seem to have developed a cabinet with a lot of lobbyists AND he then fired most of them.

“Truth” is somewhere in between the bumpers of the most liberal stories and the most conservative stories. But knowing what the bumpers are on these extremes helps me rationally evaluate the stories I see throughout the day and also helps me with #4.

4. Avoidance of clear click-bait: Armed with the most atrociously viral clickbait of the day (from step #3) I can more clearly avoid stories I see on Twitter and banner links to stories that are the viral nonsense of the day. Clicking on this stuff means the world will just produce more of it. Making these sites profitable to advertisers is how they stay in business. If I had not read some of the viral headlines on Blue Feed Red Feed, I would be more susceptible to clicking on stories that are obviously designed to goad one side or the other.

5. No TV News: TV news is designed to be entertainment. So if you’re watching TV News, I’d really consider stopping all together. You don’t realize how bad it is until you remove yourself for a while. When I am forced to watch it in airports, I find it hard to believe that it provides any real value other than making us all terrified of each other (see #6).

6. Actually talk to people who are not like you: I am making a more active effort (see Lean in to the Discomfort) to try to talk to other people who are not “just like me” more: At the gym, in the grocery store, and while out on walks. I am trying to seek out those who are from other generations, other educational backgrounds, other religions, etc. and engage in conversation. We have got to put down our echo-chamber-filled devices and apps and get to know the people in our physical proximity again.

Those are my strategies, what are yours? And if you don’t think you’re in an echo chamber … well, how do you know you’re not?

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Why Random Practice is Important

As educators, we often find ourselves in the uncomfortable position of trying to explain why students don’t seem to have learned what we know we’ve taught them. Economics instructors ask math instructors, “How come these students who have taken College Algebra still don’t understand slope?” Science teachers ask English instructors, “How come students still don’t understand basic grammar rules when they write in my science class?” The key here is to understand that students aren’t learning skills in a way that helps them to transfer the skills to new situations – the learners have compartmentalized the skill to a particular domain and it doesn’t get sufficient escape velocity due to lack of random or varied practice.

In sports, there has been some eloquent research showing that random practice leads to more transferrable and long-lasting skills than blocked practice. It’s worth taking a short dive into this research area.

shea-and-morgan-research

The gains shown in blocked practice erode when we look at longer timelines. Random practice provides short-term gains AND holds up in the long-term.

Watch the 16-min video “Motor Learning: Blocked vs Random Practice” by Trevor Ragan. He does a lovely job of walking through some of the motor learning research that very eloquently shows that “random practice” is more effective for transference and long-term retention than “blocked practice.” This is basically the same concept as massed vs varied practice discussed in cognitive science.

If you’re interested in reading the research that Ragan touches on in the video, you can find some of it in these papers:

Shea, J. B., & Morgan, R. L. (1979). Contextual interference effects on the acquisition, retention, and transfer of a motor skill. Journal of Experimental Psychology: Human Learning and Memory, 5(2), 179.

Hall, K. G., Domingues, D. A., & Cavazos, R. (1994). Contextual interference effects with skilled baseball players. Perceptual and motor skills, 78(3), 835-841.

In education we are really good at having students practice the “Do” of the “Read, Play, Do” process that Ragan describes in the video. “Do” skills are orderly and easy to monitor and assess. How can we shift to the messier strategy of having students practice all three parts of the process? For students you teach, what is the equivalent to practicing basketball shots from a variety of distances with different blockers around them?

Weekly Teaching Challenge: Consider all the topics you teach next week and design one new activity that focuses on “random” practice instead of “blocked” practice.

If you’d like the weekly teaching challenge delivered to your inbox each Friday, sign up to receive the Challenge here.

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Lean in to the Discomfort

When you walk in to a room full of people, choose someone who seems the most different from you (on the surface) or the person that seems the “scariest” to start a conversation with. Start there. Lean in to the Discomfort of having that awkward first conversation. In all likelihood, you DO have something in common with the person – seek to find it. If you always start with the conversation that you perceive to be the most difficult one to have, you will, over time, reduce your own fear of talking to strangers.

Diagram showing 10% of the iceberg above the surface

90% of an iceberg is unseen beneath the surface of the water

About 90% of an iceberg is unseen beneath the surface of the water and likewise, the majority of who we are as a person is beneath what you can see or hear on the surface. Consider all the characteristics of a person that you can’t “see”:

  • what sports do they like
  • what do they do for a living
  • what is their family like
  • what do they do for fun
  • where do they live
  • what do they do when they hang out with friends
  • what are their favorite foods

Whether at a conference or having Thanksgiving Dinner with far-flung relatives, there is so much to learn from the people that surround us. But we have to actually engage them in conversations and interact. If we want our students to interact more to learn, we need to get better at modeling this willingness to have conversations with strangers or those who differ from us.

When I walk into a room and feel the first uncomfortable feelings of having to mingle or that I will be alone in a room full of people, I remember the phrase “Lean in to the Discomfort,” take a deep breath, and begin the first conversation.

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AMATYC Keynote Notes: Durable Learning

In the 2016 AMATYC keynote, I covered three main themes:

  1. Interaction & Impasse
  2. Challenge & Curiosity
  3. Durable Learning (this post)

Three triangles surrounding a central triangle with the letters C, I, and D

Here are references and resources for Durable Learning:

What is durable learning? The learning design practices that make learning “stick” over the long-term. These include (but are not limited to) spaced repetition, knowledge retrieval, interleaving, and varied practice.

A really good book on the subject of durable learning is “Make It Stick” by Brown, Roediger, and McDaniel.

We also took a dive into some cognitive science and again, there is a fantastic, easy-to-read book I recommend “Cognitive Development and Learning in Instructional Contexts” by James Brynes.

We explored the idea of a schema – a mental representation of what all instances of something have in common (plural is schemata). In particular, schemata help you to categorize your experiences,  they help you remember what you are experiencing, they help you to comprehend what you are experiencing, and are important in developing the ability to problem solve.

Visual representation (with no numbers) of distribution - shown as a set of arcs

A schema for distribution

When confronted with a new situation, learners try to run a schema they already have. This leads to all sorts of interesting misconceptions.

not-distribution

By engaging the learner in varied practice, we hope to modify the existing schema.

No numbers representation of distribution with visual arcs and plus-minus signs to hold the spaces

A better mental schema for distribution because the spaces are now held by plus-minus signs

To help the learners refine schema, we can abandon massed practice for varied practice. In massed practice, the learner does nothing but activate the exact same schema over and over. In varied practice, the learner has to distinguish between different schemata in order to successfully complete the practice.

massed-practice-and-varied-practice

There is a lengthier talk I gave on cognitive science in the context of algebra called “Algebra is Weightlifting for the Brain” (not the world’s best recording, but you’ll hear more about the ideas of Information Processing Theory and see plenty of math examples).

We didn’t quite get to interleaving in the talk, but we will cover that during the teaching challenge.

What is the Teaching Challenge?

For the next year, I will send you a teaching challenge every week to help us, together, change the way students learn and engage. The challenge will be delivered each week by email and will include:

  1. Something to learn or ponder
  2. Best practices shared by participants in previous challenges
  3. A new challenge

Sign up for the teaching challenge here. All are welcome.

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