Teaching the Long Cut Before the Short Cut

Plus, one of my favorite companies gets new leadership.

Here is one of my kids working on a problem from the Art of Problem Solving’s Beast Academy books. Do you see the moment he experienced an epiphany?

Yep—right there at around 16 he put something together and realized he didn’t have to shade in every square individually. What do you call that moment?

A similar moment: I taught seventh grade last week here in Oakland, CA. We have this very nice lesson on equivalent expressions with some very nice interactives.

I wanted students to experience a tangible benefit of understanding that two expressions are equivalent so I did something annoying, even mean, in the warm-up:

In both cases, it would have been quite easy, nothing at all really, to share the epiphany with students, to share the short cut, to tell my kid that these are all the even numbers and here is where you’ll find them, to tell the seventh graders that if they combine like terms first they’ll see I’m asking them to do the same thing twice.

In both cases, however, it seemed useful to let the kids experience the long cut first, both so the short cut might make more sense and also because it feels good to feel your existing knowledge wake up, stretch out, and turn into something new.

Where else do you find opportunities for students to experience the “long cut” in their learning?

Featured Comments

Agasthya Shenoy was kind enough to take my last post in a spirit of constructive criticism and left a thoughtful reply:

But after my initial rush of “omg did I just kill Khan Academy??”, it became pretty clear that even if it did replace Khan Academy, it would not change the status quo: having a kid passively sit in front of a thing that’s talking at them. Add some personalization and maybe engagement goes up, but if engagement was the same as learning, every Duolingo user would be a polyglot.

SteveB confronts one of the biggest misunderstandings of math education across edtech:

It's not been my experience that each student has unique struggles with math, unique misconceptions that need personally tailored content to address the specific way they seem to be getting this wrong. Certain misconceptions crop up, over and over again, most students struggling with an idea are having the same misunderstanding about it, and it's the same misunderstanding the teacher saw come up last time they taught the lesson. So experienced teachers, before they even start the lesson, know the confusions that will come up, and sometimes try to head them off at the start or allow them to come up (may even design a question to bring this specific misconception into the light) so they can be addressed head-on.

Kelly Vaughan describes the reality of personalized videos in the classroom:

Imagine a scenario where all students are seeing different videos and different versions of videos tailored to their needs. Now a student asks for help, they didn't understand something in the video. The teacher in the room has very little insight into what the student saw and what potential pitfalls they might be encountering than they normally would. Do you have to watch some/all of the video to understand the student's misconception or area of confusion? [..] I appreciate a lot of things about it but feel that it wastes my skills and knowledge and actually kind of disempowers me from helping kids effectively.

Alex Sarlin critiques one of my points:

I think the claim that ‘there are already enough good educational videos out there, we don’t need any more’ is highly disingenuous

Immediately after Khan Academy made its splash with explanation videos, startup after startup raised a seed round to become Khan Academy + [better production value, animation, kid teachers, expert teachers, celebrity teachers, etc]. Almost all of them failed. Why do you think that is? Search YouTube for “adding integers” and you’ll find an endless scroll of videos explaining how to add integers. Alex, if we don’t have enough videos about adding integers now, how many more do we need before we start seeing transformative results? What variations on Khan Academy videos have we not yet tried? The challenge isn’t offering students better explanation videos. The challenge is offering students something better than explanation videos.

Upcoming Presentations

• I’ll be at ASU+GSV in two weeks with:

  • A 20m presentation Sunday 3:55p. Tentative title: The AI Rapture Ain’t Nigh: What To Do When You Stop Waiting.

  • A 40m panel Monday 3:00p with a collection of edtech & district types. Definite title: Let’s Get Serious: Pedagogy-First, AI-Enhanced Learning.

• Later that week, I’ll be in New York at Math for America to talk about technology, pedagogy, and student brilliance.

Odds & Ends

¶ Dylan Kane’s post on the value of Do Nows got me excited to use a paper warmup in the class I taught. He seems to use his warmups as a review of previous skills where I used mine to tee up the day’s instruction. You should probably listen to Dylan here.

¶ Speaking of The Art of Problem Solving, they just hired Ben Kornell as their CEO and Andrew Sutherland as their Chief Product Officer and I swear I do not know how to score this news. I like Ben and Andrew fine, but I love The Art of Problem Solving. Andrew ran Quizlet (classroom quiz software) and Ben was an executive at AltSchool, a company that believed children should be seen and heard and tracked through time and space with all of that telemetry sent into a giant machine learning Juicero to press out personalized learning pathways and it really didn’t work out. Best of luck here, guys. Please only do amazing things. 🙏

¶ 2 Hour Learning got some positive press recently in the Wall Street Journal and Fox News, both outlets naming the model as the solution for what ails education, neither mentioning that their positive results come from private schools that cost upwards of $40,000 per year.

¶ It’s almost refreshing, then, to hear the founders of Synthesis Tutor, math edtech software associated juuuust enough with Elon Musk for Mother Jones to lead with that angle, describe themselves as “unapologetically elitist.”

“We’re gonna try to create more runway for the brightest kids,” they say, and I, for one, think it’s helpful that they are not pretending otherwise. Synthesis Tutor is a two-part program with collaborative games and a tutor. I think it’s all quite neat and nothing close to a math education. The parents who use Synthesis Tutor will likely also need to adopt some kind of fluency software and a supplemental curriculum and stay quite closely involved with all of the above, all of which requires time and money that is most common to, yep, elites.