Month: January 2016

Total 9 Posts

Study: Implicit Instruction Rated More Interesting Than Explicit Instruction

Show the following five sentences to one group of students:

  1. A newly-wed bride had made clam chowder soup for dinner and was waiting for her husband to come home.
  2. Although she was not an experienced cook she had put everything into making the soup.
  3. Finally, her husband came home, sat down to dinner and tried some of the soup.
  4. He was totally unappreciative of her efforts and even lost his temper about how bad it tasted.
  5. The poor woman swore she would never cook for her husband again.

Then show all those sentences except the fourth, italicized sentence to another identical group of students.

Which group of students will rate their passage as more interesting?

For Greg Ashman, advocate of explicit instruction, the question is either a) moot, because learning matters more than interest, or b) answered in favor of the explicit version. Greg has claimed that knowledge breeds competence and competence breeds interest.

I don’t disagree with that first claim, that disinterested learning is better than interested ignorance. (Mercifully, that’s a false choice.) But that second claim is too strong. It fails to imagine a student who is competent and disinterested simultaneously. It fails to imagine that the very process of generating competence could be the cause of disinterest. It fails to imagine PISA where some of the highest achieving countries look forward to math the least.

That second claim is also belied by the participants in Sung-Il Kim’s 1999 study who rated the implicit passage as more interesting than the explicit one and who fared no worse in a test of recall. Kim performed two follow-up experiments to determine why the implicit version was more interesting. Kim’s determination: incongruity and causal bridging inferences.

That fifth sentence surprises you without the context of the fourth (incongruity) and your brain starts working to understand its cause and connect the third sentence to the fifth (casual bridging inference).

Kim concludes that “stories are interesting to the extent that they force challenging but resolvable inferences on the reader” (p. 67).

So consider a design principle for your math classes or math curriculum:

“Ask students to make challenging but resolvable inferences before offering them those resolutions.”

Start with estimation and invention, both of which offer cognitive benefits over and above interest.

[via Daniel Willingham’s article on the brain’s bias towards stories, which you should read]

2015 Jan 11. John Golden attempts to map Willingham’s research summary onto mathematics instruction.

Tracy Zager Offers You And Your Fact Fluency Game Some Advice

Thoughtful elementary math educator Tracy Zager offers app developers some best practices for their fact fluency games:

I’ve been looking around since, and the big money math fact app world is enough to send me into despair. It’s almost all awful. As I looked at them, I noticed I use three baseline criteria, and I’m unwilling to compromise on any of them.

She later awards special merits to DreamBox Learning and Bunny Times.

2015 Remainders

Let’s close out 2015. In this remainders edition:

  • Eight new blog subscriptions from November & December.
  • Five essential 2015 posts from this blog.
  • Three bloggers I envy.
  • Seventeen Great Classroom Action posts I never got around to posting.


  • We successfully goaded Brett Gilland into tweeting and blogging. His writing features art, wit, and insight for days. Best follow of my fall quarter.
  • Jason D’Arcangelo is an elementary math coach, making him rare company online.
  • Kendra Lomax does interesting work in elementary math education also, most recently with the University of Washington’s Teacher Education by Design project.
  • Damian Watson just came off a two-year blogging hiatus with a post featuring Malcolm Swan, Andrew Stadel, and cognitive conflict, which pushes all three of my buttons.
  • Meryl Polak likewise came off a maternity leave to post about her experience designing and implementing a 3 Act Math task.
  • Geoff Wake was one of my colleagues at the Shell Centre when I set up a tent in their offices several years ago. Great guy. Interesting thinker. I’m excited to see him maintaining a blog.
  • Jenn Vadnais does consistently interesting work with the Desmos Activity Builder. I’m tuned in, hoping to learn how she works.
  • Glen Lewis blogs thoughtfully about technology, learning, and engagement in math education.

These blogs are each low volume, producing maybe one post per month. There is zero risk of getting overwhelmed here. Just toss them in Feedly or some other RSS reader and enjoy their insight whenever they find the time to share it.

Honorable Mentions

I don’t have a lot of envy in me for other Internet math ed types — their followers, retweets, subscribers, etc. Just keep working. What does turn me green, what I do covet, though, is another blogger’s ability to stir up conversation, to mobilize and collect the intellect of his or her readers. In 2015, that was Dylan Kane, the blogger whose posts invariably had me clicking through to the comments to see what he managed to provoke from his readers, then scratching my head trying to figure out how he did it.

If your heart belongs to elementary math education, the best moderators I have found there are Tracy Zager and Joe Schwartz.

My Year in Review

If you’ve come to this blog only recently, here are five posts that received a lot of traffic and commentary this year:

Looking for favorites from the wider online math education community? Check out the #MTBOS2015 hashtag. If I had to award my own MVP, it’d be Elizabeth Statmore’s “How People Learn” and how people learn where she turns essential research into manageable practice.

Great Classroom Action

And now, shamefully presented without commentary, seventeen posts I read in 2015 that had me check myself and think, “That classroom action is great!” I haven’t shared these yet and it’s time to clean the cabinet.

“I’m gonna use my formula sheets and that’s the only way I’m gonna do stuff.”


The New York Times looks at the dismal testimony of an “accident reconstructionist”:

The “expert witness” in this case would not answer questions without his “formula sheets,” which were computer models used to reconstruct accidents. When asked to back up his work with basic calculations, he deflected, repeatedly derailing the proceedings.

Watch the video. It’s well worth your time and I promise you’ll see it in somebody’s professional development or conference session soon. It offers so much to so many.

And then help us all understand what went wrong here. What’s your theory? Does your theory explain this catastrophe? Does it recommend a course of action? If you could go back in time and drop down next to this expert as he was learning how to make and analyze scale drawings, how would you intervene?

My own answer starts off the comments.

BTW. Can anyone help us understand how the expert came to the incorrect answer of 68 feet?

BTW. Hot fire:

The motorcyclist’s lawyer filed a counter-motion to refuse payment to the expert witness. It contained the math standards for Wichita middle schools.

[via Christopher D. Long]

2016 Jan 2. The post hit the top of Hacker News overnight.

2016 Jan 2. One of the Hacker News commenters notes that the actual deposition video is available on YouTube.

Featured Comments:

gasstationwithoutpumps offers one explanation of the error:

3 3/8″ at a 240:1 scale gives 67.5′ which rounds to 68′

It is easy to mix up 3/8″ and 3/16″, which is one reason I prefer doing measurements in metric units.

katenerdypoo offers another:

It’s quite possible he accidentally keyed in 6/16, which when multiplied by 20 gives 7.5, therefore giving 68 feet. This is also a reasonable error, since the 6 is directly above the 3 on the calculator.

Jo illustrates a fourth grader’s process of solving the scale problem.

Robert Kaplinsky chalks this up to pride:

Lastly, it’s worth noting that eventually the heated conversation shifts from the actual math to whether or not he will do it or can do it. At that point it seems to become a pride issue.

Alex blames those awful office calculators:

The reconstructionist is given an office calculator, which doesn’t even have brackets. He needs to enter a counter-intuitive sequence of “3/16+3” to even get the starting point. When I was at school I remember being aware that most people wouldn’t be able to handle that kind of mental contortion. They’d never been asked to.
So what’s the problem, and how might we solve it? Well, the man’s been given the wrong tool for the job. He’s never been asked to use the wrong tool before & so this throws him. This makes him defensive and he latches onto an excuse about formula sheets.

Jeff Nielso:

The motorcyclist’s lawyer is the unrelenting classroom didactic whose motivation is based on making his student look and feel stupid. I was waiting for Act 2 where the lawyer would jump up, grab his felt marker, and demonstrate just how easy he can show the procedure.


Interesting note: my grade 7 math class is in the middle of our unit on fractions, decimals, and percents, so I showed them this video so we could work on the problem. I thought they’d get a chuckle out of it and feel good about solving a problem that the expert on TV couldn’t solve.

Their reaction was unanimous. They identified with the guy and wanted them to give him his formula sheets. Some of them were pretty riled up about it!

They’re quite accustomed to me showing them videos and doing activities that are designed to build up their understanding that everyone approaches things differently, and we’ll all get there even if we take different paths. This guy wasn’t allowed to follow his path and do it his own way, and they were unfairly putting him on the spot and forcing him to do it their way.

It’s a rich problem, so I’ll use it again, but I think I’ll set it up and frame it a little differently next time!