No one has ever succeeded
Multiplication facts, 17th century teaching, Let It Be, UBIK, and more.
Hey, friends! Let’s do this:
Thanks for reading and sharing my Q&A about addition facts; now on to multiplication facts. I just came across this paper that compared traditional drill to a flashcard routine that incrementally added new facts. The incremental approach worked better. I think this matters a lot for reasons I explored a few weeks ago in a post about my own multiplication teaching.
“During the seventeenth century, progress in teaching methods was underway. The teacher was expected not to exclusively turn his attention to students’ memorisation skills. His duty was to explain and bring forward students’ understanding and not only explain the examples in the existing book but add to them in order to enlighten understanding. The multiplication table was not to be learned only rotely without understanding,” from History of Teaching Arithmetic by Kristín Bjarnadóttir.
Math nerdery: take a bunch of regular pentagons and glue them together by an edge. From NRich, how many regular pentaons will you need until the pentagons form a completed ring?
What if you used a different shape instead of a regular pentagon? What about a regular hexagon? Or a regular 12-gon? I very much enjoyed hacking away at this problem yesterday, and maybe you will too. If you want to skip to an answer key, check out this post from Math Recreation.
I was wondering about the relationship between declarative knowledge (memories of facts) and procedural knowledge (my ability to follow steps to achieve some goal, roughly). Neuroscience expert Raj Raizada pointed me towards H.M., the partially lobotomized patient who was unable to form new factual memories but could still learn to perform new tasks. Fascinating stuff, here’s a whole video about him from TED-Ed.
I’ve been listening to Matthew Perpetua’s playlist of Beatles songs interpreted by Black artists. I hadn’t heard Ike and Tina Turner’s version of “Let It Be” and whereas in The Beatles version Paul sounds, essentially, comforted, Tina’s delivery sounds genuinely pained. The lyrics are totally different, but the most important change is a small one—there’s got to be an answer if they’ll let it be.
Reading: I read Phillip K. Dick’s UBIK back in college but am rereading it now, which is good, because I think I had forgotten pretty much everything that happens. I love how he lays out just a dozen or so bizarre conceptual contraptions in the first ten pages, but then plays with those (and just those) devices for the extent of the book. UBIK is so good.
My son asked me to read the first chapter of Hitchhiker’s Guide to the Galaxy out loud last night which is great because otherwise he’s only reading and rereading baseball facts. And how great is that first chapter! For me it’s a fantastic mix of humor and pathos and the joke about the factotum descended from Genghis Khan (mostly manifests in a confusing love of fur hats) is absolute perfection.
““Now listen,” he said, “trying to bite your own elbow’s all very well, but you know it can’t be done. No one has ever succeeded; every attempt has ended in a fiasco. Have you thought about that, you strange man?”” from “The Unbitten Elbow” by the Russian writer Sigizmund Krzhizhanovsky, in translation.
My favorite show to relax to is Grand Designs, where ambitious people try (and usually succeed) to build their dream home, and I didn’t realize that a recent season was on YouTube. You know you’re in for a good time when the couple tries to do it without an architect.
That’s it!,
Michael
From the paper you cite: Burns, M.K., Aguilar, L.N., Young, H., Preast, J.L., Taylor, C.N. and Walsh, A.D., 2019. Comparing the effects of incremental rehearsal and traditional drill on retention of mathematics facts and predicting the effects with memory. School Psychology, 34(5), p.521.
An observation noted by Sarah Hart:
"Although some have argued against practice with multiplication facts as an approach to enhance fact fluency (Boaler, 2015), direct comparisons with children who struggled with mathematics found that practice with multiplication facts was more effective than instruction in the concepts (Kanive, Nelson, Burns, & Ysseldyke, 2014), mnemonic strategies (Nelson, Burns, Kanive, & Ysseldyke, 2013), and teaching multiple strategies to complete computation (Poncy, McCallum, & Schmitt, 2010)."