Monday, October 30, 2023

Playful Math Carnival 169

 Do you want to host the 13^2 Playful Math carnival in October? A month that had a Friday the 13th

Yes, please. Should have been on 10/13 instead of 10/31 but... apologies.

169 is a palindrome in two number bases less than 16. Which do you suppose?

All odd squares are centered octagonal numbers, but 169 is also a centered hexagonal. (Visualize more with Alex CHIK's GeoGebra.)

It is the smallest square that is prime upside down! What on earth could the next one be? Also 1666666999999999 is prime. What would you call that property? (Both via PrimeCurios.)

It's the last square in the Pell sequence, which are connected to approximations of π. What numerator n makes n/129 an approximation of π?

I'm using tangrams in an elementary math ed course as our primary manipulative to talk geometry, so I maybe have been too on the lookout. Simona Riva has a great GeoGebra collection of activities. Polypad has a great tangram puzzle collection. Here are some I found on a cereal box! But most of all, you have to see Paula Beardell Krieg's amazing series of tangram posts from this summer.

Futility Closet shared a ridiculous Lee Sallows pangeomagic square.

Bakingmoomins made a Hat Hat with the new Einstein tile.


Always on the lookout for games. Tracy Proffitt has an awesome collection, well organized.

Interesting double or halve game from NRICH.

Sarah Carter shared the Ghost Game, fun logic/strategy game.

Sophia Wood and Kate Nowak with a great math game over on Brilliant: Halfsies


Jenna Laib interviewed Kindergartners about zero. Great read!

Steve Phelps is the most amazing teacher with tech I know. He has a geometric constructions Desmos activity.

Eugenia Cheng on NPR addressing "Is math real?"

Mathigon now has an online implementation of Multiply by Heart by Dan Finkel.

NCTM has a new line of kids books on Powerful Mathematicians Who Changed the World.

Karen Campe has a calendar of problems every month, solutions at the end of the month. Here's October.


Sara VanDerWerf pointed out that SNL did a measurement skit. Warning: actually funny.

Kassia Wedekind shared a McSweeney's post from a teacher about teaching a curriculum with fidelity. Warning: a little too close to reality.


Fashion? Libo Valencia has #mathplay t-shirts to go with his cool book.


Sophia Wood started #Mathober a few years ago. Art and more on a math theme. Find many posts on Twitter or Mastodon or Bluesky. I've been liking Katie Steckles' π minute GeoGebra videos.

Last Stop

Last but not least, two playful bits from my students! Corinna, Leah, Jordan, Kacy and Jill made a Spooky Monster Escape Room in Desmos Activities. Ryan, Keri, Alex, Anna, and Emma have a new headbandz inspired math game for grades 5 and up called Math Heads. And by up, we mean up to college math majors!

At the home of the Playful Math Carnival, you can find previous, like 168 at find your factors, or connect to host yourself. I'd highly recommend it! Find the next one, Nov/Dec at the Fairy Math Mother. Should be magical.

This is my stop! Hope you had fun.

P.S. This will get you to go. Ed Southall asked AI to make images of people enjoying math...

Thursday, October 5, 2023

Elicit Student Thinking

In Michigan, at least, the high leverage practices are dominating the teacher preparation conversation. For our new certification programs, the state waaants to know where are we doing it. Nothing new there, just... enumerated. Some are beyond what we can do in math classes. But where it all starts for us, I think, is eliciting student thinking. I have an interview project coming up, in an elementary teaching class I'm teaching for the first time, and thought to ask on social media what teachers do or think about this core process. (Used to just be Twitter, now I'm trying Mastodon and BlueSky.)

#classroommath #mtechat one of the main objectives with preservice teachers is to work on the practice of eliciting student thinking. What advice do you have for them? How did you get better at it? What are you working on now?

Lani Horn had a quick, impactful response (bsky). "I find that the work of eliciting needs to be followed with some work on listening and interpreting. i have seen some folks stop at just eliciting, and it becomes "what do you think? what do you think?" without any connections built."

Elizabeth continued: "OMG yes. Learning to listen is a challenge for many pre-service & new teachers, and I often wonder if this is because they feel so rushed/anxious themselves.

Listen, swallow, take a breath -- just because a student has spoken in response to a prompt doesn't mean I've heard them yet.

Another thought -- could we also stipulate that asking a clarifying question can also be also an essential part of teacher listening?"

Shelby Strong also responded to Lani: "YES. It's not enough just to hear a bunch of different ideas; what is similar and different about those ideas?"

Learners are definitely interested when they know you are interested. How many times have they had a teacher gloss over their answer while really just looking for what they want to hear. "Tell me more" is a phrase I try to use a lot.

Mike Steele said: "When you catch yourself thinking about what to say next when students are talking… don’t. Focus on listening. Take a beat before speaking."

Nick Smith noted: "I like the other replies here and I'll add, "Never say anything a student can say." 

I think too often I'm doing the thinking for them. The less I talk, the more I hear their thinking instead of my own." 

Good indicator. Especially tough as a novice, maybe, when you have to think more about what's next.

Shelby also said: "Get students to turn and talk and prep them that you are going to ask them to share what their partner said. It lowers the stakes because it's just one other person listening to their ideas, and it takes the pressure off of sharing their own ideas."

Karen Campe responded: "Oooh I like that... encourages careful listening to your partner!"

Coutney Flessner added: "I LOVE using this strategy. I also don’t have students share their work. They already know it! The class analyzes it and we ask the author if we missed anything. Kids are significantly more engaged with each other and math with both these instructional routines. Ryan Flessner introduced both to me!"

Your students who always talk will still try to say what they said, but I think this is a moment for them to hear what others see them as saying. 

Karen was also thinking about wait time: "An important step is to give Ss individual think time before talking to partners/groups or sharing out to class -- the T shouldn't solicit any responses until that essential time has happened. 

That way, everyone engages, & no priority to fast thinkers or those who can do it in their head. 

Then you can elicit their thinking.

I was so bad at wait time early in my career that I had to actual count on my fingers (behind my back) to be sure I gave thinking time before discussing. 

Tierney Kennedy also has a teacher hack: "My advice: take a drink bottle with you to groups. When kids ask a question or when you ask them one, take a mouthful. It builds in an automatic thinking moment. Plus sometimes they end up answering their own question." 

Trey Goesh thinking similarly: "I like to have students take 60 seconds to record their ideas silently before having them talk to a partner.

You can feel the tension ratcheting up as they collect the ideas they want to share."

Wait time is such an amazing tool. Really lets learners know you are really asking, not just checking 'any questions.' 

Dee Crescitelli has the objective in mind: "Listen to student thinking with an ear for the mathematical goal of the lesson… we should be thinking about the math story the classroom discussion is telling. How do student responses & representations connect to tell that story?"

Peg Cagle also thinking about what you're asking: "Make sure that you ask about their ideas/thinking not their “answer”, and make sure they know you are genuinely curious about & interested in what they tell you. Answers w/o thinking-worthless. Ideas w/o answers, immensely valuable…& to everyone in the room!" 

Tara Maynard: "Try to always find a positive in their thinking and then find the misconception. Ask students to write, draw, sketch how they found their solution, not just verbal interaction. Always trying to provide feedback that is helpful yet doesn’t take hours." 

This might violate Mike's advice to keep your mind where it's at, but I do this a lot, thinking about the summary/reflection for the lesson. I probably open floor question too much to summarize, but if there is an idea missing, I like knowing whom to call. 

Arika Byman said: "Model genuine curiosity every chance you get. Provide sentence/question stems to help students organize and articulate their thinking. Be patient and persistent!" 

The stems idea is another idea of which I don't do enough.  The curiosity is crucial. There are so many things I genuinely want to know about learner thinking, why not ask?

Another few people were thinking about the math about which you're asking:

Rose said: "# talks and visual patterns tell Ss you want to know what they 💭 esp bc everyone has dif ideas. Shifted my mindset too!

Working on: design small group tasks/materials that encourage Ss to share their ideas w/each other. Generally ⬆️ S talk. S talk = window into their thinking."

Sian Zelbo said: "One aspect of eliciting student thinking is asking questions that are open-ended enough that you get a range of answers.  If you ask something that is essentially procedural students can't share their thinking bc they have none."

Lastly, is sharing thinking a part of your class culture?

Susan Russo said: "One thing that helps is to model your own thought process out loud. Not: this is what I’m doing but: First I notice this, and that leads me to think it might be good to go this way so I’ll try that and see where it leads. But now I wonder… 

If you are also sharing genuine thinking it is a great model for when you ask for theirs. 

What did you notice about these responses? What would you add or emphasize? There's a comment section below just waiting for you.

I'm really grateful to all who responded. Whatever media site we wind up on, I'll be there, because talking to teachers is the best way to teach better.