Book Celebration

To celebrate the release of the newest great and greatest new children's math book... by which I mean Which One Doesn't Belong? by the #MTBoS' own Christopher Danielson, of course... I thought I'd recap some of my favorite math picture books. This list also has MTBoS support, as I solicited suggestions from the MTBoS for a colleague.

Get yours here.

The request was for a parent with a mathematically curious child (really, could be anyone then, am I right?) of 4 or 5 years.

Top:

• Moebius Noodles, Maria Droujkova's great book about big math ideas to explore. There were articles about calculus in kindergarten when it first came out.
• Great new book: Which One Doesn¹t Belong. OK, I'll say more. I love this book because it's clever and pretty, but also because it can teach you how to read mathematically rich literature.
• Math Curse, Lane and Scieska: just the best math book ever written. Nearly anything can be a problem, you know.

Great:

• Anno's Mysterious Multiplying Jar, or anything by Mitsumasa Anno. Just charming books, and lovely besides.
• Spaghetti and Meatballs For All, Marilyn Burns: my favorite of the explicitly mathematical genre. Tang and Murphy have their place but Burns is the queen of the genre. (Greedy Triangle, Smarty Pants, $1 Word...) 
• Princess of the genre, Elinor Pinczes: One Hundred Hungry Ants, A Remainder of One, ...
• Infinity and Me by Kate Hosford
• Tessallation!  by Emily Grosvenor
• Grandfather Tang’s Story, by Ann Tompert
• The Dot and the Line, by Norton Juster

Biography:

• Paul Erdos, The Boy Who Loved Math by Deborah Helligman
• Fibonacci, Blockhead by Joseph D'Agnese
• Eratosthanes, The Librarian Who Measured the Earth by Katherine Lasky
• Einstein usually gets lumped in here. Not a mathematician, technically, but if you're being that technical, loosen up! Try Odd Boy Out or On a Beam of Light

What to do:

• Chris Hunter has a bunch of recommendations plus how to use them.
• Another post with a lot of suggestions at Algebra's Friend
• Suzanne Alejandre suggested the old (aka classic) NCTM guide, Welchman-Tischler's book, might provide ideas? (She found a digital copy; use the NEXT button)
• Marilyn Burns (herself) just suggested this starting point from PBS

Possibly for older, but like Madeline L'Engle, I think people underestimate kids:

• The Phantom Tollbooth, by Norman Juster
• The Man Who Counted, by Malba Tahan
• Flatland, by Edwin Abbott 
• The Number Devil, by Hans Magnus Enzensberger
• The Adventures of Penrose the Mathematical Cat, by Theoni Pappas
• The Cat in Numberland, by Ivar Ekeland and John O'Brien
• A Wrinkle in Time, Madeline L'Engle (First I heard of a tesseract.) There's an audiobook where L'Engle reads it herself. Highly recommended.

And please add your own suggestions!

PS:

• Cindy Whitehead saw that I missed the Sir Cumference books, by Cindy Neuschwander, and suggested the Go Figure books, by Johnny Ball.

Math Memoirs

There's one of my favorite math teaching videos up in Keith Devlin's most recent blogpost.  (Thrilled that it's now on YouTube with several other of her interviews.) It's from the wonderful Marilyn Burns, who has really done more for math education than anyone in recent decades. Her stuff was good enough to get word of mouth sharing before there was an internet. (Dan Meyer is quite reminiscent of her in several ways.) Devlin uses the video to make the point that apparent understanding is not proof. A better assessment can uncover the truth, and Burns is excellent at questioning to get an accurate picture.




As a novice teacher I quickly found that the students giving an answer did not tell me whether they understood or not, and I moved to asking for how they got it. It took me years, however, to get to understand that how is better, but also does not get at understanding. It's their thinking that I want to hear. Then I should ask for it! Unfortunately, even spoiled university teachers don't have time to sit down and interview students over all of our major objectives. I can, however, ask questions to which I really

Dave Coffey found this excellent solution by Carl Barnard, a high school student, to the painted cube problem that crossed the line to be a memoir. We often introduce the idea of a memoir by having our students read it and comment on it. (Here's my most recent version of the workshop; Dave was almost certainly the original writer of it.) It's a start to learning how to communicate your thinking. While it's important and beneficial for any math student to do this, it is unbelievably crucial for math teachers, and a big part of pedagogical content knowledge to me.  Most students on end of term evaluations comment that this is an area where they grew significantly.

I wanted to experiment with what this looked like in elementary school, so I asked my daughter to give it a go. These are from the summer between her 4th and 5th grade. She was a bit precocious with her writing, but had had pretty traditional math instruction. (And not interested in talking with me about to a large extent.)

Just writing the method. A first attempt at memoir. I supported with a kind of questioning framework.




She was game enough to try twice more.






This is the sort of information that I want from an assessment. I get so much more an image of what ideas she has about number and operation. And it is far more interesting reading than traditional assignments where I'm looking for what I expect or not.