June 27, 2007 11:31 AM Subscribe

Books/wares to help kids think like mathematicians?

In psychological discussions of mathematical thinking, distinctions are often made between the way that innovators in math think about math, versus the way that math is usually taught in school. Does anyone know of books, software, etc. that would be appropriate for very young kids (around first grade) that would instill thinking of the former sort? Or is that too young to start?
posted by O Blitiri to Education (22 answers total) 18 users marked this as a favorite

In psychological discussions of mathematical thinking, distinctions are often made between the way that innovators in math think about math, versus the way that math is usually taught in school. Does anyone know of books, software, etc. that would be appropriate for very young kids (around first grade) that would instill thinking of the former sort? Or is that too young to start?

This might sound odd but there is a strong correlation between music skills and math skills. Teaching them piano might be a good start.

posted by chairface at 11:42 AM on June 27, 2007

posted by chairface at 11:42 AM on June 27, 2007

The Number Devil is good on the math, less good on the book part. But it goes over a lot of fun math that is simple to understand but that normally doesn't get taught to young kids - series, patterns, etc.

posted by GuyZero at 11:53 AM on June 27, 2007

posted by GuyZero at 11:53 AM on June 27, 2007

Probably the best thing is to integrate math into whatever it is that your kid loves. Soccer, art, music, dinosaurs, stars, construction trucks, dancing, cooking, camping--all have a mathematical aspect if you choose to uncover it.

In terms of books or materials, I've just read The Well Trained Mind, which is a homeschooling approach that lots of people/blogs/sites recommend (and now I recommend it, too). The math section has lots of information, and it takes an age-based approach. It tends to be laid out as a curriculum since that's the route most people are taking with the book, but it's a great resource.

I like Montessori materials. Kids that young are still working with numbers as physical things and are moving toward abstract concepts. The Montessori materials are fun, flexible (you can build with them, make patterns with them, not just count) and they have a long shelf-life.

I also just purchased The Everything Kids' Science Experiments. The experiments look fun for lots of age ranges and may give a compelling reason to learn the math for what it enables you to do, and not just as a set of times tables.

posted by cocoagirl at 11:58 AM on June 27, 2007

In terms of books or materials, I've just read The Well Trained Mind, which is a homeschooling approach that lots of people/blogs/sites recommend (and now I recommend it, too). The math section has lots of information, and it takes an age-based approach. It tends to be laid out as a curriculum since that's the route most people are taking with the book, but it's a great resource.

I like Montessori materials. Kids that young are still working with numbers as physical things and are moving toward abstract concepts. The Montessori materials are fun, flexible (you can build with them, make patterns with them, not just count) and they have a long shelf-life.

I also just purchased The Everything Kids' Science Experiments. The experiments look fun for lots of age ranges and may give a compelling reason to learn the math for what it enables you to do, and not just as a set of times tables.

posted by cocoagirl at 11:58 AM on June 27, 2007

I'm not sure I see the connection, but I was indeed obsessed with this book when I was that age and now I am a mathematician, so maybe you should try it.

posted by escabeche at 12:17 PM on June 27, 2007

chairface, that's spot on.

Get them an instrument and lessons!

Music Makes Math Meaningful

I second piano, as it's the most straightforward introduction to music. I began lessons at age 4, and it easily led to other instruments later.

posted by blastrid at 12:25 PM on June 27, 2007

Get them an instrument and lessons!

Music Makes Math Meaningful

I second piano, as it's the most straightforward introduction to music. I began lessons at age 4, and it easily led to other instruments later.

posted by blastrid at 12:25 PM on June 27, 2007

The I Hate Mathematics! Book,. Some of the content will probably go over a first grader's head, but much of it is age-appropriate.

posted by phoenixy at 12:35 PM on June 27, 2007

posted by phoenixy at 12:35 PM on June 27, 2007

I don't know if this is quite in the right direction, but U of T math professor John Mighton -- who is also an award-winning playwright -- founded a charitable organization called JUMP Math that promotes a new way of teaching mathematics. He has written a couple of books about it, one of which was just released recently. Their website is www.jumpmath.org and you can order teaching guides at various grade levels.

posted by sevenyearlurk at 12:43 PM on June 27, 2007 [1 favorite]

posted by sevenyearlurk at 12:43 PM on June 27, 2007 [1 favorite]

I'm not sure I see the connection

There's the whole section where they get to Numberopolis and meet the Mathamagican, etc. Plus the guy with a dodecagon for a head. Or maybe it was a dodecahedron.

posted by GuyZero at 12:47 PM on June 27, 2007

Not too young to start.

I recommend books such as Gardner's Aha Insight which is illustrated with cartoons but also contains some deep mathematical thinking.

posted by vacapinta at 12:49 PM on June 27, 2007

I recommend books such as Gardner's Aha Insight which is illustrated with cartoons but also contains some deep mathematical thinking.

posted by vacapinta at 12:49 PM on June 27, 2007

The Man Who Counted.

From Library Journal: "Puzzle books can be tedious (unless you like that sort of thing), but not this one. First published in Brazil in 1949 by the mathematician Julio de Melo e Sousa (Tahan is the imaginary Arab author he claimed to have translated), it is a series of delightful "Arabian nights"-style tales, with each story built around a classic mathematical puzzle. The puzzles fit into the stories so naturally that they are a necessary part of the fantasy. The hero is a Persian mathematician and mystic named Beremiz who uses his powers of calculation like a magic wand to amaze and entertain people, settle disputes, find justice and, finally, win the heart of a beautiful princess. Reading the stories is as much fun as trying to solve the puzzles. For adults and children."

posted by neuron at 12:55 PM on June 27, 2007

From Library Journal: "Puzzle books can be tedious (unless you like that sort of thing), but not this one. First published in Brazil in 1949 by the mathematician Julio de Melo e Sousa (Tahan is the imaginary Arab author he claimed to have translated), it is a series of delightful "Arabian nights"-style tales, with each story built around a classic mathematical puzzle. The puzzles fit into the stories so naturally that they are a necessary part of the fantasy. The hero is a Persian mathematician and mystic named Beremiz who uses his powers of calculation like a magic wand to amaze and entertain people, settle disputes, find justice and, finally, win the heart of a beautiful princess. Reading the stories is as much fun as trying to solve the puzzles. For adults and children."

posted by neuron at 12:55 PM on June 27, 2007

The Math Forum is a great general resource for mathematics educators. It's got links and information about all kinds of tools and curricula. Some of it is membership-based, but it has a ton of free resources too.

More directly, I just discovered a free program called GeoGebra, and it blew my mind for sheer awesomeness. Totally elegant and intuitive. Maybe a bit much for a 1st grader without guidance, though.

If you're interested in programming as well, the various permutations of Logo are great. Turtles all the way down!

posted by miagaille at 1:02 PM on June 27, 2007 [1 favorite]

More directly, I just discovered a free program called GeoGebra, and it blew my mind for sheer awesomeness. Totally elegant and intuitive. Maybe a bit much for a 1st grader without guidance, though.

If you're interested in programming as well, the various permutations of Logo are great. Turtles all the way down!

posted by miagaille at 1:02 PM on June 27, 2007 [1 favorite]

The first thing that springs to mind is Donald in Mathmagic Land, which is not a book, but rather a video. All the same, it had a huge impact on me when I was young.

posted by rush at 1:03 PM on June 27, 2007

posted by rush at 1:03 PM on June 27, 2007

The more I think about it, the more I think that there really aren't enough good materials until you get to an older audience. I keep thinking about The Diamond Age, of which this problem is a central theme.

When you talk about books, is it your intention to read them to the kids?

posted by rush at 1:11 PM on June 27, 2007

When you talk about books, is it your intention to read them to the kids?

posted by rush at 1:11 PM on June 27, 2007

Another vote for the music/math combination. More info.

posted by Cool Papa Bell at 1:18 PM on June 27, 2007

posted by Cool Papa Bell at 1:18 PM on June 27, 2007

Oh, and I'd recommend *against* the Penrose books. While theoretically written for kids, they're all over the place in terms of depth and terminology.

posted by rush at 1:22 PM on June 27, 2007 [1 favorite]

posted by rush at 1:22 PM on June 27, 2007 [1 favorite]

Flatland too.

posted by hexatron at 2:05 PM on June 27, 2007

Rush: At the risk of revealing the limitation of my own grasp of mathematician-thought, my suspicion/hope is that there might be books or programs out there that invite exploration of the patterns in and relations between numbers. Perhaps this would be a highly visual approach. For example, revealing the “three-ness” of nine, the “five-ness” and “three-ness” of pyramids; teaching multiplication through grids of dots rather than purely syntactic tables for memorization. The adult version of this, perhaps, is Rucker’s Mind Tools. Aren’t there books with thick cardboard pages out there that work with such ideas?

On preview: the Penrose books look promising.

posted by O Blitiri at 2:05 PM on June 27, 2007

On preview: the Penrose books look promising.

posted by O Blitiri at 2:05 PM on June 27, 2007

O Blitiri, 'The Number Devil' covers those exact concepts.

posted by GuyZero at 2:16 PM on June 27, 2007

posted by GuyZero at 2:16 PM on June 27, 2007

Books written by Mitsumasa Anno, such as Anno's Math Games (1, 2, & 3), as well as Anno's Mysterious Multiplying Jar, Anno's Magic Seeds, and many more books he has written combine a story with math concepts. Some of his books are out of print, but are worth looking for.

Also, One Grain of Rice by Demi.

posted by scubbadubba at 3:25 PM on June 27, 2007

Also, One Grain of Rice by Demi.

posted by scubbadubba at 3:25 PM on June 27, 2007

I second Anno's Mysterious Multiplying Jar. I know a three year old who was amazed by it.

posted by Pastabagel at 3:52 PM on June 27, 2007

posted by Pastabagel at 3:52 PM on June 27, 2007

This thread is closed to new comments.

posted by mkb at 11:36 AM on June 27, 2007