## Thursday, October 23, 2014

### Percy Jackson's Math Class

[I haven't written this post yet, and I know it's going to be more rambly than usual. Fair warning.]

My eldest child has been a big fan of Percy Jackson. Me, too, to be honest. I'm reading The Blood of Olympus now. The first Percy Jackson series is one of the few non-graphic novels my son read by choice. So this was a natural click for me: The Percy Jackson Problem at the New Yorker by Rebecca Mead.

It begins with a quote from Neil Gaiman (another family favorite):
“I don’t think there is such a thing as a bad book for children,” he argued, adding that it was “snobbery and … foolishness” to suggest that a certain author or particular genre might be a baleful influence upon young reading minds—be it comic books or the works of R. L. Stine. Fiction is a “gateway drug” to reading, Gaiman said. “Every child is different. They can find the stories they need to, and they bring themselves to stories. A hackneyed, worn-out idea isn’t hackneyed and worn out to them.” Well-meaning adults, he continued, can easily kill a child’s love of reading: “Stop them reading what they enjoy, or give them worthy-but-dull books that you like, the 21st-century equivalents of Victorian ‘improving’ literature. You’ll wind up with a generation convinced that reading is uncool and worse, unpleasant.”
If you're a math teacher, how can you read this and not connect? We've been feeding students, as a profession, "worthy-but-dull" math for ages. (Worthy when it was good, that is. When it was bad, we're talking Tartarus.)

The author's argument is the counter to this idea that all reading is good.
Riordan’s books prompt an uneasy interrogation of the premise underlying the “so long as they’re reading” side of the debate—at least among those of us who want to share Neil Gaiman’s optimistic view that all reading is good reading, and yet find ourselves by disposition closer to the Tim Parks end of the spectrum, worried that those books on our children’s shelves that offer easy gratification are crowding out the different pleasures that may be offered by less grabby volumes.
I don't like this argument for reading. But I have made similar arguments in math. After a steady diet of exercises, students have no interest in problems.

But I think what I mean is that students have no experience with problems. The engagement that comes from finding a really meaty one. The question is whether reading Percy Jackson is really reading. I would argue that spending time on Tumblr is not reading (a current teenager discussion), and wonder if graphic novels are reading. (Aforementioned comic-obsessed son.)

I think this is an issue K-12. In elementary, there is a danger that teachers don't believe that students can do real problems. In high school, a desire to have the students do the basics first. Working with preservice and inservice teachers I try to stress and give experience with contexts that are problematic, but accessible. If it's not a problem, it's not doing math, no matter how many numbers and operations are involved.

Just being letters and words doesn't make it reading?

The author isn't so concerned with the Percy Jackson books, as with the forthcoming book of Greek myths as told by Riordan, writing in Percy's voice.
While the D’Aulaires wrote that “Persephone grew up on Olympus and her gay laughter rang through the brilliant halls,” Percy’s introduction to the story of Demeter’s daughter reads, “I have to be honest. I never understood what made Persephone such a big deal. I mean, for a girl who almost destroyed the universe, she seems kind of meh.”
It seems to me that this is some of what the common core struggle is about. Parents don't recognize newer curricula as math. (Which, of course, really has nothing to do with the common core in most cases; the Common Core gave them something to be against.)

The author closes with this concern:
What if instead of urging them on to more challenging adventures on other, potentially perilous literary shores, it makes young readers hungry only for more of the palatable same? There’s a myth that could serve as an illustration here. I’m sure my son can remind me which one.
Ooh, clever. I'm sure she knows which myth. What if after doing Desmos and Three Acts investigations, students don't want to do hackneyed word problems from the end of the chapter? That's probably not fair. Will they not be interested in the real problems of calculus, geometry, analysis and algebra? I think if we had a Percy Jackson parallel in math, the greater numbers of young people interested in math would mean a boom in STEM fields. The Percy Jackson problem? We should all have such problems.

This post started when I discovered no way to comment on the article. Because I wanted to share my daughter's response. And I want to think of this in terms of math, too. Here's Ysabela:
If they were arguing against, like, Twilight, where the language use is bad because the author has no writing experience, AND the plot and ideas are unoriginal/problematic, then I would agree with them. When Twilight becomes people's standard for literature, they start accepting total crap without a second glance, which is bad.
But Riordan understands language? And his plots (at least in the original series) were good? I'm not saying it was Harry Potter, but Percy Jackson was quality, and saying it wasn't just because the language is accessible to people who aren't scholars is just... really elitist. Like I know a lot of people who find reading really, really hard, but were able to enjoy Percy Jackson because it actually made sense to them. Plus, the series was narrated by a teenage boy, it was realistic.
And don't even get me STARTED on the D'Aulaires, they're SO AWFUL. They watered down the myths so much they were almost unrecognizable, "for kids," and then wrote it at like a college reading level. Plus they organized it like total tools. I can't express in words how much I would have rather had a Riordan book of myths than the D'Aulaires when I was younger.
 Hello Katie @ Society 6
As she steps out the door now, she's railing against having spent two weeks on factoring. Because the last day before the mini fall break they learned the quadratic formula. "And it always works!" Do you know why it works? "He showed us from $$ax^2+bx+c$$. It's extra credit on the test." How much more dangerous is it that she believes math is that pointless and uninteresting?

So, I think I'll side with Neil Gaiman on this one.

## Saturday, October 18, 2014

### Such a Thing as Free

A friend found his new-to-him school in need of Algebra I and Geometry textbooks - for cheap or free. I took the Twitters, and people responded quickly and generously. Thought I should collect their suggestions.

Free Curricula
My first suggestion was Geoff Krall's (@emergentmath) Problem Based Learning maps. Amazing work. It's a worklife dream to develop a collaborative site like this where we could all link our best lessons and do some informal lesson study.

My second suggestion was Illustrative Mathematics, Algebra and Geometry (plus everything else).

Then #mtbos hit the gas:
• David Coffey (@delta_dc) reminded me of the Georgia Common Core Materials.
When he wasn't Khan-baiting.
This is where I would start. Very complete, a lot of excellent lessons and compatible web resources, even including 3 Act structure stuff.
•  Bridget Dunbar (@BridgetDunbar)  ·  out of Utah: Mathematics Vision Project.  They follow integrated sequence...but good materials.
• Engage NY, Algebra and Geometry (but complete K-12, math and ELA).
Inconsistent quality to me, but a lot of good stuff and assessments are there, too.
Lisa Bejarano (@lisabej_manitou) recommended one of these two.
Dan Anderson (@dandersod) noted it, but does not love it.
•  Macomb ISD Math (@MISDMath)  ·  have you looked at the EMATHS materials?
That's the online materials for Michigan's virtual schools. New to me.  Looks thorough, with PD materials, lesson plans, activities-based and assessments.
• @geonz  shared Algebra2go. Early, online algebra curriculum with videos and homework.
Other Ideas
• Peg Cagle (@pegcagle)  suggested: Visit Abebooks for old Key Curriculum Press materials-brilliant rigorous & coherent-a bargain at full price, now available for a few bucks.
I noticed some IMP stuff there. Love IMP.
• Justin Lanier (@j_lanier)  ·  There are the Exeter and Park School problem sets, which are freely available.
At Exeter they have been problem-based for a long time, in 12 student classes. Read more about their Harkness method.
The Park School curriculum is available on request, but you may have to nag them.
• Raymond Johnson (@MathEdnet)  ·  Not as cheap as they used to be, but College Prepatory Mathematics is worth considering.
Samples here; those are good stuff.
I also let him know about the single serving sites:
That list lives on my Reading Recommendations page. I also put in a plug for GeoGebra (of course).

If you have experience with any of these things, or know of other resources, please list them in the comments. And thanks to everybody who responded or retweeted.

## Friday, October 10, 2014

### Poetical Practices

 #35! Angelou's #1, but there's no way she'll make it through conference play without a loss.
I got a chance to hear Billy Collins last night, thanks to family friend Elizabeth.

I enjoy poetry a lot, but don't read as much as I would like.  I have virtually none committed to memory, despite thinking that would be very cool. I don't write it, but have been wondering this past year how you even get started.

He was charming, lovely voice, aware of the audience and built his set of poems like a jazz musician, making sure to hit the hits, but improvising based on conditions, inspirations and audience response. For example he read this poem, To My Favorite 17 Year Old High School Girl, which may be his biggest smash: (around 5:30)

We bought that book - it is a lovely retrospective with new poems including the one he and Colbert read.

In our reading, he had me right away; before his first poem he talked about how nice it was that we were there. That, in fact, it was nice that anyone liked poetry given the way most of us are introduced to it. By which, he meant, in school. Imagine if the first time we listened to music, it was someone picking a suitable piece, they played it for a whole group, and then sat us down to ask us questions about it.

By the same token, it's a wonder that anyone likes math, eh?

I really liked a lot of it. This poem, Aristotle, you can hear him read at the Poetry Foundation. It's about how Aristotle introduced or recognized the beginning middle and end structure for literature.
"This is the middle...
This is the bridge, the painful modulation.
This is the thick of things.
So much is crowded into the middle—
the guitars of Spain, piles of ripe avocados,
Russian uniforms, noisy parties,
lakeside kisses, arguments heard through a wall—
too much to name, too much to think about."
If there is an official poem of Three Act lessons, this is it.

Jamie Radcliffe was a young visiting prof at Penn when I was at grad school there, and an all round good guy. (Now a full prof at Nebraska-Lincoln.) In addition to telling the best ever thesis joke, he had this great line about math and poetry. Even if he had only learned enough math to write doggerel, he was glad to have learned enough math to read the classic works of poetry from the all time great mathematicians.

Sometimes I think that this is the greatest sin of school mathematics. Making people think that the worst of the doggerel is all of math, and then making the students memorize it.  Not only missing out on many of the potential future poets of mathematics, but denying most students the whole art of mathematics.

But what would be the equivalent of poetry readings in school for math? The closest I've seen, I think, is Fawn's My Math exploration of Math Munch. (See also Sam's adaptation.) In my classroom, the day they bring in their patterns they've made and share their thinking and noticing is pretty close.

And it was crucial to let them talk. Just looking, I missed a lot of their intent. Other students noticed things that even the creators hadn't. There were several comments about "what if..." that were good math thinking. I also contributed a few noticings... I think that let them know that there was some real math here.

Afterwards he did a short Q & A. One of the first questions was about his process. He said, (paraphrasing from here out) take for example "I Chop Some Parsley While Listening To 'Three Blind Mice'" I was in my kitchen, chopping parsley, listening to Art Blakey. I was thinking, who hears three blind mice and thinks it's a good jazz tune. It's hot cross buns. But then I thought, how did they become blind? Was it congenital? Think how distraught the mother would be. Maybe an accident - an explosion! Mice covering there eyes. I take the pen out of pocket and now I'm at the office. If they became blind separately, how did they find each other? I mean how hard is it for a blind mice to even find another mouse, let alone two more blind ones? And then, what, the farmer's wife?! Now they've lost their tails, too.

And I start wondering how they came to be blind.
If it was congenital, they could be brothers and sister,
and I think of the poor mother
brooding over her sightless young triplets.

Or was it a common accident, all three caught
in a searing explosion, a firework perhaps?
If not,
if each came to his or her blindness separately,

how did they ever manage to find one another?
Would it not be difficult for a blind mouse
to locate even one fellow mouse with vision
let alone two other blind ones?

And how, in their tiny darkness,
could they possibly have run after a farmer's wife
or anyone else's wife for that matter?
Not to mention why.

Just so she could cut off their tails
with a carving knife, is the cynic's answer,
but the thought of them without eyes
and now without tails to trail through the moist grass

or slip around the corner of a baseboard
has the cynic who always lounges within me
up off his couch and at the window
trying to hide the rising softness that he feels.

By now I am on to dicing an onion
which might account for the wet stinging
in my own eyes, though Freddie Hubbard's
mournful trumpet on "Blue Moon,"

which happens to be the next cut,
cannot be said to be making matters any better.
He finishes this discussion by saying, it's about curiousity. I get curious about it, and then I just have to work it out. (Here's the song; I love Blakey, and know this album well - didn't hurt when hearing the story.)

I so get that - happened to me just this week with Justin Lanier's Star Fractal pattern. I just had to work it out.

Someone asked how old he was when he started. About 10. He saw a sailboat on a drive up the Hudson River parkway that he needed to write about. He figures everyone has 50 to 300 bad poems in them; high school is good for getting through a lot of them. Someone asked if poetry was good for expressing feelings. He told her that nobody cares. You're writing to get the reader to feel things. If you're good at it, they might start caring about yours.

One of our friends with whom we went, Joanie, was a high school lit teacher among other things (see her IB thoughts). I asked her how she taught poetry. Students try, and you just read it and give them feedback. A lot of it's terrible, but you let them know if they lost their focus or what they're writing about. I do want to be a reader for my students.

So I'm still processing it, but wanted to get these thoughts down.

Do you have any thoughts on math as a liberal art? How do you teach to create an appreciation for the poetry of math, or to create a space for future mathematicians?

To close, I'll include one more of his poems. And ask if maybe we should be commiserating with poets more often.
Introduction to Poetry

I ask them to take a poem
and hold it up to the light
like a color slide

or press an ear against its hive.

I say drop a mouse into a poem
and watch him probe his way out,

or walk inside the poem's room
and feel the walls for a light switch.

I want them to waterski
across the surface of a poem
waving at the author's name on the shore.

But all they want to do
is tie the poem to a chair with rope
and torture a confession out of it.

They begin beating it with a hose
to find out what it really means.

## Friday, September 5, 2014

### What's a Problem?

We had a fun class in the elementary math course today. Introducing SMP1 - problem solving, we got to an interesting question: what's a problem?

Here's the story as told by the residue on my whiteboards.

Schema Activation: jot down about a time you solved a real problem in your life. You won't have to share with anyone if you don't want to - this can be private.

After a few minutes to write, I shared how one of the big justifications for teaching and prioritizing math in school, other than the jobs to which it gives access, is that it teaches problem solving.

Actually more yes than I expected!

People asked if I meant did math class help with the problem that they journaled about or in general. I said we want to know about problem solving in general, but they could use their instance as a specific.

Next question: is it possible that math class could help teach problem solving? Short time to discuss at table.

These were definite yesses, with a lot of confidence.

One of the reasons I like teaching teaching math is teaching is so much like math to begin with. So rephrasing: our problem is how to go from the current situation to get what we want.

So the next prompt was to quickly brainstorm. Ideas for making this happen.

I shared that I liked how many of these were things that were up to the teacher. And I paraphrased Marzano, about how there is bad news: a small percentage of factors affecting student learning are under the teachers control; good news: that percent still makes a big difference.

What did they like?
• The emphasis on real life. This brought out uniform hatred for unlikely impractical story problems.
• Logic problems: one of the students shared how engaging and powerful these were for here. I asked about the contrast with real world, but people were comfortable with the crazy logic problems because the emphasis was on how did you do it.
• Teachers can ask for multiple ways and have students compare them.
Okay. So if we're going to teach problem solving, we need problems. I asked a question, then asked them to think about if that was a problem or not. There was a tub of square tiles on each set of two tables.

After they all had answers, I asked them to think about the second part. After a short time to discuss, we went to +cheesemonkeysf 's talking points structure for the statement.
This is a problem.

We're still working on the structure, so some of my feedback was about that. The no comments idea is hard.

Pretty strong agreement. People were willing to share their reasoning with the whole class ...  even the small minority. Maybe especially the small minority?

I was really happy to see the "depends on what the teacher does" idea come up. And I added the "depends on students" too. This is not a problem for me. For first graders, a serious problem - there aren't enough tiles in the tub to cover! For them... well, they talked about methods, chose how to do it, discussed results; these are problem indicators to me.

Then we went back to the question. What answers did they find?

There was shock at the diversity.

One question I ask a lot is: is this a question where different answers could all be right?

They discussed and...

There was concern about the largest answer being too big, but that table and an adjacent table figured out the first group's table is actually larger.

I shared how measurement is one of my favorite content areas, exactly for this reason that a diversity of answers is to be expected. It can be culture setting.

So, with all this, definitely time for a problem. One of my favorites. How many pentominoes are there?

We played with domino patterns last class, so that's a natural starting point. We agreed that there was only one way to make a domino with two squares. If they touch, they have to share an edge.

With three squares, the issue came up about putting them "in the middle." That's solved by the edge rule. What about the elbows in a different direction? No, the class agrees, if you can turn it to match, it's the same shape.

So what I want to know: is how many pentominoes?

People got to work with tiles and graph paper. No group found all the tetrominoes as a step, which I was trying to suggest. A couple of times I had tables report on how many they had and were they expecting more. 8 more, 9 more, 12 probably, etc. Next time, 12, 14, 15 and a mix of have them all and think there are more. When our time was up, they sent emissaries to the board to draw what they had:

Now the best part: math fight! Are flips the same or not?

They divided up into groups based on their answer: 14 flips matter, 9 flips are the same. They shared reasoning. Flips matter because these are flat things and a flip requires another dimension. And if you try to match them up they do not line up. Flips don't matter because you can get them to line up, and what's the difference between a flip and a turn, really?

I refuse to settle the issue, and ask them to make a complete set before Monday.

If you care to comment or tweet a response, I'll share your answers with them:
• How do you recognize what is a problem for your students?
• Are flipped pentominoes the same or different? Why?

## Wednesday, August 27, 2014

### Clap Hands - a motion pattern game

This game must exist in some form elsewhere, but it came to me yesterday and we worked out a good version of it with my preservice teachers this morning.

It starts with getting to do some of Malke Rosenfeld's Math in Your Feet this summer at Twitter Math Camp, and then subsequent discussions with her that have me thinking a lot about embodied cognition. The example of this in Math in Your Feet was knowing what I needed to do but the challenge of getting my body to do. Move left foot, move! In discussions, she connects this powerfully to research and writing of Seymour Papert. She said something like:
embodied vs “non-embodied” from the research: there is no non-embodied math. Either we’re pulling from previous lived-in-the-world experience to learn, or we’re actively constructing our understanding of self moving in space. We can harness that to give students an understanding of the world.
She's deep that way.

On our first day of class, one of the things we did was watch Ken Robinson's Do Schools Kill Creativity?  (If you haven't watched it, give it a go. He's a powerful speaker on creativity, and as close to Ricky Gervais as we're going to get in academia.) The student response from my class was really focused on movement. The Gillian Lynne story especially seemed to resonate; good omens for some of the learning I hope to do this semester.

So today we're studying patterns. First activity was pulling out the pattern blocks. We used that to model how to introduce math manipulatives to elementary students, and introduce the principle that with a new manipulative you need free play. Either immediately or promise the students specifically when they will get it. (Good management meets good pedagogy.) We used free play to introduce the question: is this free play doing math? Which we discussed in Elizabeth's Talking Points structure. (Fabulous, even the first time out.) Then in whole group used our examples to discuss the difference between a design and a pattern. (Is there a difference to you? I'd love to know what you think about that.)

Then it was time to go outside...

Clap Hands

groups of 4 to 7 people

Arrange people in circles of about 6. The game is pretty simple:

Building
• One player starts, introducing a motion. Like, for example, a simple clap. Going around the circle, each player does the motion.
• After the starting player does the motion, the next player adds a motion. Clap hands, raise right hand. Each player does the 2 part sequence.
• After the second player does their two, the next player adds a motion. Clap hands, raise right hand, turn around clockwise.
• And so on, until each player has added a motion and it has gone around. Clap hands, raise right, spin right, jump, snap fingers, shake right foot twice.
Survivor
• The goal is to get the pattern to go around twice more. When it does, that pattern is complete!
• If a player messes up the sequence, they step out. Try to get twice around from there.
• If you get down to two people, the pattern is done.

I didn't get video because I needed to play this! Thanks to Jordan and other students who had great suggestions. Reaction to the game was very positive, and people were quite engaged. There was much laughter, too. Keeper!

I'm interested in your feedback on the game, and how you present patterns. So if you have time to tweet or comment, let me know.

### Dan as Assessment

First day in a class on high school math with preservice secondary teachers. A rambly story, to be sure.

 From The Duplex by Glenn McCoy
We started making nameplates and forming groups of 3 or 4.  While that seems inconsequential, I leave the markers and materials up front. And it's just the tiniest bit of culture setting when someone asks "we do that now?" and "should we come up to get the stuff?" And letting them know if the groups don't meet the parameters: facing each other and 3 or 4 members. Am I really going to be a stickler? "We have 5 is that okay?" "Nope." Student 4k+1 walks in; I ask "so what are you going to do now?" I have several occasions to say, "good thing we're a room full of problem solvers."

The next activity, Piece of Me, is robbed adapted from David Coffey. I'm now calling it 2 Questions. Each person comes up with two questions to ask the person on their left in their group. Once everyone has them, ask away. Everyone has the right to decline to answer. Some of the questions were generic (how was your summer), some were trivia (Michigan or Michigan State) (Answer was Notre Dame and a story about her family) and some sparked good discussion: "why be a teacher?" or "middle or high school and why?"

Alright!

Our first math activity was one of Sadie's Counting Circles. Regardless of how you think math should be taught, you must know what people think about math now. I shared how Jo Boaler and others have experimented with number talks to change people's beliefs about math. And how Sadie's counting circles are a good context for a number talk.

The idea of the counting circle is two-fold. One is that it helps to build a positive learning culture where it's safe to speak up, mistakes are acceptable, multiple approaches are valued, and thinking is what we want to share, and the other is to develop number sense. Sadie would probably disapprove of my choice of starter value, but I thought too easy would actually disengage this group of math majors. So we did up by 97, starting at 235. It wound up being just a little uncomfortable for a couple of people - 99 might have been better. After 1.3 times around, at 2175, I put on the pause, and asked what would Amanda say (5 people further around the circle.) When everyone indicates they have an answer, I asked for volunteers for their thinking, and then just recorded it as they spoke it, eliciting details. And I didn't take a picture!The shared strategies included noticing that the ones place went down 3 each time, adjusting from adding 100 and multiplying 97x5 and adding it to 2175. Even the computation can be interesting. 97x5 used partial products to get 485, and then he added the 5, the 400 and then the 80.

With that set up, we moved to watching Dan Meyer's TEDx talk, Math Curriculum Needs a Makeover. (It's a classic for a reason.) They were very engaged, and had intense small group discussions after watching. One of the students led the whole class discussion, which became a good assessment for me. Their beliefs about teaching stood out sharply, thanks in part, at least, to their contrast with what Dan was saying.

My notes:
Not enough time!
-planning
-class time
Some time gained from students being able to do math practice at home. Tech helps with this.
What stus know on tech is not always helpful.

Kids need too many basics to do this kind of work

Problems like this won't be on the standardized tests
I learned this way and the standardized tests were so easy. If you're taught this way, your understanding filters through standardized fluff.

Less memorization because you've created the formulas yourself.

We missed part of the process. This leads to more general methods because of questions like: How would you figure out for a tank ten times larger? Or is there a short cut for figuring it out more easily. In a class one time, for a question on the volume of a vase, why not just fill it and see? Prof answered: "what if it was 100,000 gallons?"
This kind of activity gets across the idea that you're not always going to be right. This is just one way to do it.

Grounds the math in reality. You know students are always asking 'when are we going to use this?'
I would summarized their talk as: "It would be more engaging, but..." I maintain that I do not want this course to be about me telling them how to teach, but giving them experiences that can equip them to construct their own vision of teaching and learning. Resources, reflection and a focus on student understanding lead to good teaching. But this experience helped me understand where we are starting and some of the barriers to where I want us to get.

We continued class by looking at 101qs.com and generating some questions. (Aside: read Pershan on learning to ask questions. We'll be tackling this later.)

This led into launching the meatball three acts. We watched the video, and got to our estimates, and low and high guesses.

This was cut short because we had a presentation on Lisa Kasmer's excellent study abroad program in Tanzania .  I'm interested if anyone worked farther on it.

I was moved to write this up, because I tend to think of asking questions to get assessment data, and this wasn't intended to be assessment. I might not have noticed as well if I was running the discussion, but as an observer, it put me into notice-mode.

Postscript:
Part of the homework was to look for a 101qs prompt they found interesting. What they found interesting is in turn interesting to me! Here's a few:
• Jennifer: Bowling for Pennies. "Would this be cheaper to make than buying a 'mirror ball'?":  Nicole Paris asked: Would this be cheaper to make than buying one?
• Brittany: Waterkracht "centrale". Water power plant. How fast is the stream flowing?
• Greg: Beatlemail "How many letters would each band member have to answer?"
Ken Meehan asked: How many pieces of fanmail?? What is the first question that comes to your mind?
• Sam: Brita How many water bottles are need to go around the earth once?
Dan Meyer asked: How many times around the world would all those bottles wrap?
• Kevin: NFL JumboTron HDTV's How many 60" televisions does it take to fit in the Texans television?
Nathan Amrine asked: How many 60" TV's would equal one Texans TV?
• Molly: Packing Box What is the total area of all boxes?
Elaine Watson asked: What combination of small boxes and medium boxes can fill a large box?? What is the first question that comes to your mind?
• Joshua: Angry Birds Can knowledge of quadratics improve your Angry Birds accuracy?
• Jerry: Okay, this is the first one I found: Stuck Truck This reminded me of a story I once heard of about a semi-truck that came to the opening of a tunnel only to realize it was a couple of inches taller than the opening. Having to stop in the lane with no way to turn around, the truck had traffic backed up for miles as everyone had to consolidate down to one lane and everyone slowed down to gawk at the truck to see why it was stopped there. The police and the truck driver were all standing around the truck trying to figure out how to get the truck through the tunnel or turned around and had discussed numerous things but none of them seem to be the right answer. Then a little boy leaning out of the window as his dad drove by yelled out, "Why don't you just let some air out of the tires?" The question the original poster seemed to be thinking along the same lines, "How much beer would he have to drink to allow the driver to get the truck free?" However, my question had to do with how often this happens at this spot. Either it happens often and they should fix it or there is a sign and the driver just did not see it.
Fred Jaravata asked: How much beer would I need to remove to help free the truck?? What is the first question that comes to your mind?
• Dakota: Cylindrical Tunnel How many windows are in this tunnel?
statler hilton How much glass is needed for this?
• Jim: Pickle Stack How tall can you build a pickle tower?
Krista Keats asked: What is the question?
• Brody: Keep 'Em From Fallin' How tall is the main structure?
Michele Thomareas asked: How wide apart are the columns?? What is the first question that comes to your mind?
• Amanda: Waterworks at Legoland How far will the water spray?
Rod Bennett asked: What happens to the trajectory of the water if she pedals faster?
• Christopher: Roulette Wheel What are the odds of that many 19's in a row?
Joe asked: What are the odds of the same number coming up 7 times in a row?
• Anika: Circle Square How many circles are there?
John Golden asked: What is the function for number of circles after each step?
• Nick: 2010 Guatamalan Sinkhole How deep is the hole?
Robert Kaplinsky asked: How much material will they need to fill the sinkhole?? What is the first question that comes to your mind?
• Brooke: Firing Range How many lasers are there?
statler hilton asked: How far away is the target they're shooting at?? What is the first question that comes to your mind?
• Leesha: Perfectly-timed photo How high is the plane?
Johanna Langill asked: How high is the plane?? What is the first question that comes to your mind?

## Saturday, August 23, 2014

Planning my fall pre-service elementary math course, I was thinking about books. In the distant past we've read Deb Schifter's What's Happening in Math Class? (strong teacher narratives), and more recently Jo Boaler's What's Math Got to Do It. (Here's a recount of one of our book discussions about it.) But in my other classes, it's been very good to offer choice to students. (Here's a post about that.) I'm a big believer that teacher-to-teacher reflective conversation is the best PD, and book discussions make good context for those discussions. (A pdf of some research on this by Burbank, Kurchauk and Bates in The New Educator.)

I was finalizing my list for them to choose among, and thought to ask on Twitter. As usual, unexpected generosity in people thinking and answering. (I don't know why it's still unexpected.) Here's the responses:

A Mathematician's Lament.

I don't have a long list I'm drawing from, but Marilyn Burns' "Math for Smarty Pants" comes to mind.

@j_lanier I second this. Have ordered to share with my elementary teachers in the district.

Rudin! Go big or go home ;-)

Children's Mathematics.

Euclid’s Elements, because it’s comprehensive :P

Powerful Problem Solving. Lots of great examples.

Young Children Reinvent Arithmetic: Implications of Piaget's Theory by Constance Kamii

maybe "Creative Problem Solving in School Mathematics" by George Lenchner.

I second but I also like 10 Instructional Shifts by @steve_leinwand

making sense:teaching & learning with understanding by James Hiebert - geared k-8 but great for all math teachers

#1 for me is What's Math Got to Do With It? by , #2 is Knowing and Teaching Elementary Mathematics by Liping Ma ... #3 is Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School by Carpenter, Frankl, and Levi

Van de Walle, Teaching Student Centered Mathematics

What a great bunch of suggestions. So my final list for them to choose from is below. I'm requiring at least two people per book, at most four. (24 students) In addition to the benefits of choice, I'm hoping that a variety of books enriches our classroom discussion.
• Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement, Steven Leinwand, (Amazon) [Practical, pre-service teacher approved)]
• Intentional Talk: How to Structure and Lead Productive Mathematical Discussions, Kazemi & Hintz, (Amazon) [Applies to more than math; good support for helping students learn to converse productively]
• Making Sense: Teaching and Learning Mathematics with Understanding, Carpenter, Fennema, Fuson, Hiebert, Murray & Wearne (Amazon) [Writers and researchers of the best elementary math curricula around tell what they think is important.]
• Math Exchanges: Guiding Young Mathematicians in Small Group Meetings, Kassia Omohundro Wedekind, (Amazon) [Similar to intentional talk, more strongly based in literacy routines.]
• Math for Smarty Pants, Marilyn Burns (Amazon) [Collection of entertaining problems across all kinds of math from a master math teacher.]
• A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form, Paul Lockhart (Amazon) [Not sure about putting this on. Many readers are disappointed in the 2nd part, but the 1st part people see as a powerful argument for why math teaching has to change.]
• Powerful Problem Solving, Max Ray (Amazon) [New book from a very deep thinker about how to teach math.]
• What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject, Jo Boaler (Amazon) [If I was picking one book for everybody this would be it. Dr. Boaler is doing a lot to research and share how to make math better.]
Last cuts: Moebius Noodles,  The Math Book by Clifford Pickover (beautiful history of math), and Deb Schifter's What's happening in Math Class.

5 Practices by Smith and Stein (dropped for Intentional Talk and Exchanges) and the NCTM's Principle to Actions were just not accessible enough in this structure. I think if everyone was reading the same book, those would work better.

This course focuses on pattern, geometry and statistics, with number and operation in another course. Otherwise CGI would be on for sure. The Young Mathematicians at Work books are a fine series we use with our elementary teacher math majors.

P.S. And then, like any modern story, it ends with a sequel invitation...

Good question, extend. If you could get your child's HS math teacher to read one book, what would it be?