Elizabeth Green compiles the history of math education in the United States from New Math to the Common Core:

Americans might have invented the world’s best methods for teaching math to children, but it was difficult to find anyone actually using them.

She also tours through some of the best ethnographic research you’ll read in math education but doesn’t cite two of them explicitly (that I counted) so I will.

• A Revolution in One Classroom: The Case of Mrs. Oublier (Cohen, 1990) describes how one teacher’s transformed beliefs failed to transform her practice.
• Candy Selling and Math Learning (Saxe, 1988) describes the informal math Brazilian children used to sell candy and how it failed to translate into formal classroom math.

Featured Comment:

Daniel Schneider:

It might be worth noting that the paragraph about ‘answer getting’ seems to be referring to Phil Daro and his whole take on answer-getting.

Simon Terrell writes about his trip to Japan with Akihiko Takahashi.

Dan Goldner on his resolutions:

Of all the great things to focus on in this article, this is the one that spoke to me where I am now. Student-initiated in 40%, not 100%. 41% of time practicing, not 5%. Half the time on invent/think, not all the time on invent/think. I’ve been working so hard on making “invent/think” the dominant activity in my room, that practicing, which is also a cognitive requirement for learning, has been de-emphasized. The next paragraph in the article acknowledges that Japan isn’t perfect, either, and these percentages certainly aren’t a perfect recipe. But as my personal pendulum finds its equilibrium it’s great to read this and take from it the encouragement that that all the modes of learning have to have a place during the week.

Bill Gates, via Tom Hoffman:

… the one thing we have a lot of in the United States is unmotivated students.

It’s astonishing to me how many people develop their pet education theories assuming there is little or no interaction between motivation and learning, or that motivation is somehow outside the teacher’s job description. The assumption that motivation is entirely the student’s job leaves us no way to check ourselves for de-motivating pedagogy. If students don’t like sitting in warehouses, watching lecture videos, and clicking away at multiple choice questions, it’s either their own fault, or the fault of Miley Cyrus, social media, or Kids These Days, but not ours. Our theories can’t be impeached. We just need a better class of students.

Related: Rocketship charter schools (which were last seen on this blog here) are abandoning their enormous warehouses where elementary students click away at multiple choice questions:

Teachers — who are at-will employees who can be fired at any time — also criticized Rocketship’s intolerance for dissent, saying it contributed to the disastrous redesign that placed 100 students in a classroom.

“Teachers raised concerns,” said one ex-teacher, “and no discussion was allowed on the subject.”

Those who privately expressed doubt feel vindicated [by the removal of the warehouses] although sad, by the resulting test decline.

Great.

Featured Comment

Tom Hoffman:

I was thinking that you can tell a lot about a person’s view of education by exactly when they realize the importance of motivation. From the beginning, in the middle or at the end.

I think one thing that probably strikes teachers about Gates’ quote there is how much it sounds like a cranky old teacher in the break room.

Jay Fogleman:

I find the idea that “today’s youth” are “unmotivated” is bizarre. When teenagers are “hooked” one topic or activity, they are darn near unstoppable.

Randall Munroe, creator of the webcomic xkcd, from a TED talk that’s making the rounds:

What I love is that math lets you take some things you know and just by moving symbols around on a piece of paper find out something you didn’t know that’s very surprising. I have a lot of stupid questions and I love that math gives the power to answer them sometimes.

If you want to understand the Common Core’s fourth math practice standard, “Model with Mathematics,” you could do a lot worse than studying the mental feats Munroe performs in every single post of his What If? blog.

Featured Comment

Jason Dyer:

I think the bit immediately prior is worth quoting as well, even if it’s a bit harsher:

And I love calculating these kinds of things, and it’s not that I love doing the math. I do a lot of math, but I don’t really like math for its own sake.

Jim Hays:

Like on Mythbusters, Monroe is rarely content to stop with answering the question as stated: he generally keeps going bigger, faster, taller, or hotter until something explodes.

I’m quoted this week in a piece by Vox’s Libby Nelson on the Common Core State Standards. This reminded me to empty out my collection of podcasts, vodcasts, and press clippings, for the benefit of my doting mother if nobody else.

• The Ontario Ministry of Education interviewed some of my favorite math educators, including Cathy Bruce and Marian Small. They gave me four segments there to talk about engagement, classroom culture, and applied mathematics.
• Some teachers visiting from Catalonia interviewed me about three-act mathematical modeling.
• The Boston Globe quoted me in a lifestyle piece on efficient holiday shopping.
• Remarkable Chatter is a podcast based in Hutchison, Kansas. Earlier this year we talked about the difficulties of changing practice.
• Adrian Pumphrey’s MathEd Out podcast is in its infancy but he asks a lot of provocative questions. I’m the interview subject in his second episode.

The Desmos/Mathalicious happy hour in New Orleans on Friday was a great end to a long week of conferencing with math teachers, math ed professors, and the occasional vendor. My unofficial crowd estimate puts it at something like 50x the size of their 2014 event in Denver, CO.

The Desmos team and I wrote up some happy hour questions which were fun enough that several people requested the complete list. You should feel free to use them also. Please address complaints, quibbles, or corrections to Bill McCallum c/o Illustrative Math.

1. Math Homophones

All of the answers in this round are well-known mathematical words or phrases. (Example: “It lies under the mantle and belongs to use all” is also known as the “Common Core.”)

1. Bad news at the dentist for Salman. (A: concavity.)
2. A ski run you feel really good about. (A: positive slope.)
3. A lady’s partner who’s gotten some sun. (A: tangent.)
4. Messages you send in the same direction. (A: parallelograms.)
5. Treads on the Red October. (A: subtraction.)
6. Mickey’s British mother-in-law. (A: minimum.)
7. It said, “please come aboard two by two”. (A: arcsine.)
8. A change to a military banner. (A: standard deviation.)
9. Louisiana Governor Huey drawn and quartered. (A: long division.)
10. An airplane bathroom that is not vacant. (A: hypotenuse.)

Bonus:

• Answer to the question, “Have you seen a letter jacket belonging to one of the protagonists from Monsters University?” (A: isosceles.)
• A condition in which you become a better dancer after having a organic beer. (A: natural logarithm.)
• A matching outfit you’d wear in freezing cold weather. (A: polar coordinates.)

2. Kids Say The Darnedest Things

We asked four hundred 3-5th graders some questions about math. You’re going to tell us what they said. We asked them …

1. … who invented the Cartesian plane, a) Albert Einstein, b) Carter Von Ludvig, c) Rene Descartes, d) Eric Cartman, e) none of the above? What percent said the correct answer? (A: 9%.)
2. … to name any mathematician. Name the top four answers for one point each. (A: In order of descending popularity, Albert Einstein, my teacher, Eric Cartman, Carter Von Ludvig.)
3. … which is there more of, a) feet in a mile or b) pounds in a ton? What percent said the correct answer? (A: 57%.)
4. … what their favorite number was. Name the top four favorite numbers of elementary students? (A: In order of descending popularity, 7, 10, 8, 11.)
5. … which would you rather have: $100 or a stack of quarters from the floor to the top of your head? Which was the winner? (A: $100. That got 67% of the vote. Did they choose well?)
6. … which was heavier, a) a ton of bricks, b) a ton of feathers, or c) a ton of kittens. What percent said “kittens?” (A: 5% The winner was a ton of bricks at 93%. Good job, kids.)
7. … what was faster, a) the speed of light, b) the speed of sound, c) the speed of wind, or d) the speed of kittens. What percent said “sound”? (A: 25%.)
8. … if zero was a) even, b) odd, or c) neither. What was the most popular answer? (A: In order of descending popularity, Even [46%], Odd [10%], neither [44%].)
9. … what the biggest number is. Name the top four most popular answers for one point each. (A: In order of descending popularity, infinity, one hundred million, one billion, googleplex.)
10. … to name the shape of a stop sign. Name any of the top four most popular answers for one point each. (A: In order of descending popularity, octagon, hexagon, pentagon, hectogon.)

Ӭ

3. Common Critters

Even though your students may struggle to meet the Common Core State Standards, some members of the animal kingdom are doing just fine. We’re going to match a standard to an animal. You tell us if the statement is backed up by a scientific study or if we just made it up.

1. Salamanders can “identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.” (A: True.)
2. Ants can measure lengths indirectly and by iterating length units. (A: True.)
3. Goats can prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. (A: False.)
4. Chickens can fluently add and subtract within 5. (A: True.)
5. Octopuses can tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. (A: False.)
6. Dolphins can construct viable arguments and critique the reasoning of others. (A: False.)
7. Crows can use appropriate tools strategically.(A: True.)
8. Owls can count out a number of objects from 1-20. (A: False.)
9. Parrots can correctly name shapes regardless of their orientations or overall size. (A: True.)
10. Spiders can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (A: False.)

4. Music Round

We’re going to play 10-second clips of famous songs. You need to name the number that features prominently in the song.

1. “99 Problems,” Jay Z. (A: 99.)
2. “22,” Taylor Swift. (A: 22.)
3. “Jenny,” Tommy Tutone. (A: 8,675,309.)
4. “Take Five,” Dave Brubeck. (A: 5.)
5. “Summer of ’69,” Bryan Adams. (A: 69.)
6. “Seasons of Love,” Cast of Rent. (A: 525,600.)
7. “A Thousand Miles,” Vanessa Carlton. (A: 1,000.)
8. “Sixteen Candles,” The Crests. (A: 16.)
9. “100 Years,” Five for Fighting. (A: 100.)
10. “American Pie,” Don McLean. (A: π.)