Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”12″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Team Me: 6
Team Commenters: 4

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

Mega-Grandma!

Later the text goes on to ask students to construct and graph the formula for the average cost of producing the Mega-Grandma, which turns out to be a rational function given the constraints.

But the text might have been better served by asking students to solve for generic widgets, or tennis balls, or something a little less gonzo-bananas than the Mega-Grandma exoskeleton, which is all I’m going to remember from this unit in the textbook.

BTW. Thanks to Jasper LaFortune for the submission.

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”11″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Team Me: 5
Team Commenters: 4

Pseudocontext Submissions

William Carey has offered two additional genres of pseudocontext that are worth your attention:

First:

One motif in pseudocontextual questions seems to be treating as a variable things that, you know, don’t vary.

Second:

The car question follows a fascinating pattern that shows up in lots of physicsy work: it begs the question. Physicists like to measure things. Sometimes measuring something directly is tricky (or impossible), so we measure other things, and then calculate the thing we actually want.

Questions like that have as their givens the thing we can’t measure and ask us to calculate the thing that we can measure. It’s absolutely backwards.

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

The commenters bit down hard on the lure this time, folks. The correct answer — “calculating area of parallelograms” — was selected least.

Delicious pseudocontext, right? The judges all suffered massive strokes when they saw this problem so I couldn’t get their official ruling, but I don’t think it matters. This context fails the “Come on, really?” test for pseudocontext.

“This unpredictable force of nature is threatening a precisely-bounded parallelogram? Come on, really?”

How could we neutralize the pseudocontext? I would be thrilled to see a task that invited students to select and approximate important regions with various quadrilaterals, but let’s not lie about where our tools are useful.

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”10″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Team Me: 5
Team Commenters: 3

Pseudocontext Submissions

Kimberly Robertson

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

This was a nail-biter between Team Commenters and Team Me this week, with Team Commenters narrowly tipping the scales in their favor.

The judges rule that this satisfies the second rule of pseudocontext:

Given a question, the assigned method isn’t a method most human beings would use to find it.

Reasonable people might wonder about the dimensions of a water tank. The judges rule that most human beings would use a tape or a stick or any other kind of measuring device to answer it, not a cubic polynomial.

I can’t think of any way to neutralize this pseudocontext. The number of actual contexts for cubic polynomials with non-zero quadratic and linear terms is vanishingly small.

Here is an activity I would much prefer to use to teach the construction of polynomials. It doesn’t involve the real world but it does ask students to do real work.

Featured Comment

William Carey:

One motif in pseudocontextual questions seems to be treating as a variable things that, you know, don’t vary. I have a funny video playing in my mind of some surprised fish watching the volume of their tank become negative. But happily the volume of that tank is not varying, inasmuch as it’s sides are made of glass.

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”9″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

I’m kicking the number of options back up to three. Two options simply doesn’t give y’all the challenge I know you need.

Team Me: 4
Team Commenters: 3

Pseudocontext Submissions

John Gibson

I don’t know if this is pseudocontext, but I for sure don’t know under what circumstances anyone would wonder about resultant momentum. In my head right now it’s like wondering about the middle names of the people who manufactured that car. It feels like trivia! I’m not saying it is trivia, but I am wondering if someone can put me in a position where knowing how to calculate resultant momentum would feel like power rather than punishment.

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

The commenters took this one right on the nose. The pseudocontext was in the last place they looked.

The judges rule that this violates the first rule of pseudocontext:

Given a context, the assigned question isn’t a question most human beings would ask about it.

Moreover, I just don’t see any congruent triangles in the picture. None. I know I’ll see some if you widen the camera’s angle, but there aren’t any in the frame right now, which makes this a uniquely poor context.

The only way I can think to neutralize this pseudocontext:

Show students four spaghetti bridges. They have to decide which ones are fragile and which ones are strong. Understanding congruency somehow (waves hands) makes them more accurate in their decision-making.

Featured Comment

Dick Fuller:

I like physics. And math. One without the other is school.

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”8″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Team Me: 4
Team Commenters: 2

Pseudocontext Submissions

Jennifer Pazirandeh:

Jon Orr:

Michelle Pavlovsky:

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

I lose again. (But aren’t we all winners on Pseudocontext Saturdays? No? Just you. Okay.)

The judges rule that this violates the first rule of pseudocontext:

Given a context, the assigned question isn’t a question most human beings would ask about it.

I think we can neutralize this pseudocontext by simply deleting the context. Delete the rock wall and we delete the lie that rock climbers are concerned with quadrilaterals while simultaneously preserving a task with a lot of admirable qualities.

Then ask:

Which quadrilaterals can you locate in this grid? Can you find a trapezoid? How do you know it’s a trapezoid? Show a neighbor.

For whatever it’s worth, if there were some way to help Livia climb the wall by communicating with her through quadrilaterals, I’d re-evaluate this entire post.

[via John Golden]

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”7″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Bad trend here. I do not like it.

Team Me: 4
Team Commenters: 1

Pseudocontext Submissions

Curmudgeon

Cathy Yenca

And no fewer than three people — Bodil Isaksen, Jocelyn Dagenais, and David Petro — sent me the following problem, created by a French teacher.

And I don’t know. The jist of the problem is that two soccer players are arguing about the perfection of one of their dabs. They consult a universal dabbing rulebook which says that in a perfect dab those triangles above must be right triangles. And it’s all pretty winking, right? It can’t be pseudocontext if it isn’t actually trying to be context in the first place, right? The judges give it a pass.

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

The commenters win a second straight week.

The judges rule that this problem satisfies the first criterion for pseudocontext:

Given a context, the assigned question isn’t a question most human beings would ask about it.

A question that might neutralize the pseudocontext is: “Can all of these smoke jumpers ride in the same plane together? How would you arrange them so the plane is properly balanced?”

Instead, the task here is to find mean, median, mode, standard deviation, first quartile, third quartile, the interquartile range, the maximum, the minimum, the variance, etc, etc.

Do you get my point? Yes, all of those operations could be performed on those numbers. We often assign all of the math that could be done in a context without asking ourselves, what math must be done in the context? What math does the context demand?”

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”6″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Team Me: 4
Team Commenters: 0

Pseudocontext Submissions

Michelle Pavlovsky

This is may be the worst math problem I’ve seen in my life.

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

Well well well … score one for Team Commenters.

The judges rule that this problem satisfies the first criterion for pseudocontext:

Given a context, the assigned question isn’t a question most human beings would ask about it.

Were you sleep-running the entire time? Why can’t you remember where you ran to and from?

This is Pseudocontext Saturday, so rather than overstep my jurisdiction I’ll let someone else critique the scaffolds in problem #32.

Featured Comment

Hallie:

Dan went for a run. Every 13th stride he sneezes. Every 17th stride he blinks. Every 5th stride a shiver runs down his spine thinking about his homework he has neglected to do. When will he shiver, blink and sneeze at the same time? (Ignore that it is impossible to sneeze with your eyes open.)

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”5″]

(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Team Me: 3
Team Commenters: 0

Pseudocontext Submissions

Michelle Pavlovsky

Paul Hartzer

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Answer

The judges rule that this problem satisfies both criteria for pseudocontext:

Given a context, the assigned question isn’t a question most human beings would ask about it.

I invite any commenter to rationalize the constraint that exactly 15 photos must be purchased and we don’t know which of them will be small or large. More often (always?) people begin with the photos they want, or perhaps they work from a total budget. “I can only buy 15 photos and the number of large photos I purchase can vary from zero to fifteen,” said no one ever.

Given that question, the assigned method isn’t a method most human beings would use to find it.

If most human beings were going to find out the cost of five large photos and ten small photos, they’d multiply each kind of photo by its price. Variables aren’t a useful tool.

So the textbook has made the world serve the math when math should serve the world. If the world doesn’t need math’s service, then math should be gracious enough to step out of the way.

Featured Comments

Jonathan Claydon:

I guessed correctly. The first and third choices made too much sense. Always step up to the plate thinking curveball.

Rachel:

The problem here is that the customer has no use for a general equation, but the store owner might—she’s got to deal with people who call in with all kinds of crazy orders and questions. Still, it’s unlikely the store owner would write an equation for just small and large pictures. It’s much more likely that she’d come up with a pricing scenario for unusual picture sizes.

Team Me: 2
Team Commenters: 0

Come on, team. This is your week.

This Week’s Installment

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”4″]

(If you’re reading via email or RSS, you’ll need to click through to vote.)

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer four possibilities for that connection. One of them is the textbook’s. Three of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Pseudocontext Submissions

Cathy Yenca

Dear Textbook… why not just measure Becky? #SillyMath pic.twitter.com/B4VuV5FFSK

— Cathy Yenca  (@mathycathy) October 28, 2016

David Petro

Answer

The judges rule that this problem satisfies the first indicator of pseudocontext:

Given a context, the assigned question isn’t a question most human beings would ask about it.

The judges wager that if you lined up 100 arbitrary human-types and asked them the first question they wonder about this context, no more than two of them would ask about how long the ping pong ball is in air.

The judges get the sense that the author of the problem just needed some projectile — any projectile — for the task of calculating total time in air. The tennis ping pong ball [Thanks, Paul Hartzer. -dm], the number drawn on the ping pong ball, and the prize you win for catching the ping pong ball — those are all unrelated to the mathematical work. That’s pseudocontext.

Poll

What mathematical skill is the textbook trying to teach with this image?

[poll id=”3″]

(If you’re reading via email or RSS, you’ll need to click through to vote.)

Rules

Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer four possibilities for that connection. One of them is the textbook’s. Three of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)

Current Scoreboard

Team Me: 1
Team Commenters: 0

Answer

The judges rule this pseudocontext because, given that awesome square maze, it’s very unlikely that anyone would wonder about the side length of the maze and unlikelier still that anyone would wonder if the side length was rational or irrational. An exhaustive search for a 1,225 ft² square maze in Dallas, TX, produced no results, exacerbating the judges’ sense that the textbook is exploiting the world for the sake of math. That’s pseudocontext.