Total 90 Posts

## [Pseudocontext Saturdays] Spaghetti Bridge

This Week’s Installment

Poll

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

Pseudocontext Saturday #8

• Identifying supplementary angles (42%, 186 Votes)
• Calculating angle measures in a regular polygon (36%, 158 Votes)
• Proving triangles are congruent (22%, 99 Votes)

Total Voters: 443

(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.)

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.

## Great Classroom Action

Tracy Zager illustrates a key feature of some of my favorite math tasks: their constraints are simple, but they create paths for complex thinking and ever more interesting questions:

I think my name is worth \$239. Beat me? Haven’t figured out my \$100 strategy yet.

Lisa Bejarano is a recipient of our nation’s highest honor for math teachers, so when she admits “I have no idea what I am doing” and starts sketching out a blueprint for great classrooms, I tune in:

Now, beginning with the first day of school, I intentionally work at building a unique relationship with each student. I make sure to find reasons to genuinely value each of them. This starts with weekly “How is it going?” type questions on their warm up sheets and continues by using their mistakes on “Find the flub Friday” and through feedback quizzes. I also share a lot of myself with them. When we understand each other, my classes are more productive. I still make plans, but I allow flexibility to meet my students where they are.

David Cox describes “a difficult thing for students to believe”:

Once students begin to believe that the way they see something is the currency, then our job is to simply help them refine their communication so their audience can understand them. Only then does the syntax of mathematics matter.

“Help me understand you.”

“Help me see what you see.”

Kevin Hall thoughtfully deconstructs his attempts to teach linear function for meaning, and includes this gem:

Once you introduce the slope formula, slope becomes that formula. It barely even matters if today’s lesson created a nice footpath in students’ brains between “slope” and the change in one quantity per unit of change in another. Once that formula comes out, your measly footpath is no competition for the 8-lane highway that’s opened up between “slope” and (y2–y1)/(x2­-x1).

Featured Tweet

## #CMCMath Opening Keynote Address – Practice Problems

This is the keynote address I gave at CMC North this weekend with my co-presenters Shira Helft, Juana de Anda, and Fawn Nguyen.

The premise:

For a long time I worried I had chosen the wrong career. Other careers seemed like they had so much in their favor – better pay, less homework, more flexibility on the timing of bathroom breaks, etc. If you followed this blog ten years ago, you witnessed that worry.

Then a conversation with some of my close friends convinced me why I – and we – never have to envy any other career:

We have the best questions.

At least for me, no other job has more interesting questions than the job of helping students learn and love to learn mathematics.

A career in teaching means freedom from boredom.

To illustrate that, I interviewed three teachers at different stages in their careers – a teacher in her first decade, her second decade, and her third decade of teaching. I asked them, “What questions are you wondering right now?” Then we each took ten minutes to share our four questions.

But our talks weren’t disconnected. An important thread connected each of them, and I elaborated on that connection at the end of the talk.

Chapters

What question motivates you this year? What question wakes you up in the morning and energizes you throughout your day?

The question that drives me is “How can I present this in a fashion that will be so interesting that they will not only want to learn it, but they will remember it next week, next month, and next year?”

Whether with my family (most important), the teachers I support, or students I work with:
How am I being present?

## [Pseudocontext Saturdays] Rock Climber

This Week’s Installment

Poll

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

Pseudocontext Saturday #7

• Counting to 100 by 10's (40%, 149 Votes)

Total Voters: 376

(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.)

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.

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]

## “All the time.”

Yesterday, a student gave me step-by-step directions to solve a Rubik’s Cube. I finished it, but had no idea what I was doing. At times, I just watched what he did and copied his moves without even looking at the cube in my hands.

When we were finished, I exclaimed, “I did it!”, received a high-five from the student and some even applauded. For a moment, I felt like I had accomplished something. That feeling didn’t last long. I asked the class how often they experience what I just did.

They said, “All the time.”

Featured Comment

Is there an argument to be made that sometimes the conceptual understanding comes from repeating a procedure, then reflecting on it? Discovering/noticing patterns through repetition?

Great question. I wrote a comment in response.