[Pseudocontext Saturday] Runner

This Week’s Installment



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.



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.)


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


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.)

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Neither option seems like a natural fit for the photo. I think if there was another runner in the photo, systems of equations could be more appropriate.
    When I tried to think of a mathematical problem simply based on the picture before I looked at the options, I thought about how the length of a person’s shadow changes throughout the day. But then I wondered, why would anyone care how long their shadow was? Especially if they are in the middle of running?

    • The whole point of this exercise is that these pictures are used to real worldify completely inappropriate math problems.

      Even knowing that, I remain gobsmacked by what content the textbook publishers try to associate with them.

      Side note: Hey Dan – for those of use that get this via RSS, could you provide a link to the previous week at the bottom of these articles so that we can easily go back and see just how wrong we were?

  2. Maybe I’m just sensitive post-election, but I think the *pictures* from these textbooks are not really pseudocontext trying to connect math with the “real world.” Instead, I think they are intended to operate on an emotional level, with two objectives:
    (1) insert positive pictures of women and under-represented groups into the math class experience
    (2) form a positive association between math and a wide range of situations.

    Taken at face value, these seem to me to be worthy objectives. Are they effective at changing/forming student opinions and emotions? I don’t know, I’m a mathematician, not a psychologist and 100% T (vs F) on that Briggs-Meyers dimension. In other words: someone else would have to comment.

    That aside, I strongly support Dan’s underlying messages that this path to make math interesting and relevant is neither effective nor necessary.

    • Joshua, you are completely correct. The pictures are not there to make the math.

      First, textbook writers have quotas to fill: equal numbers of blacks, latinos, whites, asians. Then equal numbers of women and men, boys and girls. Don’t ever show a girl or woman in a “stereotypical” role, so matter how common or natural. There’s more, but you get the gist. You can’t show “elite” things like yacht club regattas.

      Second, you need to satisfy the Texas groups that comb through textbooks for any mention of white or Christians in a negative light, no mention of controversial topics like using exponential functions in a way that suggests evolution, or the age of the earth. Also, the people who want a positive association demand that nothing that even slightly appears negative to anyone in any way be expunged.

      Third, you need to include all the current standards and align everything to CCSS — then write a separate version for Florida because they’re special and a version for the 25 groups who just voted themselves out of Common Core and then you need to look into a separate set of state standards for each if the school system is big enough to care about …

      Fourth, All the supporting materials, rainy-day material, workbooks, problem sets, tests, special ed materials, teacher’s editions, foreign language editions.

      Fifth, this thing has to be marketable. So you water it down even more. Don’t offend. Add more color. Another three chapters for the faster class.

      Somewhere around tenth, you get to try to make the problems into RealWorld problems even though most of your grad student writers have never actually worked in the field they’re trying to model.

      I don’t blame the textbook companies for putting out pseudocontext, but it is fun to laugh at it and it gives me some great ideas. I just know that I have to read the MTBoS and supplement and fiddle. I glad that my school doesn’t get in the way … but that problem is for another rant.

  3. Jerry went out for a 3.1 mile jog. The sun was at an angle of 48 degrees making his shadow 7.5 ft long at the midpoint of his jog. He drank .78 L of water during his jog but lost .34 L to perspiration. When he got home, his cat posed the following problem: “if x+y=12 and 2x-y=18, find x and y.”

  4. I’m gaming the system. I looked at the vote and voted for the one that’s losing. This way, assuming the vote holds up, either I win or the majority wins, so I can declare some sort of victory. ;)

  5. 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 improssible to sneeze with your eyes open.)

  6. I’d also give dollars to doughnuts that the calorie numbers in the callout box don’t take into account relative inclination changes, making them misleading.

    It’s also really impressive that you have some device that measure your speed in meters per minute. Does anyone use that unit for anything?

    This is also one where, even if you wanted to answer that question, no one would do it using an algebraic model. Because you only have ten minute increments to work with, a table of values will get you there much faster and easier.

  7. Leslie Naselsky

    November 14, 2016 - 12:59 pm -

    For teaching LCM…
    A page in a stamp album holds 18 stamps. A page in a photo album holds 8 photos. What is the least number of stamps and photos you need so that each album has the same number of items and only full pages?

    Yikes. Why???

  8. Our first win! (I guessed it correct 3 out of the 4 weeks btw) When I looked at this I for some reason looked at the guy and his shadow as two lines intersecting, so I chose system of equations…worked!

    • The commenters saw right through me with this one.

      I wish there was some way to tally up the total scores for individual voters. I’d love to pass out some “Psuedocontext Pro” badges.