I checked out your conversation with Karim on Storify (so neat to be able to archive tweets). Seems like in the specific case of the elevator photo, the student voices suggest there’s something more salient about weight in that photo. For me it’s because I have an elevator phobia and think more about crashing than squeezing in. That and I didn’t stop to think about how frickin’ huge a 31 person elevator is. Regular elevators are a tight fit with 15 people, I now recall from riding around during jury duty.

But to me, the question isnt about does the teacher ever get to assert things in the classroom, it’s about design. What do you do when a draft doesn’t go where you hoped? Edit. Maybe we need some help comparing this elevator to others. Start with video of 10 people squeezed into another elevator, then this photo. Or show people getting into the elevator and count and stop at 31 never showing the inside. Kids wonder how big is that elevator inside!

I hypothesize that it’s rare to have a scenario that’s mathematically interesting that can’t be captured in some media to provoke questions worth exploring. As a teacher, I am happy to lecture when students ask good questions, and to suggest further exploration when things are humming along, and even to tell kids about a better way to do something. But I also have to trust my subject that it is inherently interesting. If I have to tell someone “you should notice and care about this” something’s wrong and more importantly, it’s not going to work. That’s why playwrights’ mantra is “show, don’t tell”

If students aren’t seeing what I’m seeing, I need to show it, not tell them how to look.

To be honest, I find this a bit disingenuous. The 101qs format doesn’t actually gauge whether students (in this case teachers) “want” to know the answer; rather, it’s simply asks for the first — ie most obvious — question that comes to mind.

In this case, the first question that occurred to most people was, “How heavy is the average person?” We had the elevator weight (5000 lb.) and the number of passengers (31), so this question seems pretty predictable.

It’s just not that interesting. Instead, there are any number of more interesting questions, for instance How might the situation be different if it only men rode it? With 31 people getting on and off, how long would it take to get to the top floor? Sure, we can debate whether “interesting” is in the eye of the beholder, but I’m not convinced that most people really wanted to answer”5000/31.”

Again, I just think it was the most obvious. Which is exactly the point I was trying to make in the Twitter thread: that sometimes the job of a teacher is to get a 12 year-old to think like someone older than a 12 year-old. (Incidentally, this is why I think the 101qs site would benefit from some kind of “care/don’t care” rating system. You can ask me the first news station that comes to mind, but it doesn’t mean I care to watch it.)

The thing is, it seems that Dan agrees that it’s sometimes okay to trump a student’s question with a better one:

http://storify.com/mathalicious/what-does-want-mean

(actually, a few more than two words. Eek!)

One of the better pieces of advice I have read on this blog was to just ask the question if you are not willing to go with the questions the students come up. Attempting to contort their question into yours isn’t the way to go either – this is dishonest and fools no one.

I think the issue is usually that the question isn’t very good for that class, not the fact that the teacher is the one asking it (not saying student generated questions aren’t a plus).

I’m not convinced that it is necessary to have all of the students working on the same problem. In my experience, students will ask about 4-5 problems (more is usually better) and that their obvious questions are often the easiest to answer. You can then group students up by what types of questions they asked, and then have them switch up which kind of problem they are solving.

One also has to be careful about steering the class toward a specific problem. Otherwise, you will end up with a game in the class called “Let’s guess what the teacher is thinking” which is itself not a thinking activity for the students. Too many class spend their time guessing rather than thinking.

If the key is to get students thinking about mathematical reasoning, then it doesn’t really matter what problem they solve, so long as they eventually get into meatier, more difficult problems, instead of always looking for the quick, cheap, and easy problem to solve.

One way to help students work on more challenging questions is to give more context to the problem, and be willing to tell a bit of a story to get them thinking. The farmer, king and rice story is a good example of a story that justifies a discussion of exponents. Obviously population growth is another one. 101qs is a way of starting a story, surely more involved stories are necessary too. I doubt that every interesting mathematical idea can be captured by a single piece of multimedia.

We also want students to work on problems that they cannot complete in a single sitting. Mathematicians often work on problems for years, but it is rare for students to work on problems for more than 10 minutes in a single sitting. While shorter and faster problems are useful for more variety of problem solving, I also think that longer problems that take much more of a process to solve are useful.

I think we need multiple approaches to designing problems for students, and helping students design interesting mathematical problems for themselves.

Hi Dan – Thanks for all your intriguing, thought-provoking work. I don’t know how to upload it to 101 Questions, but I think a screenshot of this web page – possibly with all the contributors’ names highlighted – would prompt some perplexity and statistical thinking such as “Where are all the women?” “Is this typical?” or “Does this match the gender breakdown in our class/school/state?”

@Karim and @Dan

I think you two can both meet in the middle. I feel like where 101qs works well is that we are trying to find how we can engage those students on the gut level. To paraphrase Dan, how can we introduce these tasks to have everyone step on the first rung of the ladder of abstraction.

The more interesting questions become the sequels to these first acts. So yes, we start on a low bar, but I have a number of students who would have a very difficult time even with the average weight problem. Let them be challenged by the lower level questions, they need to experience success, and bring out the more involved questions as they work through those rungs of abstraction to the more interesting problems.

I am sure we are all well aware of that fact, but I can’t help but feel as if you guys assuming that each others methods precludes the other’s from being effective. They can both accomplish the same goal, and the question then shifts to: “How many and how rich of ideas do we want to give students at the onset?” I have been favouring the 3 acts approach, because kids start with an easy question, “How long does it take for a beam of light to go to the moon and back?” And progresses to a harder question, “How far is a light year?” To really difficult question “Based on the speed of light and the closest planet, what are the chances that we will ever find life in the universe?”

Dan wants to start on the first rung of that ladder. Karim wants the student to appreciate the beauty of the ladder in its whole glory. What is best for students?

@Karim:

I kinda cheated when I said, “media,” and I did it on purpose. I think sometimes a story or series of images or search results or lecture can motivate good questions. Now that I’ve googled Drake equation and anthropocentric I’m full of questions, like, “what the heck would non-human intelligence look like? Could there be intelligent beings the size of atoms or solar systems? Could there be intelligent rock formations? Have we found all the intelligent beings on *our* planet? What counts as communication?”

I do think good questions have to come from learners, not be asserted… but like Breedeen says, if a teacher says, “hey, here’s another question I find interesting, what do y’all think?” and the students say, “ooh, yeah! That’s totally interesting!” then those students own that question and are going to work their socks off to answer it.

Something about how you phrased reserving the right to assert what questions deserve to be worked on rankled me (and, clearly, Dan, since he put the word dum-dums in your mouth and he wasn’t talking about mystery-flavored lollipops). For one thing, the idea that 12-year-olds’ questions are less interesting than 40-year-old questions seems unverified. Less nuanced, sure, but less interesting? I had big, deep questions about fairness and justice and happiness and the future and the nature of the universe when I was 12. And if I said to a group of 12 year olds, “want to think with me about the odds of intelligent life on other planets?” and they said, “not really” I wouldn’t say, “well, that’s ’cause you’re 12 and don’t know how cool that is,” I would say, “why not? What do you want to know about?” (and they might say “how to get girls” in which case we could talk about the Drake equation after all).

All the Mathalicious questions I’ve seen are inherently interesting, and would likely interest groups of people of all ages, and you work carefully to pose them in such a way that everyone has resources to both begin to think about them and see how relevant they are to experiences they’ve had — students are prepared to think about the paradox of choice with a relevant example (custom sneakers) and equipped to think about how quickly choices grow from a few variables by working through the sneakers. It’s highly likely that the media sets them up to have just the question you predict they’ll have, and assert to them: can there be too much choice?

Seems to me like you’re starting with interesting questions and letting the math serve those questions, which I think is neat. It’s not exactly math for social justice, but it’s definitely math for good citizenship and generally being a good person.

101qs seems to have the goal of finding interesting moments that motivate the math. Making the moments interesting is super important because the math isn’t inherently interesting without a context (whether it’s a real-world context or a puzzling context: prime factorization is interesting to people who want to crack codes or make a million dollars or factor a quadratic equation or who are in any situation in which that skill is useful to a problem they’re genuinely invested in).

I find the “here’s a question” vs. “skip it” choices an okay-enough metric of a photo or video’s ability to provoke a question worth solving, and worth learning some math to solve.

I’d use 101qs to motivate a piece of math I wanted to concretize, make relevant, and get kids thinking about intuitively. I’d want to go from there to further generalizations and abstractions and thinking about the math for math’s sake.

I’d use Mathalicious to set the context for an important, interesting good citizenship conversation that requires some math skills to engage in fully.

Like you said, two really different goals.

FWIW, I think finding the average weight being used by the elevator company to be a very interesting question because I want to know how generous they’re being with their maximum capacity estimates. I don’t want to be on that elevator with 30 people and thinking, “gee what if a couple of these people are a lot heavier than average? What if none of us is skinny? Are we gonna crash?” [In a way, that’s more of a Mathalicious context: the average weight question is in the service of “what is a valid margin of error for engineering and safety?” which is a good-citizenship question and therefore more likely to be interesting no matter how it’s posed.]

The size-of-the-elevator question is interesting too, but if someone told me it was what I needed to solve after looking at this picture, I’d say, “who cares?” and then more of the lesson would be spent getting me to feel engaged than doing math with me. Whereas if I saw 31 people getting into an elevator and they just kept going and going, I’d totally be wondering, “what’s a reasonable range of sizes for the inside of that elevator,” and would be happy to answer that question — it’s not the question that’s inherently interesting or uninteresting in the 101qs case (whereas in the Mathalicious case, I think the question itself has to be interesting to “any reasonable person” or else it’s unlikely to be a question that leads to people being kinder, fairer, etc.) it’s that it was posed more or less artfully.

And that’s why it’s worth spending time improving your 101qs question ’til it screams out “care about this question!” whereas time is spent over at Mathalicious carefully scaffolding the math to get to really interesting conversations (that 12 year olds and 102 year olds care about when they’re equipped to relate to).

I worry that what’s coming out of 101qs has a sameness as far as what mathematics is being applied. I have time to spend maybe a week or two on ratios in class, but they absolutely dominate these kind of problems. I estimate overall the mathematics I’ve seen takes up 5% of what I have to actually teach.

Is there anyway we can solicit things that work with the “difficult” standards (like rational expressions)?

(Sorry iPad acted up in last comment, and I didn’t realize that part had sent. I was just starting to comment.)
For a relatively new website–not including time on #anyqs–I think 101qs is already achieving its intended initial goals. I know this because:
1) I was staring at a building for longer than usual yesterday and my friend asked, “Are you looking for math?” Ever since I got sold on 3Acts, I’m always on the lookout for “perplexing” situations. This is my 8th year teaching math and I’ve always loved math, yet I was never such a math geek like I’m now. I’m jealous of Andrew’s File Cabinet Act3 because it makes him a bigger geek.
2) Max’s and Karim’s two comments are over 7200 characters each, that’s about 51 tweets worth of words! That shows high interest and passion to me. We ask critical questions of the site and of ourselves as educators; it’s a win-win formula.

We cannot ask a kid to come up with a question and not honor it. I don’t think anyone here is saying that either. But Dan has built in a sequel and an extension to each 3Act lesson, and I see the teacher’s question can always come up at this time. When I did Andrew’s File Cabinet lesson, Act 2 was about each kid answering his/her own question in Act 1. And maybe a kid who asked a 12-year-old question liked the 30-year-old question asked by another kid and wanted to change his mind, this is okay too.

My concern is the number of WHY questions that my 6th graders have come up with. For the “Leaky Faucet,” one kid asked, “Why did he use the rubber ducky?” Another kid asked, “Why is he wasting water?” So we had a discussion about this.

The best Act 1 can go horribly wrong in the hands of one teacher, while a seemingly mediocre Act 1 can blossom wonderfully in the hands of another teacher. We have that much power.

Other ideas for trig problems: calculating distance (between two mountain peaks, say) using the Law of Sines. Then calculating distance when the Law of Cosines must be used. I can think along the lines of soccer players positioned on a field, tactical positions creating non-right triangles, etc.

As for right triangles, we once used Dan’s “How tall is the lamppost?” images (https://blog.mrmeyer.com/?p=12620) to answer the question “At what angle is the sun hitting the lampost?” using SOHCAHTOA and inverse trig functions. I wouldn’t say the experience was award-winning, but it was cool. It would have been cooler if we could have calculated what time he took the photos based on the angle to the sun. Anyone know how to do that? Right triangle trig opportunities abound in architecture, shadows, just about anything that goes up from the ground. We just have to start taking the opportunities.

I’m hoping to come up with something truly awesome that uses logs or logarithmic equations. That would make my day.

I suspect that the supremacy of rate- and ratio-type results from 101qs is in part due to the questioners, not the uploaders. I think even if presented with a good trig opportunity, most of us pose algebra-type questions. Maybe because we’re just in that mindset? Or do Dan’s blog and 101qs appeal more to algebra-ers?

I suspect that the supremacy of rate- and ratio-type results from 101qs is in part due to the questioners, not the uploaders. I think even if presented with a good trig opportunity, most of us pose algebra-type questions. Maybe because we’re just in that mindset? Or do Dan’s blog and 101qs appeal more to algebra-ers?

@lesanno: Keep in mind the point here is to have an question just begging to be answered strongly enough that even the apathetic teenager becomes curious; if anything our mindset is too complex compared with how our students will think.

Side note: Once I had a terrific lesson where I had a picture, a little extra context, and asked “what time of day is it?” No student would come on their own thinking answering the question was even possible, so it’s somewhat outside the 101qs format.

Michael P: Excellent question, especially since I have yet to contribute a single upload to 101qs. I am thus an amateur. The idea is still in the formulation stage, but here are my thoughts:
-There’s gotta be useful wilderness footage in some man vs. nature movie that involves navigating or estimating distances. I’m picturing adventurers stranded in snowy mountains.
-A bird’s eye view of a region with pins in the three relevant locations. The distance between locations 1 and 2 we know; we want to know the distance from 2 to 3; we can measure the angle.
-A picture along a line of sight between two somewhat distant objects and the simple question: “How far away is the ________.” I actually tried to construct this one on a faculty work day. I followed it up with video of me measuring the relevant pieces (a navigational compass for the angles, measuring tape for the side). It was workable, but deserves to be done better.

This is fascinating. I’m especially interested in hearing how to do this with the other 95% of the curricula, and who is building a repository of these student driven lessons, like Kelly and Jason asked. For instance, today I taught about finding the measures of a bisected angle, whose angles were arbitrary algebraic expressions. Bisected angles– sure! (mirrors, billiards) but angles of 6x-10 and 3x+5 makes it absurd.

I’m mainly posting to get notifications of the responses. :-)

@Jason Dyer I see your point and I’m certain my materials can be improved. But I also see that, not having experience in asking my own mathematical Qs as a student, I needed to be trained in this way of thinking by seeing others’ questions. Even as a young adult, I would not have asked, for example, “Which coin would be cheapest to carpet my home in?” Now I might. If a teacher can train students to ask these questions, can’t she train students in higher level courses to ask (and care about) higher level questions? Wouldn’t that be a major goal of the class?