- The speaker was well-prepared and knowledgeable.
- The speaker was an engaging and effective presenter.
- The session matched the title and description in the program book.

Attendees scored each statement on a scale from 0 (disagree!) to 3 (agree!). Attendees could also leave written feedback.

At the end of the conference, presenters were sent to a public site where they could access not just their own session feedback, but the feedback for other presenters also. This link started circulating on Twitter. I scraped the feedback from every single session and analyzed all the data.

This is my intention:

**To learn what makes sessions unpopular with attendees.**It’s really hard to determine what makes a session good. “Great session!” shows up an awful lot without elaboration. People were much more specific about what they disliked.

This *isn’t* my intention:

**To shame anybody.**Don’t ask me for the data. Personally, I don’t think it should have been released publicly. I hope the conference committee takes the survey results seriously in planning future conferences but I’m not here to judge anybody.

**Overall**

There were 2,972 total feedback messages. 2,615 were correctly formatted. With 3,600 attendees attending a maximum of eight sessions, that’s 28,800 feedback messages that *could have* been sent, for a response rate of about 10%.

**How Much Feedback Did You Get?**

Most presenters received between 10 and 20 feedback messages. One presenter received 64 messages, though that was across several sessions.

**How Did You Do On Each Of The Survey Questions?**

Overall the feedback is incredibly positive. I’m very curious how this distribution compares to other math education conferences. I attend a lot of them and Palm Springs is on the top shelf. California has a deep bench of talented math educators and Palm Springs is a great location which draws in great presenters from around the country. I’d put it on par with the NCTM regionals. Still, this feedback is surprisingly sunny.

The data also seem to indicate that attendees were more likely to critique the presenters’ *speaking skills* (statement #2) than their *qualifications* (statement #1).

**How Did You Do On A Lousy Measure Of Overall Quality?**

For each presenter, I averaged the responses they received for each of the survey questions and then summed those averages. This measure is problematic for loads of reasons, but more useful than useless I think. It runs from 0 to 9.

62 presenters received perfect scores from all their attendees on all measures. 132 more scored above an 8.0. Even granting the lousiness of the measure, it points to a very well-liked set of presenters.

So why didn’t people like your session? The following quotes are all verbatim.

**What People Said When You Weren’t “Well-Prepared Or Knowledgeable.”**

If someone rated you a 0 or a 1 for this statement, it was because:

- he was late and unprepared.
- frustrating that we spent an hr on ppl sharing rationale or venting. I wanted to hear about strategies and high leaveage activities at the school.
- went very fast
- information was scattered.
- A lot of sitting around and not do much.
- This presentation was scattered and seemed thrown together at the last minute.
- Unfortunately, the presenter was not focused. There was no clear objectives. Please reconsider inviting this presenter.

**What People Said When You Weren’t “An Engaging Or Effective Presenter.”**

If someone rated you a 0 or a 1 for this statement, it was because:

You didn’t offer enough practical classroom applications.

- I wanted things students could use.
- philosophy more than application. I prefer things I can go back with. I already get the philosophy.
- very boring. Too much talking. I wanted more in class material.

Your style needs work.

- very dry and ppt was ineffective
- very disappointing and boring
- Arrogant,mean & full of himself
- BORING. BORING. He’s knowledgable, but dry. Not very interactive.
- knowledgeable but hard to hear
- he spoke very quickly and did not model activities. difficult to follow and not described logistically.
- more confused after leaving

Not enough *doing*.

- not as hands-on as I would have hoped
- too much talking from participants and no information or leadership from the presenter. Everyone had to share their story; very annoying.
- I could do without the justification at the beginning and the talking to each other part. I already know why I’m here.
- I would have liked more time to individually solve problems.

Too *much* doing.

- while they had a good energy, this session was more of a work time than learning. It did not teach me how to facilitate activities
- I didn’t think I was going to a math class. I thought we would be teachers and actuall create some tasks or see student work not our work.
- it would be nice to have teachers do less math and show them how you created the tasks you had us do.

**What People Said When Your Session “Didn’t Match The Title And Description In The Program Book.”**

You were selling a product. (I looked up all of these session descriptions. None of them disclosed the commercial nature of their sessions.)

- The fact that it was a sales pitch should have been more evident.
- only selling ti’s topics not covered
- a sales pitch not something useful to take back to my classroom
- Good product but I was looking more for ideas that I can use without purchasing a product.
- I was hoping for some ideas to help my kids with fact fluency, not a sales pitch.
- didn’t realize it was selling a product
- this is was nothing more than a sales pitch. Disappointed that I wasted a session!
- More like a sales pitch for Inspire
- I would not have gone to this session if I had known it required graphing calculators.

You claimed the wrong grade band.

- good for college methods course not for math conference
- not very appropriate for 6,7 grade.
- disappointed as it was too specific and unique to the HS presented.
- Didn’t really match the title and it should have been directed to middle school only.
- This was not as good for elementary even though descript. said PreK-C / a little was relevant but my time would have been better used in another
- the session was set 2-6 and was presented at grades k-5.
- this was not a great session for upper elementary grade and felt more appropriate for 7-12.

You didn’t connect your talk closely enough to the CCSS.

- not related to common core at all. Disappointing
- unrelated to ccss

You decided to run a technology session, which is impossible at math ed conferences because half the crowd already knows what you’re talking about and is bored and half the crowd doesn’t know what you’re talking about and is overwhelmed.

- gave a few apps but talked mostly about how to teach instead of how to use apps or what apps would be beneficial
- good tutorial for a newbie or first time Geogebra user but I already knew how to use Geogebra so I found most of this pointless. Offer an advanced
- Good information, but we did not actually learn how to create a Google form. I thought we would be guided through this more. It doesn’t help to
- apps were geared to higher lever math not middle school

**People Whose Sessions Were Said to Be the “Best of the Conference!”**

23-way tie! Perhaps useful for your future conference planning, however.

- Armando Martinez-Cruz
- Bob Sornson
- Brad Fulton
- Cathy Seeley
- Cherlyn Converse
- Chris Shore
- David Chamberlain
- Douglas Tyson
- Eli Luberoff
- Gregory Hammond
- Howard Alcosser
- Kasey Grant
- Kim Sutton
- Larry Bell
- Mark Goldstein
- Michael Fenton
- Monica Acosta
- Nate Goza
- Patrick Kimani
- Rachel Lasek
- Scott Bricker
- Vik Hovsepian
- Yours Truly

**Conclusion**

The revelations about technology and hands-on math work interest me most.

In my sessions, I like to *do* math with participants and then *talk* about the math we did. Too much *doing*, however, and participants seem to wonder why the person at the front of the room is even there. That’s a tricky line to locate.

I would also like to present on the technology I use that makes teaching and learning more fun for me and students. But it seems rather difficult to create a presentation that differentiates for the range of abilities we find at these conferences.

The session feedback here has been extremely valuable for my development as a presenter and I only hope the conference committee finds it equally useful for their purposes. Conference committee chair Brian Shay told me via email, “Historically, we use the data and comments to guide our decision-making process. If we see speakers with low reviews, we don’t always accept their proposal for next year.”

Great, if true. Given the skew of the feedback towards “SUPER LIKE!” it seems the feedback would be most useful for scrutinizing poor presenters, not locating great ones. The strongest negative feedback I found was in reaction to unprepared presenters and presentations that were covertly commercial.

CMC has the chance to initiate a positive feedback loop here by taking these data seriously in their choices for the 2015 conference and making sure attendees know their feedback counted. More and more thoughtful feedback from attendees will result.

**Full Disclosure**

I forgot to tell the attendees at my session my PollEverywhere code. Some people still sent in reviews. My practice is to post my most recent twelve months of speaking feedback publicly.

**2014 Nov 4**. It seems I’ve analyzed an incomplete data set. The JSON file I downloaded for one presenter (and likely others) contains fewer responses than he actually received. I don’t have any reason to believe there is systematic bias to which responses were included and excluded but it’s worth mentioning this caveat.

Sam Shah’s blog has been a veritable teaching clinic the last two weeks, more than filling his own installment of Great Classroom Action.

With Attacks and Counterattacks, Sam asked his students to define common shapes as best as they could – triangle, polygon, and circle, for instance. They traded definitions with each other and tried to poke holes in those definitions.

When the counter-attacks were presented, it was interesting how the discussions unfolded. The original group often wanted to defend their definition, and state why the counter-attack was incorrect.

Trade the definitions back, strengthen them, and repeat.

Sam created some very useful scaffolds for the very CCSS-y question, “If you have a shape and its image under a rotation, how can you quickly and easily find its center of rotation?”

This is an awesome exercise (inmyhumbleopinion) because it has kids use patty paper, it has them kinesthetically see the rotation, and it gives them immediate feedback on whether the point they thought was the center of rotation truly is the center of rotation. Simple, sweet, forces some thought.

Sam then pulls a move with a Post-It note that is a stunner, simultaneously useful for clarifying the concept of a variable and for finding the sum of recursive fractions:

Ready? READY? Flip. THAT FLIP IS THE COOLEST THING EVER FOR A MATH TEACHER. That flip was the single thing that made me want to blog about this.

Finally, Sam pulls a masterful move in the setup to his students’ realization that all the perpendicular bisectors of a triangle’s side meet in the same point. He has them first find those lines for pentagons (nothing special revealed) and quadrilaterals (nothing special revealed) before asking them to find them for triangles (something very special revealed).

]]>There were gasps, and one student said, and I quite, “MIND BLOWN.”

I give out 5-6 sets of three dice. I have the students roll them and then add up all the numbers which cannot be seen (bottom, middles and middles). Once they have the sum, they sit back with the dice still stacked and I “read their minds” to get the sum.

So then I shuffled up the little slips of sequences and started saying, B, your sum is 210. C, your sum is 384. D, your sum is 2440. E, your sum is -24. They were astonished!

These moments seem infinitely preferable to just leaping into an explanation of the sums of arithmetic sequences.

Our friends who are concerned with cognitive load should be happy here because students are only accessing long-term memory when we ask them to roll dice, write down some numbers, and add them. It’s easy.

Our friends who are concerned that much of math seems *needless* are happy here also. With The Necessity Principle, Harel and his colleagues described five needs that drive much of our learning about mathematics. Kate and Scott are exploiting one of those needs in particular:

The need for causality is the need to explain – to determine a cause of a phenomenon, to understand what makes a phenomenon the way it is.

[..]

The need for causality does not refer to physical causality in some real-world situation being mathematically modeled, but to logical causality (explanation, mechanism) within the mathematics itself.

Here are three more examples where the teacher appears to be a mind-reader, provoking that need for causality. Then I invite you to submit other examples in the comments so we can create a resource here.

**Rotational Symmetry**

Here is a problem from Michael Serra’s *Discovering Geometry*. No need for causality yet:

But at CMC in Palm Springs last weekend, Serra created that need by asking four people to come to the front of the room and hold up enlargements of those playing cards. Then he turned his back and asked someone else to turn one of the cards 180°. Then he played the mind-reader and figured out which card had been turned by exploiting the properties of rotational symmetry.

**Number Theory**

The Flash Mind Reader exploits a numerical relationship to predict which symbol students are thinking about. Prove the relationship.

Here is a little trick I like to call calculator magic. You will need a calculator, a 7-digit phone number and an unwitting bystander. Here goes:

Key in the first three digits of your phone number

Multiply by 80

Add 1

Multiply by 250

Add the last 4 digits of your phone number

Add the last 4 digits of your phone number again

Subtract 250

Divide the number by 2

Surprise! It is your phone number!

A nice trick is this one with dice. A lot of dice. Let’s say 50 or so. You lay them on the ground like a long chain. The upward facing numbers should be completely random. Then you go from the one end to the other following the following rule. Look at the number of the die where you’re at. Take that many steps along the chain, towards the other end. Repeat. If you’re lucky, you already end up exactly at the last die. You’ll be a magician immediately! But usually, that isn’t the case. What you usually have to do, is take away all those dice which you jumped over during the last step. Tell them that that is “the rule during the first round”. Now the actual magic begins. You tell the audience that they can do whatever they want with the first half of the chain. They may turn around dice. Swap dice. Take dice away. Whatever. As long as they don’t do anything with the second half of the chain. [If you like risks, let them mess up a larger part of the chain.] What you’ll see, is that each and every time, they will end up exactly at the end of the chain!

A few years ago, I found this “trick” on a “maths” site, not sure which, but it was UK. You need 5 index cards. Number them 1, 2, 3, 4, 5 in red ink on the front. On the reverse side, number them 6, 7, 8, 9, 10 in blue ink. Be sure that 1 and 6 are on opposite sides of the same card…same with 2 and 7, etc. Turn your back to the group of students. Have one of the students drop the 5 cards on the floor and tell you how many cards landed with the blue number face up (they don’t tell you the number, just “3 cards are written in blue”). Tell them the total of the numbers showing is 30. The key is that each blue number is 5 more than its respective red number. Red numbers total 15. Each blue number raises the total by 5. So 3 blue numbers make it 15 (the basic sum) + 15 (3 times 5). Let them figure out how you are using the number of blue numbers to find the total of the exposed numbers.

**Expressions & Equations**

I ran an activity with students I called “number tricks.” (Okay. Settle down. Give me a second.) I’d ask the students to pick a number at random and then perform certain operations on it. The class would wind up with the same result in spite of choosing different initial numbers. Constructing the expression and simplifying it would help us see the math behind the magic. (Handout and slides.)

I do something called calendar magic where I show a calendar of the month we’re in, ask the students to select a day and add it with the day after it, the day directly under it (so a week later), and the day diagonally to the right under it, effectively forming a box. Then I ask them to give me the sum and I tell them their day.

Always a bunch of students figure out the trick, but the hardest part is writing the equation. Every year I have students totally stumped writing x+y+a+b. It’s really a reframing for them to think about the

relationshipbetween the numbers and express that algebraically.Finally I ask them to write a rule for three consecutive numbers, but I don’t say which number you should find and inevitably someone has a rule for finding the first number and someone has one for finding the middle number. I love that!

**Different Bases**

Andy Zsiga suggests this card trick involving base 2.

**Call for Submissions**

Where else have you seen mind-reading lead to math-learning? Are there certain areas of math where this technique cannot apply?

**2014 Oct 30**. Megan Schmidt points us to all the NRich tasks that are labeled “Card Trick.”

**2014 Oct 30**. Michael Paul Goldenberg links up the book * Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks*.

PhotoMath is an app that wants to do your students’ math homework for them. Its demo video was tweeted at me a dozen times yesterday and it is a trending search in the United States App Store.

In theory, you hold your cameraphone up to the math problem you want to solve. It detects the problem, solves it, and shows you the steps, so you can write them down for your math teacher who insists *you always need to show your steps*.

We should be so lucky. The initial reviews seem to comprise loads of people who are thrilled the app exists (“I really wish I had something like this when I was in school.”) while those who seem to have actually downloaded the app are underwhelmed. (“Didn’t work with anything I fed it.”) A glowing Yahoo Tech review includes as evidence of PhotoMath’s awesomeness this example of PhotoMath choking dramatically on a simple problem.

But we should wish PhotoMath abundant success – perfect character recognition and downloads on every student’s smartphone. Because the only problems PhotoMath could conceivably solve are the ones that are boring and over-represented in our math textbooks.

It’s conceivable PhotoMath could be great for problems with verbs like “compute,” “solve,” and “evaluate.” In some alternate universe where technology didn’t disappoint and PhotoMath worked perfectly, all the most fun verbs would then be left behind: “justify,” “argue,” “model,” “generalize,” “estimate,” “construct,” etc. In that alternate universe, we could quickly evaluate the value of our assignments:

“Could PhotoMath solve this? Then why are we wasting our time?”

**2014 Oct 22**. Glenn Waddell seizes this moment to write an open letter to his math department.

**2014 Oct 22**. David Petro posts a couple of pretty disastrous screenshots of PhotoMath in action.

**2014 Oct 23**. John Scammell puts PhotoMath to work on tests throughout grade 7-12. More disaster.

**2014 Oct 24**. New York Daily News interviewed me about PhotoMath.

**2014 Oct 27**. Jim Pai asked some teachers and students to download and use PhotoMath. Then he surveyed their thoughts.

**Featured Comment**

Kathy Henderson gets the app to recognize a problem but its solution is mystifying:

I find this one of the most convoluted methods to solve this problem! I may show my seventh graders some screen shots from the app tomorrow and ask them what they think of this solution – a teachable moment from a poorly written app!

I we are structuring this the right way, kids (a) won’t use the app when developing the concept, (b) have a degree of comfort with doing it themselves after developing the concept and (c) take the app out when they end up with something crazy like -16t

^{2}+400t+987=0, and factoring/solving by hand would take forever.

The point in this case isn’t how well the character recognition is. Or how correct the solutions are. Because it’s just a matter of time before apps like these solve handwritten algebra problems perfectly in seconds, providing a clear description of all steps taken.

The point is: who provides the equation to be solved by the app? I have never seen an algebraic equation that presented itself miraculously to me in daily life.

]]>ps. Photomath is just a “stupid pet trick” they did to market their recognition engine.

Here is my speaking calendar for 2015 in case anybody is interested in attending Dan’s Blog: The Unplugged Experience. Some of these sessions are private, others have open registration pages (see the links), and others have waiting lists. Feel free to send an e-mail to dan@mrmeyer.com with inquiries about any of them. It’d be a treat to see you at a workshop or a conference.

**BTW.** Delaware, Idaho, Nebraska, Rhode Island, Tennessee, West Virginia, and Wyoming will complete my United States bingo card. If you’re the sort of person who schedules these kinds of sessions for a school or district or conference in any of those states, please get in touch.

Mark has 42 coins consisting of dimes and quarters. The total value of his coins is $6. How many of each type of coin does he have? Show all your work and explain what method you used to solve the problem.

The only math students who like these problems are the ones who grow up to be math teachers.

One fix here is to locate a context that is more relevant to students than this contrivance about coins, which is a flimsy hangar for the skill of “solving systems of equations” if I ever saw one. The other fix recognizes that the *work* is fake also, that “solving a system of equations” is dull, formal, and procedural where “*setting up* a system of equations” is more interesting, informal, and relational.

Here is that fix. Show this brief clip:

Ask students to write down their best estimates of a) what kinds of coins there are, b) how many total coins there are, c) what the coins are worth.

The work in the original problem is pitched at such a formal level you’ll have students raising their hands around the room asking you how to start. In our revision, which of your students will struggle to participate?

Now tell them the coins are worth $62.00. Find out who guessed closest. Now ask them to find out what *could* be the answer – a number of quarters and pennies that adds up to $62.00. Write all the possibilities on the board. Do we all have the same pair? No? Then we need to know more information.

Now tell them there are 1,400 coins. Find out who guessed closest. Ask them if they think there are more quarters or pennies and how they know. Ask them now to find out what *could* be the answer – the coins still have to add up to $62.00 and now we know there are 1,400 of them.

This will be more challenging, but the challenge will motivate your instruction. As students guess and check and guess and check, they may experience the “need for computation“. So step in then and help them develop their ability to compute the solution of a system of equations. And once students locate an answer (200 quarters and 1200 pennies) don’t be quick to confirm it’s the *only* possible answer. Play coy. Sow doubt. Start a fight. “Find another possibility,” you can free to tell your fast finishers, knowing full well they’ve found the *only* possibility. “Okay, fine,” you can say when they call you on your ruse. “*Prove* that’s the only possible solution. How do you know?”

Again, I’m asking us to look at the work and not just the world. When students are bored with these coin problems, the answer isn’t to change the story from coins to mobile phones. The answer isn’t *just* that, anyway. The answer is to look first at what students are *doing* with the coins – just solving a system of equations – and add more interesting work – estimating, arguing about, and formulating a system of equations first, and *then* solving it.

*This is a series about “developing the question” in math class.*

**Featured Tweets**

I asked for help making the original problem better on Twitter. Here is a selection of helpful responses:

@ddmeyer I hide coins in a 35mm container & asked kids to guess the exact contents. Then I answer Qs about the total value, types of coins

— Jennifer Abel (@abel_jennifer) October 15, 2014

@ddmeyer Remove 42 coin restriction. How about.. Least # of coins? Max # coins? What pattern is there to coins needed to make $6?

— Jeff Harding (@GradesHarding) October 15, 2014

@ddmeyer If it’s only more probs like this one with numbers changed? Boo. But what about: 42 coins and $6. What denominations could this be?

— Justin Lanier (@j_lanier) October 15, 2014

@ddmeyer just spitballing: start w/ "Try to make $6 with 42 coins" (or whatever). "Can you make it w/ 43? 41?" "Can you make $3 w/ 24?" etc

— Geoff Maul (@emergentmath) October 15, 2014

@ddmeyer (Probs more like "I have 37 cents, what coins could I have?") Idea to get kids thinking re constraints, multiple possibilities.

— Katherine Bryant (@MathSciEditor) October 15, 2014

@ddmeyer Turn it into a 20-questions game: Stu reach into coin jar & grab handful, others ask Qs to find out what coins they have.

— Denise Gaskins (@letsplaymath) October 15, 2014

@ddmeyer Make a video of me taking my coin jar from home to CoinStar. Make it take a long time…until kids ask how much money did you get?

— Ryan Adams (@MrRadams) October 15, 2014

**2014 Oct 20.** Michael Gier used this approach in class.

"I'm gonna solve this one, Mr. Gier!" Students develop an almost *angry* resolve to solve the coin problem. http://t.co/KFYNegOobU @ddmeyer

— Michael Gier (@mgier) October 20, 2014

I had students literally SPIKE their paper like a football in delight when they found out they were right. http://t.co/KFYNegOobU @ddmeyer

— Michael Gier (@mgier) October 20, 2014

**Featured Comments**

]]>One of the challenges for the teacher is to guide the discussion back to the more interesting and important questions. Why does this technique (constructing systems of equations) work? Where else could we use similar strategies? Are there other ways to construct these equations that might be more useful in certain contexts?

Danielson, doing his best Howard Beale:

THE STEPS WIN, PEOPLE! The steps trump thinking. The steps trump number sense. The steps triumph over all.

Let me add to the conversation the category of “steps that are correct but useless.” These are great. They come from a conversation I had, like, fifteen minutes ago with a teacher named Leah Temes here at NWMC 2014.

Leah teaches Algebra II. We were talking about solving systems of equations. It’s really easy to teach the solution to a system like this as a series of correct, useful steps:

2x + 3y = 10

5x – 3y = 4

- Add the second equation to the first one.
- Solve for x.
- Substitute x in either equation to solve for y.
- Check that pair in the other equation for full credit.

Leah said she was tired of seeing her students mimic those correct steps without understanding why they worked. So instead of showing her students steps that were useful and correct, she asked them if she was allowed to add the following two equations:

2x + 3y = 10

5 = 5

To get:

2x + 3y + 5 = 10 + 5

Is everything still *correct*? Yes.

Was that *useful*? No.

This experience awakened her students to a category of steps in addition to the *correct and useful ones* they’re supposed to memorize and the *incorrect and useless ones* they’re supposed to avoid – *correct and useless steps*.

Alerting your students to that category of steps may make math seem less intimidating and more interesting. Math isn’t any longer a matter of staying on the right side of a line between the incorrect and correct steps. There’s another region out there, one that’s a bit less *tame*, a place for explorers, a place where the worst thing that can happen is you did something right but it just wasn’t useful. That category of steps also requires *justification* – “how do you *know* this is correct?” – which can help bend the student away from memorization and back towards understanding.

**BTW**. All of this implies a *fourth* category of steps – incorrect but useful. Can anybody give an example?

**Featured Comments**

I do a similar thing when solving equations in one variable by asking students if I

canadd 1,000,000, let’s say, to each side of an equation… or if Icansubtract 27 from both sides… or divide both sides by 200… etc. etc. We talk about what is “legal” (have we followed the rules of algebra and the concept of “balance” and equivalence?) and what is “helpful” (have we done something “legal” that helps us isolate the variable so we can solve this thing?”) Exaggerated examples like adding 1,000,000 to both sides seem to make an impression on kids.

I have long been a fan of deliberately sabotaging a solution to something that I might be doing on the board so that somewhere down the road things become obviously wrong. This is so students can start to develop strategies for what to do when this happens.

Many will tell you that it’s important for students to make mistakes (in fact, that they learn the most when they do). But that sometimes runs counter to what they see in class. That is, a teacher demonstrating flawless execution of mathematics. Even some of our best students often won’t even attempt a problem unless they are sure they will get it correct. If they are ever going to become comfortable with making mistakes as part of the normal process then we have to include managing those mistakes as part of our day to day in class.

]]>[It’s] incorrect but useful to estimate things like area problems, in order to find out a ballpark figure and check if you’ve done the math right.

In the September 2014 edition of *Mathematics Teacher*, reader Thomas Bannon reports that his research group has found that the applications of algebra haven’t changed much throughout history.

310:

Demochares has lived a fourth of his life as a boy; a fifth as a youth; a third as a man; and has spent 13 years in his dotage; how old is he?

1896:

A man bought a horse and carriage for $500, paying three times as much for the carriage as for the horse. How much did each cost?

1910:

The Panama Canal will be 46 miles long. Of this distance the lower land parts on the Atlantic and Pacific sides will together be 9 times the length of the Culebra Cut, or hill part. How many miles long will the Culebra Cut be? Prove answer.

2013:

Shandra’s age is four more than three times Sherita’s age. Write an equation for Shandra’s age. Solve if Sherita is 3 years old.

I’m grateful for Bannon’s research but his conclusion is, in my opinion, overly sunny:

Looking through these century-old mathematics book can be a lot of fun. Challenging students to find and solve what they consider the most interesting problem can be a great contest or project.

My alternate reading here is that the primary application of school algebra throughout history has been to solve contrived questions. Instead of challenging students to answer the most interesting of those contrived questions, we should ask questions that aren’t contrived and that actually do justice to the power of algebra. Or skip the whole algebra thing altogether.

**Different**

If you told me there existed a book of arithmetic problems that *didn’t include* any numbers, I’d wonder which progressive post-CCSS author wrote it. Imagine my surprise to find *Problems Without Figures*, a book of 360 such problems, published in 1909.

For example, imagine the interesting possible responses to #39:

What would be a convenient way to find the combined weight of what you eat and drink at a meal?

That’s great question development. Now here’s an alternative where we rush students along to the answer:

Sam weighs 185.3 pounds after lunch. He weighed 184.2 before lunch. What was the weight of his lunch?

So much less interesting! As the author explains in the powerful foreword:

Adding, subtracting, multiplying and dividing do not train the power to reason, but deciding in a given set of conditions which of these operations to use and why, is the feature of arithmetic which requires reasoning.

Add the numbers back into the problem later. *Two minutes* later, I don’t care. But subtracting them for just two minutes allows for that many more interesting answers to that many more interesting questions.

[via @lucyefreitas]

*This is a series about “developing the question” in math class.*

**New Blog Subscriptions**

- Tracy Zager has been one of my favorite math voices on Twitter this school year and she’s now blogging. She’s also recently announced a fight with breast cancer and has requested that we “Please help me remember that I have thinking and ideas to share, and am involved in a world bigger than this right now.”
- Annie Fetter’s work at the Math Forum has always been impressive and it’s a total oversight I hadn’t realized she writes a blog until now.
- Tim McCaffrey and I share a lot of the same enthusiasms. He helps districts run lesson studies around three-act tasks and just started blogging about it.
- Matt Bury had positively invaluable commentary during last month’s adaptive learning discussions.
- Dan Burf, a/k/a Quadrant Dan, is a new teacher who has been using my old, old lessons, which is kind of fun to watch.
- Amy Roediger, whose writing on Classkick was extremely useful.
- Julie Wright is full of promise.
- Just Mathness is full of promise.

**New Twitter Follows**

- Patrick Honner: “I’m sure Benny would do quite well at this.”
- Bob Lochel, who is a regular in our Great Classroom Action features.
- Kelly Stidham, who lit up my blog this month with a comment about online professional development.

**Multimedia Math**

I make an open offer to my workshop participants to help them with their video editing. A couple of newcomers to multimedia modeling came up with these two tasks:

- Candy & Chips, for systems of equations.
- Apples for All, for unit fractions.

**Great Tweets**

Proofs are social documents not compiled code.

**Press Clippings**

- The Ontario Ministry of Education filmed an interview series with me and other math education-types in Toronto.
- An interview with a teen writer from The Santa Fe New Mexican.
- An interview with AFEMO, a Francophone group of math educators.