Smartness and mathematics have an unhealthy relationship.
If you have been successful in math, by public consensus, you must be smart. If you have been successful in the humanities, you may also be smart but we cannot really be sure about that now can we, says public consensus.
In a world where our finest mathematical minds ruined the global economy and perpetuate unequal social outcomes, outcomes most ably critiqued by people trained in the humanities, public consensus is wrong.
This worksheet is worse.
This worksheet associates smartness with a certain way of doing math, diminishing other ways your students might develop to do the same math. Because there are lots of possible ways to tell time — some new, some old, and some not-yet-invented!
Worse, this worksheet associates smartness with a certain way of doing math that is culturally defined, diminishing entire cultures. For example, depending on your location in the world, “2/5/19” and “5/2/19” can refer to the same calendar date. Neither of those ways are “smart” or “dumb.” They work for communication or they don’t.
Try This Instead
If I’d like students to learn a certain way of doing math — whether that’s adding numbers a certain way or solving equations a certain way — I need to understand the reasons why we invented those ways of doing math and put students in a position to experience those reasons. I also need to be excited — thrilled even! — if students create or adapt their own ways of doing math when they’re having those experiences. Anything less is to diminish their creativity.
If I want students to learn how to communicate mathematically, I need to ask them to communicate.
So in this Desmos activity, one student will choose a clock and another student will ask questions to narrow 16 clocks down to 1.
I have no idea what ways students will use, create, or adapt in order to tell time. I will be excited about all of them.
I will also be excited to share with them the ways that lots of cultures use to tell time. When I share those ways, I will be honest that those ways aren’t “smart” any more than they are “moral.” They are merely what one group of people agreed upon to help them get through their day.
So I’d also offer students this Desmos activity, which tells students the time using several different cultural conventions, including the one the worksheet calls “smart” above.
Students set the clock and then they see how easy or hard it was for the class to come to consensus using that convention.
Later, we invite students to set the clock themselves and name the time using three different conventions. They make two of them true, one of them a lie, and submit the whole package to the Class Gallery where their classmates try to determine the lie.
The words we use matter. “Real world” matters. “Mistakes” matter. “Smart” matters. Those words have the power to shape student experiences, to extend or withdraw opportunities to learn, to denigrate or elevate students, their cultures, and the ideas they bring to our classes.
Defining smartness narrowly is to define “dumbness” broadly. Instead, we should seek to find smartness as often as possible in as many students as possible.
shoot. i say five fifteen and five forty five routinely. i guess i'm not "smart"— Ms.B (@MathIsNotScary) March 18, 2019
Write each time "my way."— corey andreasen (@coreyandreasen) March 19, 2019
There's nothing wrong with familiarizing students with these phrases. How about "Write each time in words in at least two different ways. Tell which way is your favorite."
Re: time as culturally bound— Idil A. (@Idil_A_) March 30, 2019
growing up in Mogadishu, Somalia my mom said they used a 12 hour am/pm system, but it ran 6am-6pm.
Makes a lot of sense living on the equator, sunrise was 0 and sunset was 12.
@ddmeyer more cultural time context. I always have to ask whatâ€™s â€œhalf sevenâ€ and thereâ€™s more than one answer. https://t.co/daR81RCAUC— Calley Connelly (@CalleyMath) March 30, 2019