Saturday, June 13, 2015

Should We Use the Term "pace" More?

I'm preparing to be one of the presenters at a 3-day NCTM Deep Dive Institute in July. Hope you can make it. Fawn will be presenting too.

I've come across some great tasks from NCTM, thanks to Peg Cagle (that's C-A-G-L-E everyone) that I've adapted to have a much lower entry point for teachers and students. However, I'm also looking to mix in some favorite Estimation 180 challenges and 3 Acts like Fast Clapper from Nathan.

I really dig this task. At first glance though, it looks pretty straightforward. Act 2 could look as simple as showing students a screenshot like this:
Then tell students to use this ratio to predict how many claps this dude will complete in a minute. We could call it a day, but what fun would that be?

Here's what I think should precede any screenshot from the Act 1 video. Have students get out their cell phones and partner up. Record their partner clapping for various increments that are less than 30 seconds. For example: 0, 5, 6, 10, 12, 15, 20, etc. Keep track of it in a table...
Then see who is the fastest clapper in the class and if they can break the record. Talk about what might prevent the students or dude in the video from breaking the record.

Here's an additional place I'd like to take Act 2. Talk about the term "pace". I really like this question I'll be using from now on with students and teachers:
How often should we check to see if he is on pace to break the record?
I think this question opens up the mathematics, especially for a table of equivalent ratios and double number lines. Forget equations (proportions) here. Furthermore, it reminds me of the pace timers that you sometimes see on television during the Olympics.

Talking about the word pace, is this the same thing as rate...?
I'd really love to hear from you about the term "pace".
  • How often do you use the word pace in math class?
  • What context do you use the word pace?
  • Are terms like rate or slope synonyms to pace?
  • Tell me everything you know about pace or how you use pace in your class?
Seriously, I want to know. Teach me!

Pace yourself,


  1. Does pace imply extrapolation? Or tends to more often than rate at least?

    1. I think we've seen some great thinking below...

  2. (Typed out train-of-thought; please take what is helpful and discard the rest!)

    A comment about the question you suggest:

    How often should we check to see if he is on pace to break the record?

    One observation about this question is that its beginning ("how often...") indicates what we have is actually a pace question about pace.

    I do not use 'pace' in mathematical scenarios in which 'rate' would suffice as a synonym (of course, the two are not generally interchangeable: consider the difference of 'pace oneself' and 'rate oneself'!). This is because I think the noun of 'rate' already occupies an important space in mathematical discourse, and don't see an obvious reason to substitute other words (you might argue it promotes vocabulary development and flexibility of thought; I would not strongly object to this.) I do, however, use the verb of 'pace' to suggest (or think about) managing resources in the context of one or more rates.

    For example: If I am thinking about the pace of a class (i.e., pacing my own instruction) then I have in mind many different rates and resources (e.g., how quickly I'm speaking, how quickly students are speaking, how many ideas students are generating, how many student-generated ideas are explored by their classmates, how much I want to cover in the given class, how much I want to cover in the course, time).

    I think you can find this phenomenon in other contexts, too. Doing a physical activity (whether clapping or running a marathon) and 'pacing oneself' requires the monitoring of multiple rates, as well.

    In pacing myself, I seek not only to maintain one rate -- I find the language of 'manage your rate of teaching' more challenging than 'manage your pace of teaching' -- but rather to strike a balance between many different rates. Again, this is a function of the connotations I have in thinking about 'pace' as a verb; however, I think some of these notions transfer to the noun form, too. Indeed, asking about 'the pace of a class' makes much better sense (to me) than 'the rate of a class'. In the former case, I proceed by trying to identify some rates to help make sense of it; in the latter case, I think: the rate with respect to what?


    1. Thanks MQ. All valuable insight. Maybe I could rephrase the question to "How often should we check to see if his rate is good enough to break the record?"

  3. When I used Fast Clapper this year, my students used double number lines and ratio tables to solve for the claps in one minute. Before the Act 3 reveal, I asked my students if they would bet a million dollars on their answers. To my surprise, many students said no and backed up their response with comments like, "His speed might change," "He might slow down if he gets tired," "He might speed up if he sees a timer and really wants to break the record," and other similar thoughts. We ended up checking the number of claps at 30 seconds, then students revised their work. The question of how often we should check brings up interesting connections to other activities in life and learning.

    Most of the time, I used pace in my classroom to describe my flexibility and give students choice. I tell students I change the pace of the day based on what they need, which is why we spend different amounts of time doing different things each day. For example, I might spend 5 minutes going over homework one day and I might give students 15 minutes to discuss and rework homework in groups another day. Throughout the day, I ask who needs me to slow down my pace and who is ready to pick up the pace based on the success I see among students. If most students want me to slow down, I usually do whatever I have planned with slower guided examples. If students want me to pick up the pace, I usually give directions with a partial example before students get to work.

    I think rate and pace are similar, but not always identical in how I use them. When I use rate, I am typically describing the change in one measurement compared to another measurement (how very mathematical of me) and a rate changes based on events that affect one of the measurements. My rate of instruction can vary based on the success of my students, the time available, the difficulty of a topic, the activities, the time needed for instructions, etc. In contrast, I tend to use the word pace to refer to instances where students or myself are actively choosing the rate of instruction. The pace of instruction can be the result of students communicating their success or struggle with a topic. The pace can also be changed when I decided to include or exclude certain activities based on the understanding of my students. I like to think of the two terms this way: rate is responsive to any changes in the classroom whereas setting the pace implies choices. Does that make any sense?

    One thing this conversation brings to my mind is assessment. How does our pacing/rate of instruction compare to our pacing/rate of assessment? Should the amount or frequency of assessment change with the pace of instruction? It's easy to just set a day of the week as a quiz/test day and write assessments that include topics up to that point in the week, but what if assessment became something that was responsive to student success? I picture a day or two in my class where students are really rocking some concept or skill, then asking students when they want to prove to me their understanding by taking a quiz. I wonder how many students would respond with a day that is sooner than I intended?

    1. Great insight here too. I love the, "Would you bet a million dollars...?" which reminds me of "Would you bet your life...?"

      I think you raise an extremely valuable point regarding assessments. How does one's pace change depending on the scheduling of an assessment or should the pace dictate the schedule of the assessment? That's a tough cookie. Thanks again!