Skills practice [#NCTMDenver]

I attended E. Paul Goldenberg’s session on Thursday of NCTM in Denver. It was not at all, as advertised, in keeping with the proof strand. But that does not matter.

What matters is this. Goldenberg shared the video below. The whole video is worth your time, but I have queued it up to the 2-minute mark, where a beautiful classroom sequence unfolds (give yourself about 5 minutes for it).

My eyes tear up watching this sequence. I am neither kidding nor exaggerating. It gives me hope for quality classroom instruction in elementary mathematics.

Be sure to notice the transition to a new task at the 4-minute mark, and how the teacher deals with the struggle that occurs at the 6-minute mark.

Also please look in the kids’ eyes. Watch their body language and their waving hands. Watch them think.

Kids are practicing facts in this classroom. The teacher is providing instruction. Contrast with this.

[NOTE: As of 5/2/2013, the video referred to seems to have been removed from YouTube. My apologies. Go search YouTube for “EDI math” and you’ll find plenty of examples that are essentially equivalent to the one I refer to below.]

You can flip this latter instructional sequence because it involves telling and choral response.

You cannot flip the first instructional activity because it involves  adapting instruction in response to student ideas, and it involves students justifying their thinking to the teacher and to each other.

You can’t flip that.

[NOTE: I have edited some of the comments below in order to focus on the practices that were exemplified in the videos (one of which is now private), rather than on the teachers in them. See my post on norms a while back. My apologies to anyone who feels their words have been altered in ways that do not convey their original meaning.]


41 responses to “Skills practice [#NCTMDenver]

  1. Thank you.

  2. Another point worth bringing up – in the first video each child has to individually consider the answer because they don’t know who will get called on, whereas in the second class, you could easily get by on relying on your peers to supply the answers for you.

  3. Great post and major differences!
    I would love to see the prequel to the first video. Do they have a visual to accompany their thoughts? Are there ten frames in their minds that they are filling to make ten, twenty and then thirty so fluently? The ones who are using their fingers, do they have another strategy to increase their mental math? Would be interesting to hear some more of their thinking!

  4. Wow, thanks for the inspiration this morning! If you have any secondary gems like those to pass along I’m game; just give a moment to grab another tissue box 🙂

  5. Neil, this one is not quite secondary, but getting closer. It’s the second of the pair of videos. Also worth your time (even though this one doesn’t make me cry…maybe when I have a fifth-grader it will?)

  6. It’s a difficult discussion to navigate well-meaning teachers through (what is teaching for conceptual understanding while incorporating basic skills). Clips like this help.

    Last thought – if flipping classes involves (devolves) into short clips of mere skill/procedure and homework-become-classwork time, that’s not true flipping. Flipping’s intent (IMO) is to free up time for deeper conversations, conceptual understanding, and real life explorations.

    Great post – thanks!

  7. Thanks so much for this post. I will be sharing these videos, even though I work with secondary teachers. It’s so hard to move teachers away from “answer getting” instructional practices, where success is measured by being right, to REAL LEARNING where students are making sense, reasoning, explaining their thinking, attending to structure (math practices, anyone?!), etc. Answers matter, but thinking matters most.

  8. Thank you so much for posting this! Administrators love the EDI method because it appears to show (and “require”) student engagement. It is not messy and loud like my claasroom (messy as in sticky with multiple approaches and even some juicy, friendly debates, that always resolves in ohhh!)

    I wish I could seat my secondary students on the floor!

  9. Agree with the other posts–thank you for these great clips.

    • Have to add, that the sequence is good, AND, it is only as good as the teacher’s closure. And I mean TEACHER led closure…that would be the piece that gives me more insight into the “stick” of it all.

  10. Thanks for sharing, triangleman! This is just the video I need to show principals who want to know what good math looks like and also how to address the fluency issue.
    Again, thank you.

  11. Hopefully I’ll find time to share this post with my colleagues and get a discussion going on around the differences between these two teaching techniques.

  12. Oh! This task gave me ideas to practice finding factor pairs in 5th grade. Thanks!!

  13. Pingback: dy/dan » Blog Archive » You Can’t Flip That

  14. I agree that I like the first video better than the second. But I’m not sure it’s quite so clear cut. A few thoughts.

    First, these are different ages of kids doing very different topics (6th grade versus perhaps 1st or 2nd?). For example, a good portion of the second video was vocabulary. We may or may not agree whether that’s important, but I’m not sure that students standing up and physically modeling the angles is the most horrible way in the world to review that.

    Second, there were some things I didn’t like in the first video and some things that were okay in the second. For example, there were several kids in the first video that never raised their hand, never participated, and other kids that dominated. In another context, folks would be criticizing the teacher for that. (I would not because one small video clip taken out of context doesn’t give me the complete picture and, even if it did, getting every kid to participate in every activity is perhaps not realistic, or even necessary.)

    Similarly, in the second video (further along) it talks about students working in groups and explaining their thinking – that sounds good to me (even if the choral response stuff earlier doesn’t sound so good). And, just like in the first video, this clip – taken out of context and clearly meant to advocate something specific for the district – doesn’t necessarily give us the whole picture of her classroom.

    Finally, I’m curious about your attempt to connect this to flipping the classroom. I can see the connection, but it’s a bit of stretch, isn’t it? Neither one of these was directly related to anything “flip” – whether that’s the type of flipping that many of us think is poor instruction, or whether it’s the type of flipping that – perhaps – is allowing the type of thinking you are admiring in the first video to happen in class.

    To be clear, the strategies in the first video appeal to me much more than the strategies in the second, but I continue to worry when we judge from afar based on isolated excerpts from very different classrooms. One might even call that “flipped evaluating” . . .

    • I was watching the girl in the checked pants, she looked very sad and confused. I thought it would have been nice for her is the teacher had a few students model their thinking process more. A choral response when they were discussing the counting up from 11 to 20 would have worked well there.

  15. I thought the whole point of flipping was that you make up time to do the things in the first video?

  16. I have lots to say in reply to the thoughtful comments here. I appreciate the pushback Karl provides. I have a follow-up blog post that will be coming in the next few days. In the meantime, one quick thing…

    Christian‘s puzzlement is interesting to me. The common rhetoric of flipping the classrooms presupposes that there is something else that kids need to engage in before they can do the thing in the video. That something-else is (again, in common rhetoric) typically described as some form of telling.

    The metaphor on which the term flip is built relies on there being two phases to instruction: (1) tell in the classroom, and (2) practice at home. The flip flips these so that we (1) tell at home via video and (2) practice and apply at school.

    Video number 1 (which is like all instances of teaching and is imperfect) shows a classroom where children are engaged in constructing methods and ideas while they practice and apply. It is all of a piece in that sequence, and it is beautiful.

    Maybe I have it wrong. Maybe the flip I describe above is not what most people mean by flipping the classroom. Maybe what most people mean by flipping the classroom is that teachers should carefully consider what aspects of their teaching routines need to take place face-to-face and what aspects could be (or should be) done outside of class. But if that’s what we mean, I have two questions: (1) how does the word flip apply? and (2) why do we need a special term for that?

    • This is precisely why I’ve distanced myself a bit from the term flipped instruction. If students are to build meaning in math that starts at the beginning. Concepts shouldn’t be introduced as isolated skills or they won’t know how to put them together in new situations. I still have videos for students but they are relied more to review things discovered by students in previous classes while at home.

  17. Looking forward to the follow-up post. I think you’ve nailed one of the big problems in this discussion, how we define “flip.” There are certainly many teachers who are applying “flipping” in the way you describe, lectures at home and homework at school. But that is not the only way it’s being applied.

    My concern is that instead of looking at what some folks (Ramsay Musallam, Jon Bergmann, Aaron Sams, et al) who are working really hard to figure out what needs to take place face-to-face and what can be done outside of class, people are going after the easy pickings of Khan Academy. I think it’s very analogous to those folks who attack “inquiry” by saying, “So, you want kids to *discover* Calculus? Right.” That’s a simplistic view of inquiry, just as many (not all) of the attacks against flipping are based on a simplistic view of what it is (or could be).

    That’s not to say that there aren’t some very valid criticisms that we need to consider. I would point particularly to Frank Noschese’s and Sylvia Martinez’ work, which I think tends to go a bit more in-depth. But I think we do a disservice to the discussion – and to our students – when we criticize from afar without diving in deeper. I’ve said this elsewhere, but how many flipped classrooms have you actually visited? And, specifically, have you visited any of the folks who are really thinking deeply about this? If not, then I think we should be careful about criticizing what we *think* it is (and, to be fair, what it actually is in some places).

    For example, many folks use the “flip” part – videos (or whatever) at home – *after* the inquiry, to reinforce the procedural stuff. Or to go after common misconceptions. Or in a variety of other ways, all designed to try to maximize the face-to-face time with kids. But most of the critiques I see just assume that they are “watching lectures at home, doing homework in class.” I think there is still some valid criticism/discussion of these other ways of flipping as well, but that’s what I’d like to see folks engage in.

    As far as do need a special term? Of course not, but that’s not the fault of the teachers who are doing what they think is helping meet the needs of their students in the circumstances they operate under.

  18. How did the students in the first video learn their match-making process? We don’t see that in the video, but it seems clear that they already know what they’re doing. How were they taught this skill the first time around? That question seems rather important in a discussion about which method of instruction is better. Video #1 is an excellent example of in-class practice that leads to individual thinking on the part of students, rather than robotic repetition without understanding, as shown in #2. But to say that flipping a classroom excludes or lessens the value of #1’s activity might be going too far, without seeing how they learned to add/subtract in the first place.

    Couldn’t a flipped teacher create a video scenario where some kids are in a store and want to buy things with their $20. Various strategies for matching items up to $20 could be shown… one kid uses fingers, one kid visualizes a break-down of $10 + $2 + $8 = two 10’s, which equals $20. The video ends with someone entering the store with $30 and looking at the shelves… cliff-hanger to be picked up in class. The instruction is done outside of the classroom in a pedagogically-sound, non-Kahn way. They don’t even have to be told, “First, do this… … …” They can just see what the kids in the video are doing. Now they have time to practice in class, like in the video, using the demonstrated strategy that they prefer. And nothing is preventing them from thinking independently and creating their own strategy, because their brains aren’t molded by 7 hours of choral response every day.

  19. In the first video, we’re not told whether this is early or late 2nd grade, which makes a huge difference, but ignoring that for the time being, we’re not impressed with this activity which they call “matching”, in particular the level of mathematics (but we know it derives from the first part of 2.OA.2.)

    We listed the examples the students chose and in 10/10, 20/0 (2x), 5/15 (2x), 11/9 the answers came quickly (except that some kids never seemed to raise their hands), 3/17 was fast, too, but with 12, there was a long delay, and one kid got confused by 9/11. We think the teacher should choose the first number by reading them from a card, so there aren’t mostly simple choices and repeats.

    It also didn’t seem like anyone is making a 20 by using subtraction or by carrying addition, instead of the silly “strategies” in 1.OA.6. It sounds like they’ve practiced this before and some have memorized answers.

    If students have learned the underlying mathematical basis for “making 20”, that is, there’s already a complete ten (a 1 in the tens place of one number), and you’re looking to “make a ten” with the two digits in the ones columns, then that ability ought to easily transfer to making 30.

    But the nature of the activity really shows its inherent weaknesses when it goes to 30. It’s like a completely different task for many students. One girl says to show 21 and 9 make a 30, you have to count from 21 up to 30, which is a kindergarten skill.

    Some kids catch on quickly, such as the one boy who shows he is using a 2nd grade skill, making a 10, which is used in carrying and borrowing. The third girl checks the answer by counting on her fingers, and in the last 5 seconds, shows she actually learned something, but can she (and others) use it universally when making a 30, 40 or 100, instead of just checking a previously found solution?

    Some of the kids were not engaged at all. In what appears to be review, those students need to be pulled in.

    • I think that was part of my point about missing the video portion that would have been “closure.” As for the kids that were un-engaged…(I would have been one of them) does having a “thing” to construct meaning here have a place? Or is the “do it in your head” an important piece? If I could see a number line, maybe the visual learners would have something to offer.

    • Hmmm … a few minutes of one classroom doesn’t show a teacher’s entire approach. This seemed like a very nice way to review in a relaxing way, which allowed all students to participate. In fact, if she read off the numbers, that would have eliminated a good portion of the class participation. It would have changed the class activity by making it teacher led, instead of student led. There is excitement in getting to participate in MAKING the problem, as opposed to always just answering the one given to you. Does this mean the teacher teaches this way at all times? Did she introduce “matching” this way? Does she plan to ever work through a way to go to 30? The inference that she never uses any other methods has to be incorrect. In fact, she reminds them of things they’ve learned so they can use it now.

      When she steers them away from counting up (but validates it as a strategy … a strategy I’ve been known to use as an adult sometimes!) and towards other ways of thinking, she is clearly showing mastery as a teacher. She validates the strategy, asks for another, reminds them of a recent strategy. She has very gently introduced going to 30 without even giving a lesson. She has very gently tested the ability of her class to transfer the knowledge to a new task. She has ended with a success. Even though she could clearly see that the majority of the class could not transfer their knowledge, she ended with them all seeing how they could get to 30 this way. Now she knows where she needs to go from there.

      I could see this being a nice after lunch or recess activity for bringing the kids back into the day. I liked her way of correcting and validating without bringing the classroom environment down.

  20. More pushback. This is awesome. I wish it weren’t anonymous, though.

    I concur with some of what CCSSIMath has to say, and I’ll push back on other aspects in a later post.

    The main thing I want to question in his/her thoughtful response is that, then that ability ought to easily transfer to making 30. This reminds me so much of when Wu writes, It should be plain to the children that this is an efficient compression of a valuable piece of mathematical reasoning into a compact shorthand. Yes, it should be plain, and yes, it should transfer, but human learning is messier than this. Human learning does not submit to what should happen, it takes time and talk and thinking. All of those are things the teacher in the first video is working very hard (but imperfecty) to encourage.

  21. Christopher, thanks for this post. Great food for thought. I like some aspects of what I saw in both videos. [I’ll play] “teacher’s advocate.” 🙂

    1. Letting kids know what is expected of them = good.
    2. Teaching vocabulary = important.
    3. Choral repetition = potentially powerful learning strategy, when used appropriately.
    4. Kinesthetic involvement = awesome. (Kids making straight angles/right angles with their arms).
    5. Finish my sentences = another potentially useful strategy. Allows a teacher to check for understanding, especially if coupled with copious amounts of wait time and an appropriate signal (ready, set, go…or 1,2,3…etc).

    If you came to observe one of my classes (I’m a HS math teacher), you’d find that I’m HUGE on teaching for conceptual understanding, promoting math reasoning and math discourse, and all that sort of thing. In fact, I’m definitely on the extreme end of the spectrum in that regard, maybe even by 19 standard deviations. But you will also find me using strategies #1-5 above…pretty much as often as possible. 🙂 Okay, it wouldn’t occur to me to use choral repetition for *everything* as Ms. Jones seems to do, but I think we need *more* choral repetition at my school, not less.

    I’ll end my remarks with this point: effective teachers have a broad repertoire of instructional skills and strategies. I think there is something to be gained from emulating the teaching in both videos. But [relying on] explicit instruction — in the ways shown in the video — to the *exclusion* of all other teaching and learning strategies — then I’ll agree [students would be missing out].

    • I like the activity in the first video, but agree that there’s absolutely, positively room for explicit instruction, too. Most of the programs I’ve seen also have a time when an individual is held accountable, so the “you can rely on your neighbors” doesn’t work then; you could do that whole first activity every day and pray you weren’t called on and never have a clue, too. I was hoping that the teacher knew her kiddos and who to call on for the first number… but wondering when the kiddos who clearly didn’t get it yet were going to get taught, and how, and wondering how much of the pre-drill instruction was rote and how much was conceptual. I’d have wanted *something* visual for support when a student struggled (a number line, perhaps?)
      When it comes to the practice stuff, I figured out a long time ago that what was boring to me wasn’t always boring to the students…

  22. To CCSSIMath, who are you? Why aren’t you “impressed with this activity” and its level of mathematics? (This was early 2nd grade, by the way.) You suggest the teacher should be reading from cards, but this takes focus away from students along with an opportunity to be clever — some students were deliberately picking more challenging examples to test their peers. It also gives any student a chance to join in, since any student can start a pair; they’ll be more likely to follow through. There are clear pedagogical reasons for the activity being built with students in control. For more information, see the two full videos (from 2nd and 5th grades) at

    Please also describe why the strategies in 1.OA.6 are so “silly”. To me they seem pretty useful for building relationships between number facts and for solving problems that might initially be out of reach, and they’ll help students in this same course do pairs to 11, 19, or 21 later in the same 2nd grade course.

    Why did you name yourself “CCSSI Mathematics” if you’re so flip to discard a standard as silly? Also: bash the activity all you want anonymously, but don’t bash the teacher anonymously. That’s just garbage. I apologize for my poor tone but I have no patience for that.

  23. I’ll admit, I was there [with explicit instruction] early on in my teaching career too. This is a glimpse of her classroom and maybe she’s made pedagogical changes or plans to.
    My favorite part from the first video (6:45), “So that’s one strategy. Is there another strategy we’ve been using for other things that we could also try?” Thanks for the comparison.

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  25. Absolutely love the first video and will try it with my year 3/4 students tomorrow and share with my staff. Thanks so much. I think I could make ‘matches’ a homework task too, as I have many supportive families.

  26. THANK YOU KeyJames!

    “1. Letting kids know what is expected of them = good.
    2. Teaching vocabulary = important.
    3. Choral repetition = potentially powerful learning strategy, when used appropriately.
    4. Kinesthetic involvement = awesome. (Kids making straight angles/right angles with their arms).
    5. Finish my sentences = another potentially useful strategy. Allows a teacher to check for understanding, especially if coupled with copious amounts of wait time and an appropriate signal (ready, set, go…or 1,2,3…etc).”

  27. Pingback: Day 130: Another change to our #countingcircle | window into a math classroom

  28. Pingback: Day 131: Student #countingcircle (Match-Match) | window into a math classroom

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  30. I love this teacher’s absolute, unwavering focus on the students. A huge part of these children’s mathematics is clearly relational, which is as it should be. This is a very subtle and sophisticated form of guided collaboration. Each child was movingly respectful toward the others AND toward his/her own learning. Just a beautiful piece of great teaching. Thanks for sharing it.

    – Elizabeth (@cheesemonkeysf)

  31. I try the matching game with my 6th graders. We were practicing adding and subtracting integers and it went great. It’s such a simple activity but its so much more effective for both, students and my own. Thanks for sharing it!!

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