Thursday, January 31, 2013

Intellectually Needy

"So does this bore the heck out of you?" a student asked me.

The problem is that this was after two days of doing the Barbie Bungee Jump activity. The fabulous Barbie Bungee Jump. (Cf. Julie and Fawn) I was assisting a very nice and competent substitute teacher.

Coming on the heels of Christopher Danielson's and Chris Lusto's #globalmath session on building intellectual need, it was clear that most of these students did not have it. Nor were they looking for it.

This is a good school with good students and good teachers. What's going on, or not going on? My first brief observations:
  1. Students were given all the steps to follow. Being told to do a, b and c and then doing a, b and c is not engaging.
  2. There was no hook. How much of a hook depends on the lesson. This one could have used the video, a discussion about bungee jumping, etc. Going straight into 'here's what you do' gives no chance for wondering. Even if it's what the students want or are asking for.
  3. There was no expectation that this was worth their time or could be interesting. There is always time to start, but this might also be about developing a culture of inquiry. Students need to learn that this is what math is, and this is what math class is like or could be like.
Day 1: Students were given a worksheet with a table, told how to assemble the rubber bands and washers and to collect data for 1 to 6 rubber bands. Then graph all of their data and freehand a line of best fit. This is the beginning of a functions unit that will end with linear functions. Then they were asked to make a prediction for how many rubber bands they would need for the drop. We didn't have the actual heights, so they predicted for 3 m. Mostly, their prediction method was pick a number that was bigger than 6. 20 seemed nice to them, though some went with 18, since 6 rubber bands was close to a meter. Two groups found the average increase per rubber band.

We weren't clear about how to do the drop in the stairwell. We didn't have a set (or maybe even one) tape measure for long distances. Two teachers wound up determining 3 drop spots and measuring the distances, between 3 and 3.5 m.

Day 2: (After a snow day and a PD day.)
The students coming back were not much more enthralled than they were Day 1. I shared how this was the start of a functions unit, the math idea of having a rule to go from input to output. I tried to phrase the question as given the input of how many rubber bands, could they predict how far it would drop. (Not much traction, as there were already instructions on the screen.) The substitute gave each group their drop height. The two groups that had figured out the averages used this to make quite specific predictions, and one group made the complete table that this would generate. At the last second they cut 2 rubberbands off of their total, to allow for the length of the disk and acceleration. They were worried that it would be traveling faster at the bottom and that would make it stretch more. Two other groups adjusted their number a bit, but without reasoning that they could share.

We proceeded to the stairwell and groups took turns making their single drop. 2 hit the floor, including one of the more mathemaical groups, 2 got about 70 cm away, 1 was more than 1 m, and the group that had made the table got to within 10 cm. Went back to the classroom, shared the results and had the winning group describe their efforts while few listened. I talked with the mathy group that hit the floor about what went wrong. Basically they felt math failed them. Double checking their work I saw the problem was that they were computing for the wrong drop height! Their calculation would have put them quite close.

So What?
The students were pretty happy. Better than a typical math class, playing with rubber bands, leaving the classroom. The sub was okay with it, as students were mostly in control and made it through all of the steps. I felt like we missed an opportunity.

So what would you change about the lesson? What would add/create/inspire intellectual need in what is a (potentially) great activity?

Post Script:
Excellent discussion! I just want a few of the shared links to be more visible here. But many people put great thinking below so don't skimp on the comment reading.


  1. Thanks so much, John, or talking more about this critical mindset of "intellectual need." I see a correlation between kids' proficiency levels and their levels of intellectual needs. This is almost unfortunate because kids become disinterested in math because they can't get the "math" right. That's why I'm sold on 3-Act lessons because they start with a perplexing task and allows for safe entries. The "math" can come later.

    Barbie Bungee. To take away all instructions, provided tables, etc, I'd do this next time: Barbie is going to jump from height "h" without dying but has the most thrilling jump. Your group gets 6 rubber bands to start with, figure out how many rubber bands for her actual jump. Go! (From this point on, I'd just throw out a lot of questions, questions that come FROM them to the whole class or to the small groups.)

    To START with all those numbers and calculations, we run the risk of drowning out the perplexing, the need to know.

  2. I know how you feel John. When I did the lesson it felt a little to "recipe" to me than I wanted. I always have a difficult time finding that balance of the "be less helpful" mantra when coming to these problems.

    As far as the initial hook goes, my step towards the horror genre, did serve fairly well as a talking point When it came to the lesson I did give a lot of directions, and I am not sure I am happy with how it went. Kids were excited to do the lab, and were quick to get to it, but then using that information wasn't exactly natural. Is that where my direct instruction comes in? Who knows.

    I wish I had more wisdom on this, but I am at the point where I am asking the same questions.

  3. Where is the connection to real life? Unless students are personally invested in the activity, it is just one more thing they are told to do.

  4. It was crazy to read your post today, when my class just started the process of doing an unstructured bungee. Given only a barbie, metre stick and rubber bands I challenged my students to create a plan that would show them how many rubber bands they would need for a final drop of an unknown height.

    I have posted about Day 1 on my blog ( and will be sharing the final proposals and results next week after Wednesday's Drop Day.

    After only one day of unstructured exploration I have overheard them ask insightful questions about what is important and how they should measure things that a structured worksheet would not have allowed them to do. Also we are using it as an introduction to linear relations. My goal is that we will share the methods of each group and then pull from those the concepts of rate of change, table of values, graphing, lines of best fit and equations of lines.

    I hope that you will follow and see the results next week and give any feedback to me.

    I also have to thanks Fawn for her blog post about the activity. It got me started thinking of what activity would be great to introduce the linear relations unit to the class.

  5. I always start this lesson by standing on a table, Barbie and bands in hand and begin silently letting Barbie "jump." I add some bands so that Barbie gets closer to the ground... usually at least one student shouts "make her hit the ground" or something like that. Usually this hooks them into the lesson.

  6. Nice Serafina! I would try that! I initially thought about some prompts, like: you are constructing a Six Flag attraction or Barbie is an extreme sports contestant... but I like your intro way better!

  7. My "real-life hook" was a paper by D.R.H. Jones, "Analysis of a fatal bungee-jumping accident" (doi:10.1016/j.engfailanal.2004.03.002), repeating some of the measurements done in that article. I also made the experiment more massive (using a 5 kg weight), and I had the students use video-analysis.

  8. Fantastic post which I can relate to, as someone who has written many well-intentioned activities which I often realize afterwards are too recipe-book to be truly effective. The teachers I work with are receptive to inquiry-driven learning, but there is a mis-conception as to what it means to encourage inquiry. For an acitivity like Bungee Barbie, the intent is that students will walk through the steps, magically make a link to algebra, and then we can get into the "real" lesson. How do we let an activity like this breathe a bit? Can't we strip away the instuctions, provide the task, and hold some check-ins where students need to communicate their ideas and progress? Fill in the gaps with the necessary math as the students express a need for it. Instead of rushing to get it all done in a prescribed number of days and steps, provide a month where this task simmers in the background.

  9. Excellent reflections here John. It's interesting what you say about students being given the steps to follow; I've just finished writing an MA assignment on Three ACT learning and I mentioned this as a possile issue. Teachers need to be more aware of this when choosing and discussing tasks with students. It certainly requires a delicate balance of more guidance in some instances and standing back in others.

    Might be interesting to ask the students what they thought about the task during the reflection phase - could get some interesting insights.

  10. What I am taking from your question is, "What do you do when students' intellectual need is not sufficient enough to complete a robust problem?” This is an issue I frequently face as a math coach who goes into unfamiliar classrooms to demonstrate the benefits of problem-based lessons. I have come to focus on four C’s (communication, curiosity, critical thinking, and content knowledge) that teachers can work on both personally and with their students. I discussed it in more detail in my blog, but the summary is:

    If students aren’t comfortable communicating their mathematical understandings, these lessons go nowhere. Most of the initial work needs to be done by the teacher to change this. Teachers need to begin by creating a safe environment and then find the right prompts and questions to get kids talking. There is some good PD out there to help teachers improve their questioning, if you are interested.

    This one kills me the most. My four year old won’t stop asking me questions about everything but by the time students reach middle school, their curiosity is nearly dead. To me this is the single biggest problem with lower skilled classes. High classes seem to do fine with this, but the low classes are often totally comfortable with not knowing and not caring. My best advice to conquer this issue is to show students the best pictures from I’ve shown them, one a day, as a warm up. I just have kids tell me a question they have about the picture. We don’t do any work on it. When kids just can’t move on without knowing the answer, you know you are on the right track.

    Critical Thinking
    This is the toughest one as students I’ve worked with seem to have lost the ability to think for themselves. Dan Meyer’s TED talk explains it best so I will leave it there. In terms of improving that, I find using some sort of Problem Solving Framework to be very helpful. Geoff at emergent math has one and I know Andrew Stadel came up with a different version recently. They are very helpful with getting students to think about what the problem is asking, figure out what they know, what they need to know, and how they are going to attack the problem.

    Content Knowledge
    This is the one that is both on the teacher and student. Students’ content knowledge may be low, so this can be scaffolded with good communication skills and curious/perplexing problems. Teacher content knowledge also needs to be high so they he or she can help students connect their different understandings.

    Thanks for sharing all of this!

  11. Having actually Bungee jumped, the hook I use is the video of me screaming like a 12 year old girl when I did(no offense to 12 year old girls)
    But then I bring up the fact that when I did the jump they weighed me and when I got to the point where they attached the bungee cord they asked how close I wanted to get to the water (I wanted to be dunked). They used both these pieces of info to choose the appropriate bungee chord (you can see all the extra cords there in the video. So clearly someone had collected some data (or at least did some calculations) before hand. So not real life in terms of everyday life but real life in terms of "used in real life".