Comments on: Rough-Draft Thinking & Bucky the Badger

By: Sven Gasser

Sven Gasser — Mon, 11 Jun 2018 14:44:08 +0000

I thought this was a great activity! I put it into Desmos if anyone wants to use it. I left off the answer video thinking I would play that for the whole class. Going to try it today!

https://teacher.desmos.com/activitybuilder/custom/5b1961e9127e270a80ec78a1

By: Dan Meyer

Dan Meyer — Tue, 29 May 2018 04:55:25 +0000

In reply to Chester Draws. If Chester is dependable for anything, it's to stop by and try to referee what should and shouldn't be considered mathematics. I don't care to argue the point with him because by the measures that matter to me (eg. do I think it's mathematics, do people whose opinion I care about think it's mathematics, do the governing bodies that decide what is mathematics where I live think it's mathematics) what we did was mathematics. For Chester it isn't, and he shouldn't spend class time on the problem. (To say nothing of the fact that American football probably won't have much purchase in New Zealand.) What I do think is interesting is that our personal and generally unspoken definitions of mathematics are very predictive of the experiences we allow students to have in our math classes. That's wild to me.

By: Rachel A.

Rachel A. — Tue, 29 May 2018 02:43:22 +0000

In reply to Chester Draws. Sorry, but I kindly disagree. Perhaps it's not applicable to the Math that you teach, but I teach Statistics and my first thought is that this would be a perfect activity for my Seniors just before introducing Hypothesis Testing.

By: Donna

Donna — Mon, 28 May 2018 03:07:20 +0000

I am impressed that students stayed on task with one problem for 90 minutes. It seems as though you could’ve spent more time on this one problem. I teach high school students and it is a struggle keep them focused on the same task for any amount of time. They tend to give up, lose focus and hence are off task. Interpretative questioning must be an excellent strategy to help students persevere.

By: Chester Draws

Chester Draws — Sat, 26 May 2018 07:05:56 +0000

In reply to Chester Draws.

Well, you can sort-of force standard mathematical contexts into Badger, but they are not good fits. You can’t really use Summation Notation for such a sequence. Any student doing Sequences and Series would be past finding Badger engaging for very long anyway.

Why not do an exercise which *naturally* fits into the curriculum we are meant to be teaching?

In a ninety minute time frame I could have *finished* teaching simple arithmetic series. Then they would have a technique that they could use problem solve.

By: Sarah Kingston

Sarah Kingston — Fri, 25 May 2018 22:39:22 +0000

I am a Math Coach at Beach Elementary and had the good fortune of sharing in this session with Dan at the helm. Although I have a fair bit of experience with and comfort in facilitating 3 Act Tasks K-5, watching Dan in action, and reading his blog and exchange with Amanda have pushed my thinking. My recent focus has shifted to harnessing the learning potential using intentional teacher moves. As Dan referenced, he knew going into the task that the relationships between points and push ups leant themselves to testing hypotheses. In the words of a student, “toying and tinkering with, and testing the math” became the work of the day. Dan deliberately, but artfully guided the process in this direction by using a series of teacher moves.

These moves aren’t always elaborated upon in these online resources, but I noticed they impact the rigor of the experience significantly. Although Dan and Amanda have highlighted a few, here is a list that another teacher and I came up with in preparation for teaching the Bucky the Badger task ourselves.

Featured Comment

–Anticipating: anticipate the student interpretations of the point/push-up relationship and be prepared to engage in the students’ thinking

–Soliciting Estimates: solicit estimates (too high, too low, just right) These become a quick formative assessment and create some productive tension and curiosity within the learning community.

–Questioning: ask an interpretive question about the relationships in the problem’s context to move students’ understanding forward.

–Withholding Act 2 Information: encourage students to make sense of the scenario so they request necessary information. Dan said, “If you have everything you need, get to work, otherwise, call me over and let me know what you need.”

–Conferring: check in with students who may be struggling unproductively. Ask them some relational questions or have them do a quick gallery walk to jump-start their thinking without over-scaffolding.

–Sharing: students share and justify why the needed information will support their investigation before the teacher reveals it.

–Identifying Critical Questions: identify critical questions in advance and bring them to the forefront when students begin to ask them.
Does the kind of score matter?
Does the order matter?

–Highlighting Efficient Student Strategies: wonder aloud if there is a more efficient way….mathematicians can be lazy! Also, efficiency oftentimes leaves less room for error.

–Reflecting: provide time for closure by asking students to privately write a response to, “What did you learn today as a mathematician?”. Then share out as teacher types them for the class to see. Was your learning objective apparent to your students?

As teachers, we are constantly trying to reflect and refine these practices and there is nothing quite like a window into these teacher moves in action. Thank you, Dan!

By: William Carey

William Carey — Fri, 25 May 2018 18:43:41 +0000

In reply to Chester Draws.

Some lovely future problem that this points to:

1. Are there series whose sum is preserved under reordering? What sorts?

2. Inevitability. If I tell you the total number of push-ups, can you develop the score of the game? Can you construct inequalities that relate the total number of push-ups to a particular score sequence? What do those look like?

3. This is a lovely segue to introduce the difference between summation notation and multiplication. Under what circumstances can we abbreviate our addition?

4. Factoring and primes. Can you come up with a (nontrivial) score where I wouldn’t have to tell you the number or order of scores to know the number of push-ups?

This is a fertile activity. At least #4 would be accessible to fifth graders.

By: Chester Draws

Chester Draws — Fri, 25 May 2018 13:53:42 +0000

Sure Dan. But that’s not Maths.

It would fall closer to Science. Hypothesis, test, conclusion.

Maths is using appropriate Mathematical techniques to solve a mathematical problem. I see neither here. I would expect a Maths problem to require a hypothesis of which technique might work, which this does not. I would expect a Maths problem to yield a link to future Maths problems, which this does not.

That it is interesting, engaging and problem solving doesn’t make it Mathematical.

Iny view it is extended guess and check, which is literally the lowest form of mathematical reasoning.

By: Dan Meyer

Dan Meyer — Thu, 24 May 2018 18:34:15 +0000

In reply to Chester Draws. I quote myself:

The point of the Bucky Badger activity is not calculating the number of push-ups Bucky performed, rather it’s devising experiments to test our hypotheses for both of those two questions above, drafting and re-drafting our understanding of the relationship between points and push-ups.

By: Chester Draws

Chester Draws — Thu, 24 May 2018 18:22:47 +0000

It’s an interesting task. Well taught it would be an engaging task. What I am not convinced is that it is Maths.

Maths includes problem solving, but not all problem solving is mathematical.

The only important part of this task is to discover the variation in how the scores accumulate. That’s about football. The arithmetic part is trivial and hugely repetitive.

At the end of the task, what mathematical concepts have they deepened? My bet is most learned more about football.

Some would argue that “problem solving” is itself a useful task. I have two counters.

Firstly, it’s probably not true. Research shows that generic problem solving skills are not transferable. Problem solving is hugely context dependent.

Secondly, there are problems which involve a useful mathematical concept, which practice both problem solving and some technique or concept. We should be using those ones.

So while you may have learned a lot about how students think, I believe the students would have been better off doing a genuine mathematical task. One that links to other mathematical skills and concepts, rather than being a stand alone task.