Barbie Bungee

7th, Algebra 1, Lessons, Linear Equations, Video , , 0 Comments

Please don't read this and think I deserve credit for Barbie Bungee. This is a well-loved, widely used activity, and for good reason. Don't believe me? Use the #MTBoS search engine, key in Barbie Bungee, and watch the hits pile up. Fawn's done it. Dan's written about it. And, so have countless others.

As luck would have it, I caught Dan Meyer's "Full Stack Lessons" talk at CMC North just shortly before I was planning to use Barbie Bungee with my 7th graders.[3]His talk spoke at length about this task as an example of how the same task can be engaging and valuable in one classroom but be drab and worthless in another. The presentation was great and pushed me to think about the types of actions and thinking my students do when they complete tasks in my classroom.

I've thought about this before, and I worry. I worry a lot about two things I deny my kids. I deny them with my too-carefully scaffolded and overly-planned lessons. I deny them opportunities to ask their own questions and to develop the method for which they will solve questions. I've fought this before (see: Fermi Estimation Problems) but a new school, a new text, new families, new students, a new coast, and more and more new stuff has made me feel like I've lost a bit of my mojo for building this into my classroom and my practice.

Dan's presentation was a wonderful reminder of the opportunity I had. The opportunity to "be less helpful" and to, therefore, help my students. So, I spent the drive home from CMC North percolating over how I would structure Barbie Bungee to de-scaffold it for my students' benefits. Here's the structure I landed on. I hope it is helpful to you as you consider implementing this or similar tasks:

  • I arranged the students into groups of 4. Partners are my preference, but I worried about handling twice as many groups
  • I purchased a unique doll for each group. This eliminated cross-copying of values and ideas since they had different heights and weights
  • I broke the task into 3 distinct "drops". Where kids did the following for each one:
    • Agreed on a number of rubber bands needed for their drop (2 x 45-minute classes)
    • Dropped their doll and recorded the results in slow-mo (30 minutes or 2/3 of a class)
    • Completed a reflection about what they did, why, if it worked, and what they wanted to do next time (15 minutes and homework)
  • I provided MORE scaffolding at each drop[4]Yes, I know this sounds wrong
    • On the first drop, I said "figure out how many rubber bands you need."
    • On the second drop, we brainstormed mathematical tools that might be helpful. Then I said, "figure out how many rubber bands you need."
    • On the third drop, I had them complete a T-table, plot the points in Desmos, graph their own line of best fit, and then have Desmos calculate a linear regression, so they could, "figure out how many rubber bands" they needed"

This is not the normal progression I follow in my classroom. But, I think it is right for this task. There were so many good conversations; I can't possible recreate them all here. But, I do have one example that I think is illustrative of what I was going for.

We had a serious lack of meter sticks in the classroom, so students got inventive and began taping rulers together. I noticed that they were taping the rulers end-to-end which, frankly, makes lots of sense. Except....

Rulers leave a length on either end (presumably for manufacturing purposes) that isn't part of the 12" distance. But, my students ignored this gap. Did I point this out to them? Yes, but only after they were done with all of their measurements.

Why wait so long? Well, I wanted it to be too late to redo the measurements. So, instead of starting from scratch because of what their teacher told them, they had to adjust their model to deal with an error they discovered in their methodology. They had to figure out if their error made their measurements too long or too short. So much good thinking and conversation came out of this. Maybe more than any other part of the activity.

Too often, I get lulled into thinking that learning is this really linear and well-defined trajectory. My kids really learn the most when I remember that class can (and sometimes should) be messy. Their own ideas lead to natural teachable moments and errors where they are curious and engaged and passionate.

At a talk, I once quoted Lord Petyr Baelish who said, "Chaos isn’t a pit. Chaos is a ladder." Like all Westerosi men of lessor houses, I certainly need reminders of this wisdom. Perhaps this could even become my house words. I need to remember to welcome chaos into my classroom when it is to the benefit of my students.

Propaganda Time: Androids (yes, I guess iPhones too) can shoot HD slo-mo video. So, of course, I had to put a video together for my school:

"Next Time"s

Next time, I want to more explicitly connect the work in Barbie Bungee to other investigations. Specifically, the stacking cups investigation we had done previously. I mentioned this in a reflection question, but I want to spend more time on this. Perhaps even make it the a key part of my assessment.

Next time, I think I want to mix up the groups between each "drop." The thing I am most proud of in my classroom is that students regularly explain ideas to one another (SMP3). Mixing up groups will allow kids to say, "Oh, my group tried this and it ___________."

Next time, I need to build in a lesson on linear regression prior to this activity. The kids thought it was cool, but didn't really "get it"

Gift Ideas for Math People

Games 0 Comments

Need gift ideas for your list or for others? You've come to the right place.

This list is heavy on games and puzzles which you might describe as "mathy". But, since there is no such thing as a math person, these are great gifts for all!

What If?

If you don't know Randall Munroe's blog by the same name, you're welcome! In this book he shares answers to his favorite questions from readers.

Wilson Wolfe Affair

Currently on Kickstarter (you won't get it until the summer), this is a detective style puzzle set in a old-timey cartoon meets film noir universe. My excitement for this has no bounds.

Hanabi

An absolute gem of a game. Players work together to play cards from their hand by color and in numerical order. The catch: only the other players can see your cards! This game is challenging and puzzle-y and fun.

Exit: Abandoned Cabin

If you like escape rooms or similar experiences, check out the Exit series. The Abandoned Cabin is the first one to try. Its got some pretty clever puzzles to solve. Lasts about 1 hour, so it's easy to find time for it.

Patchwork

A 2 player board game in which you are making a quilt out of polyominoes. You and your opponent draft pieces from a common pool and there is lots of strategy to be had in how you restrict your opponents options.

The Witness (Steam)

Don't let the fact that this is a video game turn you off; this game is incredible. The designer put together an incredibly diverse set of puzzles from a simple grid maze. You, your family, and friends will be working on this for days.

Portal and Portal 2

My all time favorite video games. The premise is so simple. You have a portal maker. It makes a blue portal and a red portal. When you go through the red portal, you come out the blue portal and vice versa. You use that tool to navigate 3D maps. The puzzles are awesome and the often hilarious. J.K. Simmons even voice acts in the second.

Martin Gardener Giant Book

Are these board and video games too fancy schmancy for you? Pick up this thick book of puzzles from the godfather of recreation mathematics. Then track down my favorite question about sectioning any obtuse triangle into all acute triangles.

Manifold

I got a demo of this at CMC North. It's awesome. You get a small square and have to fold it to match a pattern. They are tough, but not overwhelmingly so!

NMBR 9

A brand-spanking-new game about arranging polyominoes into levels. The more pieces on higher levels, the more points. Takes about 15 minutes, but you will play lots of times!

Interview Questions for Math Teachers

For Leaders 1 Comment

Interviews are a bit odd and may not work all that well. But, every teacher is going to find themselves in the position of an interviewer or interviewee at some point in their career. Regardless of your role, it is worth taking the time to think about what information you want to learn or communicate during this process.

Before we get to the questions, it is important to think about restrictions. My experience has been that interviews are short, really short. Often, they are scheduled for just 30 minutes, but by the time everyone arrives, finishes the small talk, and actually get to interviewing, there are only 15 to 20 minutes. So, let's limit ourselves to 5 questions. And, let's order the questions with the most crucial ones first. That way if time runs low, you have collected the most important information.[6]It is also important to note that, as the interviewer, there are certain questions you are not allowed to ask. Some of them are straight forward: don't ask how much money a candidate has. Others are less intuitive. Even if it is just polite small talk, you cannot ask a candidate if they have children. The assumption is that any question you ask will be used to determine whether an applicant is hired, so you cannot ask about protected traits, beliefs, et cetera.

Let's get to the questions:

If I visited your classroom for a few minutes every day of the school year, what would I notice? 

Most teaching interviews involve a sample lesson, but this only gives a small window into a teacher's classroom. I want to know the routines and practices that teachers use and build on throughout the year. Do you use number talks once a week? Do you build students' understanding of proof through structured discussions and writing? This questions gets at what a teacher believes is most important for teaching mathematics, but, by asking what you will notice in the classroom, you force the applicant to describe actions and practices not just beliefs.

What is the ideal curriculum for your classroom? How would you use it? And, when you need activities outside of its scope, what resources would you draw from?

Curricula are very powerful in transforming teachers' actions and lessons. I want to know what type of curriculum an applicant prefers because that suggest a great deal about their beliefs. Most, if not all, teachers draw from resources outside of their curriculum. So, I also want to hear that a teacher knows where to find strong tasks.

How do we help students develop a positive mindset about mathematics, particularly problem solving?

Regardless of the course or grade level, I want every math teacher working to strengthen our students' mindsets about mathematics. This does not happen by magic. It takes thought and reflection. I want to hear a candidate connect mindset to different aspects of their teaching, especially feedback.

How do you assess students? What types of feedback do you provide?

Feedback and assessment are incredibly powerful aspects of teachers' practices that impact student learning and confidence. I want any potential candidate to have a well-articulated approach to assessing and providing feedback to students. I also want to hear examples of formative assessment and how those assessments are used to guide future lessons and work.

[Insert Large Scale Content Specific Question Here]?

The details of this question depend on the position the teacher is applying for, but it should give the teacher the opportunity to demonstrate their pedagogical content knowledge (see below) for a big conceptual idea that students in their courses will be wrestling with. I want to see that this candidate knows more than just how to "do the math" covered in a course. I want to hear that they know how to help students make sense of big ideas they will be teaching.

From Ball et al. - (2008) - "Content Knowledge for Teaching : What Makes It Special?"

You might, for example, ask a fifth or sixth grade teacher the following: "5th and 6th grade students spend a significant amount of time studying operations involving fractions and decimals. Still, many find story problems that require these ideas challenging. How do help students become better solvers of story problems involving operations with fractions and decimals?"

Final Thoughts

Those are my go-to interview questions. But, like many, I adjust the questions based on how a candidate responds. When I am the one being interviewed, I am thinking about these questions too. I want to be sure to communicate my beliefs about assessment, curriculum, mindset and feedback even if I am not asked directly.

What questions do you like to ask or be asked? I asked this question on twitter and was reminded of some wonderful questions including:

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