Our Geometry Support Site

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So, I’ve talked about Khan Academy before. They make instructional videos for students to watch and learn from.


I’ve talked about #flipclass before. In this model, the teacher makes videos for the students to watch and learn from.


I like the idea of students having instructional videos to watch and learn from. But, in both Khan Academy (and other related sites) as well as flipped classes, the students are recipients of the videos. We decided that we didn’t want them to simply be recipients. We decided that we wanted them to be producers of the resources, too. So, we decided to just let the students create the math help videos.

Here’s what they did: Today I unveil the @PennGeometry Beta for your review and feedback. Currently, there are videos created from one practice test about triangle similarity. We would like to expand and continually improve.


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All of the videos are designed, produced, and completed by our students. Some of my students were sensitive to the boring math video and tried to add their personality to the video. We would love some comments, “likes”, and constructive feedback. Please check it out. Eventually, we want to add our voices to the overall mathematics community to support those in need.

Check it out and let us know what you think. We look forward to hearing from you.

Bankshot 3-Act Revised

In my previous post, I presented Act I of a 3-Act geometry lesson that I called Bankshot. I also called out to the #MTBoS to support me by offering feedback of which I received two excellent comments that were rich in suggestions, particularly in the aspect of improving the student experience.

If you want to go back and look at the first draft and/or read the comments that got left, then feel free to check it out.

Now, all three of us agreed that the action begun and ended too quickly. Danny Whitaker (@nemoyatpeace) suggested that I slow the video down. In addition to agreeing with Danny’s suggestion, Dan Meyer (@ddmeyer) suggested that there was more I could do to set the situation up and make the clear what was going on before the I roll the film.

Danny also suggested that I cut the film before the ball bounces into the wall. Another interesting suggestion that Dan made was to include multiple attempts. I thought that those are both interesting suggestions.

You will see my attempts to respond to the feedback in this second draft of “Bankshot”. I start with a more direct set-up of the situation. I also added a second attempt from when I was filming to give the students something to think about. Now they have at least four guesses they could make. “Both hit target,” “both miss target,” “first hits, second misses,” or “first misses, second hits.” You will notice also that I slowed the playback down which cost us the sound. It’s possible that a bit of background music will be needed in a third draft, but that is something that we can talk about.

All right, #MTBoS, here is my second draft of “Bankshot.” I look forward to more feedback.

Making over another typical geometry problem

It’s time to look at another typical geometry problem to make over. This time Dan Meyer (@ddmeyer) presented this problem for revision.

Dan decided to go in this direction for the revision, which, for the record I really like. I would encourage you to check it out.

I took a try at it, too. I’ll let you decide which you like better.

I like this problem’s basic core idea. Looking at the volume of a sphere (the meatball) and the volume of the cylinder (the cooking pot), in general, this is a pretty tasty set-up (pun intended). Especially considering that I am always a fan of problems that make use of food.


For this problem, food and cooking were actually more of a problem that a support.

First, the cooking pot is sitting on a hot burner and I’ll be the first to tell you, a cooking pot doesn’t have to be full to spill over. So, the question of whether or not sauce will spill over is a bit more complicated that it might seem at first.

Second, meatballs aren’t spheres. They are irregular and rarely are two of them congruent.

So, my first thought was to choose spherical objects that are all congruent: for example, baseballs. Coaches regularly carry baseballs around in 5-gallon buckets, so there is our cylindrical container.

And I figured I’d deliver the task in a video simply because videos tend to improve engagement on their own.

Now, once I made the video (and some meaningful conversation was had among those who are better at this than I am) I found that my task had one glaring drawback. When you put baseballs in a bucket, they don’t pack tightly. There is air between them. A lot of it, in fact.

So, now it seems like if we are to use this video for instruction, we would need to change the question in to multiple parts.

1. How many baseballs can we fit into the bucket? (This would likely end up being a demo or a lab where we collect data. Tricky to calculate this.)

But then we supplement the question above by…

2. How much volume is wasted by packing that many baseballs in the 5-gallon bucket.

This would get back to the original content. Likely the cylindrical volume would need to a unit conversion, and then some analysis of the collective volume of the collection of baseballs.

Now, if we could ind a way to check it. The first thought I had was to fill the bucket with water. Put the baseballs in to displace the water out of the bucket. Take the soggy baseballs back out of the bucket. Find the volume of the water that’s left.

Problems with this idea: 1. Baseballs float which is going to effect the manner in which the water is displaced. 2. Baseballs absorb water. This means that some of the none displaced water would get removed with the baseballs and not counted.

Hmm… I thought of filling the bucket with baseballs and then topping the bucket off with sand. Which would solve both of the above problems, it would also give me an opportunity to make a beach trip.

Any other ideas out there?

Pencil Sharpener Problem

Let’s start with a student sharpening a pencil as quickly as he can.



Let’s add a second student sharpening a pencil as quickly as he can.



And then, we’ll add one more student sharpening a pencil as quickly as he can.



If all these guys kept going at the same rate they were in the video, how long would it take for them to grind away 100 pencils?

The Growing Case Against Standardized Testing

photo courtesy of flickr user "Crazytales562" - used under creative commons

photo courtesy of flickr user “Crazytales562” – used under creative commons

Last August, like practically all news outlets around the country, The Huffington Post reported on the Atlanta Testing Scandal.

It seemed like it could have been an isolated incident, right? A district with a few bad apples, a little pressure, a few threats and who knows what can happen, right? Guys like Alfie Kohn would disagree with you, but on we go.

Then I read a piece on the Washington Post describing the 14 different standardized tests that a kindergarten student was subjected to.

And then, I read a post on Good.is explaining that the ACT and SAT are gradually being phased out by a growing number of 4-year postsecondary schools.

And then, Cynthia Liu wrote a piece for Good.is explaining testing as a needed fix for public education, (but advising us to not wait for President Obama or Secretary Duncan to bring it up.)

Then I saw this TED video where Sir Ken Robinson declares that innovation and creativity should be our chief concerns while standardized testing is instead forcing a model of conformity and standardization in addition to correlating to a rise in ADHD diagnoses.

Stories persist about schools putting subs in classrooms so that the highly-qualified teachers can proctor exams to be compliant with state law.

I have conversations with colleagues who explain to me that multiple choice testing is a meaningful form of summative assessment, but their rationale centers completely around preparing them for standardized testing.

What does it all mean?

Well, my thoughts are coming together on this issue and they are leading me in a few directions. While I am nothing more than a concerned educator and parent, I recognize a few problems.

Problem #1: The act of sitting down in a place for several hours and having to answer decontextualized questions in rapid succession only shows up in education. Testing during school, but also certain state certifications will require a test (driver’s licenses, hunting licenses, etc.). Many, many other industries use various other structures for their summative evaluations: past successes/failures, previous experience, interviews, credential reviews, supervisor observations, artifact collections, portfolios. The act of preparing and taking standardized testing does little more than prepare the students to take a standardized test, which is a pretty isolated skill.

Problem #2: The program most schools use to prepare for the tests require the ceasing of the entire curriculum to doing “skills review.” Which is code for rote memory exercises of detached skills and vocabulary, often at the expense of critical problem solving, which is a skill that is the opposite of isolated. Almost every situation you can think of will require critical problem solving.

Problem #3: The pressure on our students is intense and completely unnecessary. I understand pressure. Pressure is actually a good thing. A focusing effect. But, there’s no point to add pressure for the sake of pressure. Pressure is a natural feeling from something that you know is important that you need to perform well on. The pressure to perform on standardized tests is completely manufactured, especially now that universities are starting to lessen the emphasis on the ACT.

And to nobody’s surprise, I’m not the only one who notices this. The major motion picture is on shelves ready for holiday shoppers. Enjoy the trailer.