The Power of Network: Triangle Similarity

I want to share a story that shows the power of an effective PLN.

In a previous post, “proof and consequences: circular reasoning“, I begged for help solving a problem with students struggling to see their own logical crisis that was leading to predictable and consistent problems.

Several people reached out to me with suggestions. Thanks for that. I would like to highlight one specific suggestion that I tried to today and it worked just exactly as the designer predicted.

The suggestion was made by @nerdypoo.

From the comment:

“(i drew an example of this on the train home from work where i drew two isosceles triangles — the first had congruent legs 2 & 2 and the second had congruent legs 3 & 3, so scale factor of 1.5, but the first triangle was an isosceles right triangle and the second had an angle of a bit more than 90. i can send a jpeg if you want!)”

I loved this idea. And yes… I did. I did want that .jpg.

So, here’s a portion of what she sent back.

Dutch Triangle Idea Original

Today, I tried it in class. I began by putting up this image…

Dutch Triangle Idea Starter

… and asking the students to vote on whether the triangles were similar, not similar, or we don’t know. Overwhelmingly most students voted that they were similar. The thoughts they articulated were mainly that they could find the legnth of the missing side (which they claimed to be 3 cm long) and then could use SSS to show a consistent scale factor.

Then I showed them this image and asked them to vote again.
Dutch Triangle Idea

A lot of votes changed. Many changed from “similar” to “not similar”. A few others changed from “similar” to “don’t know”. An additional piece of information revealed an assumption. The assumption was that finding a consistent scale factor in two pairs implied the third. Perhaps an assumption that the angles were congruent.

It was essential that I made sure the students knew that I wasn’t changing the situation from the first question to the second. I was simply revealing information that was hidden. Those angles were never congruent. They simply didn’t know that, but most them assumed they were. But every person who voted that the first two sets of triangles were similar were making an assumption, an assumption that they didn’t recognize before. An assumption that shouldn’t be made because sometimes it’s incorrect.

7 thoughts on “The Power of Network: Triangle Similarity

  1. Many of my best ideas come from listening to shared ideas. I think that is why common license is so important in education. Your lesson just got better. My next lesson on this will now be better. (I saved the idea and put it in my lesson book for triangle proof). I feel more knowledgable about the ideas I can expect from students because you and another teacher have been there and shared!

    • Yeah, there’s a sense that some have that announcing success is nothing more than a form of bragging, until you realize that when you do that, you are contributing to a conversation with lots of people listening with specific questions in their heads.

      I’m just glad that I can finally start adding somethings to the conversation because I have spent a while being a taker.

  2. very cool! though now i feel renewed guilt about having a blog that i never ever blog on and a twitter account that i’ve tweeted from exactly once. ah the best laid plans.

    • It can be really hard to get started. If you go and read my oldest blog posts, you’ll see an entirely different focus and target audience. Only after I’d written a couple dozen posts did I start to get an idea of what I was going to write about and for what purpose. Once I figured those things out, I feel like my network has grown in number and productivity.

      • it can also sometimes feel like talking to the void, i suppose. i do read a number of blogs but mostly lurk and rarely contribute unless i think i have something (possibly) of interest to say, so it’s hard to establish a presence (and then i am still a little at the stage where i question if i want a presence, especially considering the school’s social media policies and privacy issues). but yes: perhaps i will make a post this weekend in an effort to be more a part of the conversation (even if it’s one-sided for now).

  3. This is a great story – I enjoyed both posts … I just never got around to commenting on the first. Thanks so much for writing and sharing!

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