## Monday, February 26, 2018

### Productive Struggle

Alternate Title:  Standing on the Shoulders of Giants

A few weeks ago, a Twitter conversation with @JennSWhite and @Teachmathtorr started the wheels a'spinning...

I knew right triangle trig would be coming soon, so I quickly bookmarked Michele's Desmos Activity Builder (Go check it out here).  I *loved* the idea of exploring the trig ratios without mentioning sine, cosine, or tangent.  I loved the idea of tying into similar triangles and dilation.

But that was a few weeks ago and the whole conversation slipped my mind.

Until this weekend.

Right Triangle Trig was upon me... I started by looking at the MTBoS Search Engine, which is my go-to starting place for a new unit.  That led me to Tina C's blog and Lisa B's blog, both of which referenced a Geogebra applet similar to Michele's Desmos AB.

I'm not a huge Geogebra person but I liked the simplicity of the applet, so I decided to try it and do Desmos tomorrow.

Like Michele's Desmos AB, I decided to focus just on the opposite / hypotenuse ratio, letting them explore by creating different triangles and hopefully noticing that all of them had the same ratio (or very close.. rounding issues ya know...)

And things were going pretty okay...

Until they weren't :(

I had started them with exploring with angle A set to 35 degrees, then asked the following questions:

Holy moly - you would have thought I had asked them to perform major surgery! :(

It did not end well :(  Either they just used the applet and totally ignored the instructions to try to figure it out first OR they just made up some random number and ignored the applet OR they got mad because I wouldn't just tell them what to do to find the value.  (cue whiny voices... But Mrs. T!!! Do I multiply or divide????)

By the end of the first hour, I knew that tonight would be a blogging night... I needed to process what had happened.  I also needed to regroup and figure out how to fix it tomorrow.  Thankfully I have a long commute and it was a beautiful night for a walk, so I spent most of that time working through what had happened today.

Here's a summary of my conclusions...

Thought #1:  Students are not used to thinking like mathematicians - looking for patterns, making conjectures, then testing those conjectures.

Thought #2:  As teachers, it can be super frustrating, especially when the whining starts.  This often results in throwing our hands up in the air and giving in to the "just tell me what to do" mentality

Thought #3:  I need to provide my students more chances to make sense of the mathematics.  Had I given them the equations of 3 / x = 0.573  and x / 6.5 = 0.573, they probably could have found x with minimal issue.  However, having to think about "Okay, this means that 3 divided by some number has to equal the ratio of 0.573" was quite the stretch for them.

Thought #4:  I am a strong believer that students need to grapple with a concept, but for the sake of time and for the sake of my sanity, I don't do it often enough.  This has to change.

So tomorrow is a new day...

We are going to discuss the work from today, then go back to the Geogebra applet to try to "build" the trig table by looking at angles from 10 degrees to 80 degrees and the 3 ratios, then comparing those to an actual trig table.  Along the way, we will explore a few more problems and see if it goes any better.

Today, the struggle was real.  Both for my students and for myself.  I just hope it pays off in the end :)

Here are the files if you are interested.  Many thanks to Michele, Tina and Lisa for the inspiration behind these files!
H3.1 - More Side Ratios (Day 2)
H3.1 - Practice Problems - Dry Erase Sheet