Coming off of Thanksgiving break I feel ready to go. In Algebra, we are just starting to work with slope. I am excited for tomorrow’s lesson… stay tuned for that.

I graded Geometry’s concept tests over the break, and a majority of the class bombed Triangle Congruency… Hard.

The fact that 7/8 of the classes scores didn’t raise tells me I messed up somewhere along the way. We spent about 40 of the 49 minutes in the period reviewing different problems on whiteboards. I think it helped them quite a bit.

For the last 9 minutes I threw this up on the board:

They were giggling and having a great time. I thought it was interesting that none of my 20 students tried to make the side at a slant… Taking the easy way out I guess.

After about two minutes I revealed the bottom of the slide:

It is really interesting to me that after about 3 seconds, most of the class decided it would be too much work and checked out.

Did I ask the wrong question? Were students not perplexed by this? Is there a lower entry point into coordinate geometry that would have been more effective? Was a bad idea to give this problem with 7 minutes left?

Maybe.

I don’t regret asking students to find a place to start on this for homework. I set the bar high… Students should see that I want them to struggle and be challenged.

This summer I went to one of Dan’s workshops. One idea that stuck with me was **you can always add to a problem, but you can never take away.** I believe that if I led students through a coordinate geometry problem before hand, it would take away from the magic and struggle that makes math so great. Working at a problem for a longggg time then finally getting it, ya know?

I had parent teacher conferences a few weeks back, the only talking point I had planned was to project my class goals up on the board for parents to see. These were on my syllabus this year and I refer to them constantly to make sure I am excited and passionate about what I am teaching…

Here they are:

**Encourage the development of mathematical reasoning by:****Incorporating multimedia into lessons.****Presenting students with low entry and high exit problems.****Focusing on student work.**

**Develop patient problem solving skills.****Make math social.****Provide the appropriate level of mathematical rigor for each student.**

I believe there is an appropriate place for guided examples, notes and repetition; after the struggle. After students discover and apply the mathematical tools that make their lives easier.

Tomorrow I am planning on having students talk about the problem for a few minutes, creating a plan of attack with their groups, then trying it again. I will work in examples along the way according to where they are at in the solution process.

Sometimes I like to phrase it “Convince me …..” “Provide evidence……” “Show….” instead of the word “prove.” Some of the stigma associated with “proof” overflows into how the students approach the “proof.”

By asking them to informally provide a convincing argument, they can start with whatever they think is logical to convince their reader. (low entry point) I will then circle the room and provide guidance and reveal my high expectations by saying things like “You need more support than that” “Eyeballing the sides of the rectangle is not convincing enough.”

I can work with their format of the proof after they have invested time and thought into the logic of the proof.

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You asked: “were students not perplexed by this?”

I guess I’m missing the point, but I don’t see what they would find perplexing. Though it also isn’t clear why they found the previous instruction to create a rectangle with those dimensions to be so much fun.

That said, I strongly support your thoughts about letting them struggle and letting them find a way to engage with the question.

Since you are working on coordinate geometry, I suggest you take a look at pencilcode. Logo-inspired, it provides a natural source of motivation for the kids to learn more about geometry and a place to apply what they’ve learned. For example, here’s some simple code that creates a slanted parallelogram with side lengths 3 and 5.

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As always thanks for the comment!

I was trying to challenge students thinking by asking for more than just a visual description of why their shape was a rectangle. Now that I have some distance for the lesson and more time to reflect I agree that there isn’t anything perplexing about this sorta question.

I am going to look into pencilcode right now!

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