# Day 126: Speed Dating

Algebra still needed some practice on Properties of Exponents. Yesterday, I passed around answer keys to a worksheet students had. There ended up being a few mistakes on the answer key. Two periods passed without any students picking up on those. To me this says that most students straight up copied off them then called it a day.

So today students experienced speed dating; here is how things went.

• I passed out a note card to each student
• There was one expression on each side, a black one (the problem) and an orange one (the answer).
• On a sheet of paper students simplified the expression in black.
• A couple minutes passed
• They then flipped their note card over and checked their answer (Almost every student actually listened here or didn’t recognize that the answer was on the backside)
• We moved the room around into two long rows of desks, facing one another.
• I set a timer for two minutes, during that time one student held up the side of their note card with black ink and the person across from them simplified, if they were wrong they tried again.
• Timer goes off, repeat 10-15 times

This is the bare bones of the activity. I played it up a lot before hand and told ’em about how they needed to be masters of solving the problem in black ink. They had to own the problem and know it inside and out.

A couple other things I said: “You can’t just give your heart, or answer in this case, away to the person, they need to understand you”

“While they are trying to get to know you, just hold up the problem and smile back, helping them along the way”

“If you didn’t have a good experience with a person that is okay, move on, another may work out better for you”

I also mixed things up a bit by playing a cheesy gong sound that I found on Youtube at the end of each session.

The main reason I liked this activity: Quite a few students struggled with their problem, throughout the period, they were able to see other students struggle with the same problem, but this time help others out in understanding it. Also, students were able to get immediate feedback and self correct. I heard a lot of comments today about how students didn’t get the problems at first but they became easier after practice.

Two of my four algebra classes seemed to really like the activity, while the other half never wanted to do it again. I know for a fact though that 90% of my students walked away from today knowing more about exponent properties.

# Day 30: Proofs?

I have a sub tomorrow. Last year it would have been no big deal. Probably because I was so focused on surviving. Now I am kinda disappointed I don’t get the spend the day with my students and frustrated at myself for giving them all the same worksheet when they really need to keep moving forward.

Today in Algebra I was planning on taking the easy road and giving students a day to practice. I wasn’t feeling great about it because that would mean back-to-back days of practice on a concept they have almost mastered already. What is awesome about my students is they would have done this without any thought. But just because they are willing to work for me without question, doesn’t mean I should take advantage of it.

Instead I did a sort of speed dating activity. We rearranged the room so there were rows of desks facing each other. Students had two minutes to work on a problem with their partner then one partner rotated. I threw other questions in there like state flags and capitals of states; they loved it.

Afterwards I asked them for feedback; didn’t want to change much, just maybe a little more than 2 minutes on some problems (that doesn’t mean there isn’t any room for structuring it a little better on my end though!).

In Geometry we started proofs. (Actually, first there was an awesome visual pattern found here)

And I was worried about how today would go.

At a workshop this summer with Dan he talked about how you can always add more, but after all the mathematical structure has been added you can’t take it away.

I went with it and put this up on the board:

I asked students what they could conclude from this.

There wasn’t any complaining or distractions or groaning. They jumped right on it.

Some threw numbers into the mix;

And eventually we were able to reach the conclusion. I talked about how this was a specific case and how 6.1 and 83.9 is another. If we want this to be true for every case, we would be spending a lot of time plugging in numbers making sure they work.

After I asked students for to write out a game plan for how they could use the provided information to reach the conclusion we wanted.

They did it.

And it was awesome.

I guess all my emphasis on how the process is so much more important than the solution is paying off. Those whose game plan fell short didn’t care; they learned from it and hearing about other’s approaches. I wrapped the discussion up by writing a formal proof using THEIR rules.

For the rest of the period students worked on Justin’s Formal System Proofs. (Provided by a co-worker) This is a great way to introduce proofs and reinforce logic in general.

Here is the direct link to the goods.

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Featured comment:

Joshua provides two great suggestions for fostering student interest:

…encourage your students to have opinions about proofs. Which ones do they like, which ones do they find most convincing, which ones do they find easiest to understand, for two proofs of the same result, how do they compare, etc…

Prove or Disprove and Salvage if Possible (=PODASIP, inspired by the PROMYS Program in Boston.) Give them at least a couple cases where they’ve been asked to prove something that isn’t true. This ambiguity is common for working mathematicians and many non-mathematical situations…