Ready or not, here we come!

This weekend is the ICTM High School Math Contest State Finals. Friday afternoon I’ll be one of two coaches driving a bus¹ of math team students down to U of I. Six students qualified to compete individually. Our 5 person calculator, freshman-sophomore 8 person, and junior-senior 8 person teams qualified too!

It should be a good weekend (although I admit, I detest driving the bus - I’ll be much more relaxed once we get there). Friday evening is always fun - we’ll eat dinner and then just hang out at the hotel. Last year we had “math team family game night”. This year promises to be just as enjoyable. It is one of the senior’s birthdays. A cake has been ordered that says “Happy th Birthday”.

We’re hoping for good weather so we can hang out on the quad Saturday between events. Although we can always check out the math library in Altgeld too.

A couple of years ago², I told two of the students that it had been one of my favorite places to study when I was there. Their eyes lit up. A whole library, just for math?… and off they went to investigate. I love coaching math team. Kids excited about a math library. Gotta love it. Now one of those “kids” is a college freshman - majoring in math. The other is a college sophomore - he wants to be a math teacher.

Have I mentioned I love coaching math team?

Wish us luck!

¹It’s sort of a bus. A mini bus. The kids lovingly refer to them as the ice-cream-trucks.
² Even though this is my first year teaching, it’s my fourth year coaching the math team.

Photo: IMG_5648 by mrkw via flickr, cc

Proof Update

Things have gone much better the past two days with the trig proofs. Much much better.

Yesterday, I asked for volunteers to put up the solutions. Not every problem was done correctly (most were though). Having the students explain their thinking as they were presenting helped. They did a nice job asking questions of one another. I also stressed multiple methods so we saw different ways of doing things. Some were a bit convoluted, but they worked.

Today was more of the same, except this time I called on the, uhm, hesitant students. I told them they could use a lifeline if they got stuck. One girl clapped and cheered when she did it correctly on the board. One student initially said no. I told him it was his choice. So, of course he then got up and did it.

We have a quiz tomorrow. We talked about how to study for math. I’m still surprised by the number of students whose plan is to “look at” the problems. I suggested to take out a new piece of paper and do the same problems again. Then compare results. I shared that I’ve done the same problems over and over until I understood them.

We’ll see what tomorrows brings in terms of quiz results, but I’m really happy with the way classes have gone the past two days. The students have been doing the math, explaining the math, and asking questions of each other. Yay!

“Teaching” Proofs

We recently began trig proofs. I love trig proofs. To me they are a joyful puzzle.

My students don’t quite share my sentiments.

/understatement

Today I heard: “I don’t know where to begin“, “This takes too long“, or “Show me what to do and I’ll do it“. Friday I worked out some examples. Students worked out examples. They worked together. I walked around and offered guidance. My suggestions included: finding a common denominator, factoring, using the identities (I gave them a sheet with them all listed - I’m not assessing their ability to memorize). Today was more of the same. We’ve seen multiple methods of proving the same thing. I find joy in this - yay, there’s more than one way! The students seem to find this annoying.

Aside from the open-endedness of the steps, what is giving them the most problems is the dreaded f-word.

One student summed it up pretty well, “The darn fractions finally caught up with me.”

I don’t know how to “teach” proofs. They want a step-by-step procedure. Unless I’m missing something, there isn’t one. Just play with it. Try something.

Grasping at Straws

We’ve been exploring the ideas of similarity and congruence in my freshmen classes. Today the students developed congruence by SSS - with straws.

Supplies needed: drinking Straws (1-2 per student), string (dental floss was too slippery), and scissors.

Question 1: Are all quadrilaterals with congruent corresponding sides necessarily congruent?¹
Students began by cutting a drinking straw into four pieces, threading the string through, and tying it off to form a quadrilateral. They quickly realized that they could “move” the angles, so nope, this is not true. Unexpected bonus: discussion of concave/convex.

Question 2: Are all polygons with more than four sides that have congruent corresponding sides necessarily congruent?
Repeat the bit with the straws. Some of them realized they could easily create this by carefully cutting one of the straws from their quadrilaterals. Conclusion, nope, more “moving” angles.

Question 3: Are all triangles with corresponding sides congruent necessarily congruent?
Make the triangle with straws… conclusion, yep, this does guarantee congruent triangles as the angles are “locked”.

We spent the rest of the period trying to explain why this is the case (and formalize the language after a bit). We also discussed whether of not this constituted a proof.

On the way out, one student thanked me for the lesson. He said it was fun to really understand why it worked. Wow. I was thanked. For a math lesson. Wow.

Up next: SAS congruence with straws and pipe cleaners.²

¹We’ve spent the past few days on “if-then” statements and counterexamples as a lead in to this.
²I thought it was time to start sharing.

Image: popping colors via flickr under cc