This comment of Dan’s started my thinking (he’s good at that, isn’t he?).

One of the most surprising, reoccurring events this year was my constant battle with my students’ attitudes toward math. Not so much that they dislike math– the fact that they believe they can’t do it. Not that it is difficult. Not that they have to work at it. So many firmly believe they can’t do math.

I’m not sure from where they got those messages. I’m not sure how they internalized them. But they have.

I had many a conversation outside of class with individual students about this problem. It usually went something like this.

Then we’d work on changing their thinking. We’d come up with some replacement messages and ways to integrate that into their belief systems.

Did it work? For those that took it seriously it did. Now that I think about it, it was mostly the seniors who had this entrenched negative belief system. I wish I had talked about it more in class with them. I mean, really, what’s the point of learning a new lesson if they are sitting there telling themselves they can’t do it?

Interestingly, I didn’t get this from too many of the freshmen. I need to take another look at the end of the year surveys now that school has been out for a whole week.

Do your students come to you with the same beliefs? If so, what do you do to try and change them?

I did something different for the “review” for the final exam today. Instead of giving the students a packet of problems, I created review stations.

Eleven different pages were posted around the room. Each page was identified by a capital letter and had anywhere from one to four problems listed. Like this:

As the students walked into the room, they were handed a mostly¹ blank table. On top of each I had written where they should begin. I alloted about three minutes per station. I had a total of 11 stations, so with the beginning instructions, transition time between problems, and instructions at the end of class, it worked out pretty well.

In the past I found that when I’ve given review packets, students don’t use them well. They either start at the beginning and work their way through, only do the problems they know how to do, or just stare at it. I liked this as it encouraged the students to work on each question/set of questions, without spending too much time on any one question. It also encourages them to think about what they need to study. The column on the right was a place for them to write notes to themselves about each problem: “Uh-oh I don’t know how to do this” or “Easy” or “Double check tonight”.

Their homework is to look over their comments and try to answer their own questions. Tomorrow we’ll go over the solutions.

I liked the way both classes went. They worked well with their partners, they were actively working the whole time, they know what they need to review tonight, and what they know well.

A better teacher would have had a bunch of three minute songs cued up to signal station changes. Oh well, there’s always next year.

¹Mostly blank. Any geometric figures were already in the table for them. As were the axes for the graphing problems for C.

2D

Phun is out for OSX! Okay, it came out a few weeks ago, but I just got around to downloading it. Phun is a 2-D Physics sandbox.

At this time, I have no idea how I’ll use this in class, but I have a new prep to plan for next year and a summer that is mostly unplanned.

3D

Via information aesthetics I ran across Tag Galaxy, a 3-D¹ representation of photos on flickr by tag. Each planet represents photos of related tags. Of course I had to see what the math tag looked like:

I had planned to post the screen shot of the “planet” of photos. However, the first photo I checked was not licensed under a Creative Commons License. So, be careful.²

4D

I’ve got nothing, sorry. Although I do keep bugging a friend to work on a time machine. Alas, he hasn’t come through yet.³

¹Obviously it is really two dimensional. Also, I think it is more of a planetary system than a galaxy.
²In a strange coincidence, the first photo I checked for CC belonged to Courtney.
³I know, I know. He hasn’t built a tesseract either.

Today was the first day of senior finals.

One particular student was very anxious about the test. She had worked with a friend on the review materials. Actually she worked near a friend. When the friend sat next to her, she felt confident enough to try each problem. She didn’t do them perfectly, but she was willing to try. When the friend moved away, she stopped trying.

So her friend came to the final. She sat next to her and read a book.

I have remarkable students.

At the end of 3rd period study hall on Thursday, I got a phone call that necessitated my leaving the building, so I had to throw together sub plans on very short notice. At the beginning of 4th period, I apologized to the kids, explained that they’d have to look in their books for examples of the Law of Cosines and try to do the assignment. I told them I fully believed they could figure it out. I asked them to help each other.

I was trying not to show the students that I was upset/worried/nervous. Apparently I didn’t do a very good job of that. I apologized again on my way out. This is what I heard as I was leaving, “Don’t worry Mrs. B, we’ll figure it out. We love you.”

It’s a good thing I was walking out the door. Darn kids - making me all teary.

I haven’t forgotten about this space where I’m allegedly reflecting about my first year teaching.

I’m just buried in work. Grading, mid-quarter grades, reports to case managers, parent contact, first year portfolio, preparing for final exams… you know, the usual. I don’t do well with little sleep.

There are many changes happening too. I don’t do well with change. I still don’t know for sure what I’m teaching next year. I don’t do well with uncertainty either.

I’m also getting a bit wistful at the thought of not seeing some of the seniors anymore. I’ve grown attached to quite a few of them. This happens to me every year.

I need to figure out how to better deal with these things. I don’t think they are going to change much from year to year.

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

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!

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.

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