Math-itude

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.

Student: I can’t do math.
Me: What do you mean, I’ve seen you “do math”?
Student: Well, I’m fine when we’re doing the problems in class or if I’m at home. I just can’t take math tests.
Me: Huh. Well what do you say to yourself when a math test is put in front of you?
I usually got some variation on the following:
Student: I’m gonna fail… I’m no good at math… I can’t do this… I always screw up.
Me: Huh… what do you say to yourself before a game/performance/show/English test/whatever it is they’re good at?

Student: I’m going to do my best… I can do it… Just like in practice…

Me: So, you don’t say… I’m going to fumble/forget my lines/trip on stage/forget how to write an essay?

Student: Uh, no Mrs. B, then I’d fumble/forget my lines/trip on stage/forget how to write an essay.

Me: Oh.

Then I wait.

Student: But this is different!

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?

Review Stations

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.

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.