Algebra I: Still Hazy After All These Years

This isn't good. One homework problem took me 32 minutes and two entire sheets of paper. As there were about thirty problems in the entire homework assignment, it should only take me...um...sixteen hours to do my homework. Did I do that right? 32 times 30, then divide that by 60? Good lord, I hope that's right, because if I can't figure that out, I am dead in the water in Algebra I. The scan above is the cleaned-up version of the problem, the version I re-copied so I could actually how the heck I got to a final answer.

I knew I would struggle in Algebra I, when I returned to class in order to get over my math anxiety, and not just because I have a lot of trouble visualizing how numbers work. The bigger problem is that due to my overloaded teaching schedule (I teach two sections of composition 8, one of composition 7, English 8, English 7, Latin 6, Latin 7, and Latin 8), I can only attend two of the four Algebra I classes held in a week. I do my best to keep up, and as I have mentioned, my students fill me in on the important lessons I miss.

The biggest hurdle I face at the moment is the lack of continuity. I jumped into Alison Gorman's Algebra I class halfway through the year, and missed all of the lessons that inform our current chapter (11). When Alison says, "Don't forget to use the discriminate factorability test! You will have to keep it in mind when you do tonight's homework!" I have to quickly and surreptitiously flip to the index in the back of the book to understand what she's talking about. D...D...Directly proportional...Disappearing variable...Discriminant...ah - Discriminant, test for factorability, 436.

"A quadratic [oh, crap, look that up, too] trinomial can be factored if an only if the discriminant [...and that, too] is a perfect square."

Lovely. As clear as swamp effluvia.

My biggest worry at the moment is that I am going to need the quadratic formula to do some of the work in this chapter. I remember learning it once, long ago...something squared over something else with b and 4ac and...

Q....Q...Quadratic degree...Quadratic equations...solving by factoring - here we are. Formula, 214. Way the heck back in chapter six.

Okay. I kind of remember that. But come on, it was thirty years ago. Apparently, Alison teaches the kids a song about the formula. I remember hearing them singing during class back in December. I have to remember to ask my students to teach it to me the quadratic formula song on Monday.

What has been fun is the opportunity to see my students in a new context. Alison witnesses different aspects of these kids in her math class than I see in English and Latin. I am getting an education in my own students, and that alone has been worth the effort I've put into Algebra. This new knowledge has really paid off this trimester. One of my students was having trouble in math, and when I met with Alison to discuss what was going on, she was able to show me in the students' math notebook exactly what mistakes she was making. I never would have understood the nature of her mistakes before, and it allowed me to sit down with my advisee and offer up more than general advice about diligence and "doing your best." We were able to untangle her specific issues with the unit and devise a game plan. We laughed together over her misunderstandings and I empathized over the time spent working through the more confusing problems on her last test.

But she's still in better shape than I am. She had never spent 32 minutes on one problem.

This weekend's homework: catch up on relative rates problems. Alison calls them "sitcom problems" because whenever a sitcom character wants to freak another sitcom character out with a complex math problem, they give a relative rate problem as an example.

"A kisses B goodbye and leaves home on his bicycle, going 30 km/h. Half an hour later, B realizes that A left her briefcase at home and so he starts from the same house, going after A in his car, at 50 km/h. How long does it take B to catch up with A?"

Alison insists that these problems only sound complex, but are really just a matter of common sense. Alison's reassurances make one huge assumption, however. The small detail of common sense, which I fear I lack. As there are around thirty problems assigned for this weekend's homework, I'd better get to work. Monday is only 72 hours away.

Part VI of my math odyssey can be found here.

Exponents, Products and [my mathematical] Powers

"Everyone who beats Mrs. Lahey on this problem set will earn extra credit points."

Oh, dear. Extra credit points will be flowing like New Hampshire spring runoff thanks to Mrs. Gorman's misplaced faith in me.

When I decided to return to Algebra I in order to get over my math anxiety, I knew I'd have some catching up to do. I stumbled into class on the last day before a unit test, in the last week of the second trimester. I paid little attention in Algebra I the first time around, and that was 30 years ago.

Helpful hint: If you plan to return to Algebra I in middle age, start on the first day of a unit, not the last.

I did my best to catch up with the kids, and Alison Gorman is the best math teacher I've ever seen, but if you glance back up at the scan of my first practice set, you can see how badly I tanked. The red "C" in the middle of the sheet was the one problem I got right on the first try. I had totally forgotten what to do with exponents, could not remember what the distributive property was let alone how to use it, and my hand cramped up about four pages into my notes.

That one correct problem turned out to be my only correct problem. But it reveals I learned at least one new thing yesterday, and that's good, right?

The students loved it. My students taught me. One taught me about domain and range, another explained why you add exponents when the bases are multiplied, another whispered the number of the problem we were supposed to be working on when I missed Alison's instructions. Hey, come on, I was taking notes. It's hard to listen to write and listen at the same time. I will try to remember that next time I start talking when my students are still writing.

I can't attend Alison's class every day because my teaching schedule overlaps with some of her math classes, so a fair amount of confusion is to be expected. But that first day was just silly.

Today was better, though. The class started a new unit, "Exponents, Products, and Powers," so I stood a fighting chance. We were all on the same starting line, give or take thirty years. As we moved through the exercises, I started to see it. I have my list of properties - power of a product, product of a power with equal bases, power of a power, power of a quotient...and on and on - and I have to refer back to them, but they are slowly sinking in.

I got some insight into my basic issue with math when I proudly told my son Ben about my day. We have a tradition at dinner - "high, low, funny." The best thing in our day, the worst, and the funniest. My best and my funny were both math class, but Ben provided the worst. I recounted the properties I'd learned, and told him how proud I was of myself for remembering that when you multiply variables raised to a power, you simply add the exponents. Ben looked at me like I was an idiot and said,

"Well, that just makes sense. Of course you add the exponents."

And there you have it, ladies and gentlemen, the difference between my brain and the brain of someone who naturally gets math. I can't see it. I can repeat the steps if someone shows them to me, I can replicate the process, but I don't think any of my teachers spent much time explaining the "why" of the process to me.

For example, we did this problem today:

Look at the one without all the scribbles and crosses through it. I have no problem leaving the exponents well enough alone when they are next to an X or a Y, but put them next to a number, and they call out to me. The 12-year-old in me has to DO something with them. Create something. Find an answer, multiply all those threes, no matter what. That's the part under the big cross-out. I made mistakes because I solved for all sorts of unnecessarily large numbers. 

Must. Multiply.

But today, the grown-up, rational teacher in me had a breakthrough. If Alison, teacher extraordinaire, hands her students a problem where the exponent is higher than 3 or 4, and she's not letting them use their calculators, and she's not particularly in the mood to torture them, she probably does not mean for them to do the multiplication. She's probably hinting that there's a simpler method. 

So, two things. I learned two things today. 

But now I have to head out to the dining room table. I have a lot of homework and a teenage son to impress.

Part IV of my math odyssey can be found here. 

Quantifying the Unknown

I have a recurring dream: I am in college, or law school - sometimes high school - and I have not attended classes all semester. I don't know where my locker is, let alone the combination, and I'm not sure where the classrooms are. I certainly don't know what material we have covered. It's exam time, and I know I won't even be able to find the classroom so I can take the exam. I know that if I don't pass the exam, I will not be able to graduate, so I have to find the main office and I can ask them where my classes are. I wander around the school, often in that slow, stunted, underwater way, and get nowhere as the minutes of the exam period tick by.

One fun twist on last night's version of the dream is that while I was digging around in my materials, looking for any clue as to my class schedule, I found an application for an internship with Billy Collins. Despite that nice surprise, I still woke up nervous and flummoxed.

The class I fail in my dreams is usually math, which is absolutely predictable if you know me at all. I have never done well in math, and as a result, I have serious math anxiety. I can grade papers and calculate percentages, but anything more complex than that brings on the shakes. So when I woke up this morning at 4:32 A.M., drenched in sweat, I decided to return to the place of my defeat (again) and go back to school.

Fortunately, the math teacher at my school is amazing. She's the math teacher I wish I'd been lucky enough to have when I was in middle school. She's organized, demanding, witty, and kind, and every time I poke my head into her classroom, her students are enjoying themselves.

I know! That was a new concept for me, too.

I checked the middle school schedule and realized I have a prep period during her Algebra I classes on Wednesday and Friday, so starting next week, I'm back in school. I will have my own textbook, and I will even try to do some of the homework once I catch up to the kids (if that even happens).

It's time to put my money - well, my pride, I suppose - where my mouth is. I encourage my students to be brave, diligent, and never back down from an intellectual challenge. I try to model a love of education, a genuine thirst for knowledge that drives what I read, watch, and listen to. They know I am a frequent buyer at The Teaching Company, and that I listen to lectures on my iPod when I stack wood, fold laundry, and chop vegetables for dinner. Currently, I'm listening to a course on the evolution of the English language, and I love to share the tidbits I've gleaned with my students. They know I listen to courses on English, history, and science, but they also know about my math aversion. They joke about it. I joke about it. But it's not really that funny; it's actually quite sad.

I am hoping that my efforts to remedy my math anxiety will put weight behind my words. I hate math, yes. I hate the obsessive attention to plusses and minuses. I hate the inflexibility of numbers. But the excuse that "my brain just does not work that way" doesn't cut it when I simultaneously tell my students that they can do anything - anything - they want to do.

Well, dammit, so can I.

Part II of my math odyssey can be found here.