Credit Cards & Recursive Geometric Formulas

This is my first lesson post with materials, so please comment if you need more information, or if things don’t work.

Learning Targets:
1. Students will be able to write a recursive formula with a percent increase or decrease.
2.  Students will know how a credit card balance is calculated (hindsight:  they need to know how a credit card works)
3.  Students will know about credit card fees, APR, interest and monthly payments.

Background: Our textbook (Discovering Advanced Algebra) uses recursion to build into linear functions and exponential functions.  Our district decided at the beginning of the year that we could take the geometric recursive sequences and teach them at the intro to exponential functions.  The student teacher I’m working with had the idea that we could use credit cards to make a real-world connection.  Unfortunately he got saddled with all of the lesson planning for PreCalculus and never got to flesh out the idea.  So I hopped on that train and made it into a groupwork jigsaw activity.
What makes it a groupworthy task:  credit card calculations involve a lot of separate pieces of information, and you don’t need to be an expert on every aspect to grasp the whole, but you do need the basics.  By dividing up the resources of content knowledge, the final group has a reason to seek a contribution from each member.

Activate Prior Knowledge: We opened with the warm-up to make sure students were all clear on percentages, and finding increase and decrease.  In years past this was tricky, but it was smooth sailing this year.  The discussion questions at the end of the warm-up helped a ton to prepare them for presenting their work to the rest of the class.
Grouping: Each group of four students were assigned individual expert tasks.  They split to meet with their matching experts from other groups & work through their sheets.  The FEES experts have an actual credit card offer on the back of their sheet.

Products: After completing their requisite tasks, they head back to their original groups, and get the overall Task Card.  In a 100 minute period, this is where we had to stop and we’ll continue on Monday.

The final product will be a public vote tally on which credit card is “better.”  I haven’t figure out how to guide that into a mathematical argument.  Perhaps each vote needs to put up 2 reasons for the vote, and discussion will ensue?  I have to see it play out once and then decide what can be added.




Reading Process

We devoted an entire 100 minute class to practicing this process (it’s on three chart papers on the wall now).  It was myself, a student teacher and a literacy coach in a class of 32 students.  We chose a problem in a future section, and told students to base their reading off solving this problem.
We gave all of the students 3 minutes of private quiet think time to read the problem and assess their level of understanding.  They held up fingers (1-4) and we grouped the students by their level of understanding.  I re-explained the rest of the process and how they should expect to repeat it multiple times.
I sat down and worked with the small group of 1’s to get them started on understanding the question.  I pretty much kept repeating the two questions:  “What do you understand?”  “What information are you looking for?”  Even the IDKers could say what information they were looking for.  If it was from before the section, I directed them to the index after they couldn’t find it in the index.
  1. Read the problem (or example)
  2. Assess your level of understanding (this is on a second poster)
    1. I don’t understand the question –> I’m reading to understand the question (you may need help from a classmate or teacher)
    2. I kind of understand the question, but can’t start the problem -> I’m reading to find an example
    3. I understand the question, but I need an example –> I’m reading to see possible solutions
    4. I understand the question and know what to do –> Go for it!
  3. Prepare to read (this is on a third poster)
    1. What information do you know?
    2. What information do you need? (just one thing at a time)
    3. Run your eyes over the section of the textbook and find several places where that might be located
    4. Choose one location
  4. Read
  5. Did that answer your question?  Yes – solve the problem.  No – repeat!

We (the student teacher and I) need to devote another 40-50 minutes in a month or so to reinforce this process.  But already we’ve learned a lot about where students get stuck reading and locating information.  Just breaking down the “prepare to read” was a huge eye opening experience for me.

First Week

Although this blog is for my own personal reflection, I have to pretend I have a vast audience that is chomping at the bit for regular postings.  Perhaps this can be another avoidance strategy to lesson planning on Sunday nights.

What’s different and wonderful about this first week of the school year?

To begin, I know nearly all of my students already.  Those that I don’t know, know a fair amount about me and how demanding and strict I can be.  I gave an exit slip on the first day of each class asking for questions about me.  I didn’t give any spiel about who I am and how I teach.  I figured if they were interested, they would ask.  When the question, “are you strict?” came up, I was in a great position to explain how I am strict, but I’ve gotten very good about not being a jerk.  Yes, I will hold you to a high standard.  No, I will not let you pass just because you’re sucking up.  But there’s just no good reason I would need to be mean while enforcing my rules and standards.

Also, It’s wonderful to know the curriculum I’m teaching.  I taught Algebra II last year, I taught PreCalc two years ago, and this is my third year teaching Physics.

I’m very excited about standards based grading.  The concept is not new to my students.  Most of them have had SBG in their language arts classes for the past two years.  The shift for them is from pieces of evidence to make the grade, to multiple assessments.  I’m not grading homework, and I won’t accept homework as evidence of learning.  There has been a strong culture of copying for the past several years and I’m not going to forget.

Finally, it’s wonderful to have a student teacher to work with.  I couldn’t help but step in when he was leading an activity on the first day, but I do think that we’ve established to the students an expectation that we are partner teachers.  As time goes on, I’m sure I’ll need to step in less, and I think that’s appropriate.  Planning the first days of lessons was incredibly productive.  We’re both tossing out ideas, we’re both weighing in on what we think will be effective.  I still have the final say, which again will change when he takes over the class.

Goals for curriculum:

– Make something cohesive out of the first semester of Precalc (before trig)!

– Document the heck out of Physics, so someone else can step in and take over next year.  I just realized that video is going to be important there!

Right.  Enough procrastinating.  And check out Baths – Cerulean, excellent working music.

Being cool sucks, or everyone’s a geek

I have spent my entire summer learning.  I have been reading a ton of blogs, taking classes, reading books, visiting the radiation department in a hospital.  It has been great!  I get in this mode where I binge on information.  I’ll read one article, which will set me off on a several hour journey where my mind is in overdrive and I can’t read fast enough to satisfy my now apparent hunger for information.

What I like even more about this is how much more fun and easy this is as an adult.  Let me explain by contrasting with a teenage mind.

You can find this in the brain research, or if you’re very introspective you can recall this about yourself.  As a teenager, when I learned something new it went into my brain as “this new thing.”  There were no connections between “this new thing” and what I’ve learned before, unless it was made explicit for me.  That could be from a teacher pointing out the connection, or a question leading me to that connection, or an experience.  Did you notice how “this new thing” has dink in common with “that old thing?”  Point is, as a teenager I would learn something new and LATER connect to previous knowledge.  (it’s pretty obvious that this is our jobs as teachers)

But as an adult, I don’t learn brand new things!  Everything I learn is a branch from something I know already.  Many times this is due to exploring something deeper based on my own curiosity, which will immediately make anything I learn a branch off previous knowledge.  I am made aware of this when I am talking to people at parties about what they do.  There is an awkward first minute or two where I am struggling to keep up, then I’ll ask or they’ll volunteer the connection.  “Well it’s similar to BLANK.”  “Oh!  I know about blank!  How is it different?”

In both cases, once I had a starting place, I could keep adding on new information.  Even as a teenager, if I had a starting place I could tack on a ton of new knowledge, so long as I followed the path I saw ahead.  As an adult the path forward a little clearer (i know where to look now) and I know where I am!  Everything has a connection, and I’m never more than an arm’s length from comfortable knowledge.

Okay, so about how being cool sucks.

Every time I’ve tried to be cool, it meant either proudly proclaiming a lack of knowledge (“what is dungeons and dragons”) or pretending to know something I didn’t (“yeah, they do sound like sonic youth mixed with velvet underground”).  And that makes it very difficult to learn what I want to learn.  If it’s not cool to learn too much about something, it’s like trying to go for a walk and having a cop stop you 1 block from your house in every direction.  Every time that I pretended that I knew something, I spent the entire time in an awkward space.  Like knowing that I’m in a pine forest, but not knowing if I’m in North America or Europe.

I want to communicate this problem in the clearest way possible to my students.  I feel like I had to actively fight the tendency of the school system to make me fit in, to make me learn what they wanted and not “waste my time” learning more.  And all of my classmates made it very uncool to geek-out and learn something really in depth.  But EVERYONE geeks-out on something.  Just because you geek-out on football and I geek-out on music and math doesn’t make you better than me.  It doesn’t make me smarter than you.

This is our* model for humans and learning.  Everyone wants to geek out on something.  So my job is to create a culture that removes most** of the inhibitions to geeking out.

our* – I can’t take all the credit, this has been an ongoing discussion with my wife

most** – well I don’t want everyone totally absorbed in their little world.

What does that final grade mean?

I have control on how a final grade is calculated – but not how it is used.

When my students leave my class, they’ll get one of five letters on their transcript.  It’s a secret code that is distilled from my teaching, their learning, their performance and the heavy thumb of my value system (do I count zeros, allow re-takes, grade homework?).

The really crazy part about this whole process is how that code gets shipped off to some college, scholarship, university or whatever.  They ship the code – but NOT THE KEY!  How crazy is that?

And to make it worse, they do their best to break the code based purely on assumptions!  Some people count a B in an AP class as more than an A in a regular class.  How do they know that?  I assume they treat all Algebra II grades as the same.  How do they know that?  They don’t.  It’s a huge assumption that leads to a loophole for students to game the system.  Some students have caught on to this, and they know it’s all about the letter grade until they finish their undergraduate degree.

I don’t think the problem is grade inflation – the problem is the grade is meaningless.

next – what this means for my grades

Educational perspective

I’m going to be working with a teaching candidate (student teacher) this coming year.  I’m already psyched, because the two conversations that we’ve had have left us both wondering where the time went.

As I automatically reflected on the second meeting, I realized that I’m already starting to, sort of…. groom him into my philosophy of education.  That sounds sort of sinister, but once I explain a bit more it might not.

Over the past two years of teaching and from psychology classes before that, I’ve come to a couple of tenets of dispositions that I think are essential to being a good teacher.

1)  Every student can get it, and getting it is only dependent on their previous experiences (inside and outside the classroom).

2)  People are logical creatures.  They may have false premises, or those premises may be simply emotions, but in the end what they are doing makes sense to them on some level.  I feel that this is critical for empathy.

3)  Every answer to any question is right on some level.  I mean even silence is an answer (it could be “I’m scared of you” or “I have two conflicting possibilities” or “I’m bored”)

3a)  People can tell when their incorrect answer doesn’t match up.  If they ask, point out what parts of their thinking are correct, and they will be able to identify the rest.  Let them know help is on offer, but do not help unless you are asked.  Respect them enough to let them think for themselves.

4)  I can control my behaviors.  Through these, and only through these can I do anything about my attitudes.  The same is true for everyone else in the world, so it’s pointless to talk about changing attitudes or intentions unless it is through changing behaviors.

5)  More important than relevance for getting students interested is success.  If they don’t feel successful on some level, then no amount of relevance is going to make them try your subject.

I know there are a few people already reading this blog.  What needs to be added to the list?  What needs to be clarified?  What are your fundamental dispositions?

thank you teaching for…

totally stolen from dan meyer.

Teaching has taught me when to be a leader, and to be extremely good at sussing out true motivations of behavior.

Outside of the classroom, I used to take charge simply for the sake of leading.  This has lead to some hostile situations.  Now I’m much better about hanging back, waiting until the moment when someone taking the lead is actually necessary, rather than simply what I want.  (not perfect, but much better)

Because of teaching education, I had a fairly deep theoretical background in adolescent psychology and counseling.  But in the classroom, I had to figure out something to do for the millions of times “i don’t know” comes up.  Now I’m pretty good at asking “is [blank] what’s really going on” without being a total dick about it.

There is plenty more, but time management definitely isn’t one of them yet.  Sorry teaching, but I’m good with the first two.