## Saturday, April 30, 2011

### Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

## Wednesday, April 27, 2011

### Factoring schmactoring.

I swear I titled a blog post this exact same way a few months ago because I was complaining that my precalc kids can't factor.

Right now we're factoring in Algebra 1.  It wasn't something that I was looking forward to; we've been struggling a lot lately with both behavior and material.  (I'm still trying to forget about the weeks we spent solving systems.  Sheer torture.)  Last week we talked only about GCFs, which I thought were going well until I graded half of the quizzes.  There were 4 - 5 kids with 100%+ (I had a couple of bonus problems) and everyone else was below a 50%.  A little disparity, anyone?

This week we've been factoring quadratics (just $x^{2}+bx+c$ ) using the X-box method.  We make an X to find the two values whose sum is b and product is c (have you seen the product-sum puzzles on ilovemath.org?) and then make a box to finish up the factoring.  I was worried that it was going to be too much writing for the kids but things seem to be going well.  Today's plan was to practice some more.

I wanted four of those five kids to do a little more today, knowing that they would get bored quickly with doing the X-boxes... and that's when they go crazy and drive me crazy.  (The fifth boy is super smart but is autistic and OCD.  I didn't want to push.)  so I wrote up a sheet with a combination of GCF and trinomials mixed up... and problems with both a GCF and then a factorable trinomial.  I had the chosen few work on the first couple of x-box problems with the rest of the class so I could make sure they were comfortable, then gave them the second sheet.  The amount of work and concentration that they showed that assignment was amazing!  The one boy who is constantly up and around and bugging everyone else got every problem done... with help.  I didn't have to tell him one time to sit and work and stop talking.

Him on the way out the door:  You know, I just get everything down and then you make it harder.
Me:  Yep.  Think about how much smarter you’re getting!
Him:  Think about how much harder I’m working.
Me:  Yes!
:)

I promised him tomorrow would be more of the same... and then I'm going to move them on to solving the equations that they're factoring!  Hopefully this will be the end of the behavior issues....

I can't believe that I almost forgot!  Got my new ipad today at school!  Woo hoo!  Now if any of you can tell me how to use it in class I'll be forever grateful :)  (Someone on twitter mentioned that I might be able to use it with geogebra... definitely need to figure that one out!)

## Tuesday, April 26, 2011

### Random stuff

1.   We started limits yesterday in precalc.  I'm taking it slowly - just did them graphically yesterday, numerically today.  It was actually kind of funny...  we were doing $\inline \lim_{x\rightarrow 2}(3x-2)$.  I set up a table so we could see the values from both the left side and the right side, and we ended up getting an answer of 4.  I could see wheels turning.  Finally one of the girls was like, "Can't we just plug it in?"  Yes!  Big sighs of relief ensued.  Of course, then I had to show them that everything's not pluggable.

(I found the latex editor here.)

2.  As we were discussing last night's assignment (checking out graphs and limits from them), one of the girls asked if we could watch Mean Girls in class.  After discovering that several of the kids have the movie at home, I said sure (at least the part where they reference limits!), we'll do that tomorrow.  They were all pretty excited until they realized that the juniors have an academic awards breakfast tomorrow during first period and won't be in class.  Then they got mad. :)  (Several asked if they could skip the breakfast!)

3.  I got my possible classes for next year from my department head yesterday.  Because of people moving from our school to the other school in the district, there's no one else that wants to teach the Honors Precalc.  (Can you imagine?!  It's my favorite!)  So it looks like I'll be teaching all three of those (down from 4 total this year, 2 are mine), 1 college prep Algebra 2, and I'm picking up the Honors Algebra 1.  I'm iffy about the Algebra 1 - I've taught the Honors class before, but the problem is that it's not really honors.  The "real" honors kids are now taking Algebra 1 in 7th grade.  The next level takes "Honors" Algebra 1 in 8th grade.  So these are kids whose parents want them in an honors class but weren't ready for Algebra 1 when the brightest of their class was.  Twice.  And they're freshmen.  Double whammy.  The good thing about the class is that I'm getting out of teaching the Integrated Algebra 1 (our general level) but unfortunately, that means my class size will go from 12 to 22-ish.  Yuck.

## Saturday, April 23, 2011

### Getting back to NCTM

I've avoided it long enough - I need to get back to summarizing my NCTM trip before I forget what all happened!

Session 2:  Trig Tricks You’ll Love (with Ann Coulson)

I got there late but was in time for sin/cos spaghetti, trig cut-ups, patty paper exponential folding, patty paper conic folding. The place was packed – I sat in the “gallery”.  People seemed to be enjoying the session, but I'd seen it all before.  I left early.

Session 3:   Supporting Productive Struggling in the Mathematics Classroom (with Susan May and Kathi Cook)

Problem:  Anxiety about Algebra 1  (Students have trouble transitioning to hs level, math)
Students don’t believe they can be successful
Academic Youth Development – help students work on concept skills and identity at the same time
Mathematically proficient students… make sense of problems and persevere in solving them.
How do you build students who persevere?
Students who persevere… understand the role of challenging tasks in learning.
Understand that setbacks can be a natural part of learning
Engage in self-monitoring
Learn from setbacks and struggles

Two views of intelligence:  fixed and malleable
Fixed:    (Their intelligence is their identity… whether good or bad)
Avoid challenges and seek easy successes
Desire to look smart at all costs
Worry about failure and question their ability
Malleable:  (Have control and can change their intelligence)
Pursue and enjoy challenges
Careless about “looking smart” and self-instruction
Engage in self-monitoring

Need to break the cycle of kids thinking they’re stuck.    (Carol Dweck , 1999)

Metacognitive strategies – internal dialogue prompts… chart in packet
Make a plan, Monitor work, Evaluate

Delicate balance between productive struggle and frustration… need to baby step kids into it.
The Bucket Problem  (How to split up 8 liters using only 3 liter and 5 liter containers)
(Use clip from Die Hard)
Strategies:  clarify question, trial and error (brute force), discuss with others

Why do we need persistent learners?  Because the problems get bigger.
Problem solving tool is intended to be used side-by-side when they’re working on a challenging task.

And then you move on to problems that might take several days to solve….
Miles of Tiles: The Value of Persistence
5 levels of problems (A, B, C, D, E)
Your role as a teacher is to help them be a problem solver, not to tell them the answers to the questions.
NOYCE Foundation

These are my (somewhat disjoined) notes from the session... there's a better summary at Lisa Henry's blog.

Session 4:  Fortifying the First Five (with Robert Gerver and Richard Sgroi)

Need some help getting your class started?  Check this out.  This was the one session I attended where the documents were online.  Isn't it nice?

Session 5:  Student Centered Projects to Enrich a Precalculus Class (with Masha Albrecht and Dan Plonsey)

These two had some great examples of student projects for precalc.  I need to get together a list of these and the ones from my last session to help me plan out my precalc course next year.  They gave a handout (but no link, darnit).

Session 6:  Conics with patty paper and the TI-Nspire  (don't know name of presenter)

Using the TI-Nspire to mimic the paper folding that is used to illustrate conics.  I was getting a little frustrated with it and left early.  I definitely need to see if I can borrow one from school for the summer (we have a new class set that no one knows how to use) and figure it out.

Session 7:  A Day in the Life of a Fractal (with Neil Cooperman)

zzzz.....  Oh, sorry about that.  I was expecting a lot more out of this session.  The speaker went through a lot of the upper-level math that creates fractals and examples of them.  What I was looking for was how I could use this in my classes (I'd just done something with the Koch Snowflake in class in regards to the geometric sequences formed) and he didn't hit that at all.  Fortunately, in the last 5 minutes his wife stood up and showed us a website she uses with her 6th grade classes to create fractals.  That saved the session from being a complete washout for me.  The website is Aros fractals.

Session 8:  The Unit Circle and Geogebra (with Zyad Bawatneh)

I'm wondering if this was the guy's first presentation... he seemed very unorganized, though he did have a flash drive to share his presentation/documents on (I'm glad that I'd taken my laptop and actually had a battery long enough to use it during the session!).  He went through the "making a sine graph out of the unit circle" process (that I do in class using string and spaghetti) using geogebra.  It was pretty cool and showed me that I need to spend some more time with geogebra this summer.

Session 9:  More Precalculus Projects (with Luajean Bryan)

GREAT ideas.  Need to summarize them for my own use.  We were given a book of her projects (including student work, rubrics, etc) and a disk with all of the files on it.  Very cool.

### Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

### Thanks!

I was just checking out my blog stats for the last year and was amazed at what I saw for the past year.

I realize that these numbers are nowhere near some of the blogs I read, but honestly, I'm still amazed that anyone actually reads this.  Thanks to those of you who take the time!

## Thursday, April 21, 2011

### Prom is in the air!

At the school where I teach, some of the kids go crazy in asking each other to prom (and answering those queries).  Sometimes they get the teachers involved.

A couple of days ago, one of my students from last year stopped in after school to ask if I would help her out in saying yes to prom.  Her date is in one of my classes this year.  Of course I agreed - I'd never want to stand in the way of young love!  (gag.)

She brought in a list of statement that she wanted me to say to the class.  I was to have them stand up and if the statement wasn't true for them they were to sit down.  It started out pretty general (you're taking precalculus; you're a boy;  you're a senior. . .) and after 7 or 8 of these we were left with only the intended recipient.  As the winner, he was given a 5 lb bag of flour with a note on it that said to look inside.  The girl had told me she thought he'd wait until he got home (because I didn't want a big floury mess) but the other kids urged him to open it up and check it out.  He headed up to the trash can (thank goodness) and slowly emptied the bag.  Nothing in there.

Today the girl came in with a pretty red flower and asked me to give it to him in class.  So as we were getting started, I told him that there'd been a mistake yesterday and he'd gotten the wrong flower (flour... get it?).  It had a note taped around the stem.

Overall, a cute idea.  I guess the days of just asking and saying yes are gone!

## Tuesday, April 19, 2011

### Super size paper

I'm going to divert from NCTM talk for a post... I'll get back to it, I promise!

Yesterday in Algebra 2 I wanted to take a day and give them a chance to ask questions.  We'd started exponential functions last week right before I left and then they had a couple of activities about them while I was gone Thurs/Friday.  I knew there would be some questions (that were hopefully cleared up in class!).

So after taking questions, I showed them a clip from Mythbusters where they dispell the myth that a piece of paper can only be folded seven times.  Here's what I showed.

Then I gave them all pieces of patty paper and had them start folding.  We looked at the number of layers and the surface area.  They all seemed to enjoy it while looking at the exponential functions formed.

Of course, then, there were a bunch of kids that wanted to give it a try.  On the clip they have a football-field size piece of paper.... I'm not sure where to get that!   Where did I go?  Twitter.  It seems as though a bunch of the kids are now on twitter, so a couple of them pulled out their phones and tweeted the question.  Almost immediately I had a response from @sarcasymptote, who said that his dad is local and works for a paper company.  He suggested that I contact them about it.  (I did... we'll see what happens!)

The funniest thing is that when the kids found out that I was on twitter, we started comparing numbers.  They were super jealous when they found out how many followers I have and how many tweets I've made.... they finally realized that I'm cooler than they are! :)

I also heard from @jamestanton, who did something like this with his kids in class, but they used a roll of toilet paper.  That could be an option if the kids are really interested... though we don't have a miles-long hallway to work with!

I just got response from Smart Papers!

Ms. Fouss,

future generations. Your class project sounds interesting.
What SMART Papers could give to you is a sheet of paper approximately
10ft' wide, the width of our paper machine. We can vary the length. How
long of sheet do you want?

Woo hoo!

## Sunday, April 17, 2011

### And we're off....

NCTM, Day 1

1st session:     Differentiating for Gifted Learners
Craig Russell
University of Illinois Laboratory high School

He started out by telling everyone that it was "National Poem in your Pocket" day and gave us a little green piece of cardstock with a poem called "Mathematical Mind" on it (written by a former student).  Ok....

NCLB has left behind the gifted students.
NAGC:  “Regular classroom curricula and instruction must be adapted, modified, or replaced to meet the unique needs of gifted learners.”
CCSS:  No references to what to do with gifted students.

What he does:  Daily group work; group work often differentiated; group assignments change at least once per unit; homework assignments include required and suggested problems, most include “alternative” problems (required for certain students if going to calc, etc.); assessments may be differentiated

How do you select the "gifted" students?
Students self-select for “alternative” homework
May be based on pre-test results  (determines groupings in classroom… ex. change focus from graphing linear equations to parametric equations, etc.)
Students may be “re-directed”, both on in-class work and on homework
Assessment: continual, with evidence for parents
“open questions” and “parallel tasks” allow for self-selection and re-direction

Differentiation basics:
1.  Product: gifted students may produce more sophisticated work with less structure in instructions
2.  Process:  Gifted students learn through exploration, problem solving
3.  Learning Environment: Different students have different learning styles and respond to different stimuli

1.  Product differentiation:
Student choice vs teacher choice (mandatory or suggested?) on projects
Amazing Race – Roadblock.  Choose one of two options.  (Create or Crititque)
Smaller-scale activities may be more open-ended for some students
Tests/quizzes may cover enriched curriculum
Amusement park: students choose which ride, with knowledge that some are tougher  (design ride… basic is roller coaster, pirate ship is easiest, double ferris wheel, scrambler (toughest) – rates of change, parametric eq, accel, vel

2.  Process differentiation:
Problem-based learning
More open-ended problems, less clearly defined
Different resource materials
More emphasis on “why” than on “what”

3.  Learning Environment Differentiation
Flexible furniture locations – grouped or individual
Whole class vs small group instruction
Time allocation:  “sweep” or “anchor” activity/exploration

4.  Content examples
What product might be expected:
Modular arithmetic
Absolute value inequalities
Multi-variable functions
3-d conic sections
Hyperbolic functions
Partial fractions
• Math forum pow
• QELP (from community college in nw) – environmental data sets keyed by math topic

Differentiation by unit:
We do this now:  What are the goals?  How much classroom time is devoted to each goal?  What lesson activities do you use?  How will learning be assessed?

We also need to think about:  With which of the unit goals are gifted students already comfortable?
What additional goals (enrichment? Acceleration?) related to this unit might be appropriate for gifted students?
Should (or could) the planned lesson activities be differentiated?

Challenges
Time
Materials (time?)
Peer/parent pressure
Balance:  time for pre-testing, de-emphasis on “routine”

Some lessons learned
Develop a “few” differentiated lessons per year
Study non-traditional textbooks:  COMAP, Core Plus, SIMMS, IMP, UCSMP, Discovering Geo, college texts (iffy?)
Use conferences to examine the literature
Look into NCTM Illuminations and math forum PoW
Find a partner

Rewards
"Differentiating an insipid curriculum results in a differentiated insipid curriculum." – Carol A Tomlinson

Thinking about how to differentiate for gifted students actally caused us to think about how we challenge all students, and we have tightened our curriculum overall as a result.

***************************************************************
Overall, I enjoyed this session - it gave me a lot to think about.  I'm not usually one who enjoys the philosophical-type talks, but this guy was entertaining and kept me interested.  I've tried to do a bit of differentiating in precalc this year by offering options for assignments, but there's obviously so much more I could do.  I'd like to incorporate pre-tests next year and differentiate based on those, but that's a big plan that will take a lot of work to pull together.

More to come:

Trig Tricks You’ll Love
Ann Coulson

Supporting Productive Struggling in the Mathematics Classroom
Susan May and Kathi Cook

Student Centered Projects to Enrich a Precalculus Class
Masha Albrecht and Dan Plonsey

And this was just from Thursday!

## Saturday, April 16, 2011

### Things I've Tagged (weekly)

• Http://commoncoretools.wordpress.com is doing the analysis of standards across grades and domains by CCSS writers. #nctm11

tags: nctm11

• tags: precalc sequences

Posted from Diigo. The rest of my favorite links are here.

## Friday, April 15, 2011

### Before I get in too deep...

I got home this afternoon from a fun two days at NCTM.  I have several (8? 9?) pages of notes and other worksheets to sort through before I post any thoughts, but I was just catching up on my google reader (it was around 480... ugh) and wanted to pass along a few items I read that are definitely sharable.

1. A  post at dy/dan by Dan Meyer referencing a clip from The Daily Show.  Just thought it would be fun to throw at my Algebra 1 kids and have them check the math.

2.  Kate Nowak at f(t) brought back Qbert (created by Jason Dyer last year in a response to a challenge thrown  out by Kate to create something fun for the binomial theorem).  I'll be covering the binomial theorem on Monday in precalc and it might be fun to use something like this with them.  That's assuming I find the time this weekend to check it out.

3.  A semester review project from Mimi at I Hope This Old Train Breaks Down (which I think I'll refer to now on as IHTOTBD because it takes me forever to type that :) ).  They're going to make a geometry magazine.... I thought that sounded cool!  I guess it's time to think about what I want to do for the kids to review this semester - that'll definitely be on my list.  A guy mentioned to me today at a session that last year he had the kids each pick a topic and they were to make a 5-8 minute presentation on it.  He said that most made videos and they LOVED it.  Another on my list.

4.  I don't know where she finds the time, but Julie Ruelbach just made her first imovie with her class singing their Equation of a Line song.  So cute.  So totally can't see my high schoolers even giving it a shot. :)

5.  I'm going to be hitting conics soon with my Algebra 2 kids and just saw this post on Square Root of Negative One Teach Math from Amy.  It talks about a deck of conics cards that she says really helped her kids understand (and like?) conics.  Definitely something to try!  (I just e-mailed the originator and asked for the files.)

One last thing before I crash.  I don't know what happened, but all of a sudden my google reader looks different.  It used to have the navigation stuff in a column on the left side of the screen.  While I was just reading, I guess I clicked something and that's gone.  Does anyone know where it went and/or how to fix it?

## Tuesday, April 12, 2011

### How much will it cost?

I'm heading off to Indy tomorrow after school and was wondering if the gas reimbursement money that school is going to give me will be enough to cover the cost of the gas for my car (which is sky-high right now around here...).

So I decided I'd let my Algebra 1 kids figure that out for me.

I googled directions to Indy from school to get a total number of miles one way (122).  I found the specs on my car to give them an average mpg, and I gave them a chart showing the price of gas at some local stations.

It was a fun little exercise, especially when they figured out that I'll get a nice little overage!  (I recall there being a nice mall in downtown Indianapolis....)

## Monday, April 11, 2011

### Change of plans!

I spent waaaaay too much time in class today having to go over arithmetic and geometric sequences.  Unfortunately, I didn't have time for mathematical induction (which I know I'll need lots of time for) so for probably the first time all year the kids didn't have an assignment to work on.  They were rather upset.... not.  I'm hoping that the cheering and applauding didn't disturb the classes around us!

I'm going to be out on Thursday and Friday for #nctm11, so not getting done what I wanted to today changes my plans.  Originally, I was going to do this:
Mon: Mathematical Induction
Tues: Review/practice
Weds: Binomial Theorem
Thurs/Fri: Review all (plus sequences) for quiz next week
 I found this picture on flickr... the caption said it's from a subway station in Portland.  Random.

Now what I'm thinking is this:
Mon: Sequences
Tues: Mathematical Induction
Weds: Review/practice
Thurs/Friday:  Exploration into Pascal's Triangle

This new version will probably be more fun for the kids (hopefully).  I'm going to give them some stuff about the history and patterns in Pascal's Triangle for Thursday then the application of it (expansion of binomials, combinations) on Friday.  I think this'll work.

When I decided to do this during my plan bell 2nd period today, I checked out my links on diigo as a starting point (they're here if you're interested).  It's so nice to have resources available!

## Saturday, April 9, 2011

### Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

## Friday, April 8, 2011

### What a week! And my new bird.

This has to have been one of the strangest weeks of the year (never mind that it's our first week back after spring break!).

1.  I was only here 3.5 days.  I had a sick boy at home on Tuesday and was out for a half day on Thursday because we had to grade the practice OGT that was given to the freshmen.  (Oh the fun.)  The good thing about the grading is that it usually only takes us as a department about an hour, but we're out the whole afternoon.  That gave us another 1.5 hours or so to catch up on work, chat, and keep tabs on the Reds score.

2.  My sub for both days was a retired teacher from school that's a peppy, fun, interesting lady.  The kids normally really enjoy having her here, and she likes being here.  She actually sat with my Algebra 1 kids both days and did the work with them.  She had a ball doing it (she told me) and they're still talking about how much they like her.  (And my Algebra 1 class was crazy amazing this week.  They were so good.... I asked them what was up with that and they told me it was because they like what we're working on now.  Freshmen.)

3.  I was looking over some Algebra 2 assignments (solving radical equations) this morning and noticed that a lot of the kids are making the same mistakes, so I pulled out an old favorite activity of mine that I definitely don't use enough.  I copied down a few problems, worked them out, and made copies so everyone had one. The key was that every problem had a mistake in it.... and of course they were mistakes that I was constantly seeing.  (Note to self:  error analysis is the way to go!!)  They got really frustrated with me as they were trying to find the mistakes because they didn't see what was wrong.... I'm hoping that I made some headway today!

4.  As I was grading those assignments, I noticed two that were identical.  (Ugh... more cheating.)  One of the boys involved was the first in the room, so I asked him about it.  He denied copying and said they'd worked together.  We had a little talk about the difference between the two (copying vs working together) and he continued to deny.  The other boy involved was in the room at this time and wouldn't answer the question to say that there was no copying involved.  Boy #1 sat in his seat and pouted the whole class.  I was surprised, though, that at the end of class (after everyone had left) he stopped at my desk to tell me that I was right;  he'd copied and he was sorry.  Said he just gets so caught up in the moment that he lies and then regrets it later.  I was really amazed at the maturity of that and gave him the opportunity to do the assignment over the weekend.  Hopefully he won't do that again to me.

5.  (This just happened as I was typing)  One of our math teachers is going to the other high school in our district next year to teach because of different cuts that have occurred.  I have her daughter this year in Honors Precalc.  I know the daughter has enjoyed having her mom here and is bummed that mom won't be here for her senior year.  The daughter just came into my room offering me presents - either salt & pepper shakers or a foam bird that she'd made in an art class in exchange for being her "mommy" next year.  Isn't that sweet?  I was going to offer my services anyway (though I said I'd stop short of lending money because I never have any) but thought it was cool that she asked. :)    (I chose the bird, obviously.)

## Wednesday, April 6, 2011

### duh.

Student after returning from missing 2 days:  "What did I miss?"

Me: "Nothing.  We just sat here and waited for you to come back."

Student:  "Really?"

Duh.

(P.S. - If you don't "get" twitter or think it's dumb, check this out.)

## Saturday, April 2, 2011

### Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

### Hi ho! Hi ho! It's back to work I go.

Don't you think that the week of spring break is the quickest one all year?  (Unless it's winter break, anyway.)

I didn't have a whole lot planned for break except for a 2-day vacation from my children.  Unfortunately, my mom got sick and sent the kids home early.  (She's actually still in the hospital but is expected to go home on Monday, thank goodness.)

I did a little bit of work while I was home.  In my Integrated Algebra 1 class we're going to start factoring soon... and I'm not looking forward to it.  At this point, the only thing I'm looking forward to in that class is June 3rd.  Is that horrible?  I'll keep going and try to keep as peppy as I can and find stuff that they might actually enjoy doing, but they're dragging me down....

In precalc we're going to do a little bit of sequences and series then jump into limits.  It's been several years since I've had the opportunity to get to limits, so I was doing some searching the other day to see if I could find anything interesting to at least intro them.  (They'll get the boring version next year.  Oops.  Did I say that?)  I had some help from @mrhodotnet, @samjshah, and @dansmath (in my comments here).  Still trying to piece things together.

There was a conversation (on twitter, of course) about what you expect students to know when they take a certain class.  For instance, I would expect anyone entering Algebra 1 to be able to add, subtract, multiply, and divide numbers (like fractions, negatives, etc).  With my class this year that was a dumb dumb dumb assumption.  At this point in the year I make sure they all have calculators; they can usually do the algebra, it's the adding and subtracting that messes them up.  Julie put a request on her blog for topics that she called "Math's Greatest Hits".... what do you think they should know?

After my frustration in precalc earlier this year about them not being able to factor (see here and here) I made up a list of all of the skills I would expect my students to have when starting out the year.  I gave a copy to the Honors Algebra 2 teachers who would be sending kids my way.  My plan is to quiz them in the first week of school on some of those skills and if need be, get them reviewing on their own.  Here's my version (if you have any suggestions, please let me know!):

Precalc skills