Monday, December 31, 2012

Great Movies

I was just thinking about some great movies that I like to show in my classroom.  My favorites are:

Stand and Deliver

October Sky

The Freedom Writers

Pursuit of Happyness

The Blind Side


Notice a theme?  They're all based on a true story.

What are your favorites?

Wednesday, December 26, 2012

Saturday, December 22, 2012

Door Decorating Contest


This is my entry in our school's door decorating contest.  Wait until you see next year!

Thursday, December 20, 2012

Shifts in Classroom Practice - Stepping Out Of My Comfort Zone

In my department, we have PLCs (Professional Learning Community Meetings) lead my an outside group called PARLO.  We meet once a month and sometimes our coach assigns us something for the next meeting.

This past month we have been given the assignment of attempting to make a shift in our classroom:  "From mathematical authority coming from the teacher or textbook toward mathematical authority coming from sound student reasoning."

I don't know about you, but I'm hurting here.  If you read my last post about the real world sucking, this is right up there with that.  I'm one of those people, who needs (I mean NEEDS) validation.  So, in my classroom there are my students who want validation and have always received validation, and there's me who wants to give validation.

So, I need help with my assignment here.  I can't wrap my head around this and could use some advice.

My ideas so far:

1) Students should try to make an educated guess right after reading a problem.  This way when they finish, they can validate their answer on their own.

2) Students can look over each other's work and offer comments and advice.


Perhaps this assignment was made for me.  We don't grow unless we step out of our comfort zone.



That's all I have.  Any thoughts?  What does this shift mean to you?  Do you do this in your classroom?  How did the students respond?





Friday, December 14, 2012

The Real World Sucks

Yesterday I finally did my own 3-act math task with the students.  We have been studying linear programming and this past summer, my son and I created a little movie to help with this topic.

Here is act 1:


And act 2:





Finally, act 3:




The First Thing I Noticed:

While walking around to see how the students were doing, I found one of the students crying.  She was upset because the answer didn't come easily to her.  A nearby student was trying to help her make sense of the problem and go over step-by-step where she may have gone wrong.  

At the end of class the girl came up to me to talk about the problem.  It really frustrated her that the work didn't come easily, since all the previous problems we did in class on this topic did.  First she thought that maybe it was because the information was given in photos rather than words.  She walked away and a few seconds later came back and declared that she didn't eat a good lunch and that could have contributed to the problem.  She walked away again only to return and said, "I know what the problem was.  I didn't know what the problem was asking."  

Ah-ha!  My response:  "In real life, we don't always know what the question is."  

To many of my students, especially the college prep students, math is this neat, tidy, little box of rules and procedures.  The questions are clear, the work is precise, and the answer is solid.  Once we step out of this little box of perfection, it gets frustrating.  

I like to escape from the real world once in a while to a nice long math problem (you thought I was going to say bath, didn't you?).  The joke in my family is that to keep my mind off of the pain while in labor, my husband would give me math problems to do in my head.  Okay, that's not a joke.  


The Second Thing I Noticed:

When I played the third act, no one was surprised.  You have all seen Dan Meyer's videos where the students watch the third act and there are oh's and ah's.  Not here.  They didn't even need to see the third act.  The problem with this 3-act math task is that it's too perfect.  Life isn't perfect.  



I think that I will keep this 3-act math task.  I believe it is a nice stepping stone into more life-like problems.  



Tuesday, December 11, 2012

No Seating Chart Update

I haven't updated you on my lack of a seating chart since the beginning of the school year, and I think it's about time.  You can read the original post here.

I don't have a seating chart for any of my classes.  Nope.  I have class lists for substitutes, but that's it.  What's the point anyway?  The students think that it's funny to switch seats on a substitute teacher, so then a seating chart is useless.

I started the year with seating activities where the students would have to work together in order to find their seats.  Things like sitting alphabetically or by height.  It was fun, the students were engaged and working together.  Everyday before they came into the classroom, I would write the directions on the board.

My intentions were to do this the first week, so that I would remember the students faces rather than their desks.  One day everything changed, a student walked into the room, immediately looked at the board and asked, "What are we doing today?"  I remember wishing that the students would do this with my bell ringers.  All they would do was sit in their seat and ignore the warm-up problems.  So, I put the two ideas together and no one has ignored the problems to date.

As the students walk into the room, I hand them an index card with a problem on it.  The students need to answer the problem in order to find their seat.  I didn't think I would last this long with this idea, but a few things are keeping me going.  The obvious, the students are finally doing the bell ringers without begin begged.  Also, once I make a set of cards, I can use them over and over because the chances of a students getting the same problem twice are rather small.

The types of cards that I have are mostly multiple choice in order to prepare for the state tests.  I write on the board that students are to sit in row 1 if their answer is A, 2 if B, etc.  I sometimes instruct the students to get into groups so that each group has an A, B, C, and D.

I also have cards where the answers are an integer from 1 - 24 and then the student sits in the corresponding seat.  OR if I have 24 students, I will tell them they need to sit in groups of four so that the sum of their answer is 50.

There are my logic puzzle cards.  I try to find logic puzzles with 3-4 clues.  Each clue is written on an index card and students need to create a group making sure they have all the clues within their group.

A few things I like about this idea are the flexibility and control that the students still have with this arrangement.  If a students gets an answer of A and has to sit in the first row, he can sit in the front or the back of the row.  And with groups, the students still have a little control over which group they form.  I may say they all have to have different clues, but they have some say in it too.

I still have some students who complain, but I'd have that regardless.  At least I have cooperation.  I will work on the complaining next.

Wednesday, December 5, 2012

Sabotage

I have this game in mind, but there's something missing.

I call the game SABOTAGE.  The game helps students to practice solving linear equations.

Download the game and instructions here.

Here is a quick rundown of the game:

Each team is given an equation that is written on the board, 4 operation cards, and 5 number cards.

On each turn the team uses one of their operation cards along with a number card to get one of the equations closer to being solved.

When an equation is finally solved the scoring goes as follows.  If x is negative, the team that "owns" that equation will get that many points.  If x is positive, then the points (value of x) is split between the team that solved the equation and the team that owns the equation.
For example, suppose that team A solves team D's equation and x = -6.  That means that team D loses 6 points.  And suppose that team B solves team C's equation and x = 3.  That means that both team B and C will receive 1.5 points.

Initially, I told the students that they could work to solve equations or sabotage equations.  What happened was a bunch of sabotaging and only one equation was solved the entire period.  So, I changed the rule so that a team must "help" and equation if possible.  If they cannot "help" an equation, then they may sabotage.  What do you think?  Or should I change it so that if they cannot "help" an equation, then they may forfeit their turn to trade in cards?

I'll try play testing again and see what happens.

Your thoughts and suggestions are MORE than welcome.

Monday, December 3, 2012

Slope Christmas Tree


This is my classroom Christmas tree, totally decorated by the students.  My Algebra 1B students decorated it using slope.  I created two types of ornaments where students use slope to create the them.   The paper chains are created by solving linear equations.  

The tree is a Walmart special $20!!


Saturday, December 1, 2012

Assumptions and Graphing Lines

In our state (Pennsylvania), we are gearing up for the first round of state tests which are next week.  Yikes!  Right now our state is switching to only an Algebra 1 exam for high school math.  Between classes a few of my colleagues and I were discussing the tests and how we were going to spend our class time the last two days before the exams begin.  We had mentioned skipping a review in classes like Calculus and Pre-Calculus.  After all, it's only an Algebra 1 exam.  But, we backtracked quickly.  It has happened in the past where a Calculus student failed the exam!  Algebra 1!

I teach Pre-Calculus and here are some assumptions that I had that were wrong!

1) Students can order numbers when they are given in different forms, like this.


What I found was that students didn't realize they needed to convert all the numbers to the same form (decimal) in order to compare.  They thought they should know just by looking at them, and of course felt stupid when they couldn't.   Some students didn't know how to convert the numbers to decimals even with a calculator.


2) If students can factor, then they can simplify a rational expression like this. 


In problems like this, students are looking to cancel individual terms rather than factor then cancel.


3) In my Algebra 1 class:  If I teach students how to find slope given two ordered pairs, then they can find slope given a graph.  

Again, I discovered that students aren't comfortable with converting forms without instruction.  To take a graph and, on their own, find ordered pairs, then find the slope, was something they didn't think was "allowed".




This year I decided to teach graphing lines to my students a little differently based on these incorrect assumptions that I've been making year after year.  

First, I can't teach topics in isolation, I need to help students make connections between the methods of graphing.  I always assumed that students were making these connections because they were obvious to me, so they should be obvious to the students.  

I started teaching graphing of linear equations with tables.  To me, that seemed to be the easiest entry point into this topic to help the students feel comfortable with graphing.  Once students were proficient with this I asked them to start picking out patterns in their tables.  I encouraged them to keep their tables organized.  We discussed the change in y (delta y).  We discussed the change in x (delta x).  We looked for these numbers in the equation.  Low and behold, the students noticed that delta y over delta x was the fraction next to x in the equation (after we solved for y).  

Next, we went over how to graph by finding the intercepts.  We noticed that this was very similar to graphing with tables, except that we filled in two zeros in the table immediately (one for x and one for y).  Discussions on why to use zero were completed.

Now we're back to slope.  We know that we can find slope from a table and from an equation when it's in slope-intercept form.  What about other forms?  What if I give you two ordered pairs?  One student suggests putting those numbers in a table **Angels start singing**.  We discovered the slope formula.  Next I give them a graph and ask how we can find the slope.  Another student says, find two ordered pairs and use the slope formula  **An entire choir of angels sing**.  We discover rise over run.  

Helping students make connections is time consuming, but oh so worth it.