Monday, August 15, 2011

First Days of School

Most of the people close to the teacher side of me would probably agree that classroom management is my biggest struggle.  Notice, I didn't say biggest "problem" because struggle is a better word for trials, failures, and successes I've found in my first 9 years of teaching.

In my ideal world, students respect me because they admire my content knowledge.  They are studious students because they want to attain knowledge.  Instead, I've learned that students respect me when I show concern and respect for them and build relationships.  But building relationships is such a broad topic, that I'll focus first on the things I can do or avoid doing during the first days of school.

Keep kids busy from bell to bell at the beginning.  Show them that we've got things to accomplish.  I saw great success with a class when, for the first week or two, they came in to find materials already on their desks.  They knew I meant business.
Use your personal sense of humor.  If that includes sarcasm, go for it, as long as students aren't the target of the humor.
Call out behaviors in front of the whole class.  Kneel down to address them, or take them to the hall if necessary.
Joke around with the jokesters.  It blurs the line so that neither of you know when the relationship got out of hand.
Poke fun at students.  Instead, poke fun at yourself.

I was once told by a principal that I needed to sit down with the class and establish a list of norms.  I tried and it failed miserably.  As I tried to find out what "setting norms" looks like, most techniques seemed to elementary, too artificial, and (worst of all) could probably be taken to a level of manipulation and terrorizing by students inclined to do so.  I did an opening activity with 8th graders once where they brainstormed what the teacher should/shouldn't do and what students should/shouldn't do.  Possible reasons for the chaos and failure that ensued?  Handing over power to 8th graders before any relationship had been established?  Whatever the reason, I found the following article, and it sounded much more like my style.

Are Classroom Rules Needed?
  • I love that the author spends the first weeks forming relationships and building a team atmosphere.  He actually makes more headway on the curriculum than the teachers who raise an eyebrow at the beginning.  A good class really does learn more and has fewer distractions.
  • He doesn't make a list of classroom rules.  He tells his students "I only create rules if we need to have them. We only have them in my classes if students can’t respect one another and me."
  • Once you know your students, you can address problems with questions like "“I know you’re better than this” or “I know you aren’t really acting like yourself".  You can't ask questions like that if you don't know your students.
  • When it is time for the "Come to Jesus" talk with a student, it may go like this:
Me: Why are you here?
Student: Because I have to take this class.
Me: Why do you have to take this class?
Student: ‘Cause it’s required to graduate.
Me: Why do you want to graduate?
Student: ‘Cause I want to get a good job.
Me: Why do you want a good job?
Student: ‘Cause I want to make money.
Me: Why do you want to make money?
Student: ‘Cause I want to buy stuff, and I want and to take care of my family.
Me: That’s your goal. That’s the dream. This class is not what you’re after — it’s the family and money. This is just a step on the way. What happens if you don’t complete this step?
Student: I don’t get to my goal.
Me: That’s your motivation. Close your eyes and picture the dream and think about that while you’re here. You don’t have to like me or the class, but you do want to reach your dream. Let’s do it together. I’m here to help you reach your dream, but I need you to help me, too.
  • I often have trouble finding the right wording during these talks, but this sounds like something that would fit in my comfort zone and be believable.

Part of our beginning-of-the-year PD is PBS (Positive Behavior Support).  I'm really hoping that what I hear gives me more ideas for building relationships and handling misbehavior.  I'm nervous that it will be another annoying acronym presented in a theoretical, feel-good way that doesn't transfer to teaching my students.

Saturday, August 6, 2011

Algebra 2 Intervention

I have the exciting opportunity to be one of the first teachers at my HS to lead Algebra 2 Intervention this coming year.  Another teacher is doing Algebra 1 intervention, and together, we will invent this new class which is designed to support students who have a likelihood of struggling in their math class.  Students are enrolled in intervention before the main class even begins.  I've decided to try to bring together all of my thoughts and ideas about the class here before I begin planning with my colleagues.

Personalized Computer Instruction
The district is shelling out a good chunk of money for a computer program called PLATO Learning that will be our resource for remediation on pre-requisite skills that individuals are lacking.

Having taught many of the students on my class list in 8th, 9th, and 10th grade, I know that building a relationship will be essential for having them buy in to the intervention class.  I want them to know that I am their coach, cheerleader, and fan.  And they are a team.  This will likely be slightly easier with the Algebra 2 kids than the Alg 1, which is possibly why I'm so eager to experience this new support class.

I know this class CANNOT be students sitting in front of their computer clicking away (most likely disinterested, possibly angry) for 50 minutes a day, 5 days a week.  In order to make sure I provide enough variety, I'd like to have a plan which is (necessarily) flexible based on the students needs.  A sample weekly plan is included below.

Weapons of Math Intervention
     Preteaching/Previewing  I've always preached to my students to spend 5 minutes previewing an upcoming section from the textbook.  I doubt anyone has taken my advice.  I see using this idea in the form of a rapid-fire intro to several upcoming lessons in their main class, including actual example problems.  The goal is not for them to come away from the session with any skills (an interesting concept for me!), but to build confidence and some vocabulary for the presentation of the "new" material in their main class.  *They have an advantage for likely the first time in their math career.*
     Journaling  Self-reflection is a main theme of many of the articles I've read on this topic.  I see the journal being used in a once-a-week, prompted writing session combined with short entries throughout the week.  Possible entries/prompts may include:
  •  Safe, opinion questions such as "Is it important in this day and age to be able to compute a 20% tip in your head?"
  • Reflection on homework, note-taking, or participation habits from the week
  • Reflection on what has helped in Intervention
  • One new thing you want to try next week, reflection on something new you tried since last time
  • Do this problem and explain your thinking step-by-step
  • Quickly jot down 3 things you caught during the Preview Lesson
  • Name one type of problem you feel confident about, one you need more practice on, and one you really don't understand.
     Grouping  Partners-of-the-week solve a warm-up problem from the curriculum together each day.  Small groups (halfs or thirds of the class) solve problems at the board while talking through their thinking (as the rest of the class does PLATO).
     Celebrating   Possibly a box where students can brag about successes, indicating whether they want their name shared or not.  On Fridays, have a "brag party" to share and celebrate with the class.  Noisemakers?  Snacks?  This is so stepping outside my box! 
     Skill Building  Explicit instruction on skills successful students possess (for use outside of math class too!).  For example: note-taking, test-taking, test anxiety fighters, study skills, homework skills, self-advocacy, class participation.
     Sentence Sense-Making  I prepare sentences such as "The discriminant of a quadratic function tells us how many real roots it has" and "Since 10 cubed is 1000, the common log of 1000 is 3".  Students rate each sentence on how much sense it makes to them.  I can pull small groups based on their answers to remediate.
     Correcting Errors  I make up a homework assignment completed by some fictitious and goofy-named kid.  Students must find the pre-determined number of errors on the paper.  Bonus "Packer Pride Points" for finding extras.

Weekly Sample Lesson Plan
Each day, a warm-up problem from the current curriculum.
Mondays: Review in the form of... "Tell me everything you know/remember about ________."  Brainstorming as someone records ideas/examples on the board.  PLATO for remaining time.
Tuesdays: Preview/Preteach, Journal, then PLATO
Wednesdays: PLATO, then Sentence Sense-Making
Thursdays: Small groups presenting problems at the board/PLATO
Fridays:  Celebrations, Correcting Errors, Skill-Building, weekly Journal entry

Other thoughts
I have a student teacher for the first semester.  This will make small groups so much easier!
The schedule will depend on what I learn about PLATO.  I have zero experience.  If it's a pain to get into the program and get started, I'll likely have 2-3 days per week for just PLATO.  I like that Friday is PLATO-free.  They'll probably welcome the break.
I don't want to give any time for homework from their main class.  It sends the message that they'll have unlimited time to get homework done, and that I'm there to make sure they get everything right.

Things I read that inspired my ideas
Teacher Interventions-To-Go Series, Intervention Strategies for Mathematics Teachers, Math Intervention at Cascade MS, Samantha Douglas - Give 100%?

Tuesday, June 14, 2011

Developing a Plan for a Proof - An Analogy

We begin by presenting a strategy game in which there is a key moment before winning where you have already won.  For example, Tic-tac-toe.
Get yourself set up with two possible wins.  Your opponent can only defend one of them, so you win.
But then we have to think of how to get yourself in that position.  There is definitely more than one way to get there.  One way might be more efficient in certain circumstances, but as long as the end goal is achieved, all methods are valid.

This type of thinking will (hopefully) get kids to think about intermediate steps on the way to the end of the proof, but always keeping the end in mind.  And help them to see that you must start with some sort of plan of how you could get to "win".

Hmm, maybe I could even present the discussion with an #anyqs following a heated competition...

I got this idea from a grad class discussion of what another grad student did in collaboration with a geometry teacher.  Bottom line, it's not my own idea, but I can't be sure of where it originated either!

A New Take on Assessment

Consider grading each problem on a test* on a scale from 0 to 4.  Not with a point for each step like I normally do, but more as a rubric ranging from
0  "blank or irrelevant"
1  "did something legit, but far from solution"
2  "going in the right direction, but didn't make it to target"
3  "essentially correct"
4  "completely correct"

I like it because it could be a quick way to assess students' work.  The rubric would be known to them.  They would know how far off from a correct solution they were without me having to necessarily indicate their mistake or misconception.

I don't like it because the overall test grade cannot be the total number of points earned out of total possible points.  This is because some problems are of higher difficulty than others.  So consider classifying the level of difficulty of each problem.  Could I then calculate a weighted average?  But would I weight a novel extension sort of problem twice as heavily as a standard knowledge/procedure-based problem?  Is that what I want the percentage to represent?  The jury is still out, but the ideas have me thinking!

*This post is a reflection on the grading practices of my professor Dr. Bill Martin when he taught at an International Baccalaureate school in India for a semester.

Thursday, May 26, 2011

Wednesday, May 18, 2011

Instantaneous Rate of Change

Ten days from the end of the school year, it is not only the students who have lost some focus.  But a good lesson introducing derivatives to my precalculus students today got me pumped up like it was the first quarter again!

Although I didn't start the day with this idea, it's going to be a permanent addition to my instruction!  I try introducing the idea of instantaneous rate of change by talking about police radar detectors and how they must be measuring split-second changes in distance and time to calculate speed.  Inevitably, this leads not to thoughts of derivatives, but to police, speed traps, and how to argue one's way out of a ticket.

Apparently my explanation got through to some students.  Student comments of speed being zero/zero sparked some interest since we just talked about limits and the indeterminate form.  It was one student's comment about instantaneous speed being like a photograph that really led me to this new approach.  Lately I've been following the #anyqs project on Twitter, and this was a natural extension.  Here's how it works:

Present the above picture, and ask if anyone has any questions.  The photo is supposed to be enticing enough that most students will have the same natural question.  I plan to take a picture of a car driving past a speed limit sign to further encourage "How fast is the car going?"  (Today, a bad drawing of a photo of a car on the board even did the trick.)

Some questions I'll ask to lead the question:  How do we normally calculate speed?  So what's the distance and the time in this picture?  So the speed is 0 divided by 0?  What is that... undefined?  Zero?  (A small discussion today of shutter-speed ensued, but nothing compared to the side conversations about getting pulled over.)

Then they get another picture of the same car taken a small period of time later.  Again, any questions?  What do you want to know?  They answered today that they wanted some landmarks.  One kid cut to the chase saying he just wanted the distance.  Or a distance reference (like Mythbusters) in the background.  I suggested that it'd be especially convenient if the cars were at mile-markers on the highway (not to scale!).  So we agreed the distance would be useful.  One boy wanted to know the time interval.  I took that opportunity to introduce the "delta t" notation, which they seemed very comfortable with from science class.

The whole thing was such a nice, intriguing discussion that a senior even commented that it was really a great example.  Of course, I gave credit to my student in the previous period who gave me the idea, and they were equally impressed with him.  For a 7th period class in late May with senioritis spreading rampantly to the juniors, it was an amazing discussion with students showing clear, innate understanding.  It brought me joy that they were excited to see elements of limits in an actual real-life concept.  Great period to end the day with!  On top of that, they even liked my Geometer's Sketchpad secant-turned-tangent line example I made.

So, a thank-you to Dan Meyer and the Twitter community for keeping my imagination fresh.  I realize this probably isn't a monumentally new approach to this lesson, but it was the first time it occurred to me, and it was pure gold!!

Monday, January 10, 2011

State of the Department Address

Our math department has taken a beating this year.  For the most part, it has been the individual battles that several of us have had to fight.  Parents are more demanding, administration is more demanding, students are more needy.  We all feel completely maxed out and can't imagine what more we can give, yet that's what is expected when students aren't doing well.  I chalk it up to either students being coddled too much in previous years or our society where values are changing.

It's hard for us to focus on the good.  The good students, the good lessons, the good parents.  It's even harder to reflect on improvement when we're constantly thinking of what parent is going to call next or whether administration backs us and appreciates what we try to do.

My professional goal this year is to balance my sarcastic personality and laid-back style with respect and order in the classroom.  I'm doing this by observing other teachers and making notes of specific things I take away.  The first teacher I observed did a lot of SMILING.  She let students tease her, but didn't tease back.  She spoke quickly and got down to business, yet it felt un-intimidating because of her happy demeanor.  I wonder if I can get to that point... When I'm always feeling a bit disorganized, behind, and over-worked, is it possible to keep a smile on my face?  Maybe I just need practice!

The new semester starts in 2 weeks.  Since my precalc class is only a semester course, I get a second round this year.  I also did both geometries last year, so I have hope for feeling organized, prepared, and on top of things.  I'm looking forward to the fresh start immensely.  I'm also looking forward to the time I have during the review and final exam weeks.