Big Changes coming to Geometry*

With the start of a new semester, and with the framework from and guidance of teachers more experienced than I, there will be big changes to my geometry classroom beginning next week.  I am both excited and nervous about these changes (like starting teaching all over again), and so I thought I would use the opportunity to share them with you.

Here is the big idea: Although you will never hear me deny the importance of geometry, as I believe the skills and mathematical content knowledge is essential for my students if they hope to to move forward in their mathematical endeavors, much less survive high school.  But there is a host of 21^st century skills which are also valuable for my students to learn as they move through high school.  These skills include:

• —  Critical thinking and problem-solving
• —  Collaboration across networks and leading by influence.
• —  Agility and adaptability.
• —  Initiative and entrepreneurialism
• —  Effective oral and written communication
• —  Accessing and analyzing information
• —  Curiosity and imagination

Now the challenge (which is by no means new challenge) becomes this: How do we teach the geometry content while paying heed to these underlying skills?  With this question in mind, I present a new structure to my mathematics classroom.

The (very general) schedule:

Monday: We will introduce a new task to our groups of students which my colleague and co-teacher has come to call BIPs (Big Important Problems).  These problems are complex, big-picture problems which will require students to use skills which they have not yet seen, much less mastered.  However, the students will also receive a packet of problems which guide them to the necessary skills which will allow them to solve the BIPs.  Students will have the opportunity to work in their groups to formulate a plan for modeling and solving their BIPs.

Tuesday-Thursday:  Students will be working in the school computer lab watching videos which present tutorials and solutions to their packet problems, reformulating their strategies on the current BIP, and compiling progress logs / clarifying questions which will help them move forward.  Groups of students will have consultations with me regarding their progress in the packet problems as well as the BIP of the week.

Friday: This is where the reveal is.  Groups will present their solution to the BIP and see if their solution matches the real-world data.  They will then be asked a few individual and group extension problems to further assess their understanding of the content.

There are a lot of moving pieces to this structure, and I am grateful for the work that teachers have put in to compiling the problems, creating the videos, and working out many of the the kinks over the course of the previous year.  I am also grateful for the opportunity to merge one of my (ridiculously small) classes with another teacher who used this structure last year.  I am sure I will undoubtedly meet my own challenges along the way, and have to make changes as I go, but that is part of the excitement.

I hope to write more of the nuances of this structure (such as what the problems are and what consultations and assessment looks like) as well as continue to reflect in blog form as things develop in class.  For now, next week is going to be a significant amount of norming of the students (especially the ones merging classes).

*Note: I am not the creator of much of the structure, nor the curriculum.  I owe this structure to the greatness that is my colleagues, and am merely doing what teachers do so well: stealing good ideas.

Good / Bad ways to address off task students

I was reading Jason’s blog the other day and I was struck with guilt by  something he said:

The downside (of new teacher blogs)  is I get that “parent whose daughter is going to be out past midnight for the first time” feeling when a new teacher goes more than a couple of weeks without posting.

Seeing as I haven’t posted almost a month, I thought I’d write to say that at the very least, I’m still here, still teaching, and still (at the very least) reading others blogs.

When I used to post I followed a general principle: regardless of whether org not anyone will ever see it, post as though the whole world is reading.  A coworker described first year teaching as drinking from a firehouse.  I’ve found that since becoming a teacher I have had a hard time turning down the pressure.  I have this fear that if I write a post everything would come pouring out, and much of what I tend to think about is not for the world wide web.

But I that doesn’t mean I haven’t been thinking about a lot of things, working on improving daily, trying new strategies and structures, and learning lots and lots and lots.  What I learned discovered most recently is that when I need to intervene on behavioral issues during a task, it’s much more effective to redirect the conversation towards the mathematics than directly address the behavior.

Good (task related questions):

• Have you read the problem?
• Have you drawn a diagram?
• Have you made a plan?
• Have you written an equation?
• Which problem are you on?
• What questions do you have about the problem?

Bad (behavior related directions):

• I need you to be focused/on task/working

What other strategies do you use to keep kids focused?

A Classroom For Next Year

[this post is about a project I have been working on for this summer.  If you would like to read more about it / join in, follow this link.]

Even though it’s the middle of summer, my job as a teacher seems to be unavoidable in my day to day life.  I’m not just talking about the unavoidable questions of “so what do you do for a living,” but the places my mind drifts to when I have nothing else to think about.  During silences in conversations, or when I close my eyes at the end of the day thoughts of my soon to be classroom are constantly filling my mind.  I am finding that years worth of warnings, suggestions, and advice are all bottle-necking at the brim of my consciousness and creating a gridlock keeping me from actually making progress towards my goals.  Luckily, in instances like these I find that I can always depend on the help from close friends and other teachers for guidance and support.  That is exactly what I have done with this issue, and hope to continue to do.

Over the past couple weeks I have worked with one of my closest friends from my credentialing program to write a comprehensive list of questions to try to answer about the classroom next year.  This includes the big dilemmas of teaching, the concrete rules, less concrete systems, and slightly vague norms of a classroom, as well as how to successfully implement such strategies inside the classroom.  We’ve included over fifty questions so far, and will most likely add more as we go.

Over the next few weeks (until the end of summer, and possibly beyond), I hope to answer these questions one by one.  Perhaps, by the end of the summer, I will have a fairly coherent vision of my classroom for the year.  At the very least I will be proactively doing something to fulfill such a vision.  I will have an outlet for my unquenchable educational mental meanderings.

But if there is one thing I’ve learned about unquenchable educational mental meanderings, they cannot take place in a vacuum (or at least those which do are of inferior quality when compared to the alternative).  The truth is that these questions do not get answered in a nutshell, but through conversations with differing viewpoints, more experienced teachers, and an abundance of ideas.  in the past I made a call for assistance. Here is what I was speaking of.  I hope that this will not just be helpful for me, but for anyone who struggles with specific features of their classroom.  I hope this site can become a forum for ideas and a testament to the holistic nature of group thought.  Otherwise it will become merely a road-map of my classroom (which is definitely not a bad thing).  I invite you to browse the site, read it’s aims, and hopefully partake in valuable discussions.

The Difference between Teaching & Graduate School + A Call for Assistance

I suppose that it would be a gross understatement to equate earning a master’s degree in education to beginning a career in teaching.  Even today, months before I begin my job, I am experiencing the glaring discrepancies between these two distinct stages of my life.

In recent days, I realize that I have made the mistake of trying to treat this career as I have treated my entry into my master’s program.  Although a parallel may exist between being accepted to a graduate program and receiving a job offer, the truth is that the responsibilities attached to the two decisions could not be more different.

After being accepted to a master’s program, I consciously worked to maintain as few expectations as possible.  I treated my new life as an interesting surprise, and I gladly handed my time and freedom to an educational institution.  The professors of my program described it as a well-oiled machine. I imagine a function machine in which the inputs were students and the outputs were teachers.  As an input, I was churned through the machine without having to focus my life decisions, or even worry about where it was going.  I made one decision, an acceptance, which essentially lasted me an entire year.

After accepting a job in April and completing my graduate program a week ago, I turned off my brain to education.  For a short time I stopped being a graduate student – or a student at all – and enjoyed my freedom.  I remember going to a Greek festival and feeling that I was getting away with something by not reading, writing, or reflecting.  I stopped reading educational theorists, I stopped thinking about school, and I stopped posting on this blog.  I needed a vacation from academic thought, I had the time to take it, and most importantly, I had the available distractions that make life so great; and so I took a week off.  I hold no regrets.

But I can’t just turn off my mind to my future.  The one decision to enroll in graduate school was, essentially, the only difficult decision I had to make.  Accepting a job was just the start of a long line of decisions.  After a vacation of thoughts about teaching, I am now ready to return to educational thinking.  And boy, are there a lot of thoughts to be had.

I have a huge amount of information on education floating around in my head right now – my graduate program has made sure of that.  I have a ton of experience inside the classroom, which has begun to give me the pedagogical tools, subtle skills, and essential practices that productive teachers need – my students have made sure of that.  I have quite a wealth of resources, support, talent, and information easily accessible – you, as the reader and commenter, have made sure of that.  So the challenge of accepting a job now becomes that of distilling down the huge amounts that I’ve learned about education and who I am as a teacher to realizing how exactly it all translates into a productive environment for student learning.

What has become apparent in my experiences as a teacher is that there are a number of essential practices and structures which make up the classroom.  Before setting foot in the classroom, I need to have a plan for all the systems I will use, from seating arrangements, to collecting and returning homework, giving assessments, monitoring absences and tardies, and dealing with students on a day to day basis.  I need to build the norms of my classroom (as well as develop strategies for reinforcing those norms); I need to figure out how I will ensure all students have the opportunity (and understand their obligation) to learn; I need to know what I will do when everything goes wrong.  I need to build my classroom before I begin to teach.

When I tell experienced teachers that I am beginning my first year as a math teacher, more often than not their advice is some form of “don’t reinvent the wheel.”  I have built a collection of strategies for dealing with each of these questions, but I expect that my inexperience has provided me with a very narrow scope of possible solutions.  A very close friend of mine had the idea to send out a “question of the day” to be discussed by a listserv of mathematics teachers.  I love this idea, as I cannot think of a better use of time than to contemplate and discuss with others how I will realistically deal with the problems and dilemmas of teaching.  However, why use a listserv when you can include the entire world.  With that, I call on you, the reader/commenter, to help me turn my ideas into a well-formed plan of action.  I hope to post the ideas I am wrestling with regarding questions about how to build a productive classroom.  Perhaps you can help me turn my hodge-podge set of disconnected, half-baked thoughts into a working classroom.

Moving: It’s like the mathematical process…

Since 2005 I have lived in two countries, four states, and fifteen different dwellings (I use the term dwelling so I can include the trailer in a church parking lot and the tent that I stayed in for two months).  I bring this up, because for the past week I have been preparing to move again.  This move is unique to me, as it is the first time I am going somewhere without explicit plans to leave again.  Although I have changed locations so many times, this move is by far the hardest relocation I have ever put myself through – it seems that when it rains, it pours.

But that is not what this post, nor this blog, is about.  As a mathematician (who can only think in analogies), I tend to equate everything to mathematics.  Such has been the motif for the past week and the focus of this post.

When I got here last Monday, nothing seemed to make sense.  I missed California… California was something I knew.  There, I could get around with relative ease; I rarely had to look at maps; I had friends and family and a life there.  Every day since I arrived here I have oscillated between thinking of this move as an adventure and wondering if I’ve made the biggest mistake of my life.  This past week I have felt more lost, confused, and alone than I have in as long as I can remember.

I can’t help but wonder if this is how my unconfident mathematics students feel when they walk into my classroom.  I feel safe with mathematics because it makes sense to me and I know how to navigate and control it.  But I don’t think that safety is the feeling commonly associated with my field of study.  I think that the general gut reaction to mathematics (at least when it comes to those whose response to me being a math teacher is “I suck at math”) is that of fear, confusion, and a general lack of control.  It’s not just a question of being bad at math, but being afraid of the mathematical wolverine - the new place outside of one’s comfort zone; an unexplored, dangerous landscape.

Allow me to provide an anecdote to my experience (and attempt to put a slightly more positive twist on this post).

One evening I had to get from where I was staying to a colleague’s house for dinner.  I had a plan to bring along a friend with a car, but in the spirit of this crazy week, my plans fell through.  With a vague idea of the general direction of where I wanted to go, and a basic understanding of the types of public transportation in the city, I set off towards my destination.  I rode buses in the wrong direction, took trains to trains to buses to dead ends, and walked miles when I probably could have gone feet.  But in the end, I made it to my goal.  I was confused most of the way, not sure if I what I was doing was right or wrong.  I didn’t even know what systems I was working in, what was allowed or not, what went where or how to master my own direction, but somehow, against all odds, I made it.

When I got to where I was going I still felt lost and confused, but I also felt a sense of power.  I had mastered a route from one place to another.  It wasn’t the fastest way, nor the cheapest, but it was a way – my way.  My domain was expanded as I could now freely move between two places.  This was the first time since arriving here that I felt some semblance of control of my life.  I still knew almost nothing about the city, but I knew I could learn and that I was getting better.

If I didn’t know public transportation existed I never could have made it the twenty miles to my destination, and attempting to walk there would have been like trying to solve trig functions on my fingers.  I understood the existence of public transportation, so, with enough effort, I could solve my problems.

I wonder how often students walk into a math classroom without an understanding of the rules of mathematics; How many students don’t even know that something exists to help them solve their problem – I bet even less understand the painful and frustrating process of mastering those tools.

I wonder how often we give students a goal when they don’t even know the system they are working in.  How often do we miss the forest for the trees? Miss the process for the destination? Miss the tools for the end product?

Navigating Chicago is like mathematics, not because it is built like a Cartesian coordinate system (with Northeast, Northwest, Southwest and Southeast  equivalent to quadrants one through four respectively), but because getting around doesn’t make sense until you have spent enough time fooling around, being lost, and screwing up.  Only through the arduous and painful process of making mistakes can one really understand how to navigate a new land, be it physical or mental.

An Arbitrary Collection of Books That I May or May Not Read

I don’t remember the exact date that I started blogging, but I do know that around now is my one year blogoversary (see? I can make up blogging words too!).  I haven’t really been keeping track, but the conditions right now seem to mimic what they were when I started.  For example, when I started, Riley Lark was hosting his first ever virtual conference.  Today we’ve come full circle.  Last year I didn’t have any experience, and therefore, little to say.  Perhaps I’ll be able to add my input in this year.

A couple weeks ago a friend received a gift card to a bookstore and a note that said “this is to take advantage of one of the best parts of teaching: summer reading.”  I recall an abundance of reading lists last year, but haven’t seen many pop up yet this year.  I’ve been working recently on my own list.  This summer I’m generally trying to avoid books about math and education, since that is what has consumed my life for the last twelve months (though they always end up creeping in).

It should be easy for me to create a reading list – my dad is a book dealer**, so I am inundated with books every time I go home.  Nonetheless, I can never seem to find a genre/writer/style/font face that I regularly enjoy.  Yesterday, with a laundry list of recommendations and an abundance of recommenders, I went with my dad on a run to the local thrift shops and picked up a number of books at various people’s recommendations.   I like this because I didn’t have to pay more than $1 for a single book.  On the flipside, I was at the mercy of what I could find in the unsorted piles of rejected books.

So after a day of hunting, I picked up a pile of books that might be worth reading…  And with that – Behold:

• Brave New World
• Forrest Gump
• Childhood’s End
• The Kite Runner
• The Millennium Problems
• The Collector
• Logicomix

And then there’s a few books that I was sort of looking for but couldn’t find:

• Stranger in a Strange Land
• The Brothers Karamazov (Pevear and Volokhonsky Translation)
• The Yiddish Policeman’s Union

And then there’s books that I know little about, but have been recommended since this post:

• Candide
• A Clockwork Orange
• The Moon Is a Harsh Mistress
• Crime and Punishment
• The Immortal Life of Henrietta Lacks?

I only vaguely know what most of these books are about.  If you read and liked/disliked any of these, or just have some advice/words of wisdom, let me know.  Feel free to tell me what’s not worth my time, or what’s a must read.  I’m just looking for books to enjoy, to think about, and to pass the time.

**For those who don’t know what a book dealer is, my dad goes to garage sales and book stores where he buys books at absurdly cheap prices.  He then turns around and sells them online for anywhere from $4 to $4000.

Reflections (or Lack Thereof)

A friend of mine pointed out to me yesterday that I seem to have fallen off the face of the blogosphere.  While I do still read peoples’ posts, it is true that I have not been posting or commenting as much as I used to.  What better way to illustrate this phenomena than with a graph?

Numbers don’t lie, but they rarely illustrate reasons why phenomena occur.  I have been asking myself recently why I haven’t posted much.  Do I have nothing to say? Definitely not that Am I lazy? Maybe a little, but I think we all are.  Am I burnt out on talking about teaching? I think I’m getting warmer.  Am I having to reflect on my teaching practice every waking hour for graduate school and not wanting to go home and continue to reflect on this blog? Bingo.

All I ever seem to do is reflect.  For PACT (the Performance Assessment for California Teachers) I had to teach a lesson, reflect on it daily, reflect on the assessment tools and the learning structures and the balance of procedural and conceptual.  I had to reflect on the process of writing my paper and write a summative reflection on all my reflections.  I wrote 93 pages of reflection for that assignment.  Now that that’s out of the way I need to reflect on the rest of the year (including my 93 page reflection).  Sometimes I wonder if graduate school is just reflections all the way down.

“But Zach,” you might say, “aren’t you all about the reflections?  Isn’t that the purpose of this blog?” and of course the answer is a resounding yes, but I enjoy a specific kind of reflection.  When I am required to spend pages upon pages answering questions such as “how have I learned to support all students in learning?” and “how have I developed as a professional educator?” I feel I am given a cookie cutter reflection template.  I don’t get to talk about the things I like to talk about or even ask the questions I want to ask.  I suppose I only like to reflect on that which I enjoy reflecting about (who woulda thunk it?).

To build off of Kate’s ideas, the questions I’m reflecting on don’t stem from my own curiosity; one might say I am being required to do “real” reflecting rather than “fun” reflecting.  I want to reflect on an amazing finance unit we gave; I want to brainstorm ideas on how I can actually build safe spaces in the classroom rather than talk about them; I want to talk about the amazing job offer I got and flesh out the details of how I am going to take on my own classroom next year.  But instead I am answering questions that all seem congeal into one mass of cookie cutter responses.

Here’s where I make Sean burst into Cornally-Hulk.  From a grade / masters degree / teaching credential standpoint, this blog is worthless.  From a pedagogical standpoint, this blog is one of my most valuable tools to becoming a professional educator.  Nonetheless, when I am faced with the option of completing a series of mind-numbing graded reflections versus reflecting on the things I want to think about, I will always acquiesce to the graded task.  If I didn’t, I wouldn’t be where I am today.  It’s ironic to be both a student and a teacher – to watch myself work to avoid subjugating my students to the things I personally despise.

If I were a stronger man I would take it all on.  But when my eyes burn from staring at a screen too long and the arthritis in my fingers rears it’s ugly head, all I can do is dream of a day when my reflections are unbridled – when I can be proud of, and want to share the things I write.