Pick a piece of candy!

I try to change seats often in my classes (every three weeks or so). Sometimes I choose their seats for them, but most of the time it is random.  I usually use a deck of cards (well, part thereof), kids pick a card when they walk in and all of the Aces, Twos, … sit together.

A few months ago, I for some reason had a lot of leftover candy. So I divided into groups. One of the five groups I created was this one:

First period, kids walked in, sat in their usual seats and began working on the warm-up. As they were working I walked around and asked each person to pick one piece of candy but not to eat it yet. There was a bit of grumbling about having to wait to eat the candy, but they played along.

You can see where this is going, right? I next announced, okay pack up your stuff and find all the other people with the same type and flavor candy. It was a nice change of pace from my usual “pick a card”.

So, I repeat the process second period.  I get to the first table, and the first cherub looks at the bowl and says “I think this is how we’re getting our new groups! There are only three or four pieces of each type.”

I neither confirmed nor denied that this was the reason for the candy. They then proceeded to shout out which one they were picking so their friends could grab the same kind. It was a bit chaotic for a few minutes, but they quickly settled down and refrained from eating their chosen piece of candy.

With an evil grin I then announced, “You guys figured it out! We’re forming new groups today. First thing you’ll need to do is pass your candy to the person on your right, then find everyone who has the same type and flavor of your current piece of candy and pick a table.”

A collective groan arose. Silly kids really thought they’d outsmart me.

Posted in General, teaching | Tagged | 4 Comments

Advice For New Teachers: Goals

Adding my (late) contribution to Letters to a First Year Teacher

To a new teacher,

As you plan for your first year, my advice to you is to have concrete goals — and very few of them.

Some of us began our first year with goals such as:

  • All of my students will love math!
  • My students will be excited, engaged, and enthralled every moment of every class period.

These are neither concrete nor realistic goals for a first year teacher. Going into my sixth year, I’m not sure if they are realistic goals for any teacher.

Not all of your students will walk in the door loving math. Nor will they leave with this love. This is okay. Hopefully some will learn to love it, some will learn to enjoy part of the process and the rest will learn that even if they don’t enjoy math, they can be good at it.

Engagement is a good goal. As is excitement. Every moment? Not so much. Planning effective lessons is hard. Really hard. The only way to this is to write, implement, reflect, revise (and sometimes the reflection leads you to simply scrap and start over again), then repeat.  You probably will not be very good at this your first year. You will have moments of good.  Examine those moments. Figure out what made them work and how you can build upon them.

Aside from not having lofty goals, don’t set too many goals. Do not tell yourself I’m going to … implement Standards Based Grading, write and use entrance and exit slips every day, write all of my curriculum from scratch, have my students journal about math, flip my classroom and make videos for every prep, ….

You’ll never be able to do it all let alone do it well. You will be exhausted (not that that won’t happen anyway). You will feel like a failure. Do not set yourself up for this.

Pick one or two or three things to focus upon doing well. Write down your goals. Decide in advance how you’ll know if your goal is met. Write this down too. Be willing to revise this. Throughout the year, reflect upon your progress. If necessary, revise your plan for meeting your goal.

Once you’ve written down your goals and the way in which you will measure your success in meeting them, figure out why these things are important enough to be your goals for the year. Knowing why you value them enough to implement them is important. Implementing something in your classroom because “everyone else” is doing it is not a good reason. Your goals should have meaning for you (and of course, your students).

So this summer, reflect, ponder, plan, and recharge. Start the school year refreshed with your goals in mind.

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Summer Prep: Progress

Next year I have three preps:  Honors Accelerated Advanced Algebra (sophomores, two sections), Honors Pre-Calculus (juniors, two sections), and what we’ll call Algebra I (freshmen, one section).

Pre-Calc is the only prep that isn’t new. I taught it last year and have a pretty good foundation.  Skill lists for each unit are good to go.  Unit Exams are in decent shape (AP style: Free Response and Multiple Choice, calculator and no calculator sections of each).  Last week our course alike team met and went through all the modified AP Calculus problems we have written thus far.  We decided which we’ll use and where. We each left with a couple of new questions to modify and will meet again in July to do more work with these.

What I still need to do for pre-calc:  Rewrite all of our individual skill assessments.

Advanced Algebra: This is somewhat of a new course.  Previously, our honors students began with Advanced Algebra as freshmen, then took Geometry, Pre-Calc, and AP Calc.  Last year we switched to Geometry as freshman.  The honors team met and reworked our plan for Advanced Algebra and Pre-Calc, to make it more of a two-year course.  We decided which topics would be taught in which course. So we have a lot of work to do on this “new” course. I’m excited that we will now be able to embed Geometry concepts into our problems.

What we have done:  decided on the order of the units, written skill lists for all of the first semester units. Began writing individual skill assessments.

What we still need to do: Write the final and unit exams for first semester. Write all of the individual skill assessments. Write modified-AP style problems. Make our supplemental materials. I wish we had enough time to begin working on second semester, but we’ll make time do that during the year.

Algebra I… for lack of a better name.  This will be our course for our ‘average’ level freshmen. This will be the first year we are not using IMP in this course (although much of what we have planned includes many of the activities from IMP1).  We’ll do some algebra, some geometry, and some prob/stats, using ACT’s College Readiness Standards as our framework.

What is already done:  breaking the course into units and rough outlining of the skills in each unit. We have more than a few workshop days scheduled in July during which we’ll get quite a lot of the work done for this “new” course. We already have a lot of materials written (we won’t be issuing textbooks).

What needs to be done: finalizing the skills lists… and then everything else. Organizing the materials we’ve already written (deciding what we’re keeping/modifying/trashing), writing the rest of our materials, writing unit/final exams. I am very very fortunate to have an incredibly strong team on this course.  We all worked together last year and do an incredible job of bouncing ideas off one another and dividing up tasks.

Writing this all down makes (part of) me regret not doing much work during the month of June. But only part of me. I really needed these past three weeks of … actual summer. Relaxing was very much needed. I haven’t had a stretch of time with so little that had to be done in a very very long time.  However, it is time to get back at it.

Posted in Math | Tagged | 2 Comments

End Behavior of Rational Functions

This is the activity I used a couple of months ago to help students investigate the end behavior of rational functions.

The second part of the activity (not shown) asks them complete three statements:

  1. If the degree of the numerator is greater than the degree of the denominator, then…
  2. If the degree of the numerator is equal to the degree of the denominator, then…
  3. If the degree of the numerator is less than the degree of the denominator, then …

I thought it worked rather well to help them understand why the three different cases occur. We were able to have great conversations about rates of growth. “Weird stuff happens in the middle, but in the long run, the bottom gets bigger faster, so the function goes to zero.”.  I like this approach much better than presenting the “rules” for the three cases and just asking them to use them.

The students conjectures were not a precisely worded as I would have liked. I think that when I use this next year, I’ll still include the conjectures in Part II. However I’m thinking of changing/adding another part that we’ll complete as a whole class where we formalize the wording together.

Any suggestions for improvement would be greatly appreciated!

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National Boards, Reflecting and Writing

Ever have a friend that you’ve thought about often, but somehow lost touch?  Things come up, you mean to call, but somehow… you don’t. This continues, then it gets to the point where it seems too awkward to call. And unless someone reaches out to make the first move, the friendship just … fades away.

That is kind of what happened with this blog.  I’d think about it, but somehow never got around to making the first move to write.  It has been a crazy year for me (but aren’t they all?)  My mom passed away on the first day of school and for the first month of school I was just trying to … survive. Writing was not high on my list of priorities. Then as I came out of my fog, I meant to write. But I didn’t.

Then someone reached out. I recently received an email asking why I had stopped blogging. This person didn’t blame. Didn’t accuse. She simply reached out. And somehow, I was ready to hear what she had to say and ready to write here.

Despite not posting here, I have been writing this year – for National Board Certification. It was a  stressful experience for me (but mostly because I procrastinated and didn’t begin writing as early as I should have). It was also an incredible learning experience.  I started “planning” for it last summer. The portfolio requires 4 entries — with very specific requirements and questions to address. These questions were in the back of my mind just about every day in every class.

I did manage to complete the portfolio and am scheduled to take the test on May 20th. I’ll find out late next fall if I “passed” or not. Either way, I am very glad I did it. I chose to try to become a National Board Certified Teacher as I wanted to focus upon exclusively upon my teaching this year. I finished my masters last summer and wasn’t ready to begin the next one, so National Board’s seemed like a good fit.

It was a good fit. I was forced to video tape my classes and critically examine my practice. “Entry 2: Instructional Analysis: Whole-Class Mathematical Discourse” and “Entry 3: Instructional Analysis: Small-Group Mathematical Collaborations” require one to submit two 15 minute video clips of a whole-class discussion and small group discussions respectively. The video were painful to watch. Even more frightening was asking someone else to watch them in order to edit my writing for each entry.

Despite the fear factor, taping myself and my students and then writing about it was a great learning opportunity. It forced me to examine the way I respond to student statements and questions. To examine the way I  foster peer-to-peer communication about mathematics. To examine how I respond to misconceptions. To examine every thing each student says or writes for evidence of mathematical understanding. To examine how my feedback helps to develop and refine each student’s understanding.

I wish I could say that I had begun taping early in the school year as I had planned. But I didn’t. I did however think about each class as if I had. I guess I was taping in my mind. And reflecting upon each class as if I were writing about it for my portfolio. I can’t say that I drastically changed any of my practices for this process. I did however become much, much more aware of each comment I made and how that comment helped (or hindered) student understanding.

The effect this process has had on me this year really hit home for me recently.  A week or so ago, one of the students in my class shared an alternate way of answering a problem involving ratios. In response to his method, another student said, “That was nice evidence of mathematical thinking. Thank you for sharing it with us.”

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The Ways We Learn

Recently I asked people to list five verbs that describe the way they learn. There were 25 responses (including my own).  The top four verbs reported were discuss (8), read (8),  experiment (7), and practice (7).

I wonder how the way(s) in which we each learn influences the way we each structure our classes.

I also wonder if I incorporate enough different modes into my own classes. While I try to structure each class so that there is individual, small group, and whole class work/discussion time, I’m not sure there is enough time given to individual work. Then again, I want them discussing their work with each other. I’m sure there is a good balance. I’m also sure I haven’t found it yet. Something to watch closely next year.

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There are approximately 1,059,000 high school teachers in the United States, according to a 2007 estimate.

There are approximately 90,000 members of NCTM.

Winter Kiss by mubblegum via Flicker CC-A-NC-ND 2.0

I have 87 people listed under my math teacher list on Twitter.

I have about 50 blogs listed in my “Math Teacher” folder of Google Reader.

While I value those I converse with on Twitter and what I learn from what y’all write, I have lately come to realize that my view of what “everybody” knows/has read is highly distorted.

Posted in General, Math | 11 Comments