of mathematics and beauty

I love math

I really do. I think it represents a profound aspect of humanity that is both beautiful and surreal.

What I love even more is seeing that same excitement I feel reflected in my students, and also pushing them to proofs, because this, ultimately is what mathematics is about.

I had two students jump out of their chairs today when they discovered that the number 35 can be written as

17 + 18 = 35

and

2 + 3 + 4 + 5 + 6 + 7 + 8 = 35

Students were also excited by the fact that their peers hypothesis were either totally correct, or that there were some exceptions to the rule. (such as triples of consecutive sums add up only to an odd number.


Students today worked on a continuing problem from Friday. Here was the challenge:





One of the major conjectures students came up with today was the following:

An odd number plus an even number is always an odd number.

I asked them if they would bet 2 million dollars that this hypothesis was true. Some decided to renege on the answer, while others were more insistent. The next step in this is me asking them to prove it.


Here is the formal proof below for my mathematically inclined readers.

Conjecture: An odd number + an even number = odd number

Let k represent some natural number in the natural numbers set.
Let m represent some natural number in the natural number set.
Let n represent some natural number in the natural number set.

Therefore, we want to show the following:

(2k + 1) + 2m = 2n + 1

Proof:

By commutativity, 2k + 1 + 2m = 2k + 2m + 1 = 2 (k + m) + 1

Let n = k + m, such that n is a natural number in the natural numbers set.

Therefore, 2(k + m) + 1 = 2n + 1

By definition, 2n + 1 is an odd number. proof complete.

Thus, an odd number + an even number is ALWAYS an odd number.

Beautiful, elegant, and simple no?

In any case, this is where I want my students to head towards; the idea that there is truth and elegance in this world.

I strongly recommend this book:





It has really rich and insightful problems that can cater to a wide range of mathematical curricula.

I have found that updating grades is a lot easier when listening to this song.

today....

first brief glimpse of what my students deal with on the outside.

it ain't pretty.

and it makes me sad.

tomorrow I start advocating for them, one day at a time....

undermining bridges

Today would rate as a B - or translated into a 'meh'

Activity went okay. I did all the good utepy things you're supposed to when doing a group building activity:

- job roles for students
- clear expectations
- modeling positive and negative behavior
- clear worksheet with directions
- materials ready in advance to be passed out
- job helpers to pass out materials
- and it goes on....

however, this was all undermined by something very foolish and obvious. I did not explain that the job roles they were being given were IN ADDITION to the group discussion they were supposed to be having...

sigh*

well at least I've learned my lesson...and now will refine that idea for tomorrow.

I bravely look towards tomorrow with sniffles and a head cold.

plans have been made
photocopies need to be hurriedly rushed in the morning.
charts need to go up.
greetings, addresses, and the daily tumble begins.

triumphs and tedium

I am very exhausted this week, and have one more day to go still tomorrow.

It has been a week of realizations, battles, and brief moments of getting it right.

Too tired to type deeply, so I'll speak with pictures.

Here are some of the 'positives' for the week:


Group D's Hopes and Dreams. I need to put up Group E's and F's, but I am waiting for the imminent arrival of the SmartBoard and its subsequent placement before I tape up 60 more of these...


My very simple but effective rules for the classroom. To make it actually concrete as opposed to abstract we did the following activity below:



Students, in their study teams, received a packet of 'anecdotes' of behaviors I had seen last week, both positive and negative. They then arranged them according to category. This became quite powerful as there were some negative stories that fit into all three rules of being broken. Students realized that their actions affected more than themselves. (Of course, not everyone got this, but it was still a powerful exercise nonetheless)

This was a time-heavy activity to make with all the materials. I made envelopes of about 20-30 stories for group, 20 groups in total. At least two hours of prep time, but it was worth it, I feel.


We've started bar graphs and our graphing unit this week. Middle school girls apparently really like Chris Brown....so let's put him into mathematics eh?

I've also been purposely making mistakes on my graphs, so that I can ask students during share out what problems they are noticing about my graph. This is leading up to an activity where they look at different graphs to find errors....still working out the details on it however.....



Yay! I am using my math word wall, and used it to jump start Math Simon Says today. Tomorrow, they begin formally defining the words for themselves. Math Simon Says went well, despite some disruption and behavioral problems.

Okay....bed time

Sara

realizations for today

1. girls really like to chat. you might as well capitalize on it and do something constructive. Today, they did an activity in which they had to put together anecdotes with my classroom rules. Even though many groups were talking about a lot of different things, they definitely understood the idea at the end that if one of us chooses to be disruptive, it effects the whole community.

2. I feel a lot less scared, but definitely still overwhelmed. one step at a time. I am beginning to believe that I can actually do this teaching thing....


3. I am realizing that my transitions are terrible. What can I do to help fix this problem with a bunch of very loud girls? The problem is, is that it's hard for me to get them back together after a group activity. I use the hand raise signal, but I feel like there's already a rate of decay happening with its efficacy. Should I use music? a bell? lights? Janet's head tapping strategy? Or do I just stick with the hand raise. Help....


That is all.

Till tomorrow,

Sara

deep breath in.

Check:

1. The week is officially planned. We begin our intro unit on graphing and organization this week. I am hoping it goes well.
2. I am excited about incorporating Math Simon Says this Friday. Since we are doing graphing, I am planning on using horizontal arms for the x-axis, and vertical arms straight up as the y-axis. (so on and so forth)
3. Study teams of four have been made. They are not mixed ability, which is a new concept for me. Another teacher at the school has set her classroom up this way, so I am willing to give it a try to see if it works for me.
   
4. I am ready to start the math. Tomorrow's activity is kind of a precursor, where they put little anecdotes I created in the right rule. Tuesday is when the mathwork begins.
5. I have been at this since 2 p.m. today, and worked appx 4 -5 hours yesterday. I feel like that's alot...I am hoping once basic things are set up (like how to use Easy Grade Pro), I might be a lot more efficient with my time.
   

Okay. That's about it!

Sara

roller coasters

today was better....

how well we learn from our mistakes. I broke students off into groups systematically. My morning group was amazing!! They did the broken circles activity in almost complete silence, which was what my original expectation for them had been.

I have scrapped my plans for next week. I am beginning math content work and plan on emphasizing rules and routines, but I, and my students, feel a need to start the math.

Let's go!

Also, this is the comic I was referencing in my previous post to those that read my blog and were unaware of it. This is something I do want to discuss next week...Maybe the word 'suck' is not such a good choice however...

-- www.xkcd.com

it's truly amazing how one day can be absolutely great, and the next can be a total maelstrom.

I am disappointed both in myself as well as my students. The behavior today was truly awful, but in part, was due to my own faulty lesson planning.

Andrew, the Spanish teacher, next to me is full of teacher aphorisms, and the one he told me today has really been making me think.

'If you don't plan well, the kids plan the day for you'.

I think it all had to do with how I am breaking off students into groups. My room feels very small now, and I need to think of a better way to rearrange my seats, or think of some way where students can get into groups easily. It was too much chaos for a small activity.

I need to stop telling myself that I am a bad teacher, and start believing that I can do better than this.

all right. trying not to cry...

sara

laughter and better days

I decided to scrap my original plans for today, and instead work simply on having my students enjoy their day.

It went well! There were some minor issues, but by and large, talking about what has been working so far, and what they were having challenges about helped. We then went right into playing Statue.

I used my popsicle sticks that they had written their names on to pick students fairly. This also helped reinforce the idea of the right to pass. Many students elected to pass, but since we were playing the first time, I kind of knew this was going to happen.

This also lends itself to an idea I had about preconceptions. There were a lot of 'don't pick her! She's not funny!'

Next week, I am planning on giving out that comic I showed over the summer about girls being terrible at math.

We're going to talk about judgments, stereotypes and misconceptions, and how it relates to both girls in math, and how the girls themselves were basing their presumptions today playing Statue.

We'll see how effective it is, but I have a feeling that if I do it well, it will really be powerful.

In any case, tomorrow I am going to attempt Hopes and Dreams. We'll see how it goes.

Below are pictures of my ever-evolving classroom






Community jobs students will have eventually: Pass out person, hall leader, plant waterer, and journal distributor. I do not have lesson plans yet in how to begin incorporating these, and would love to hear suggestions about how you all are introducing job roles into the classroom. Please, please share!


Bathroom sign out, as arranged by color coded groups, and attached pen. yay to yarn.




Our very first activity involving Silent Birthday Line up with and without a bar graph structure. Girls had to figure out what was 'easier' to do. Brief lesson in how symbols around them can make life better....


I absolutely love this method. It eliminates all tedious complaints about not being picked fairly, and also lends itself to discussions about probability once we get to that point in math. huzzuh.

okay, hope all is well in the Midwest.

Back to planning I go,

Sara

before bedtime thoughts

realizations/thoughts/goals all melted into one giant fondue of pedagogy

1. I need to talk less
2. I need to enjoy this more
3. It is overwhelming. I have to realize this, and not panic.
4. I want my students to smile in my classroom
5. I want them to enjoy being there
6. I want them to get to know each other.

rethinking and refocusing plans for the week. I have rearranged seats. we'll see how it goes tomorrow.

pictures will be up soon, so people can see what structures I'm trying to get going.

Goal for today:

To have a better day

and have my students have a better day too.

monday crazy monday

Today was a bit of chaos sprinkled with too much nonsense. 

Mondays are going to be rough on me. 

I have all three classes and a study clinic with entirely too many people in my class on the same day. 

Being a teacher means juggling 40 different objects that in turn are being juggled. 40 to the 40th power perhaps...

Can you tell that I'm a little flustered?

I was not on my game today. For example, I was expecting one group to come in during 2nd block, but another came in, instead. Of course they're on a completely different lesson, so I had to scramble to be ready for them. It wasn't too bad with this group, but I think my management is already shot to some degree. 

There are lots of very loud, overbearing girls in one of my groups that kind of take up alot of my attention. This worries me because I have many girls in the class, whom I still do not know what their voices sound like. How can I make their voices heard if I am constantly having to ask girls to quiet down? I came up with a signal for one of my especially loud girls today. She gets two signals before I call her out on a behavior. We'll see if that works for her, or if I need to try something else. 

I am eager just to get into the mathematics, but I know I have to calm myself down a little. This week is a continuation of socialization, rules, routines, and the creation of their hopes and dreams. I have a feeling that content work will start next week, but I am not sure honestly if all of my plans this week will happen. 

I only got through half of my lesson today. However, it went really well. It involved a puzzle in which 4 circles are cut up into various pieces. Groups of 4 students have to put the circles together without talking. Other rules include no doing the puzzle for another student, or snatching etc. The girls really felt empowered doing this activity and I think it'll go well tomorrow with my other groups. 

I think I need to be a lot more hardline about management however, especially for one of my groups. 

There is so much more to say, but I'll wait until I can express it a little better. 

Hope all is well in Chicago,

Sara

I have no idea what to do for 45 minutes with a bunch of girls in study hall.

On the one hand, the idea is quiet time to do work.

On the other hand, there is no work....

I tried to do a study habits mini-lesson last week using the multiple intelligence theory. That didn't go over too well.

Maybe I will just go with social-interaction skill games....tribbles anyone?

Sara

wanted:

pretty technology

This contraption looks amazing. too bad I can't afford it right now.

Product Description:

NeatReceipts Mobile Scanner and Digital Filing System for Mac (White)

Scan in documents to:

• Create searchable PDFs
• Capture text that you can edit
• Organize documents into collections

Organize Your Information:

• Create separate libraries for multiple businesses, projects or time periods
• Organize documents by collections so you can keep relevant items organized together
• Create Smart Collections of receipts or documents based on specific criteria
• Import PDF copies of receipts and documents stored on your hard drive

How amazing if I could store all my student work digitally, and then burn onto a cd with the work they've done over the year. This would eliminate my propensity of losing work (which I have not done yet thankfully), and make everything so much more portable.

One can dream...

Back to grading diagnostic exams I go.

hark

the D.O.E. angels sing

"Thank you for your application to teach in New York City. We are pleased to inform you that upon reviewing your application, you are eligible to teach in our public schools. Congratulations!"

I believe all is well now in terms of my being able to teach here...

In other news, I am very lucky to be teaching at my school. We have a meeting structure specifically where I meet with my other math teachers. Thanks to talking to them, I now have an idea of how I'm going to have a homework plan, and what I am going to do about the hopes and dreams components I have planned for next week. The 8th grade math teacher suggested I have the girls create their hopes and dreams, but, instead of having my 7th graders create the rules, I have some explicitly in place for them. In turn, they figure out how their hopes and dreams relate to my rules.

of course...Now I need to figure out my rules, but I think I will follow the mantra of keeping it simple, but explicit.

Already, I am seeing the signs of 7th grade girldom: ipods, lip gloss, gum, lotion, sparkly things, etc....none of which I want in my classroom. Any ideas on a good way to make sure they don't bring these into my class?

Today went well for the most part. Study hall was somewhat of an issue, where many more girls showed up than I had a list for. Understandably, things will be somewhat confusing for the first week or two, but I'm hoping I can organize myself so that I can help my students get where they need to go. So far, I have kind of not done so well on that front.

I've been posting reminders and schedules for myself on the wall, replete with color coding. This has helped to some degree.

On a more positive note, I am doing a better job with names. I'll say that I have about 60 to 70 % of each class' names down, which is pretty good considering I am just not that good at it.

I think the handshake before entering my class has really helped out in this front.

What else..what else...Me Bags went well today, although I think when I do it again on Monday, I want to make it a lot clearer about what I expect when a girl is presenting her Me Bag. A rubric might be a good idea as well, for both the class and the presenter. (all of these ideas are just popping into my head right now of course)

There was a common thread of girls bringing in their childhood stuffed animals, pictures of family and friends, perfume that they like, etc.

There were some issues with girls not listening and being rude when a presenter was up there. I had a student share some really beautiful pictures that she had drawn about people in her life that had passed away. I thanked her for being brave, and had the class give her a round of applause. Of course, someone laughed sarcastically as soon as she was done, which was really not okay.

Ah...middle school. the fun never ends.

Hope everyone survived their first week okay,

Sara

wow. what a difference

What a difference structure makes.

I came home yesterday about to weep because of the sheer attitude I had gotten in one my classes. Joe comforted me to some degree, but I went to sleep with a heavy heart and not much confidence in my plans, and how successful I was going to be today.

but wow!

I had my girls line up before they were welcomed into my classroom. I took a page from Bob's post, and decided to give each girl a handshake and started greeting them by their names in an effort to learn them better.

They dutifully walked inside. One of the girls, whom I knew was going to be an issue, started having issues with me from the get go, but I finally moved her desk in a somewhat isolated spot, gave her a job where she could be a leader, thanked her, and again...change in attitude was pretty amazing.

I also introduced a time policy in which if my hand signal is not completely respected in 5 seconds, I put a tick mark on the board for the time they are taking from me. After 4 tick marks, I start giving out individual detentions. Again, this authority idea has taken these past few days of getting into, but actually doing it today and seeing what a difference it made in my classes has made me want to continue being strict.

Materials were ready in advance, so girls were good to go with all the various activities I had them do. In particular, the Silent Birthday Line up went really well. I loved the on the spot thinking and decision making I was seeing the girls do as they tried to find creative ways to line up according to birthdays without being able to talk. I was not as hardline as I could have been. (I had promised to have girls sit down if they chose to talk) but all in all it went really well. I had the girls give themselves a round of applause at the end of this activity. I could tell they were proud of themselves and I was proud too.

Most importantly, I was told today that I was 'mean'. Hooray! What a compliment, and I say that with all sincerity. When I asked my student what she meant, she stated that I was strict. Yes! Yes! Yes!

So lesson (re)learned for today: structure = happiness.

Now I am trying to figure out all the mounds of paperwork I have received and an organizational system that will actually help me keep track of my plethora of papers. any ideas would be really appreciated! The question being essentially, how do I keep track of three different classes, where one of the classes is CTT (most of my sp. ed students are in this one)

I have posted pictures below. I miss you guys.

Sara






















My as of yet, undecorated math wall. Hopefully, this year I will make good use of it.
















Today's Board, with the messy scrawl that I call my handwriting.

The girls really appreciated this I think. What was most amazing was that I got through everything except for the exit slip.
















I have posted every schedule up on the wall nearest to the door. Each of my groups can look at where they need to go instead of asking me thousands of times. I also have my own schedule up....which is coming in a lot more handy than I realized.

the first 48 hours

The first day of school was fraught with chaos and some disarray, but by and large went well. These first two days of middle school have been rather frenetic, but there have been some pros and cons that have ensued.

I am so full of today that I can hardly think about yesterday, but I will try my best.

8:10 - students enter their new building and we have our first morning meeting.

students are then dismissed and go off to various advisory rooms and group rooms. again, lots of chaos with girls not knowing which groups they're in. I received an updated class list the night before, so of course I was unable to tell girls which new groups they were in yesterday morning.

The morning was spent doing ice-breaking/social activities in which students introduced themselves and played a variety of games (think TRIBES amped up)

The next activity was where they set up expectations. I met one of my classes at that time, and I can already tell which students are going to vie for my attention this year. We set up the expectations by talking about mottos and slogans. The girls then briefly discussed what they expected of themselves, and what others expect of them.

This seemed a bit superficial to me, since the girls were simply not that vested in the discussion and also were meeting me for the first time, so I really can't say how well it went. There were no major disruptions so that was okay.

I have been working with the Spanish teacher next door in reinforcing behavior and proper line order. That is going to be worked on tomorrow as well. For now I am letting them line up in whatever order, but I wonder if I should structure it more by making them line up alphabetically. There are pros and cons to each...

Today was a bit more complicated.

• Lots of names to remember
• Several new girls showing up today that weren't there yesterday, which meant my seating arrangement is simply no longer applicable.
  
• One of my groups was especially rambunctious, and I had to pull two girls aside and have a brief discussion with them about their attitude and following directions.
  
• I did have the rambunctious group for appx 2 hours today, which was a bit too long imo.
  
• I finally got my act together with them, by having them line up by the door. Since they were not doing the lining up like I had asked, I had them sit down and try it again. They did it better that time, which basically showed that I need to be a lot stricter with them from the get go. (classic newbie teacher mistake I suppose)

My first impressions of this whole teaching thing:

• It is hard. very hard.
  
• I feel overwhelmed.
• There are parts I have enjoyed, which wasn't something I was expecting.
  
• New York is hard on you, especially on your feet.
  
• I need to find a way to take care of myself. (I've already skipped lunch two days in a row, and have been going to bed too late, and waking up entirely too early)
• There will always, always, be work but you need to know where the line you stop for the night is.
  
• I wish I had prepared more.
• It doesn't matter how much I have planned, because new information comes in everyday that changes your plans.
  
• I don't think I have control (obviously enough...since it's been two days of chaotic orientation), so I need a way to make it clear that I am in control)

and the list goes on ad infinitum.

I am trying to keep the small melodic voices of self-doubt at bay, but their tone is getting louder.