Wednesday, April 30, 2014

Day 148: Math in the Rain

Warning: This post contains a photo at the end with profanity.

Today was Act 2 of my lesson on angles, perception and distance.

On Monday, we talked about how the eyes work in terms of depth perception.  We didn't talk much about the calculation, but more about the concepts.  The discussion was excellent and I was VERY excited for today.

When students showed up to school today, they saw this:

Once we got started, I asked them about a problem we did last week that used angle measurements at two points to determine the height of Ayers Rock.  It was a complicated problem and required them to move out of their comfort zones.  I asked them to identify exactly how much information we were given in the problem.

S: "The angle from the one point, the angle from the other and the distance between the two points."
Me: "Ok, so if we had that information, we could, in theory, find the distance to an object, right?  It may be a complicated set-up, but we could do it."
S: "Yeah we could."

We talked about ways that you could create depth perception if you only had one eye.  One student suggested that you could move back and forth, looking at the angles that changes.

Me: "If I were going to do that, should I move a little bit, or a lot?"
S: "The more you move, the bigger the difference will be and it will be easier to calculate the distance."
Me: "So if I wanted to calculate the distance to something far away, should I use two points that are close together, like my eyes?"
S: "No, you should pick ones that are farther apart because the angle will be bigger and easier to see."

We did some extensions of this through diagrams, without numbers, on the board.

Me: "What if I wanted to actually do this? What if I wanted to find the distance of something far away.  What should I do?  What would I need?"
S: "I guess you would need two points, like your eyes, but further apart, the distance between them and the angles from the sticks to whatever you're going to measure."

So we did it!

I gave each pair of students a protractor and two sticks and we went outside.  I had brought my mallet so I could pound the sticks into the ground, but it was wet and soft enough that they were able to push the sticks in.

The directions were:

You're to pick two objects in the middle distance (further than your thumb, but closer than downtown Pittsburgh).  Find a good place to plant your dowels and measure the angles to one object at a time.  I will come around and measure the distances between the sticks for you while you measure the angles.

They were awesome!  There were a few groups who didn't quite get that they could leave the sticks in the ground for both objects as long as the object wasn't in the same line as the sticks, but overall, it went VERY well.  In 20 minutes, 28 students had gone outside, planted dowels, taken measurements, gathered data and returned to the classroom.

Did I mention that it was raining almost the entire time?

Me: "Great! Now show me how far away those objects were.  I want to see everything! Diagrams you used, calculations you made, everything.  If you're not sure how to set it up, talk to your partner and look at the Ayers Rock problem."
S: "I don't know how to set this up! What do I do?"
Me: "This is a problem solving activity. We talked about what you needed and that it would be enough information.  Use the resources you have to determine the distance.  Check your notes, experiment with different triangle set-ups.  It's a puzzle and you can do it!"

It was an amazing activity.  If I think about it, maybe I'll write it up all professional-like and charge the people a dollar and a half to see it.  Then I'll be rolling in dough!

Period 4/5 worked very well on the word problems with percent change.  Volunteers walked us through the problems step-by-step.  We had a very good back and forth discussions and had friendly interactions.

Period 8/9 came in rowdy and destructive.  Within 20 seconds of the start of the period, they had done this:

And they seemed genuinely confused as to why I was upset.  I assigned them to work independently on the next topic, simple interest.  While the introduction to this happened through discussion and examples in the other class, I wasn't able to push my annoyance and frustration away to stomach a conversation in this class.

The student who complained that I don't grade enough items once again did not complete his homework.

I'm going to take deep breaths and swim through the joy that my successful lesson brought me this morning and not let my pre-algebra class drag down my spirits.  Tomorrow is another day.

Warning: The following picture contains profanity and has been rated "Dull" by the Education Association of America

The following was written on my classroom door.  The paper is list of school-wide expectations.  Instead of taking the graffiti down, I decided to respond in an educational way.

Tuesday, April 29, 2014

Day 147: Testing...again

These tests never seem to end! At some point, I should put in the effort to calculate exactly how much instructional time is lost to standardized testing that provide no immediate feedback for students or teachers.  I know that I have missed my geometry class about 8% of the school year for testing and various activities.

Along those same lines, I just found out that a large portion of my Geometry class will not be in class on Thursday for a field trip.  I have yet to receive a list of how many and who will be attending. "They (the students) were supposed to tell you."

In pre-algebra, I asked a student to do a problem on the board and he insisted that he had no idea how and didn't want to.  I patiently egged him on and, once he realized I wasn't moving on, let me drag the answers out of him.  It was an interesting moment because he fought it every step of the way, but he clearly knew what was happening.

I wonder how much of student reluctance to do the work is laziness and how much is lack of confidence.  We frequently see students who are quite good at mathematical thinking and calculation who claim that they are terrible at it.  One of the girls in my class says that she hates math and she's terrible at it, but when she decides to put the effort in, she produces amazing results.

It's so frustrating to watch that happen, watch her do great work and at the same time say that she's terrible at it.  It's not modesty.  She honestly thinks that she's bad at math.

Yesterday in period 8/9, a student started yelling at me about how he wanted more graded items.  He wanted credit for the homework and classwork that he claimed he was doing.  So I gave them an assignment to work on for a grade.  When I checked it today, he hadn't done it.  When I asked him about it, he said that he had completed part of it and he should get full credit.

I just looked at him and he started yelling about how he didn't care.

I don't have any idea how to take them out of their situation and have them examine it as an outside observer.  I know that if it were someone else with this same problem, this student (and others) would recognize the fault and tell the other student that he or she was wrong.  I know this because it happens daily.  When this student started complaining, those around him told him he was wrong.

How do I get them to understand?  When he failed to complete the assignment for today, he yelled that it was my fault and that, again, he didn't care.

When you have toddlers, they will ask you to make something for lunch.  The conversation usually goes as follows:

Parent: "What would you like for lunch?"
Child: "I want peanut butter and jelly."
P: "Sounds good! I'll make you some peanut butter and jelly."

**A few minutes later**

P: "Here's your peanut butter and jelly!"
C: "I don't want that! I hate peanut butter and jelly and I hate you!"

Some days, teaching is this conversation writ large.

Perhaps this is normal for the age group, but it seems to me that the maturity of the students has been declining over the years.  I don't have idea how to combat this thinking.

Monday, April 28, 2014

Day 146: Perception and Perception

I spent the last week or so figuring out how I wanted to do the culminating lesson for the chapter on right triangles.  I received a TON of help from various math teachers around the internet, including Jen Silverman, Wendy MenardAudrey McLaren and Megan Schmidt for which I am extremely grateful.

I have the basic outline available for anyone who wants it.  This was a lesson in three parts, Act 1 of which was today.

My lead-in was my whiteboard drawing.  I told the geometry students that I wanted to talk about eyes.  I asked them about the different kinds of eyes they could think of.

Eventually, we were able to put them into two categories: side-facing and front-facing eyes.  We then started listing animals of each type and I asked them what those animals had in common, other than eye placement.  The students (faster than I had hoped) identified that, for the most part, animals with front-facing eyes were predators which those with side-facing eyes were prey.

We had a discussion about the advantages to each of these types.  The side-facing provided a view almost entirely around the animal, allowing it to see danger no matter where it originated.  But what are the advantages of front-facing?

S: "Depth perception!"

Sweet!  The discussion moved in to why predators need depth perception, but prey might not.  We talked about lions pouncing on prey and how, if they missed, they would go hungry.  Prey, however, only need to see danger and don't care much how far away it is.

Me: "What about people?  How are our eyes set?  Are we predators or prey?"

I had student hold up their thumbs in front of their faces and look at objects further away as they opened their eyes, one at a time.  We talked about what they saw and why.

S: "Each eye is seeing something slightly different so it looks like your thumb is moving when it isn't."

I had them hold up their thumbs and focus on a far away object, noticing that their image of their thumb was doubled and transparent.

After having them talk about their observations and theories, I asked them to draw diagrams of what each eye was seeing.  Then I told them about my weekend.

After doing a fair amount of yard work, building a raised bed for a garden, raking soil, moving rocks, I collapsed into a chair and began looking over my yard.  I noticed a tree stump at the top of my property.  I closed one eye and covered the stump with my thumb.  Then I opened that eye and closed the other, noting the movement of my thumb.  I estimated the angle between the stump and my thumb to be about 3.5 degrees (in reality, it was about 5.5).  Knowing the distance between my eyes and the distance from my face to my thumb, I was able to calculate the distance to the stump.

I told them about this, but it would be effective to show them.

Thanks to the brilliance and patience of Jen Silverman taking the time to show me how to use GeoGebra, we were able to develop an applet to demonstrate exactly this!

When I got to school this morning, I realized that GeoGebra wasn't installed on my laptop and I had forgotten to upload my applet to GeoGebratube, so I had to recreate it before the kids got there.

Jen is an amazing teacher and I am SUPER excited to learn more from her this coming Saturday!

I explained that in my messing around with the numbers, I discovered that my angle measurement was WAY off and, in order to accurately determine distance, it needed to be very precise, as in to the nearest 1/10 of a degree, not something that can be done without proper instrumentation.  As a result, I opted for this demonstration rather than a hands-on activity.

The students were deeply engaged and I could tell that they weren't sure where we were going with it to bring it back to math.  THAT will be in Act 2.  They will driving stakes into the ground and using those stakes (a much larger, further-spaced version of their eyes) to determine distances of objects outside (weather permitting.)

The original plan was for that to be tomorrow, but we have yet another round of standardized testing that will take up my entire geometry class.

Act 1 went VERY well and I'm glad that I at least made a basic list of the questions I wanted to ask.

Pre-algebra, however,...

Remember the AWESOME activity that we did on Friday? The one where all of the students were engaged and doing work?

In both classes, one group turned in a finished product.  Two other groups tried to turn something in, but it wasn't even half finished and I wouldn't accept it.

I talked to both classes about my frustration and, much to my exasperation, the students who are the most disruptive, least on task, least prepared, were the ones who claimed that I had a bad attitude.  I asked if they thought there might be a correlation between their behavior and my attitude towards them.  I asked them about specific times when they were on task, or at least not disturbing other students and they acknowledged that I never "get an attitude" with them at those times, but I still "get smart" with them.

I asked students who put in great, or even good effort and they thought that I didn't have an attitude.

Even as I'm typing this, I know I've written it before.

I told them how badly I didn't want to give up on them.  How much I didn't want to hand them worksheets and have them work silently.

I was interrupted by a girl who had been talking over me the entire time.  She asked me if I would please just teach.

It feels very much like watching my children playing roughly.  The older one will hit the younger one who will, of course, hit her back.  The older daughter then comes crying to me about her sister hit her.
"You hit her first."

Students come into my room being disruptive, rude, unprepared and unwilling to control themselves.  Then they are confused about why they are treated as though they are disruptive, rude, unprepared, and unwilling to control themselves.

I think period 4/5 understood where I was coming from, but I think it missed period 8/9 completely.

We have less than 35 days left and I want to make the best out of them.  I'm not sure that having these heart-to-hearts is the best use of my time.  The kids that are attentive to them always are and the ones who aren't are the ones who need it the most.

All in all, a great day in Geometry, a frustrating and tiring day in Per-algebra.

Friday, April 25, 2014

Day 145: A Great Week

A stray comment at the beginning of geometry about students smelling bad lead into an hour and a half long discussion about rape culture, gender roles and double standards.  I had been noticing more and more the way that the boys in my school treat the girls and vice versa and I don't like it.  We talked about, not individual biases or individual behavior, but how we view men and women as a society.  What we see as standards for beauty, manliness, appropriate conduct, objectification, etc. were all dissected and discussed.

I think that some parents and teachers might see the discussion as inappropriate for the age group and the math class, but I disagree on both counts.  My school doesn't have a comprehensive sex education program at the age when studies say it is more necessary.  It's also the age when gender roles are being solidified and emotions run high.

It was an excellent discussion and they asked great questions.  I felt that they were very receptive, joking when things were funny and serious when they were not.  I caught looks of agreement and even relief from several of the female students.

I have more thoughts about this, but they aren't fully formed yet.  I shall think on it some more.

When I covered an English class later in the day, several of my students told me how much they appreciate my class and how they really enjoy going (or at least aren't excited to leave.)  They said how I'm not like other teachers because I care about them and I'm interesting.

This was a class that is known for being rowdy and loud and unproductive.  During the time that I was watching them, they worked hard and well.  They didn't disrupt each other and they were kind.  I attribute this to the fact that I was the one covering the class and that I have spent the year building respectful and caring relationships with them.

Relationships are everything...

My pre-algebra class knocked it out of the park today and I will give all of the credit to Fawn Nguyen for the amazing activity that kept them engaged.  We are finishing up our unit on percent change with discount and mark-ups in stores.  I brought in the class set of iPads (upon the cart of which I would never ride down the hall, boogie board-style) and had them look up the prices of items at Target.  I told them that the person who got closest to $500 (after discount and tax) without going over would get a bunch of jelly beans.

In the 144 prior days, I have NEVER seen them work as hard or ask as great questions as they did today.

They worked SO hard, in fact, that I did something I almost never do: I extended the deadline.  Instead of being due at the end of the period, I let them take it home.  I made it very clear that it would be counted as a quiz grade and if they didn't think they could remember to bring it in, that maybe they should finish it.

I had one group hunt me down later in the day to turn their in.

They used the iPads responsibly and well.  I didn't have to ask a single kid to get off of games or music.  They were on task and engaged for the entire class.  Conversation may have wandered a bit into the realm of which gaming system was better, but it didn't hinder the work.  They were so engaged that half of the students didn't utilize the break at the halfway point.  They worked right through.

It was fantastic, except that half of period 8/9 left them on their desks and so will get a zero on Monday...

Clearly I need to hire Fawn to design all of my activities.

It always seems so random to try to figure out which activities will engage students and which will flop.  I think it's 100% possible that this exact activity would have failed horribly on another day.  So much of what we do is a reflection of things beyond our control.

I am incredibly grateful to Fawn for this amazing lesson that my kids loved.  I am grateful to my students for having an "on" day and being engaged.

This was a great week.  Now I'm REALLY going to buy a lottery ticket!

Thursday, April 24, 2014

Day 144: Buy A Lottery Ticket!

Why, yes! Math DOES own bunny slippers. You wanna fight about it??

I was really scared to come to school today.  I am wary when lessons go well because I'm always waiting for the other shoe to drop.  It's an awful feeling and I wish I could kick it.

I want to wake up in the morning and think "Man! Yesterday was awesome! I can't wait to push it forward today into something even better! I'm going to ride that momentum as far as it goes!"

I hate that I wake up and think "Man! Yesterday was awesome! I wish I could continue that momentum."

I deeply worry that many of my students think "I worked super hard yesterday! I'm done for the week."

I worry that they think this because I've heard them say it.

So today, riding on my own energy high from yesterday, and capitalizing on a large number of students out for various events, I kept my energy up and pushed forward.

And it worked!!

Geometry ended up being another stand-up comedy routine with some trig thrown in here and there.  I do feel badly about not covering as much content, but I think it's vital to build relationships with students and making my classroom a positive place for them to be a huge step in that direction.

There was a track meet at a neighboring school district today, so a large portion of my pre-algebra students were gone, making the class a very manageable size.  There were two students hitting each other right from the beginning and I had them both step outside the room until they calmed down. Once they returned, they were fairly productive.  I had to remove one of them again for instigating with other students, but another couple of minutes outside to think about his behavior and he was back to being awesome.  I need a time-out space...

Once we got into the lesson, we continued from where we were yesterday and talked more about percent of change.  I asked if any students had jobs and how much they made.  Donald works with his dad and gets paid $100 a week.

I set up the scenario that after a hard week of working, Donald gets his $100 and goes to McDonald's. He orders $4 worth of food.  A homeless man, after a day of begging, has made $10 and orders the same food as Donald.  Who is more effected by the amount of money spent?

We were able to draw back on the example yesterday where I took 1 jellybean from a student with 10 and 1 from a student with 2. We talked about how, even though Donald and the homeless man spent the same amount of money, that money had different value to each person.

I extended the example where, with his $100, Donald could choose between the $1 cheeseburger or the $2 double cheeseburger.  The students agreed that the burger he chose would have little or nothing to do with the price because how small a piece of his total it was, but for the homeless man, the piece would be much bigger and he would almost always make a decision based on price.  It was an excellent discussion and I was incredibly proud of the logical progress than many of the students displayed.

In period 8/9, however, I got about 15-20 minutes into the lesson before I had to remove several disruptive students and the ones remaining began arguing with me about the price of the burgers and the color ink I was using on the board.

When I said that the student was going to McDonald's, they started yelling about how they don't like McDonald's and they would rather go to Wendy's and they would order a chicken sandwich instead of a burger.

It annoyed me so greatly that I put myself in time-out.  When I cooled down and re-entered the learning space, I pulled up the practice problems that we got to in the last 5 minutes of the other class.  We spent the next 40 minutes working on those, grinding through the calculations and not having any application or higher purpose.

They were engaged.  They asked good procedural questions and I was able to branch out a little bit with multiple approaches to the problems.

I was disappointed at the lack of higher-level thinking, but satisfied with their level of engagement.  I will be content with what I was able to get out of them, regroup and attack again tomorrow.

I think they were able to sense that I was done messing around with them.  When I had brought myself back from time out, I was polite, kind and understanding, but not friendly.  They knew they had pushed me too far and they were excellent for the rest of the class.

I'll thank them tomorrow for their hard work and ask if maybe we could start that way instead of getting there after I get too pissed off to teach.  I think they will be receptive.

Bonus: Here is yesterday's picture that I forgot to take...

Wednesday, April 23, 2014

Day 143: Pointed Questions and Jelly Beans

Somehow, I forgot to take a picture of my whiteboard...

I HAD A VISITOR TODAY!!!!  My good friend, Jami, came to observe my classes!

In geometry, we continued our work of angles of depression and elevation.  I gave them a critical thinking problem that will be the lead-in to the astronomy project I want to do next week.

Kwan-Yong measures the angle of elevation from the ground to the top of Ayers Rock to be 15.85 degrees.  He walks 500 meters closer and measures the angle again, finding it to be 25.6 degrees.  How tall is the mountain?

I LOVE this problem because of the extensions we will use with it next week.  It was also a MUCH more difficult problem than we've done in that class.  It requires some lateral thinking and playing around with the numbers and trig functions.  Students need to be ok working with multiple equations at once and not getting an answer immediately.

I love this problem.

The pre-algebra classes started by going over the homework word problems (which no one did).  I sat in the back while I had students put the work and answers on the board.  I battered them with questions about why they set up the problems in the manner that they did and what each number represented in the problem.  When they finally got the end, my standard statement is "Great! Tell me what that answer means in the context of this problem."

S: "So X is equal to 7.1"
Me: "Great! Tell me what that means in the context of the problem. In a complete sentence, please."
S: "On a bill of $35.50, a 20% tip would be $7.10."

After we finished up the word problems, we started talking about percent error and percent change.

I put up an #Estimation180 problem from earlier in the year and asked the students to estimate the number of cheese balls in 6 containers.  I wrote my estimate of 4200 on board.  Then we looked at the answer, which was 4416.

Me: "Aw man! How far off was I?"
S: "216 off."
Me: "Would you say that's pretty close, or no?"
S: "Yeah, that's pretty close."

Then we looked at the one from today and made the estimate that the roll of quarters contained $226.  It actually had $10.

Me: "Aw man! How far off was I?"
S: "216 off."
Me: "Would you say that was pretty or no?"
S: "NO! That's SUPER far off!"
Me: "But wait! You just told me that being 216 off wasn't that far off?  Why was is close for the cheese balls but not for the quarters?"

When they didn't quite get where I wanted, I brought out my giant bag of jelly beans.

Me: "I've given 2 jelly beans to Anton and 10 to AJ.  I don't think that's fair, so I'll take some back."
**I ate one jelly bean from each kid**
Me: "So, I've taken 1 jelly bean from each of them.  That's fair, right?"
S: "No! You didn't take the same amount!"
Me: "But I did! I took one from each of them.  Isn't 1 jelly bean the same as 1 jelly bean? Why isn't that fair?"

We continued along this conversation until I got the response I wanted.

S: "1 jelly bean to Anton is worth more because you took half his jelly beans! It was a bigger percentage."

I was incredibly pleased with how this example worked to get them to understand the idea.  We continued it with the idea of grades.

Me: "In the first marking period, Niya got a 50% and Malik got a 70%.  In the second marking period, they both worked harder.  Niya brought her grade up to a 70% and Malik earned a 90%.  Who had the bigger improvement?"

There was an excellent discussion about how they both went up 20% and how that means they should have equal improvement.  So I asked about the jelly beans again.  This lead into a talk about percent of change.

The additional example that I used in period 8/9 was that if you were to give $1 to a homeless man and $1 to Bill Gates, who would appreciate it more.  I think more than the others, this extreme example helped to solidify the point I was trying to convey.

Period 4/5 was ON THE BALL today! They rocked every aspect of today's class and the participation was excellent.  Right before period 8/9, however, there was a huge fight right outside my room.  A situation that had been bubbling all day finally spilled over and I ended up dragging some girls apart.  It was very difficult to keep that last class where I needed them to be after that, but overall, they did very well, especially when I brought out the jelly beans.

My lesson from today: Teach Like You're At Seaworld!  Bribery will get you everywhere.

Knowing that there was the possibility of jelly beans, my students were much more likely to participate and do what I asked of them.  I was temped to dangle some jelly beans and see if they would balance a ball on their noses.

After we completed the 8 word problems, I asked a simple question:
Me: "What did I not see in any of these problems? What tactic was not used?"
S: "Cross-multiplication."
Me: "Did anyone even think to use it?"
S: **silence**

YES!!! One trick nixed! Tina would be so proud of me and I had Jami as a witness!

It was a great day with lessons that went well and interactions that I enjoyed.  It's a shame that it had to end with a fight...

Regardless, I'm so happy that Jami was able to join me and I look forward to hearing her reactions and thoughts.

Seriously, if you can get someone to spend a day in your class, watching what you do and being a part of your environment, do it.  Do it ASAP!

Tuesday, April 22, 2014

Day 142: Back To It!

My geometry class ended up being a talk about history that covered thousands of years and multiple civilizations.  We discussed the advances that the Japanese have made since the 1800's, the allegory of Godzilla, why the situation in the Ukraine is happening, and many other topics.

We did actually talk about geometry a bit, discussing angles of depression and elevation and how they relate to the activity that we completed on Wednesday.  They were highly engaged and asking good and important questions.

I frequently feel bad about the number of tangents that I take in this class.  Part of me is deeply concerned about the content and making sure it's all covered.  I worry that someone will walk into my class and fire me on the spot.  As absurd as that may be, I worry about it.  I worry that my students will go home, full of energy and enthusiasm and, in talking about class, give the impression that we aren't "doing math."

Being an "at-risk" district, everything we do focuses around test scores.  As a result, there is constant pressure to be covering content rather than skills.  I have justified my approach to the parents on multiple occasions and they have been on-board.

But I think something in my personality makes me constantly in fear of being fired.

Well, we hit content AND skills in pre-algebra.  I gave them a 4-question open-ended quiz on Wednesday.  I "graded" it on Sunday and it ruined my day.

After my initial upset about the lack of progress on the tests, I took a few hours to think and analyze the answers.  I discovered something interesting.

The calculations that they were doing seemed ok.  Not great, but acceptable and level appropriate.

The reason that all of the answers were wrong fell squarely into two categories:  They either didn't know how to set up the problem correctly, or they didn't answer the question that was being asked.

For example, in a question about price mark-ups, they were asked to find the new price and 75% of the students found the mark-up (correctly).

So today, I handed back the tests with my comments and feedback and we did them again.  I re-wrote the questions in an attempt to make them more relevant (percentage of jellybeans rather than survey respondents.)  I put one question at a time on the board and set up a timer.  I had someone read each question out loud before they worked on it.

One girl sat in the back and shredded her re-test.  Two boys stared at the wall.  One claimed he didn't have a pencil, so I gave him one, he refused to sharpen it and sat there.

But the rest worked very well.  Before they got started, we talked about how to organize an open-ended test so that they made sure they hit every part and answered every question.  I was very pleased with the majority of the work that I saw.

In period 8/9, 15% of the students didn't bother redoing their quizzes, even knowing that failing to do so would result in a zero.

It will take a lot more practice to get there where I want them to be and we only have about 7 weeks left, but I'll keep at it.

Apparently, our new web filter thinks that Estimation 180 is WAY too entertaining...

Wednesday, April 16, 2014

Day 141: Applied Trigonometry

Apparently, allergies make you look like Hitler...

The Scene: 31 hours before school is closed for  5 days.
The Mood: Anxious

"What would you ever use trig for?" he asked me morosely, not having any idea about my plans for the following day!
"I have no idea. Maybe we'll figure it out" I replied, having a clear plan for the following day.

**cue steepled fingers and foreshadowing look into the camera**

The Scene: 7 hours before school is closed for 5 days.
The Mood: Barely contained excitement (mostly on the part of the teacher)

My geometry students built clinometers!

During the first class, we used washers, string, straws and protractors to create a device that would measure the angle of inclination or depression from our eyes to an object.  We did a quick introduction on how to operate and properly read the device and how to take the calculations to determine the height of an object that was some distance away.

During the second period, we went into the gym!

Working in pairs, students picked four objects around the room, measured the angle of inclination and recorded it on their data sheets.  Then, once I could get to them, we measured the horizontal distance to the objects and, through the power of mathemagic, were able to find the height of the objects!

I cannot express how well this activity went!  During the introduction, I did an example and measured the height of the ceiling.  I messed up the angle measure twice while the kids watched so I got to talk about the importance of precision and accuracy as well as running multiple trials.  They also got to see my thought process on how I correct my mistakes.

In the gym, they picked a wide variety of objects, not the just obvious ones like the basketball net, the scoreboard and the windows.  They picked points on bleachers, clocks, security cameras, chin-up bars, etc.  They worked hard and well, checking their answers with their partners and engaging in the "does that answer make any sense?" discussion.

I was VERY proud of them and VERY impressed with their work.  After the success we had today, I have confidence that they can handle an activity on parallax, which would be a similar activity, except in the dark...

Now I just need to figure out how to set it up in a way that would effectively demonstrate the proper use.  It will clearly need an intro lesson, but I need to decide how much to reveal before do the activity.

I LOVE hands-on activities, especially in math where students are often unaccustomed to it.

The pre-algebra students took a quiz today.  It was a 4 question, open-ended quiz and they could work with a partner, but each person had to turn in their own work. Even this late in the year, I'm still trying to get them to do more than just calculation.  I haven't given up on them, but I am easing them back towards where I want.

I think that my major short-coming with that class this year has been my desire to move them out of their comfort zones WAY too quickly.  I know they are capable of amazing things, but throwing them in the deep end of the metacognitive pool was probably not the best choice.  A few of them swam, a few flailed about for help, inadvertently slapping their would-be rescuers, and some angrily crossed their arms and sat at the bottom of the pool.

We spent the last week or two in the shallow end and they did very well.  Now, I am slowly trying to walk them into deeper water.

I started the class by helping them to review ANY questions from the chapter that concerned them.  They asked some good ones and we talked again about how to effectively set up fractions using words first.

Period 4/5 (with half of the students missing) worked VERY well in the partner groups.  There were side conversations happening, but they were mostly on task and working quietly.  This was one of the first times this year that I felt they truly cared about doing well.

It was short-lived, but it was a step in the right direction!

Period 8/9 did not do as well.  Three or four students simply refused to stop talking in spite of my repeatedly asking them to.  The behavior of the two pre-algebra classes between yesterday and today seemed to have flip-flopped.

In addition to all of this, I found out this morning that I was nominated for a Bammy Award!  I am deeply honored that someone, let alone several, feel that what I write is good enough for an award.  If you feel so as well, you can vote here.  I would greatly appreciate it.

Tuesday, April 15, 2014

Day 140: Where Have All The Students Gone

We continued our work on trig ratios in geometry.  We had a cool discussion about the roots of words and the benefits of taking Latin if you plan to do any work in math or science.  Today's lesson was primarily to get them familiar and comfortable with using the ratios and the trig tables.  We got to talk about my new favorite topic: the difference between doing calculation and doing math.

"The trig table does the calculation for you, so that you can free up your mind to do the math."

A student, in a fit of confusion and frustration, asked what we would ever use this for.  I almost never get this question in the geometry class, so I did a simple example of a wheelchair ramp and went into depth about the other applications.  I could tell how anxious he was, so I tried to make it as real as possible.

Since this group is pretty great at going along with me in my theoretical journey's in math, I sometimes forget that they need the application to tie the concepts to.

Weather permitting, tomorrow we will be making clinometers and calculating the heights of buildings and trees outside, or in the gym.  I'm pretty pumped about it.

In pre-algebra, 1 student attempted the homework.  Between 2 classes, only one student did what I asked them to do last night.  I don't mean that only one completed the assignment.  Only one student even had anything written in their workbook, let alone brought it to class.

My class has somehow become a spectator sport and I don't know how.  I gave them the benefit of the doubt, thinking that maybe the word problems were too complicated.

A coat that normally sells for $90 is on sale for 45%. If you have $45, do you have enough to buy the coat? Explain your answer.

After 5 minutes of pulling teeth, I couldn't even get them to tell me how they would start it.

I am struggling deeply with determining if they don't understand, or if they are simply too lazy to make an attempt.  I go back to the concept that if I ask the class for an answer, or a method, or input, I don't get any sort of response.  If I ask a specific student, they certainly seem capable enough, but getting them to take a moment to think about what they're saying is, as I said, like pulling teeth.

They have gotten into the habit as well of setting up fractions by putting down the numbers in random places.  I've been drilling into them that we need to think about, and write down in words, which number represents which concepts.

What I've been asking them to do, as in the example above is to look at 45/100 (for the percent) as (discount amount)/(original amount).  But I'm having tremendous trouble getting them to do it consistently.

They are so anxious to get an answer that they don't seem to care if it's right or not, or even if it makes sense.  The MOST frustrating part is that the entire section that we're covering right now is about finding a reasonable answer.

Period 8/9, while they hadn't completed the assignment, or even attempted it, for homework, did amazingly well with the discussion.  It was NOT pulling teeth with them.  They were eager to do the work and we had some pretty great discussions about places when estimations are useful, such as gas mileage, determining if you have enough money to buy a few items.

As much as period 4/5 got me frustrated today, period 8/9 went swimmingly.  I would rather they had done the work at home, but I'll take active class participation any day of the week.

Monday, April 14, 2014

Day 139: Interruptions

In preparation for an intense 3 days of trigonometry, I worked on a modified version of the Trig Intro from the brilliant Tina Cardone.  We got about 10 minutes into the lesson when they began calling large groups of students to the auditorium to take yearbook pictures for clubs.  Since the majority of my geometry students are in a majority of the clubs, I once again, lost almost an entire day's worth of instruction. 

With the few students who were left, someone made the foolish and excellent mistake of asking "Mr. Aion, what's the deal with Pascal's Triangle?"

As a result, my geometry students, many of whom will be in Algebra 2 next year were treated to a quick tangent (haha!!) on number theory, rabbit reproduction, Sierpinski Triangles and binomial expansion.  As I showed more and more examples, my excitement grew.  I explained to the students that THAT was what I loved about math: not that there was an answer, or that it followed certain rules, or that I can do calculations in my head.  I LOVE the patterns that exist in nature and the multitude of places that the reality of mathematics can be found outside of the classroom.

Once enough students came back from pictures, we were able to get underway with the activity.  I got through enough of it that I asked the students to figure out the relationship between sine, cosine and tangent.  After a minute or two of staring at it, one of the kids came up with the fact that the tangent was the sine divided by the cosine.

So I was able to show them these:

I used to have the idea that I wanted to put up a math comic or joke every week and offer bonus points to whomever could explain why it was funny.  We have talked about how learning can be defined as the ability to ask a question that you couldn't before.  I would add that you've learned something when you can understand a joke that you didn't previously.

The weekend must have been rough on the pre-algebra kids.  They were sluggish and aloof, much more so than usual.  They also got stuck on a problem that I thought was fairly basic and got stuck in a spot where I didn't think they should have.

Latoya gave 35% of her allowance to her sister and 25% to her brother.  She was left with $12.  How much does Latoya get for her allowance?

Even as I type this, I hate the problem.  There are MUCH better ways to deal with percent and no one thinks about giving their allowance away in percentages...

In any event, period 4/5 could get to the point where they knew she had given away 60% of her allowance.  What they COULDN'T get to, even after several minutes of directed questions, was how to relate the 60% that she gave away with the $12 that were left.

I have gotten much better at the kinds of questions that I ask, making sure that they direct student thinking instead of simply asking for an answer.  Even so, I couldn't find the right question to ask that would get a kid to say anything like "She has 40% of her allowance left, so 40% of something is $12."

Since I moved the pre-algebra classes back into rows, their attention to task has been much improved.  In contrast, the attention in geometry has gotten worse.  I think the groups were very beneficial to them, but the layout of my room doesn't really allow me to switch desks around every period.  Perhaps we'll try it when we get back from Easter break.

The pre-algebra kids managed to retain much of what we talked about last week in terms of doing certain percentages in their heads and I was really proud of them for it.  They are all bright enough, but retention of material something that we need to work on.

For the most part, it was a pretty good day.  I'm still tired though.  I need to sleep more and eat more fruits and vegetables...

Saturday, April 12, 2014

Letter From a Reader

I got the following the email from one of my readers.  This person wanted to talk to me about their first year as a classroom teachers and the struggles that they went through.  The story tugged at my heart and helped me to remember that teachers are never alone in our struggles.  No matter what situation we find ourselves in, there is someone else out there who is facing similar trials.

I have removed identifiers from the email, but otherwise have copied it here.

Sorry this took a while to write. It's finally here.

It is your daily reflect that I admire. I have always felt introspection/reflection is what has allowed me to grow to become a teacher, and from there grow to become a better teacher little by little. When I shared your blog earlier today afterI discovered it, I likened it to how photographers do 360 photo-a-day blog projects to rekindle their creativity. It's not everyday that someone can be so honest about themselves--even more so in a public way--it takes a lot of bravery and the willpower of someone who genuinely wants to improve. Needless to say, I was inspired.

Onto my story--earlier this year, I had been hired for my first full-time teaching position to teach all subjects to 8th graders. I had a self-contained class of 35 students who stayed with me all day as I taught them all topics like elementary school classrooms do. I had everything you could wish for in your dream school: an enormous classroom maybe the size of 2 regular classes, a copier machine outside my “door” (I had no door), cabinets full of card-stock to use for printing at will, etc.

I liked 8th grade because I got to teach US history and algebra--and most importantly, leadership. Having the oldest students in the school meant I could give them a sense of responsibility as role-models for all the others. That was my classroom management strategy: inspire leadership and students will manage themselves. That went hand in hand with just having a well-planned lesson would keep everyone engaged in learning. With so much riding in my favor, like fully stocked supplies, I thought nothing could ruin the experience.

Yet it was before I taught students anything, or even had an icebreaker with them did things already begin to sour. My school had a tradition of having a day where students could meet their teachers before the first day of school. Each teacher had a booth where they had goodies to give out as they spoke with each prospective student. It was only after the event that I learned from my fellow 8th grade teacher that students wanted to move out of my classroom--or rather, it was their parents who made the call. They complained that they did not want to have a first year teacher for their children.

It didn't bother me too much since it turned out that many parents wanted to move their children into my class since I made a pretty good impression to many. The big idea is that parents wanted to have control over these decisions, yet in doing so, it undermined the authority of the school and furthermore, it painted a picture of me as ineffective and novice.

My administrators blocked all requests to move and my students got along with me for the first week or two. I had break-throughs in getting kids excited about physical science. Yet more parents continued to make requests to get their child out of my class. I sat in on a meeting with one of them. They cited things like how their child learned best with competition and rewards and how he was more of a bodily kinesthetic learner. I was able to cite many examples of how active we were in reviewing integers with physical movement, yet could not agree with them on using competition and rewards since that was like suggesting to me how I should teach. I solved this “PR” mess by inviting the parents to stay after the meeting to observe my teaching. All went well and I didn't hear anymore complaints from those parents.

Then my principal started visiting my classroom every day for observation. I’m very comfortable with visitors, and he offered good feedback that he liked what he saw. It was around this time, a few weeks into school that my students impression of me started to change. They didn't stand in straight lines (we walk students back to class), they took longer to recognize my attention cues, and they would pass around notes in class. My vice-principal suggested that I should take some time from instruction to do more icebreakers, just to get to know them more. This seemed out of place since given the timing. She gave me some questionnaires to use for gathering information I could integrate into lessons. I thought to myself, that there are some things that I could change about myself to make learning happen.

Yet spending that time on those activities pushed some other subjects off my planning. My students would talk to the students in the other 8th grade classroom and learn that we were “behind.” This inevitably spread to the parents who, again, took action to complain. This vicious cycle looks like this: parents had low expectations of me -> they complain -> I implement changes -> unintended consequences -> students start to have low expectations -> respect is lost -> classroom management is a nightmare.

In one incident, a boy had taken a red ribbon from Red Ribbon Week and put it in his hair. I asked him to remove it because it was distracting to those around him. He responded by asking why it's not okay. I repeated that it was distracting. It went in circles like this similar to one of your blog posts in a back-and-forth you had with a girl in your class. It was a mistake to go back and forth on such a ludicrous issue that should have been a simple situation. It just reinforced the defiance. I felt so angry at being disrespected, having an argument with a student. Then slowing down, I realized kids keep asking the same question because they just disagree with your reason. Only when I brought up that the ribbon symbolized something important and that much time had been wasted in the moment did he then remove it. The easy way out would have been to send him up to the principal right away, but I felt I “lost” no matter what.

In another incident, some girls were caught passing around notes in my classroom. I had a small conference with them after class, and before I uttered a word, the girl in question said “why are you singling me out?” as if I was the culprit and that she was the victim. I was reminded of an incident like this in your blog when it seems like students don't understand how harmful they can be to the learning time of other students. She proceeded to tell me that “other students were passing notes too,” and did not give away names. I was not happy with this and so I told her I would notify her parents. Unfortunately for me, the apple did not fall too far from the tree as her mom defended her daughter, asking, “you do know that you have students texting in your classroom?” I learned later that her mom was very vocal in a ring of daily emails between parents that nitpicked on everything that happened in class.

I started to feel that students didn't like me, that when parents complained, it started to bother me. I tried to take action to get on everyone's good side. I reorganized my classroom, got new furniture, set up classroom stations, even going so far as to seat more friends beside one another (that was a huge mistake). My principal explained that I was what he would call a “people-pleaser” since he was one too. A people-pleaser is someone who teaches or works best when everyone gets along or when everyone likes you. It really started getting to me that I could not manage my classroom because students had lost their respect for me. I had exhausted everything I felt I could do to please them.

That's how I burned out.

When I read your blog about the things you do in class, it seems like you, too, might be somewhat of a people-pleaser--which is not necessarily a bad thing. You've got fun cartoons on your white boards, you try new ways of learning/teaching, etc. I visited my university supervisor and shared all this with her and she said it was a cultural phenomenon. Depending on where you live and work, some places give more respect to the teacher, and others “worship” children. I happened to be working in a place that placed children on pedestals--such that it made me feel like if something was wrong, that it was a problem with me and that I had to change myself to fix it. By being too much of a people-pleaser with all my actions, it subverted my own self-respect. So not only did parents and students not have respect, but I too was contributing to my own demise by giving in to them.

I had received anonymous hate mail. My principal was not around to investigate and administrators from above him started visiting the schools, asking, “have you seen what they have been saying about our school on” subtly communicating that I was the cause of it all. In trying to find out who was the sender, I started being suspicious of my students. It made me feel uneasy that I had to find out who hated me that much--that I too might not like my students. Then inside me, I started to hate teaching: I set up such a great learning environment, why don't they like it, and why don't they learn? How could my first job teaching be so malignant?

I phoned in a day-off just like you mention in your latest post. I thought taking one day off work would help me get myself together. Then I took another. It still wasn't enough, so I took one more. On that last day, I scheduled to meet with one of my administrators. At the time, I was distraught, telling him to “please find a good teacher for them” as I had lost confidence in my own ability to teach. I submitted my letter of resignation thereafter.

Since then, I went back to substitute teaching, which is where I originally fell in love with teaching and others discovered my talent. It has helped me regain my confidence and, most importantly, my love for students and teaching. Gone are the days of suspecting students of hate mail and being the gossip of bitter parents. I have concluded that somewhere out there is a school that can really appreciate the thoughtfulness I bring to the classroom. Resilience in the face of all those pressures is important, but you need to know your limits and how to uphold your dignity.

When you said you were feeling ineffective and helpless, that's like how I was when I thought I had done everything I could, yet it wasn't reciprocated or appreciated. I don't have much in terms of wisdom or advice, but I want to let you know that our stories might take different paths, but they seem to have that similarity. I guess, if I do have anything to share, it would be to take steps that make it so you like teaching, and that you're happy. For me that was taking a few days off and ultimately resigning. That might not be for everyone.

Friday, April 11, 2014

Day 138: Newton's Laws and Mental Percentages

We are about to delve into trig (my favorite topic) in geometry, so instead of starting a new section, I decided to hold off until Monday.  Instead, we covered a few questions about special right triangles and watched another episode of Cosmos.  Several students quietly asked some very insightful questions about the mathematics of Newton's Laws of Planetary Motion.

In pre-algebra, I continued my plan to keep the lights low, and side conversations to a minimum.  The students were a little bit more boisterous, but got back on task when I needed them to.

In period 4/5, we had an extended conversation about lottery winnings and whether it made sense to take your winnings as a lump sum or as an annuity payment.  Several students felt they would be willing to take a lower value of winnings to have a guaranteed check every year, in case something happened.  Others felt they would rather it all because they it would be worth more if they invested it.  The discussion was very interesting.

We moved from lottery winnings to the banking system, interest and how banks make money.  In the examples I used, I had the banks paying 1% interest to depositors and charging 10% interest to the borrowers.

Using nice round numbers, I was able to help them boost their confidence and spend more time on math rather than calculation.  In both classes, we did a ton of verbal practice with me calling out questions and kids rushing to answer them.

"What is 10% of 230?"
"What is 25% of 12?"

I made sure to emphasize that the purpose was not to force them to do all of this in their heads but to let their heads do the work so they can think about other things.  There were several who claimed they would rather set up proportions and do it that way.  Who am I to tell them they can't be less efficient if they want...

In period 8/9, we had a discussion about the reasonableness of an answer.  I demonstrated the value of that using Google Earth.  I asked the students to pick a city that they couldn't find on a map.  They picked Indianapolis.

Me: "Great. What DO you know about where it is?"
S: "It's in Indiana."
Me: "So would it be reasonable for me zoom in on France?"
S: "No, because it's in the United States, so zoom in there."
Me: "Now what?"
S: "Now zoom in on Indiana (which was labeled.)"

We did several of these types of examples with me picking Crimea and Toronto.

Me: "So, how does this help us?"
S: "It helps us to narrow down the space to look."

And then there was a fight outside of my classroom.  One teacher was sent to the hospital after suffering an asthma attack and one of the girls was sent back to class.

It's the weekend.

Thursday, April 10, 2014

Day 137: Analyzing A Change

Since we have missed 2 days of geometry this week, I decided that we needed to cover some content to catch up, so we delved into special right triangles.  We had an excellent discussion in which we derived the rules for 45-45-90's and 30-60-90's, starting with Pythagorean Theorem.  After we calculated the sides on several, I asked if anyone was able to identify a pattern.

I then asked them, if I were given side lengths of 4 times the square root of two and a hypotenuse length of 8, how could I draw the triangle without a protractor to measure the angle.  We had a great discussion about creating smaller right triangles of side length 4 and using the hypotenuse of those to make the legs of the new triangle.

I was very pleased with how they worked together, bouncing ideas off of each other to develop a theory.  What I said a few days ago about having them trust me is, I think, very accurate.  They ask clarifying questions that might be considered risky in other classes.  They put out there what they understand and what they don't in an effort to make the amount of the former grow and the latter shrink.

It takes a ton of courage for anyone to ask for help or to admit weakness, let alone a 13-year-old.

In pre-algebra, we had a discussion about depreciation and the value of being the first owner of a car, or pair of shoes, or anything.

Me: "You go to the store and they're selling a brand new pair of Jordan's for $180.  Right next to it, is exactly the same pair for $140.  What question do you have?"
S: "Why is the one less?"
Me: "That's a good question! When you ask, the salesperson tells you that the $140 pair was worn once and returned.  Looking at them, you can't tell the difference. Which one do you buy?"
S: "You gotta buy the new ones?"
Me: "Why?"
S: "Those are used shoes.  Even if they look new, you'll know that they aren't and that they weren't yours first."
Me: "And that feeling is worth $40 to you?"
S: "Absolutely. They have to be your shoes."

It was an interesting discussion and helped me to understand my students a little bit more.  In my mind, I would rather save the money, but I look at shoes as shoes and not as a status symbol.  I think it's enlightening to be reminded that I frequently have very different priorities than my students.

They were VERY engaged in the discussion, but as soon as I asked them to produce something, about half shut off.  This is very typical of what I've seen.  They are interested in the discussion, but then...

The biggest challenge that I have had consistently with my 8th grade students in this year, as well as previous years, is transitioning them from talking to doing.  Either that, or I need a MUCH better way of assessing knowledge verbally.

Period 8/9 had an amazing discussion along the same lines, but I think it was more effective in helping them to understand the concept of percents.

I proposed two scenarios.

In the first, they went into Best Buy and saw two identical TV's.  One was labeled $300 while the other is labeled "Used!"  We went around and discussed how much the used TV would have to cost for the students to choose that over the new one.  How much would you have to save in order to give up the idea of being the first owner?

After some discussion, we came to a consensus that it would take a savings of $50 to get them to buy the used TV.

In the second scenario, they went to the dealership to buy a MiniCooper with a sticker price of $16,000.  At the dealership, they also found an identical Mini labeled "Used."  I asked them if they would buy the used Mini for a price of $15,950.  They very adamantly said they would not.

Me: "Why not? You just said you would buy a used TV to save $50. Why wouldn't you buy a used car to save $50? $50 is $50!"
S: "Yeah, but with the car, $50 is nothing!"
Me: "Isn't $50 the same $50 no matter where it is?"
S: "Yeah, but on the car, it doesn't really mean anything because the car costs so much more."

After a bit of coaxing and directed questions, I finally got someone to say the word percentage.

It turns out, the $50 was 16.6% of the TV's price and only 0.3125% of the car's price.  This lead to a longer discussion about marketing strategies and why it's important to understand the math behind advertising.

Overall, another great day!  A student with whom I had a very combative interaction yesterday was on amazing behavior today.  At the end of class, she said "Man! Today went by so fast! Were we really here for an hour and a half?"

We had a brief conversation about how this is how I WANT the classroom to be.  When she asked why it wasn't, I just looked her in the eye and waited.

"It's cause I'm too loud, right?"

I smiled and thanked her for joining our learning environment today.

So I have changed the look and feel of my classroom.  It is now much more like it was last year.  The students are back in rows, although the sit in pairs in those rows.  I've also been keeping the lights off.  I used to keep the lights off because I couldn't see my projector with them on, but now I keep them off because it conveys a sense of calm.

One of my colleagues came to observe my class yesterday.  He made a ton of notes about the atmosphere, the environment and my movements and interactions with the students.  It was fascinating to see what he saw in terms of the ways that I spoke with students and where I was, physically, in the room.

Doubly interesting was how, if he had come last week, he would have seen something MUCH different.  By having the students in rows facing the board, I am very limited in where I can be and still interact with them and the board.  He also noted that the few negative interactions that I had were primarily with male students.  I attribute this to the fact that the primary disruptions (both female students) were no in the room, but it is something to think about.

It was the kind of observation that I've been craving since day one and I am deeply grateful to him for taking time out of his day to do it.  I hope that I'll get the chance to sit and have a longer discussion with him.  I need to make a conscious effort to listen to his feedback and not try to justify my actions.  I know that he came in because I put out a cry for help and his only interest is helping me to become a better teacher.  I trust him implicitly, but I know that my first response will be "Yeah, but this is why..."

I'll need to keep a rein on that if I want to learn anything, which I desperately do.

In totally unrelated news, one of our teachers went out on maternity leave.  The sub they hired to fill the spot quit before our teacher left.  The sub they got to replace her quit after 2 days.

Wednesday, April 9, 2014

Day 136: PSSA Day 5

These are the tests that neveeeer eeeeeend! Yes, they go on and on MYYY FRIIIEEEEEEND!  **Everybody sing with me!**
Some people started taking them, not knowing really why! And they'll continue taking them until everyone cries!
**insert joke about puppets, proctoring and proctology**
After my near melt-down yesterday, I thought long and hard about solutions.  I had some great conversations with some amazing people on Twitter that helped me to clarify my goals and ways that I can achieve those goals.  I spoke with my principal about specific students and my plans for them and she supported my choices.

I am desperate to not make decisions out of anger this year, so having the night to think it over, I've made some choices that I think will be educationally beneficial to my pre-algebra students.

I put the room back in rows and assigned seats.  The choice to go back to rows was a difficult one because I don't feel it's the best way for students to learn, but until the behavior gets under control, no one is learning anyway.

It was...


The lesson for pre-algebra was VERY basic. (What is 30% of 50?)  I kept the lights off, and started with a basic question.

"You go into a store to buy a $30 shirt.  When you get there, you find that it's on sale for 20% off.  How much are you going to pay for it?"

We had a good discussion about what 20% off actually means and if, depending on how you think about it, would it make more sense to find the new price first, or find the amount of the discount and then subtract from the original.

We spent some time as a group going over setting up proportions and I kept reminding them that this is what we've been doing for a few months now.  90% of the students were engaged. Whose who didn't have their books were writing things of pieces of paper.  As I called on random students to give me answers, others yelled out to show that they knew it too.

They were arguing over who got to answer and were asking good clarifying questions.  It was as though it was a completely different class.  I wonder if they read my blog yesterday...

After we did several problems as a group, I gave them a short break and then an individual assignment that we would go over at the end of the period.  Most of them worked very well on it and I made sure to shower praise for their efforts.

In period 8/9, I had to remove three students in the first 5 minutes.  After that, I had an almost identical experience to period 4/5.  Students were engaged and participating.  They weren't afraid to answer questions when they were unsure.  They were willing to take risks by volunteering and were disappointed when someone answered before they did.

In both classes, the atmosphere was positive, supportive, energetic and happy.

This is the point where every teacher reading this will say, out loud, "Well DUH!"

The removal of one or two students will completely change the dynamics of a class.

A part of me is trying to be upset about having a day of direct instruction, but I'm going to push that away and bask in the glow of an amazing day!

Middle school students are fickle.  I'll happily take it though.  Today gave me hope and renewed some of my energy.

Today was a great day!

And then I got interviewed by a reporter at the New York Times.  I'd better go to bed now before I jinx everything!
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