Wednesday, September 17, 2014

Day 17: Defining Success and Rectangles

I've been thinking very heavily about the conversation that I had with my geometry students on Monday.  They are, in my mind, overly concerned with getting into college, to exclusion of all else, including the actual act of "learning."

I expressed my discomfort with this notion on Twitter and had a very interesting conversation about teaching and parenting with Kory Graham.



How do I help my students?  How do I help my own daughters?

I think this is part of a much larger discussion about how we as teacher define success versus how the parents of our students do versus how the students themselves do.

A few weeks ago, I was asked for my opinions about Common Core and standardized testing by a reporter from the New York Times.  One of the things that I told her was that I don't see how, effective or not, standardized tests can even be designed until we have a national, or state, or local conversation about the basic question of the purpose of education.

I don't know how we can create assessments until we have answers, or at least discussion, about the following questions:

What is the purpose of education?

What does success look like?


My thoughts on those are constantly shifting, which is why I have discomfort with my current assessment and grading practices.

I'd like to write more about this, but my head isn't on straight at this point, so I'll talk about my classes instead.


My pre-algebra student demonstrated proficiency with calculator use, about which I have mixed feelings.  We are working with fractions, fraction to decimal conversion, and ordering rational numbers.  I've been giving my students to the opportunity to do some independent work, but I think today may be the last day for that.  The advantage was that I was able to sit with a few students and talk about ordering fractions.

As is the case with much of my brilliant lessons, I channeled Fawn Nguyen. I plan to spend the next week (month, year) talking about fractions in terms of rectangles.

As I was working with my students about how to compare 4/7 and 3/5, one of the girls started talking about how she learned to compare fractions from a previous teacher.  Her explanation included phrases like "since the denominators are both odd" and "then you add the top numbers."

At that point, my eye was twitching so heavily that they had to call the nurse.

I should also state that, had she been able to solve the problem using this method, I would have been more likely to listen and try to figure it out, but she couldn't.  Not only couldn't she solve the problem, but she admitted that the process didn't make any sense.

So we talked about rectangles.  We did it slowly.  It was a conversation, rather than a lecture.  They took great notes and asked great questions.  Perhaps most encouraging of all was what one of them said.

"I really feel like I learned something today."

I''ll admit that I've been lost for the last several days, feeling as though I was killing time and watching unproductive struggles.  I think this could be a bit of interest that I can leverage into a more productive discussion of fractions.

Tuesday, September 16, 2014

Day 16: Nose to the Grindstone

After the conversation that I had with the geometry students yesterday, I had been thinking about the amount and type of practice that I've been having them do.  While I think it's fair to have my class be a different style than what they are used to, I think it would be beneficial for me to offer a transition to the unfamiliar territory.

After reading the letters that I asked them to write this weekend, It's obvious that they are much more comfortable with working through lots of practice problems.  Clearly, this is not true for everyone, but many expressed this concern.

So today, I gave them some options.  I printed out several worksheets with practice problems from the current chapter.  They could work on those if they wanted the practice.  They could continue working in the guided notes, if they chose.  They could work on revising their assessments from Friday.

I also told them that, if they chose to do so, they could waste their time.  As long as they weren't stopping others from learning, they could spend the time as they wished.  I explained that I am trying to move them in the direction of self-directed learning and being responsible for their own education.  Since they are still 13 and 14, I don't expect that they will always make good, mature decisions, (especially because in my 30's I rarely do that myself) but I believe that there are lessons to be learned from failure and making bad choices.
These jive turkeys made bad choices today...

And so I gave them those options and let them go.

The geometry kids, with a 10% error, all worked very hard on the assignment of their choice.  I made myself available for those who had questions, or simply wished to talk things out.  I was able to circulate and watch their efforts, talking to them as more of a peer than an authoritative figure.

THIS is how relationships get built.

And yet...

As I sat there, casually hanging out, waiting for students to engage me as they saw fit, I couldn't help but think that I wasn't teaching.

While I know that this is not true, the part of my mind that is a product of a direct instruction education was telling me that I needed to get up and address the group.  I needed to be conveying wisdom or standing over kids while they work, like teachers do on TV.

I wonder what an observer would think if they walked into my room and saw me hanging out at a student desk.  As much as I want to claim that I know (or at least think) that what I'm doing is in the best educational interests of my students, I wonder what a parent would think.  What would an administrator think?

Why should I care?  If I believe in what I'm doing, why do I care what other people think?


How long do I have to teach before I am truly confident in my work?

Overthinking is exhausting...



Monday, September 15, 2014

Day 15: Communicating Philosophy

This is my 4th year teaching 8th grade, my 6th year teaching in my current district, my 8th year as a classroom teacher and my 10th year working in some capacity in education.

I'm not sure how to teach.  I'm not even sure what my style is...

In previous years, I would lecture and consistently utilize "I do, we do, you do" strategies.

Last year, I did much more project based activities, interspersed with lecture and group work.

This year, I have found that I'm giving the kids problems to work on, talking to the group very little and allowing them to work on their own or in small groups while I walk around and answer questions or guide them back on track.

I think there is value in all of these.  I know which one I prefer to use, but I'm not sure that it's the best for my students.

In reality, I'm sure the answer is "a balanced mixture of all three approaches is most beneficial."

I like lecturing, but I don't want to be a lecturer.  I love watching the kids solve problems at their own pace, but something deeply engrained in me makes me very uncomfortable with that.

I find myself constantly asking myself "is this actually teaching?"


So this is what I believe:

I feel that it is NOT the job of the teacher to simply share knowledge.

A teacher should be more than a textbook or a video.

"Christ! All he does is shows videos all day!" goes the conversation in the faculty room.  Then we return to our classes and talk at our students for 45 minutes straight.

But we hold equal contempt for teachers who hand out worksheets and then sit at their desks for the whole period.

I feel that it is my job as a teacher to collaborate on learning with my students, helping them to explore their interests and become better critical thinkers.



What I have been trying to do has been to minimize the amount of time I spend talking and maximize the amount of time they spend working.  Some of that work has been grinding through problems, but most has been abstract, critical and reflective.  I am having them do writing and thinking about their process.

This shift in what they are used to receiving from a math class has split my students into three camps, that I can tell.

1)  The first is those students who are used to lecturing from their teachers.  These kids feel that if I'm not in front of the class, telling them how to do a problem, that I'm not teaching.  They take the time that I give in class for them to work on practice problems as free time.  I don't blame them or think that they are lazy because of this.  I recognize that in the past, they have been conditioned to think that when the teacher stops talking, the class is over.  They feel that doing the problems is a task for homework and, when given time to work on something in class, frequently respond with "I'm going to do it tonight."

They have very little experience with efficient use of class time for independent or group work.   For the most part, my pre-algebra students fall into this category.

2)  Other students are used to grinding through worksheets and practice problems.  These kids have great ability to work independently and, given textbook or worksheet problems, will solve them efficiently and happily.  They are comfortable with assignments that read "do these 50 problems."  For the most part, they prefer the type of teaching style that is "I do, we do, you do."  They excel in situations where they are asked to recreate methods and strategies that have been shown to them.  They take comfort in formulas and prescribed plans of action.

For the most part, my geometry students fit into this category.

3) The third group is much smaller.  These are students who preferred either lecture or worksheets, but received the other.  This group wants to talk about the problems, discuss what they know and then practice independently.  From these students, I frequently hear "alright, I want to try it on my own."


Perhaps it is misguided of me, but I would like this third group to grow.  I know that my students are going to face such a variety of challenges in the coming years and, really, for the rest of their lives.  They will not always have situations that are ideal to their learning styles or preferences.  But that doesn't mean that they CAN'T learn that way.


We had a VERY long (both periods) discussion about the geometry quiz on Friday.  Their homework over the weekend was to write me a letter about the class, telling me what they've learned, what they like and what they don't.  The results were...interesting.

The students came in distressed that they had not aced the test on Friday.  Much of what we discussed is in the preceding paragraphs.  I tried to address their concerns and explain my view point and teaching style.

They expressed the sentiment that the world cares about grades, and so should they.

My counterpoint was that they should care about the learning, the knowledge and the skills.  My claim was that if they master those, the grades will happen on their own and they will have the ability to build upon them.

We had many disagreements about educational philosophy and I hope that they felt as though I heard them.  I tried very hard to express my sympathy for their points of view and to explain that my own.

I expect that we will have many such discussions over the course of the year.  I know that I am different from any teacher that they have had before and, most likely, ever will again.  I know that my teaching style doesn't work for everyone, so I'm trying to develop alternatives for those who need or want it.

Bree Murray introduced me to the format of the Recycle Assignment where students are able to correct their mistakes and talk about why they made their initial mistakes.  I gave this to the geometry students and expressed that, since I care about the learning and they care about the grades, I would give them the chance to earn better grades by demonstrating knowledge and reflection.  They seemed amenable to the process and I have faith in them.

There will be growing pains.
No, not these...

I just hope no one cuts my legs off to keep those pains at bay...




I'm so tired, but my skin looks amazing!!!
It was a long and exhausting day, but a good one.

Friday, September 12, 2014

Day 14: Technological Integration

This past week, I started having my students recite the 8 Standards of Mathematical Practice before we start each class.  I've been calling it the Pledge to Improved Mathematics because I don't have a better name yet.  My geometry students asked whether they should put their hands over their hearts, like they do for the Pledge of Allegiance.

After some discussion, it was decided that a more appropriate gesture would be to place their hands over their minds.

So my classes now begin with student placing their right hands on their heads and reading the 8 Standards of Mathematical Practice.
A student who came in late asked if she had missed the Pledge and was very disappointed when we said that she had.

The other thing that we've been doing at the beginning of class is #Estimation180, as we did last year.  This year, however, I've added a few new procedures.  Going off the four steps that I'm emphasizing in all of my classes, the conversation goes something like:

Me: "What's the first question we ask?"
Students: "'What am I looking for?'"
Me: "And what are we looking for?"
Ss: "The number of staples in a single strip."
Me: "What information might be helpful in order for us to make a good estimate?" (Emphasis added because I think this is an incredibly good question, if I may humbly say so.)
S: "How big the staples are."
S: "How long the strip is."
S: "How often the strip has to be replaced."
S: "How much it weighs."
Me: "Those sound like they would be very helpful in making good estimates.  What are your estimates for the number of staples in the strip?"




I realized also that I don't have nearly enough grades in my book to satisfy my administration, so we had a quiz in all 3 classes.

The pre-algebra classes took a simple version of a test from the text book.  It was 20 questions, multiple choice.  I have very mixed feelings about multiple choice tests because, traditionally, they only provide the students "right" and "wrong."  In an effort to incorporate more feedback, I decided that just because the test was multiple choice didn't mean that I couldn't use it to develop skills that I find important.

So the students took the tests.

While they were doing so, I handed out Plickers cards.  Plickers provide a unique QR code to each student that can be turned 4 different ways to indicate 4 different answers.  They are then scanned by a phone or tablet and the data is displayed in real time on the computer.  I found out about this program this past summer at TMC when the amazing Pam Wilson presented about how cool it is.  She was right!

I had them printed on blue cardstock cause it's purdy!
Each student was assigned to a specific number and, once they had completed the test, we went over it.  I had them hold up their cards to indicate which answer they had chosen while the display showed who I had scanned and who I had missed.  The beauty of this was that no one knew what anyone else answered, but we were able to look at the data to see the distribution of answers.  As the graph started to display, I asked the students if they thought it was a problem that we needed to go over as a group.

They quickly picked up that if the majority of the class had selected the right answer, they could ask me about it individually if need be.

Answers were revealed, kids cheered for themselves or sounded disappointed.  I had them mark their own papers, keeping track of the ones they got right or wrong.  I did the same for problems that more than 20% of the class got wrong so we could discuss them together.

Their homework assignment for the weekend was to take the test home and, as we have been doing for almost 2 weeks now, take the ones they got wrong, correct them and write an explanation of what they did.  Doing so would give them the credit back for the ones they missed.

S: "Mr. Aion, can I just keep the score I have?"
Me: "Did you get all of them right?"
S: "Nah, but I'm ok with what I got."
Me: "If you didn't get a perfect, then you still have room for growth and improvement, right?
S: "Yeah."
Me: "Good! Then work on those."


Quote of the day: "They didn't cheat! It's called 'Number 8,' son!"
SMPs are sinking in!

Thursday, September 11, 2014

Day 13: Classroom Cardio

After the success of the whiteboarding activity in pre-algebra yesterday, I decided to try another variation today.

Last night, I went to Home Depot and bought two 4x8 pieces of 1/8 panelboard and asked the kind gentleman in that department if he would cut them for me.  I ended up with four 2x2 whiteboards and twelve 1.5x2 whiteboards. (all units in feet)  Those, added to the whiteboards that I bought last year, the ones I found in my classroom 4 years ago and the one so very kindly donated by Stephanie Reilly and Jen Silverman last year, brings my total to a whole bunch.

Yesterday, I barely had enough for each group to have one, but now, I have enough for each kid to have one and various sizes of each, ranging from Personal Pan to Big Daddy, to mix my pizza chain references.

After reciting the Pledge to Improved Mathematics and our #Estimation180 warm-up, I handed out 12 word problems and told them to get to work.  But there was a catch:

They would only get credit for the problems on which I signed-off.

How would they get my coveted signature?

They had to show me how the obtained the answer.  They could work in groups or individually.  They could use the whiteboards or not.  They could start on whichever problem they chose and work at whatever pace they wanted.

When they finished a problem and wanted it checked off, they would call me over and we would talk about it.  If I liked what I saw in terms of work, explanation, picture, whatever, I would put a smiley face and my initials next to the problem.  If I didn't have the time to get to them, I told them to keep the work somewhere, grab another board and work on another problem until I made my way to their workspace.

They did an incredibly good job with this assignment!  They sectioned themselves into groups of 2, 3 and 4, spread throughout the room, snatched up whiteboards and got to work!  I spent 70 minutes running between the groups asking probing questions and making them explain the work that I saw.  They were eager to show me what they did and explain their efforts!



Along with the activity yesterday, I may have hit on a way to get them working consistently!  At no point did I have to tell kids to get back on task because those who were off didn't get their papers signed and then had a ton of homework.

This group was VERY small.  Several young women spent the first 15 minutes organizing lipstick and finding the best combinations for the day.  I left them alone and devoted my attention to the ones who were working.  After the initial grooming session, those girls got to work as well.  Great questions were being asked and there was always someone to help.

I barely noticed that it was 85 degrees in the room and that I had sweat through my pockets!
The kids thought I had peed on myself, which I thought was flattering, but silly.

My only real problem was that, since I was requiring that I sign every problem before they got credit, I had to be everywhere.  I needed more me.  This activity might be better with a co-teacher or an aide, but I'm still going to do it again, even if I'm alone.  Also, I made several mistakes in the math and reading the problems since I was coaching on 12 different items at once.  I tried my best to go back and correct it, but I know some slipped through.

It also helped me to see which students were really struggling with the concepts of translating words to numbers.

My absolute favorite part was that I was able to compliment students on their mathematical, problem solving and group choosing abilities.  Genuine praise that doesn't feel forced is vital.

I think that today went a LONG way to building relationships with my pre-algebra students.

The geometry class is very...energetic.  I like how enthusiastic they are about answering questions, but coming right out of lunch, it's hard to get them back in the mode of learning productively.  I keep reminding myself that this is a different group of students from last year, but that's just not sinking in.  I have to treat them differently because they have different needs and different dynamics.

Wednesday, September 10, 2014

Day 12: Showing Vulnerability

Several factors of frustration built up this morning before the students even came into the building.  There were a few that were school related and a few that weren't.  The end result was that I was already irritated and short-tempered by the time my homeroom got into my class.

This has happened before, so why was today different?

For whatever reason, it was just too much to swallow.  Normally, I'm able to force it to the back of my mind and be present for my students, but no matter how I tried, I couldn't separate them from my frustration.

I responded to several students in ways that were not how I wanted.

They used to tell teachers that you shouldn't smile until after Thanksgiving.  I suppose this was to establish the seriousness of education, or remind students that you are the authority in the room.  I don't believe this.  I believe firmly that relationships are what build education.

Students will work for a teacher they like, even in a class that they hate.  I want my students to learn from me and they won't learn as much as they could if they hate or fear me.

So I talked to them about it.  I told them that for reasons unrelated to them, I wasn't feeling great.  I was annoyed and irritated, but it was by no means anything that they had done.

"I am feeling off today.  I wanted to tell you so that you know it has nothing to do with you.  There are other things going on that have me a little upset.  I'm trying to keep it separated from here so that I can be the best teacher I can be, but if it leaks through and I seem upset, I wanted you to know ahead of time that it's not about you at all  You guys are doing what I've asked and I greatly appreciate it.

"With that said, I would appreciate if you would be your normal charming selves and not pretend to be jerks."

My homeroom REALLY stepped up!

I want to be incorporating more presentations and explanations into my lessons, so I tried something new today.  I broke the class into groups of 4 and assigned each group one problem from the homework.  Each group got some whiteboards and markers and were told they would be presenting their problems.  Each group used a different method to present, but all did a great job! I had the students applaud afterwards and will be emphasizing the importance of supporting each other.





At the end of each presentation, I asked the class to "tell me something that I love about what they did there."  They always had something.

"You loved how they wrote down the 4 steps."

"You loved how they showed all of their work."

"You loved how they used a picture to solve the problem."

The only one I had to drag out of them was how, in the last picture, the group used a variable to represent the unknown quantity.

8th period did not do as well with this activity.  There were several students who, not being in class yesterday to receive the assignment, tried to claim that they couldn't help their groups.  I'm still having trouble modifying my expectation for a class that meets in 85 degree heat after a day of being cooped up in 85 degree heat.  I allow them more latitude in terms of conversation and off task behavior, but I'm feeling as though the time for that is coming to a close.

I also think that the social make-up of that class is vastly different than period 1.

We talk a ton about differentiating lessons, but I would like to hear more about differentiated behavior expectations.


In geometry, while going over one of the examples, a student expressed that she felt defeated by the math.  I thanked her profusely for her willingness to admit her feelings to others as I'm sure that other kids felt the same, but didn't want to say so.  I also pulled up the link to this great post from Megan Schmidt.  It talks about empathizing with students who feel this way.


In addition, starting yesterday, I'm beginning each class by having a student read the 8 Standards of Mathematical Practice.  Eventually, I have the class recite it as a group.  We make them stand and say the Pledge of Allegiance every day, so why not these?

I consider the 8 SMPs to be the Pledge to Improved Mathematics.

Tuesday, September 9, 2014

Day 11: Digging and Filling Holes

One of the things I find most frustrating about teaching 8th grade is how uncomfortable and unfamiliar the students are with negative numbers.  They have tremendous difficulty with subtracting negatives.  No matter how much I get them to talk about the properties of negatives and subtraction, they have a mental block against what to do when they are together.

This is probably why math teachers have a tendency to ignore the underlying concepts and jump straight to "two negatives in a row make a positive."  **cough cough Nix the Tricks cough Section 2.3 cough**

As a result, I try to use analogies to explain this concept.  Normally, I use money.  My students over the last few years responded very well to the idea that positive numbers represent money that you have while negative numbers represent money that you owe.  This usually works pretty well until we get to the idea of subtracting a negative.  Then the analogy falls apart because I end up using phrases like "If you have 5 dollars and you take away a debt of 4 dollars..."  Then I'm trying to get that sentence to make sense and it's an issue of confusion and grammar and monetary policy.

Today, we digged holes!
"You digged holes... Well, now you're going to fill them."
The discussion went something like:

Me: "Imagine a pile of dirt that's 1 foot high. What would be the opposite of that?"
S: "A hole?"
Me: "How deep would the hole have to be for it to be an opposite?
S: "1 foot, if the pile is 1 foot."
Me: "Alright, so let's say you have a hole that's 1 foot deep and a pile that's 1 foot high.  What could you do with them?"
S: "I guess you could put them together."
Me: "And if you did? What would happen?"
S: "The hole would fill up and you'd get nothing."
Me: "So let's say you have a bunch of holes and a bunch of piles."
S: "You should fill the holes with the piles and see what's left."

So we looked at the expression -14 - (-18).

Me: "What does that negative 14 mean?"
S: "That we have 14 holes.  The minus is the middle means 'take-away'."
Me: "So what are we "taking away from our 14 holes?"
S: "We're gonna take away 18 holes.  But we don't have enough holes to take away, we only have 14."
Me: "So, is there another way to get rid of holes?"
S: "We could add piles."
Me: "What are you saying?"
S: "Adding a pile would be the same as taking away a hole because to take away a hole, you need a pile.  So if we start with 14 holes and then have 18 piles, 14 of those piles will fill in the holes."
Me: "Keep going."
S: "Then we will be left with 4 piles."


The idea of difference in heights (What's the difference between a mountain that 10,000 ft tall and a valley that's 500 ft deep?) was a bit more elusive, but we worked on it.

By the time 8th period came around, it occurred to me that mountains are just very big piles and valleys are just very deep holes.

Of course, I had to draw someone falling from a mountain into a valley...


In 8th period, a group of very loud boys gathered together and were arguing about who the one kid liked and how that girl used to go with this other guy and ...

I was listening to their conversation, getting more frustrated with them being off task when their discussion suddenly was on task and they were arguing about the math in their assignment.

It was an important reminder for me to see that students are able to multitask.  Just because they work in different ways than I do that doesn't mean they aren't working.

I was very proud of them and I made sure to tell them so.
Related Posts Plugin for WordPress, Blogger...