Today the afternoon was a work day. And I so needed it. I spent the last 3 hours or so grading, and I'm still behind. Ugh. At least I feel semi-caught up - meaning the stuff I still need to grade is all from this last week. Nothing older than 4 days to grade. Yay!

There are a couple of reasons grading is getting to me this year - 1. I started collecting and grading homework, rather than just checking for completion and marking down a score. I think it's more valuable for the kids this way - but man, it takes a lot of time! 2. I don't have any after school work time. All of my days (M-Th, anyway) got booked up with one thing or another, and so I don't get any planning or grading done between when school ends and when I go home.

But, I'll get through it. It might mean taking some work home, or maybe just staying 15-30 minutes longer each day, but I'll make it work. That's what teachers do, right?

On a separate note - this morning was a PD session, and we spent the morning watching and discussing a Webinar by Grant Wiggins on the Common Core. It was some good stuff. I got a lot out of the Webinar, and we had some good discussion around it. It gave me a good format to start thinking about incorporating the Practice Standards into my curriculum, and it was a good reminder to keep making kids think deeper - even in the little things I do during my lesson.

We also did a close read of the Practice Standards, and I kept thinking of Dan's Ladder of Abstraction. There is a lot in the Practice Standards that asks kids to abstract situations into math symbols. I like the idea of having ways to help kids build up to being able to do that, and do that well.

# Proof in the City

## Thursday, October 11, 2012

## Friday, September 21, 2012

### Geometry: Unit One

**So, I wrote this a few weeks ago, and just realized that it never published. I scheduled it to publish, but it's just sitting here as a draft. Anyway...here you go. A follow-up of sorts to my Geometry Test post.

My first unit in Geometry is called Lines and Angles. We are introduced to a lot of vocabulary (lines, points, planes, rays, etc) and a lot of notation. We talk about angle relationships with parallel lines and a transversal and we calculate the midpoint and distance of segments on the coordinate plane.

Not a lot in this unit, and it's pretty straightforward (at least, I think so). I expected test scores to be overall pretty high.

So, I've been doing some thinking about the unit, and how I could have improved test scores.

Here's the good:

My first unit in Geometry is called Lines and Angles. We are introduced to a lot of vocabulary (lines, points, planes, rays, etc) and a lot of notation. We talk about angle relationships with parallel lines and a transversal and we calculate the midpoint and distance of segments on the coordinate plane.

Not a lot in this unit, and it's pretty straightforward (at least, I think so). I expected test scores to be overall pretty high.

So, I've been doing some thinking about the unit, and how I could have improved test scores.

Here's the good:

- I made the students take notes. I checked as often as I could that they were actually doing it during class. I made it a part of their grade and allowed notes use on the quiz.

- There was a lot of chances to practice what we learned. I gave homework nearly every class period (every other day because of our block schedule), and we also did some class work.

- Homework was (somewhat) spiraled. I did give some homework about transversals when we were studying midpoint and distance in-class.

- I collected and graded nearly every assignment. If I didn't check for correctness, I gave students a chance to check their own work against an answer key.

- I gave a quiz and got it back to the students in a timely manner. I encouraged them to fix what they missed.

- I gave out a Study Guide with a list of all vocabulary and skills that would be on the test.

- Shorter, more focused homework along with more of an emphasis on in-class work, so I can see how they are doing right away.

- Two quizzes. The unit was 5 weeks long. Two quizzes would have been more appropriate.

- A review day of some sort.

- Fixing mistakes on a quiz is assigned and not optional. Perhaps for students who scored below a certain score.

For the next unit, I am going to put some of these things into place. I am going to continue to make them take notes. I am going to give more quizzes more often, and make kids fix mistakes as an assignment. Maybe kids who score below a 70%? 80%? I am still debating on the review day. I just don't like them. I'll probably do one anyway.

Here's to great scores next time around!

As for these current tests, I still haven't figured out what to do.

## Wednesday, September 19, 2012

### Tests this week and preliminary results

So, I gave a test this week. Two, actually. One in Algebra and one in Geometry.

In Geometry, I felt really good when I handed the test out. I felt like I had given the kids plenty of feedback on their work, and lots of practice. I didn't do a review day (which I dislike anyway), but I felt that we had still spent time learning and practicing what we needed to learn and practice. I felt good about the test I wrote. It seemed fair and that it would provide a good reflection on the students' understanding.

When I handed out the test the next day in Algebra, I didn't have the same feeling. I'm teaching a new unit that I just created, and it's iffy. I knew exactly what I wanted the kids to end the unit knowing and doing. I wasn't sure about how to teach that and even less sure about how to assess that. I wrote and gave out a test anyway. We'll see how they do.

I paused grading the Geometry exams to write this post. So far, scores are either really high or really low, mostly even split. I'm not sure what to do with that. I'm not sure I'm willing to spend class time re-teaching when half of them have it, and I'm not willing to move on if half of them don't have it. Ideally, I could re-teach half of my class, while the other half stayed home or something. Wouldn't that be great?

I am more than a little disappointed with those Geometry scores. Post coming soon about how class time went during this unit, and my ideas about what to change/fix/keep. Also a post on Algebra results.

In Geometry, I felt really good when I handed the test out. I felt like I had given the kids plenty of feedback on their work, and lots of practice. I didn't do a review day (which I dislike anyway), but I felt that we had still spent time learning and practicing what we needed to learn and practice. I felt good about the test I wrote. It seemed fair and that it would provide a good reflection on the students' understanding.

When I handed out the test the next day in Algebra, I didn't have the same feeling. I'm teaching a new unit that I just created, and it's iffy. I knew exactly what I wanted the kids to end the unit knowing and doing. I wasn't sure about how to teach that and even less sure about how to assess that. I wrote and gave out a test anyway. We'll see how they do.

I paused grading the Geometry exams to write this post. So far, scores are either really high or really low, mostly even split. I'm not sure what to do with that. I'm not sure I'm willing to spend class time re-teaching when half of them have it, and I'm not willing to move on if half of them don't have it. Ideally, I could re-teach half of my class, while the other half stayed home or something. Wouldn't that be great?

I am more than a little disappointed with those Geometry scores. Post coming soon about how class time went during this unit, and my ideas about what to change/fix/keep. Also a post on Algebra results.

## Monday, September 10, 2012

### Small change with a big payoff

Alright, so I'm a little slow, but something I've realized this year is that kids don't remember what we did in class last time. At least not without a little reminder. I've been getting much better about building that into the beginning of my lessons, and it is so paying off!

What I've realized is that I spend a lot of time planning and thinking about the flow of my lessons, both in each class, and from class to class. I'm also the one teaching and the one who is already good at math. As a result, I am hyper-aware of what happened last class period when I go into today's class period. I've been assuming my kids are also aware of what happened.

But, they aren't. They don't hang on my every word, they don't look forward to what new math knowledge they can get today, they don't take a moment to reflect on where we are and what we are learning before class starts. So I have to make them pause and reflect at the beginning of class.

I've been noticing that kids seem to understand more. I feel as though I'm able to move forward instead of spend the class time reviewing things that "they should know by now." All because of 1-2 minutes that I take at the beginning to refresh their memories.

It can be as simple as saying and asking, "Remember last time, we were talking about parallels and transversals? Can you look back in your notes and remind yourself what a transversal is?" "List the 5 relationships between angles we talked about." I've mainly been calling on a few kids (randomly...I don't pick volunteers for this one!) to answer my questions, but I also have the idea of having them write it down at the beginning of today's notes.

I really like this small change, even though it makes me feel a little dense that I didn't figure it out sooner.

What I've realized is that I spend a lot of time planning and thinking about the flow of my lessons, both in each class, and from class to class. I'm also the one teaching and the one who is already good at math. As a result, I am hyper-aware of what happened last class period when I go into today's class period. I've been assuming my kids are also aware of what happened.

But, they aren't. They don't hang on my every word, they don't look forward to what new math knowledge they can get today, they don't take a moment to reflect on where we are and what we are learning before class starts. So I have to make them pause and reflect at the beginning of class.

I've been noticing that kids seem to understand more. I feel as though I'm able to move forward instead of spend the class time reviewing things that "they should know by now." All because of 1-2 minutes that I take at the beginning to refresh their memories.

It can be as simple as saying and asking, "Remember last time, we were talking about parallels and transversals? Can you look back in your notes and remind yourself what a transversal is?" "List the 5 relationships between angles we talked about." I've mainly been calling on a few kids (randomly...I don't pick volunteers for this one!) to answer my questions, but I also have the idea of having them write it down at the beginning of today's notes.

I really like this small change, even though it makes me feel a little dense that I didn't figure it out sooner.

## Tuesday, September 4, 2012

### Math Quotes

One of my hobbies is collecting quotes. I love it. I even found a quote to explain why I love quotes:

"I love quotations because it is a joy to find thoughts one might have, beautifully expressed with much authority by someone recognized wiser than oneself." -Marlene Dietrich

Here is one that is among my favorites:

"The simplest schoolboy is now familiar with truths for which Archimedes would have sacrificed his life." Ernest Renan

I like this quote because it reminds me about what I am teaching my kids. I have a whole long list of facts for them to memorize, and if I wanted to, I could just spout them out and make the kids write 'em and learn 'em.

But, the truth is, that list of facts represents years and years of real mathematics work. Math work that is relevant and interesting, not just created to make high school kids groan.

So, when I read this quote, it reminds me to let kids 'experience' math and come to their own understanding of why math is the way it is. I want to let them learn from trial and error what the most efficient way to solve an equation is. I want them to decide that arrows and tick marks and such on geometric diagrams are worth learning and using, because they make things so much easier. I want them to decide that we need a word for "the side of the triangle that isn't next to the angle" I want them to know that true math knowledge is hard earned, but so worth it. I don't know if that was it's intention, but this quote reminds me of that.

## Wednesday, August 29, 2012

### Upcoming Project I am Super Excited About

So, later in Algebra 1, when we get to Functions (probably around early November), I am going to have the kids do this super awesome project!

The current title is, "Is It Linear?", but I am hoping to change it. That's just what I've been calling it in my head.

I haven't typed anything up or hammered out all the details yet, but the basic idea is that kids will make a hypothesis about a relationship they think is linear. For example, the temperature of water vs. time in the microwave or the distance of the water vs the number of pumps on my Super Soaker. Then, in their science class (I'm already in cahoots with the 9th grade Science teacher!) they will develop an experiment, perform it and collect data. Lastly, in my math class, we'll use the data to create a scatterplot, find the line of best fit, determine how "linear" the relationship is, etc.

I'm stoked! I love that they will get to work on this project in two classes. I love that we will start it relatively early in the unit, before they really have a grasp of what functions are, and use it to help them come to that understanding. I love that it will (hopefully) clarify and deeply define what "linear" is, in a way other than "it makes a line."

I've been working on it here and there since the middle of the summer, and will keep doing so until we do it, so I hope it turns out to be as valuable as I am imagining.

Anyway, what I'd love from you are some ideas for students to test. I'd like to have my own list to prod kids along if they are having troubles coming up with something. Truthfully, it doesn't even have to end up being linear, just something kids might think is linear beforehand. That actually might be pretty cool if someone gets results that aren't linear.

The current title is, "Is It Linear?", but I am hoping to change it. That's just what I've been calling it in my head.

I haven't typed anything up or hammered out all the details yet, but the basic idea is that kids will make a hypothesis about a relationship they think is linear. For example, the temperature of water vs. time in the microwave or the distance of the water vs the number of pumps on my Super Soaker. Then, in their science class (I'm already in cahoots with the 9th grade Science teacher!) they will develop an experiment, perform it and collect data. Lastly, in my math class, we'll use the data to create a scatterplot, find the line of best fit, determine how "linear" the relationship is, etc.

I'm stoked! I love that they will get to work on this project in two classes. I love that we will start it relatively early in the unit, before they really have a grasp of what functions are, and use it to help them come to that understanding. I love that it will (hopefully) clarify and deeply define what "linear" is, in a way other than "it makes a line."

I've been working on it here and there since the middle of the summer, and will keep doing so until we do it, so I hope it turns out to be as valuable as I am imagining.

Anyway, what I'd love from you are some ideas for students to test. I'd like to have my own list to prod kids along if they are having troubles coming up with something. Truthfully, it doesn't even have to end up being linear, just something kids might think is linear beforehand. That actually might be pretty cool if someone gets results that aren't linear.

## Sunday, August 19, 2012

### First week and new ideas for the year

One week down! The first week of school went by so quickly, and it was pretty fun. I enjoyed getting to know the new Freshman class. A few of us 9th grade teachers decided we have a crush on them. The sophomores did their first homework assignment! As a class, they really struggled with homework last year. I made tearful remarks to the Juniors about how I won't get to have them in my classes anymore.

Classes went well the first week. All of that planning and preparing over the summer paid off. I thought a lot about how I wanted my classes to run, and how to introduce that to the students, and I think it is going to work out! I've never felt this way at this point in the school year - super-confident, pleased about how the year started, and more excited to keep it going than ever. I mean, I've had good starts to the year before, but something about this year feels different. Of course, this is the most experienced I've ever been, but I think this year will be so much better than previous years, more than just typical "I've got another year under my belt this time around" better.

A couple of things I'm going to do differently. Or just plain do.

1. Homework Sets. In my Algebra classes, I am going to give the same amount of homework, but make it due less often. I still plan on assigning nightly homework, but I will just hand out and collect a week to a week and a half's worth at one time. That's actually another change - collecting homework. In the past, I've checked for completion, and given a kid a grade without ever collecting his work. Less paper I have to deal with, right? But I found that it made kids start to slack a bit on their homework. And not care as much if they didn't get things right. I think 9th graders are still pretty young, and need some more accountability. So, I'm collecting and grading homework. (Just a few problems from each assignment.) But I also like the idea of giving them more than a night to do it, so that they have time to come and ask me for help before it's due. And, truthfully, I'm not good with organization and keeping track of papers. So I decided that I would give them a packet, and give them lots of time to complete it. One possible drawback: The kid that waits until the day before it's due to attempt a week of homework. To prevent this, I'm still going to assign nightly homework ("Do page 3 tonight...") and get parents on board. And I'm sure I will also have to make some accommodations for some students. ("Your homework is due everyday.") Last year's Freshmen were not good at doing homework, so I've decided to not try this system with the Sophomores. I'll keep you posted on whether I like it or not.

2. More Problem-Solving. I want to make kids think! I've been wanting to include more problem solving days in my classroom, making kids figure things out and then share their solutions. I am going to do it this year! I found quite a few ideas over the summer, and I'm getting better at "being less helpful." I started out my Algebra class with a problem-solving lesson and it was a hit!

3. Common Core (-ish) I didn't dare touch Geometry this year, but I am doing a cross of current Arizona standards and Common Core standards in Algebra 1. I feel like the kids won't be prepared for a full-on Common Core curriculum, as they'll be missing quite a few pieces. But I tried to get some of the major ideas in, and took out Arizona stuff that will not be on Common Core.

4. Super Good Projects. My school is a believer in Project-Based Learning. Last year, I tried to do a few projects, and they were mediocre. They didn't have a lot of meaning or purpose, and weren't executed well. But I learned a lot, did some research and planning over the summer, and have some great projects coming this year. I'll be sure to blog about all of them. One involves students doing an experiment to see if two quantities have a linear relationship. I can't wait!

5. Blog more. Duh.

Classes went well the first week. All of that planning and preparing over the summer paid off. I thought a lot about how I wanted my classes to run, and how to introduce that to the students, and I think it is going to work out! I've never felt this way at this point in the school year - super-confident, pleased about how the year started, and more excited to keep it going than ever. I mean, I've had good starts to the year before, but something about this year feels different. Of course, this is the most experienced I've ever been, but I think this year will be so much better than previous years, more than just typical "I've got another year under my belt this time around" better.

A couple of things I'm going to do differently. Or just plain do.

1. Homework Sets. In my Algebra classes, I am going to give the same amount of homework, but make it due less often. I still plan on assigning nightly homework, but I will just hand out and collect a week to a week and a half's worth at one time. That's actually another change - collecting homework. In the past, I've checked for completion, and given a kid a grade without ever collecting his work. Less paper I have to deal with, right? But I found that it made kids start to slack a bit on their homework. And not care as much if they didn't get things right. I think 9th graders are still pretty young, and need some more accountability. So, I'm collecting and grading homework. (Just a few problems from each assignment.) But I also like the idea of giving them more than a night to do it, so that they have time to come and ask me for help before it's due. And, truthfully, I'm not good with organization and keeping track of papers. So I decided that I would give them a packet, and give them lots of time to complete it. One possible drawback: The kid that waits until the day before it's due to attempt a week of homework. To prevent this, I'm still going to assign nightly homework ("Do page 3 tonight...") and get parents on board. And I'm sure I will also have to make some accommodations for some students. ("Your homework is due everyday.") Last year's Freshmen were not good at doing homework, so I've decided to not try this system with the Sophomores. I'll keep you posted on whether I like it or not.

2. More Problem-Solving. I want to make kids think! I've been wanting to include more problem solving days in my classroom, making kids figure things out and then share their solutions. I am going to do it this year! I found quite a few ideas over the summer, and I'm getting better at "being less helpful." I started out my Algebra class with a problem-solving lesson and it was a hit!

3. Common Core (-ish) I didn't dare touch Geometry this year, but I am doing a cross of current Arizona standards and Common Core standards in Algebra 1. I feel like the kids won't be prepared for a full-on Common Core curriculum, as they'll be missing quite a few pieces. But I tried to get some of the major ideas in, and took out Arizona stuff that will not be on Common Core.

4. Super Good Projects. My school is a believer in Project-Based Learning. Last year, I tried to do a few projects, and they were mediocre. They didn't have a lot of meaning or purpose, and weren't executed well. But I learned a lot, did some research and planning over the summer, and have some great projects coming this year. I'll be sure to blog about all of them. One involves students doing an experiment to see if two quantities have a linear relationship. I can't wait!

5. Blog more. Duh.

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