Missing the Point

Recently, I wrote about my system for assigning practice. I give students an answer bank with every assignment so that they can find mistakes and revise their work.

I know why I do it this way. The purpose of these assignments is practice, so I want to give them feedback while they are working. I want students to keep practicing until they are doing it correctly. I want them to learn from their mistakes.

We have only been in school for 8 days, but I have spent a lot of time trying to communicate this to students. I keep getting responses that tell me students don't really get it, like these:

1.  Extreme excitement, because having the answers feels like legalized cheating.
2.  Confusion (usually from the high achieving students), because they don't think it is fair that everyone has an equal chance of getting all the answers right.
3.  Resistance, from students who feel like it is pointless to show their process since they already know the answer.

Practice is a process, dear students! I will assess you soon, I promise.

I am not sure how I can help my precious Algebra 2 students to understand.

It seems obvious (but not all inclusive) to use some sort of sports analogy:  If you are learning a new football play and you totally mess it up, the coach doesn't mark a D- in the grade book and call it a day, does he? No, he doesn't. He sends you back out there to try it again until you get it right.

That is all I have for now . . . I am going to keep working on it.

Sticker Survey

I have always done some kind of survey-type thing at the beginning of the year. My lofty goal is always to collect the data and learn valuable information about my students. Sadly, most years the surveys get filed away. I get busy with the planning of lessons and the grading of quizzes and such, and I never look at them.

This year I decided to put the survey questions on card stock and post them around the room. I gave each student a strip of stickers.

I think these two are interesting, placed right next to each other. (The grade I usually get in math is . . . , and My goal for a grade in math is . . . ) I assured them their responses would be anonymous.

This was kind of a last minute idea, so I had to work with what stickers I could find. I think next year I will try to find something real distinctive for each hour, so I can easily compare the data for a single class.

Anyhoo, it was a fun first day activity and it was definitely more useful than my old survey.

My Thoughts On Homework

Lately I have been thinking about how I assign, collect, and give points (or not) for homework. (For the record, when I say ‘homework’ I really mean ‘practice’. I want my students to practice every day. Sometimes they practice at home.)

I know a lot of bloggers have had success with not giving points for homework, but I am not ready to go there yet. I tried not giving points once during my first year of teaching and it was a disaster. Then again, lots of things during my first year of teaching were a disaster. But if giving students a score on a paper helps them to reflect on the quality of their efforts as they practice math, then I’m okay with using points.

So this is what I do . . . In bold is the thing I am trying to accomplish, and after that is how I attempt to make it happen.

1.     The perfect system emphasizes quality practice. Students need to reflect and make corrections as they are working:  I spend a lot of time teaching students how to practice. I want them to work out a problem, and then check the answer and find any mistakes and revise their work as needed. I hate to say just “show your work”. I do emphasize the importance of justifying your solution so that you can communicate to others how you found it, and prove it is correct. I make up a page of problems where some are perfect, others are missing work/justification, others have a wrong answer, and some have a right answer but the work/justification is incorrect or incomplete. Then students work with a partner to critique and discuss the quality of the practice. This takes time, but it is worth it.

2.     A good system gives students feedback while they are working, whether at home or at school. Ideally, they can find out if their answer is right or wrong without being told the actual correct answer: I put the answers to the problems in random order in the margin of the assignment. When students finish a problem, they find the answer in the margin and cross it out.  The only drawback here is that they can use the process of elimination to know the answer to the problems at the bottom of the page. Still, it works pretty well. I am thinking of tweaking this a little this year using the sum of a couple answers (sort of like Kate’s Add ‘em up). Instead of writing all the answers in the margin, I think I will try something like “the sum of #1 and #2 is _____”.  Then they will know if they need to fix their work without giving away any answers.

3.     If points are given, the points should reflect the quality of the practice vs. the number of answers that are correct on the first try:  A problem counts for points if it has correct work (or justification of some kind) leading to the correct answer, regardless of how many tries it takes you to get there. I don’t really even think of it as a “homework” grade. I want the point value to help students think about how well they are practicing. Hmm, maybe I will start calling it the “quality of practice” grade. Or something like that . . . I will have to think of something more catchy.

4.    If points are given, the system minimizes teacher time spent grading and recording:  My students spend so much time learning what good practice looks like that they know whether a problem they have finished qualifies. It has correct work leading to the correct answer and it counts, or it doesn’t. So students take the number of problems that qualify as good practice divided by the total number of problems times 5 (because I want a practice assignment with 20 short problems to have the same value as a practice assignment with 4 or 5 lengthy ones). I will even put that formula at the top of the paper to make it simple. Round the number to the nearest tenth and hand it in. Teacher records that number.

I am pretty happy with this system, but I still have a few problems. Sometimes students put a score on their paper that isn’t accurate (pretty easy to catch). Sometimes students rely too heavily on clues from the answers in the margin (maybe my little tweak will help that). Sometimes students copy their friend’s homework in the hallway before school (but at least they have to copy the work, too).

What's your homework system?

Common Core Response: Panic?

Last fall, when I heard about my state's adoption of the Common Core State Standards, my response was panic. But it wasn't the "Oh no, we have new standards" kind of panic. It was the "Oh no, we're gonna have a new assessment" kind of panic. Yes, it is true. I suffer from a fear of high stakes testing.

I set out to learn as much as possible about the new standards. I attended a couple of webinars, I enrolled in an online class, and I attended a two-day conference. I spent a lot of time during the month of June reading documents, writing papers, and participating in discussions. I felt like I was learning quite a bit, and I resolved to blog my thoughts.

Each time that I sat down to write about CCSS, I had nothing to write. I was completely blank. Weird. But I did notice that the panic was gone, so that is a good thing. The best I can do now is a bulleted list of random thoughts . . . which seem to have led me away from the panic I was feeling:

1.  The CCSS are not just about WHAT we teach, but also about HOW we teach. There are now 8 practice standards to guide our teaching methods. Students need to learn how to think, not just follow a set of steps. That is something I need to work on anyway.

2.  The new standards are more rigorous and more complete than our retired standards. In Kansas, our standards only went through the 10th grade. We've only been testing a limited number of these standards. A more rigorous update was needed, no question.

3.  The thing we want to know about the most (assessment!) is the thing about which we know the least. There are two companies working on the new assessment, and it is in the early stages of development.

4.  We most likely have 3 - 4 years before the new assessment rolls in.

5.  I know I am going to need to do some things differently, but three years is a relatively long time to make the necessary adjustments. I am going to make a list of things to change, and a time line for myself. One. Step. At. A. Time.

6.  I want to believe that if I work towards helping students be better thinkers, and make sure that the standards are included in my curriculum . . . if I focus on good teaching vs. state assessment preparing . . . that everything will be fine . . .

7.  I believe that this is a positive change, even though the transition will have its challenges.

8.  Panic isn't going to help.

Dear Summer, Please Slow Down

I can't believe that four of my precious summer weeks are gone! Here's what I've been doing:

1.  Moving:  My husband has taken a new job. He is leaving his position as principal of a small K-12 school to be an administrator in a larger district. So, we moved to a more centralized location between our schools. My last day of school was May 26th and we moved the very next day.  

2.  Unpacking, Sorting, Organizing, Tossing, Putting Away . . . On the bright side, our new home is located in a town 20 times larger than the old one. It has multiple grocery stores and multiple stop lights. Now we can walk to the park, dentist, hardware store, library, pool, and more. The mail is delivered right to our front door. Not to mention, there is a place down the street with half price ice cream on Tuesdays. We are living large, for sure.

3.  Recovering from a hail storm:  Five days after moving in, we had baseball-sized hail. I have never seen anything like it! We needed a new roof, new gutters, paint on the house . . . Oh, and new cars (both were totaled in the storm). Garages are only helpful in these situations if you park inside of them.

4.  My other full-time job:  Mama to this curly-headed cutie. She is almost 2. Full time job, indeed! She is growing up so fast. If some things on my summer list don't get finished because I spent too much time playing with her, I am not going to feel bad. 

5.  Common Core, Common Core, Common Core:  One of my biggest professional concerns has been our state's adoption of the CCSS. It means there will be a new assessment, when we are pretty comfortable with the current one. It means there will be changes to what I teach and how I teach it, but I am  not sure what kind of changes. I just finished an online course, and I will be attending a two-day conference this week. I plan to post some of the things I am learning. Soon, I hope.

Lost Treasure, Found! (a fun way to start class)

Most of my teaching career has taken place at my current school, but my husband's job took us away for a couple of years. During that time, I taught at Bulldog High.

There was a really great chemistry teacher at Bulldog High, Mr. S. He was a tough teacher, but the students loved him. He opened every class period with an enthusiastic class chant. If the classroom door was open, you could hear it all the way down the hall.

It started like this:
Mr. S:  Good morning Bulldogs!!!
Students:  Good morning Mr. S!!!
Mr. S:  How are you today?
Students:  Super great and getting better!

The chant when on and on for awhile. Over the years, students had suggested additions and it became a tradition in Mr. S's class. The students loved it!

Anyway, I really wanted my own chant for my class -- but that was Mr. S's thing and I didn't want to take away from its uniqueness. When I left that school, I asked Mr. S to write down the entire chant. I thought I would modify it for myself and start using it, since I'd be in a different school. I was super excited to do this!!!

Sadly, I lost my copy of the chant. Then I forgot it existed . . . until today! The hubs and I are packing up for another move. I found a small box, never unpacked, full of personal stuff I'd packed up from my Bulldog classroom. The chant was in that box!! Woo Hoo!

I am already thinking of how I can use it next year.

Here is the entire chemistry cheer, as written by Mr. S:

Mr. S:  Good morning bulldogs!
Students:  Good Morning Mr. S!
Mr. S: How are you today?
Students:  Super great and getting better!
Mr. S:  How far?
Students:  All the way.
Mr. S:  How much?
Students:  All of it.
Mr. S:  How many?
Students:  6.022 times 10 to the 23rd particles per mole
Mr. S:  What's our favorite class?
Students:  We love chemistry!
Mr. S:  What's our motto?
Students:  Can do!
Mr. S:  What's the truth of the matter?
Students:  The impossible takes a little longer.
Mr. S:  What's the platinum rule?
Students:  If you mess it up, clean it up.
Mr. S:  What's our philosophy of life?
Students:  WE NEVER GIVE UP!!!

So fun! Thank you, Mr. S!

Color Coding: For Sketching Piecewise

I tried a new (for me) approach for introducing piecewise functions in my Algebra 2 class, and it went over pretty well.  There is nothing really earth-shattering about this method, but it does involve color-coding -- and that is totally on my list of favorite things!

First of all, I am using only basic parent functions and their transformations that my students are already familiar with (linear, quadratic, and absolute value).  They do not need to plot points, because they already know how to sketch these graphs. I spent some time reviewing these before the lesson.

I start out with the idea of a restricted domain.  Students sketch the function, using the entire coordinate plane . . .

Then we worry about this "if" that comes after the function. Students color the restricted domain, and the corresponding portion of the x-axis.

Then they draw vertical lines to enclose the restricted area and shade it in completely.

And then they erase everything that is not in the restricted area.

We practiced these for a while before moving on to piecewise.

For piecewise, we shaded each restricted domain with a different color. Then shade in the corresponding restricted areas.

By the time we reached this point, most students could draw the graphs within the restricted areas without drawing the entire graph and erasing.

I've taught this lesson before, but pairing it with colored pencils was a first for me. I am pretty happy with the results, especially considering that a bunch of them are *DONE* and have started to shut down for summer.

Secret to motivating students this time of year, anyone?

Or, to get everyone to at least bring a pencil?