Summertime Reading

One of my favorite things to do in the summer is to read and one of my favorite books to read once the reality of Back-to-School sets in is a trio of books by David R. Johnson. I found Mr. Johnson's first book "Every Minute Counts" early on in my career and quickly bought the sequels "Making Minutes Count Even More" and "Motivation Counts". I don't even know if these books are in print any more, but they have been my summer staple for years. I also lend them to student teachers and new teachers to read. The books are short, more like booklets, with around 100 pages in them, so they are quick to read but they definitely pack a punch.

Last night, I decided it was time to start my yearly re-read and decided to pick up the third book. The first two are more about classroom management and how to set up your routine, while the last book is more about best practices in math. "Motivation Counts" was published in 1994 and while I was reading it, it really struck me how slow education is to embrace change in our teaching methods. Other than the fancy technology that now populates classrooms, I would venture to guess that most classrooms have the same structure that they did 50+ years ago. Even with the research on best practices, how to engage learners, teachers that fully agree that change needs to occur, it is sometimes so overwhelming that we quickly fall back into old habits and comfortable routines. We tend to teach the way we were taught by teachers who taught the way they were taught by teachers... (rinse, repeat).

Here's the quote that got me: (remember, this book is close to 20 years old now)

Lesson plans for the traditional classroom routine, as you can see from this list, detail *my* activities; they do not include what *the students* should be doing during class....

..In a recent television interview, a CEO in a major industry cited the main objectives for our schools as follows:

• Teach problem-solving experiences and skills.
  
• Teach communication skills.
  
• Teach students how to learn.
  
• Teach students how to work effectively as a team member.
  
• Give students an ability to handle change.
  

...it is very obvious that what industry wants, and what the traditional rountine offers, are not at all compatiable - or even complementary. Industry wants involved, active thinkers who can work together and deal creatively with the unexpected....

I think most of us know and agree with the above and even strive to accomplish those goals. For years, this quote has really hit me in the gut. I know I start the school year with big plans, but as reality sets in, it can be easy to fall back on that traditional routine where *I* am doing the work and the students sit back passively. I find it wild, though, that today's goals are still what they were 20 years ago and that little progress has been made in changing what a traditional math classroom looks like.

I can easily say that, of all the professional books I've read through the years, this trio of books have had the most profound influence on me as a teacher. Even though I've read these books numerous times, they never fail to inspire me and make me think about how to be more effective in the classroom.

What is your must-read book for teachers?

Incorporating Writing in Math

With students returning in just a few weeks, I am digging through old materials looking for lesson ideas. Tonight, I ran across this...

The question "why so much writing?" can be answered in three basic ways:
1. Writing promotes clear thinking.
2. Writing promotes effective and long-term retention of what has been learned.
3. Writing provides individuals and groups in a complex world with a voice and a record.

Students need to understand that writing is the single most powerful tool for thinking, learning and participating in the broad culture of a society.

Source: Write Path Mathematics from AVID

Now my question... how do you incorporate writing in your classroom?

Using SBG in AP Stat

Last year I implemented SBG in Algebra 2 and loved it. However, I just could not wrap my head around how to implement it in AP Stat, so I spent a lot of time this past year thinking on how I could make it work. This is more of a mind-dump of ideas than a complete plan - a way of getting my thoughts down on paper and put it out there so that I can analyze it further.

This Past Year
For SY 2010-11, grading in AP was pretty traditional for me. I had three categories in my gradebook - Tests/Quizzes (65%), Assignments (20%), and Final Exam (15%). The Assignments Category contained pretty everything that wasn't a test or quiz. This included weekly AP MC practice, POWs (Problem of the Week AP problems), worksheets, labs, etc.

Tests and Quizzes
I already set up my Learning Targets (LTs) and provided them on my assignment sheets for each unit over this past year. (See Unit 3 HERE). I think each LT Quiz will cover 2-3 LTs. Where I struggle here is how to set up the LT Quiz. In Alg2, each LT has 3 problems (basic, average, and advanced levels), and I don't know how well that will work out with AP. I'm thinking maybe a MC question and then two FR questions. Of course, the layout will be different than the current Alg2 layout, allowing a question stem to be used for multiple LTs. I would still use a 4 point scale for each LT, like I do in Alg2. I think Unit Tests would pretty much stay the same as they are currently are, with a MC and a FR section, with the grade being a traditional test grade. This would allow the quizzes to be more skills based and assessed, whereas the tests would be more summative.

Remediation and Reassessment
This past year, students could retake a different form of a quiz *if* they provided proof of remediation, which was the practice problems on the assignment sheet for that chapter. They could also make test corrections if they did at least one problem from each objective on the assignment sheet. For the most part, I liked this plan. This next year, it would roughly stay the same, but to reassess a Learning Target, they would have to work the problems specific to that LT, rather than the entire chapter. For test corrections, they would still have to do at least one problem from each LT, PLUS have completed the Unit's Summary Sheets (see Unit 3 HERE)

Issues I need to figure out

• What percentage breakdown do I want to use for Tests, LT Quizzes, Assignments, and Final Exam? The Final is district mandated to be at least 15%.
  
• Actual AP questions often cover multiple topics. While I could edit them for the LT quizzes to only include the current objectives, I would like to have that cumulative element. This could be a reassessment opportunity, but with only one data point, how would I grade it on a rubric? Maybe those "mixed-bag" style questions should be on the summative tests, not the quizzes?
  
• What to do about the Assignments category? I could leave a small percentage of the grade devoted to this category. In Alg2, their grade is purely assessments, and all of their assignments are non-graded, feedback only. I'm not sure I'm ready to go there in AP just yet. I do see value in the items placed in this category, but would not want them in either assessment category since a lot of it is lab investigations, partner work, etc. The other issue with this category is anything that isn't done in class has the potential to not be turned in on time, which leads us down that "late work" rabbit hole.
  
• Should the tests be unit based (like they currently are), or time based (like every 6 weeks)? I like unit based tests because things seem so neatly packaged, but I worry that that last chapter being quizzed won't be graded/returned/processed/remediated/reassessed prior to the unit test date. I like the idea of every 6 weeks (covering LTs up to Chapter X), but worry it might feel awkward and not flow well, but theoretically would give that cumulative element needed in preparation for the AP exam in May.
  
• One of my biggest issues is that I'm a pretty slow grader in AP. With Alg2, I almost always had their quizzes back to them the next day, sometimes it took two days, but rarely more than that. With AP, there is so much reading that you have to do that it really bogs down the process.
  

New idea for next year One thing I've done for several years is a weekly POW that is a previous AP problem. I take these up on Friday and provide feedback and an AP score. This has worked fairly well for years, with the exception of a few kids here or there not getting them turned in, etc. This year, however, I had one class that was the class from hell when it came to turning these in. Seriously, out of 20 kids, it was pretty common to have less than half of the class turn it in. This really pissed me off, especially since they were assigned on Tuesday, given 10 minutes to work with their partner to read, discuss, and sketch out a solution, then 3 days until it was due in final format. After some thought and an "a-ha" moment earlier this summer, I think I am going to do two things to hopefully fix this problem. First, I am going to do daily warmups that consist of parts of AP problems. I can give up a few minutes a day to have the kids write a solution to a part of an AP problem. Then, I will either provide the scoring guideline to the class for whole-class feedback or sometimes take them up for more individualized feedback. Second, on a regular basis (maybe once a month?), we will have an AP quiz with maybe 4 AP problems and they have to choose 3 to completely answer and I'll grade it using the rubrics. I'm not sure where these will fit in my grading scheme yet though :) Wrapping it up
I don't have the details all ironed out, but overall, I think this is a plan I can live with for a year while I refine it. I think this provides me the detail I want on the individual objectives while still maintaining the big picture/integrated structure needed in Statistics. Now that I've identified the big issues and concerns that I have, I think I will be able to work on strategies to fix those issues. As always, I appreciate any feedback and questions to help me guide my thinking.

My Summer To-Do List

Oh my gosh, it's now July!!! Back to school aisles and sales are popping up all over and I have NOTHING done!! So, thanks to some inspiration from some blogger/twitter friends, I decided I had better put my to-do list down on "paper". There is just something satisfying by crossing things off of a list!

You will note that my to-do list is not something that easily lends itself to crossing off items. Most of these are a work in progress that will continue through the year. The idea behind this list is to help me focus on what I need to work on, rather than the nitty-gritty details. Some (most?) of these will not get done by August 15th, but I can make headway on putting together a plan for them.

• Read. I am working on UbD, but have several others in line as well, including some on Habits of Mind. Need to do some personal reading too:)
  
• SBG. I need to figure out how to make it work for AP, which isn't as skills based as Alg2. I also need to do some minor tweaks to Alg2.
  
• WICR. I really want to work on incorporating Writing, Inquiry, Collaboration, and Reading in my math classes. I usually start off the year fairly well, but need to keep this going throughout the year.
  
• Active Learning. I did this in AP and was mostly pleased with how it worked. I need to do some revisions in AP and increase this component in Alg2. I am in the process of going through and finding labs to add to my binder of ideas.
  
• Warm-Ups. This year, I really struggled with Warmups and I really need to go back to them. In AP, I think I am going to do formative assessments using parts of AP problems. I'm not sure on Alg2 yet.
  
• Cumulative Work. This has been a goal for several years, but it often goes by the way-side due to time crunch. I want to make a consious effort to have assessments and assignments that have previous knowledge involved.
  
• Technology Integration. Supposedly we will have access to laptops in our new building, so I would like to beef up my class website to be more of a learning portal. I would like to integrate tools like Flubaroo (Thanks Fouss!), G-Docs, Wiki, etc. However, until I have full confirmation that this technology really is going to be available, this is kind of low on my priority list.
  

I'm sure there are more things to add. I've worked a bit at most of the ideas listed, but I don't have anything concrete yet, which is a bit frustrating. I have a jumble of ideas floating in my head and lots of dreams of what to do, but the nitty gritty details just haven't settled down yet. *sigh* I need July to go slower than June did :)

Active Learning and UbD

Our bookclub has been reading Understanding by Design. The first few chapters really gut-punched me in several places and I marked next to them "BLOG POST!!". However, I was out-of-town at the AP Reading and a workshop, so it's taken a while to actually get my thoughts down on "paper".

Here's what got me in Chapter 1...

"How will we distinguish merely interesting learning from *effective* learning?" (pg 14)

"But many teachers begin with and remain focused on textbooks, favored lessons, and time-honored activities - the inputs - rather than deriving those means from what is implied in the desired results - the output. To put it in an odd way, too many teachers focus on the *teaching* and not the *learning*. They spend most of their time thinking, first, about what they will do, what materials they will use, and what they will ask students to do rather than first considering what the learner will need in order to accomplish the learning goals." (pg 15)

That still has the power to take my breath away. How many times have I been that teacher? How many times I have thought about what *I* will do without considering the end goal? One of the design tips suggested going up to a student mid-lesson and asking them "What are you doing? Why are you doing it? What is its purpose/connection?" and I want to do that more this year. I want to be more explicit in the WHY, so that at any point kids should know the purpose of the lesson/activity.

A few days later, we read and discussed chapter 2... again, I felt convicted:

"Doing something correctly, therefore, is not, by itself, evidence of understanding. It might have been an accident or done by rote." (pg 39)

"Students should not be able to solve the new problems and situations merely by remembering the solution to or the precise method of solving a similar problem in class It is not a new problem or situation if it is exactly like the others solved in class except that new quantities or symbols are used." (pg 41)

"We cannot *cover* concepts and expect them thereby to be understood; we have to *uncover* their value - the fact that concepts are the results of inquiry and argument." (pg 46)

I am guilty of coverage. Especially this year :( After 11 snow days, I was in a race against the clock to cover it all. I cringe to even use that word, but it's what I did :( I am also guilty of the new problem issue, although not as bad as I used to be. Early in my career, I was bad about giving a worksheet of 20 problems that were all alike, then giving a quiz with 2-3 more and declaring a success because the kids were able to repeat a process like a trained monkey. Thankfully, I have gotten away from that as much, but it still can creep up on me if I'm not watching.

The next few chapters in UbD weren't as exciting to me, but now we're on Chapter 5, which is about Essential Questions (EQ). I'm about halfway through the chapter at the moment and am eager to finish it and discuss it with my bookclub buddies. Last week, I was at an AVID workshop and one of the cornerstones of the AVID system is the use of Cornell Notes (CN). This year, they rolled out an updated version of their CN template that includes a space at the top for the EQ. I know a lot of districts around the country have adopted UbD as a planning tool and require their teachers to post the daily EQ on their boards at the beginning of the hour. I really like this new addition to the AVID CN template because it helps focus the students in their note-taking and their summary should be a direct link back to the EQ of the day.

As always, when I leave an AVID workshop, I feel challenged to do more WICR activities in my math classes. (WICR = Writing, Inquiry, Collaboration, Reading). I really feel that the use of WICR activities may help the issues mentioned above and aid in student understanding of concepts. Today, as I was working on some literacy strategies in math, I saw a link being tweeted about PBL, which lead me to another link about Student Centered Learning. (link here) The idea behind this article is that this teacher writes a step-by-step lesson plan and has his students teach themselves. That's not a very good explanation, so please go read his article for yourself. :) I do something very similar in my AP class, where students work through lab activities to gather data, learn vocab and concepts, and work collaboratively with their groups with me acting as a facilitator. I am eager to try something similar (on a smaller scale) with Algebra 2. All afternoon, I tried to visualize this classroom dynamic and the pros/cons of it. I'm not there yet, but so far, I think this could work for me.

It's been a busy summer and while I love going to workshops and learning new methods/ideas, sometimes I walk away feeling pretty down on myself. I don't know if it's something other teachers feel or if it's the perfectionist in me. I know I always have room for improvement and I think that quest for continuous improvement is a good thing. At the end of the day, all I want is to be able to answer "YES" to this question... "Have you done everything in your power to be the best teacher/person that you could be today?"

SBG - Reflections on SY 2010/11

Last summer was a changing point for me as an educator. Fed up with my then method of grading, irritated at the "points-game" that my students played, and a lack of consistency in grading amongst teachers led me to reach out to the twitter/blog-o-sphere to build a better mouse trap. As a result, I became drunk on the Standards Based Grading (SBG) Kool-aid and I'm so glad I did.

If you go back and read the posts from last summer, you will see a lot of uncertainity in my posts as I tried to figure out how to best implement SBG in my classroom. Now that a full year has gone by, I want to provide some information on implementation, what worked for me and what didn't, and how I plan to modify it for next year.

Disclaimer #1: I only did SBG in my Algebra 2 classes and I'm still working out the details on how to implement in my AP classes for this upcoming year

Disclaimer #2: I am writing this post with the assumption you are already familiar with the basics of SBG. If not, I would definitely recommend Robert Marzano's Classroom Assessment and Grading that Works. A lot of my ideas are borrowed from his research.

How SBG works in my classroom...
At the beginning of a chapter, students are provided with an assignment sheet (Click HERE) which has a list of Learning Targets (LTs) and practice problems for each LT. In general, the LTs were from the lesson objectives of my textbook, but I did sometimes combine or even eliminate smaller objectives. For each LT, I broke down the traditional assignment from the textbook to 5 or so problems per LT, trying as hard as I could to provide a range of difficulty for each LT. I also tried to select odd problems so the students would have access to the answers in their textbook.

After 2-3 lessons (roughly 4-5 LTs), we would have a quiz over the material. Each LT had 3 problems, the first one was fairly straightforward and basic, the second problem was of average difficulty, and the third problem was of more advanced difficulty, often asking them to apply their knowledge in a new way or combining multiple skills. (Click HERE to see a sample quiz). Each LT was graded as a C (for Correct), P (for Partial), or I (for Incorrect). The C/P/I's were then combined for a rubric scale grade for each LT, with the more advanced problem's score weighing a bit heavier than the basic problem's score. I used a 4 point rubric, which I then converted to a 10 point "gradebook" grade due to limiations with my district gradebook.

In general:
CCC = 4 = 10/10 - You totally have this concept mastered!
CCP = 3.5 = 9/10 - You are almost there, just a minor error (usually a sign issue!)
CCI = 3 = 8.5/10 - You've got a pretty good grasp on the material
CPP = 2.5 = 8/10
CII = 2 = 7/10 - You have a basic understanding of the material
PPP = 1.5 = 6.5/10
PPI = 1 = 6/10 - There is a glimmer of knowledge of the concept
III = 0.5 = 5/10 - You have no clue, but you gave a valid effort
--- = 0 = 0/10 - You left it blank or no valid effort
**Note, not all combinations of C/P/I are listed... this is just a general guideline of what I did. Sometimes a CPP was a 3 depending on the strength of the Partial.

The night of a quiz, I went home and graded them, then recorded them in my gradebook on the 0-4 scale. I kept a paper gradebook (Blank copy HERE) because I wanted to keep track of student scores and reassessments, plus we don't have online access to our gradebooks at home :) Each square in the gradebook is large enough to write several scores, so it worked well for me. (See Sample GB HERE)Probably the most difficult thing for me was that I've always been a slow grader so I really didn't know how well I would do at getting quizzes back the next day. However, after a few quizzes, I was amazed at how speedy it was to grade, and so it wasn't the dreaded chore that it had been in the past.

The next day I handed the students back their quizzes. On the first few quizzes, I took the time to re-explain the system and what the rubric score meant. I really think that the time I took to model and explain the SBG system paid off in more ways than I could have expected. In the past, students had looked at their overall grade and then thrown their quiz away (or in their backpack, never to see the light of day again). However, with SBG, students really took the time to read the feedback, do an error analysis, check with a buddy to compare methods of solving, and rarely did I find a quiz in my trash can or recycle bin. In fact, most students kept their quizzes in their binders, in numerical order and even in May, they were able to produce quizzes from the fall semester when they were asked to. I had *never* had that happen in the past!

After the students received their quizzes, we discussed as a class what it meant to remediate and reassess. We talked about their score was a reflection of the mastery they had demonstrated, and if they felt their mastery had improved, then they needed to come in to demonstrate that improvement to me. On my podium was a weekly sign-up sheet (Click HERE for a blank copy) for students to schedule reassessments. I only allowed reassessments on three days of the week so I would have some off time for tutoring, meetings, etc. We also have a built in Advisory period on Thursdays that students could come in, but since I already had 20 Advisory students, I limited reassessments to the first 10 students that signed up.

When a student showed up for reassessment, they had to provide me proof of remediation. The idea behind this was that I didn't want them wasting my time or theirs on reassessment if they had not put any effort into mastering the material. Initially, I had planned that their remediation would be the practice problems from the assignment sheet, but as the year went on, that idea was modified to include an error analysis of their quiz, notes/problems worked with a tutor, etc. Overall, I was pleased with how students handled their remediation. As the year progressed, you could definitely see the students taking more control of their learning as they decided the amount and type of remediation they needed to do in order to master the material. We did have a few big rules regarding reassessment - the students could only do the LTs from a single quiz during a single session, and they could not received tutoring and reassess during the same session. These rules helped us keep our sanity and helped with the short-term memory issue :)

The Lessons We Learned
I was really shocked and amazed at how easy parent communication became with SBG. Since their grades were totally based on quizzes, there were no discussions on extra credit, turning things in late, etc. The gradebook was laid out in a very clear manner about their student's level of mastery per objective, so most parent questions were easily addressed.

At first, I was really dreading the actual grading, but I quickly adapted and overall I ended up with less to grade, yet able to provide my students with more specific and detailed feedback about what they knew or didn't know. I was also able to grade much faster, which let me have more time for planning interesting lessons.

In our original design, we had planned to continue with traditional chapter/unit tests, but this quickly went by the wayside. Part of this was a time issue, part of it was keeping all of the terminology straight, and part of it was just that traditional tests didn't seem to fit in well. We ended up going to just quizzes, which were every 5-8 class days and it worked out just fine in the end.

Definitely have a partner to try this with! If I had gone at it alone, I would have bombed out early just from being overwhelmed. However, I had spent most of last summer reading, researching, blogging, tweeting, discussing SBG before I ever stepped into my classroom. Having Neighbor Teacher there to try it with me, to help shoulder the responsibilities of writing quizzes, coming up with LTs and Practice Problems, asking advice while scoring a quiz was simply invaluable.

Changes for Next Year
One change I would definitely like to make for next year is an easier way for students to keep track of their scores. The assignment sheet has boxes for this, but I wasn't very good at insisting that students write their original score and their reassessment scores in those boxes. I need to look at some of the other blogs to see what they do for student recording.

I would also like to look into using tiered remediation. In other words, if you scored a 3.5, you only had a single minor error, so you don't need to do as much remediation as a person that scored a 0.5. I'm not sure that I could keep up with this paperwork, but I did have a few kids that did the minimum amount for remediation and then were shocked when their reassessment still wasn't very good!

Would I do it again?
Heck yeah! This was a long process but SO worthwhile. I've grown professionally through this process and I don't regret a minute of it. I just hope that this record of my journey helps someone out there as they start sipping the Kool-aid :)

In the Good Ole Summertime...

It's official - summer is here! Today's highs were in the upper 90s and it's downright yucky outside!

Last Friday was our official last day of school, but I went back for a two day workshop this week. To say I'm conflicted would be an understatement... As I had understood it, the goal of the workshop was to work collaboratively on inquiry based lessons. However, most of my inquiry focused more around the "Huh??" realm. :) One definitely positive outcome was having conversations with the science teachers on how they use math in their classrooms and what I can do to support their program within my math classroom. I think the key challenge will be finding places in our math curriculum where the science fits naturally as to not create a "square peg/round hole" forced situation. It was pretty natural to find places where statistics fit in (duh!), but it was challenging to find areas for Alg2. The best we came up with was literal equations, parabolic motion, and graphing stories (distance vs time, etc).

After our workshop, several Alg 2 teachers got together to plan out the first part of next year. One of our frustrations is that we spend too much time on Alg 1 review, which then creates a bottleneck when we get to the actual Alg 2 material. Our goal was to try to condense the first few chapters of material while reviewing the Alg 1 material in the context of Alg 2. For example, instead of reviewing slope and writing equations of lines and such, we would do linear piecewise functions and have them write equations and find slopes of the various segments. I'm very excited about the changes and reorganization that we worked on and hope that it really helps with making connections for our students.

By the way, for those naysayers that think teachers have all this time off, today was my first day with nothing planned out and what did I do? I cleaned my office and worked on some activities for next year. I did get a nap in though! :)

Edited to add....
I asked my twitter PLN for any examples of how math can support what they are doing in science. For sake of my memory, I am cataloging the responses here...

macsmath - linear & quadratic eq's --> 3d position & prediction - I'll post what I do with it soon (hopefully)

jsb16 - I'd be happy if my students came in with Alg1 concepts solidly understood. Most of my sophomores can't solve F=ma for m.

torquedu - direct/inverse/inverse square/sqrt/logarithmic/exponential variation as common relationships among variables (not x &y)
- Not strictly Alg2/Precalc, but stus could always use practice with unit conversions, sci notation, non-integer numbers & graphing

fnoschese - equation of line, slope, area under graph (by hand, no calculus), solving equations, systems of equations, right tri trig, vectors.
- stop using x and y as variables eg if height is unknown use h not x.
- Truck starts 100 m north of school going south at 20 m/s. Car starts 40 m south of school going north at 35 m/s. When/where meet?
- Another is when they need to use slope eqn and area equation for a graph at the same time b/c of unknowns.
- for example: slope = (10 m/s/s) = v/t, area = (45 m) = (1/2)(v)(t) . What is v and t?
- You have a graph of velocity vs. time. Slope is acceleration (given). Area under graph is displacement (given). What's v and t?

I really appreciate the information given by the science teachers!! Thanks to you all!