## Monday, June 28, 2010

Last night, I had the chance to chat online with my teacher-next-door buddy. She and I often are partners-in-crime when it comes to trying new things, so I was so eager to share the idea of SBG with her and get her feedback. After chatting some and sending her off to view @k8nowak's Jing video and to view some blogs, she was totally on board with trying it. Today we met for a very long lunch to hammer out some of the details and figure out questions we are still fuzzy on.

Our Plan of Attack
After thinking through some of the articles we had read, we decided to start with our textbook and set up our learning targets for the first few chapters. Our state is adopting brand new textbooks this year and we are pretty limited in terms of the order of topics and sections we have to teach. We started with Chapter 1, and using the objectives for each section and the homework problems as a guide, we came up with the following list. LT = Learning Target, then the numbers represent the Chapter.Section.Objective

Chapter 1: Equations & Inequalities
LT 1.1.1: Use order of operations to evaluate expressions
LT 1.2.1: Simplify expressions using properties of real numbers
LT 1.3.1: Translate verbal expressions & equations to algebraic and vice versa
LT 1.3.2: Solve 1-variable equations
LT 1.3.3: Solve literal equations for a specified variable
**Note: All of the above LT's are going to be assessed using a quiz, but will not be taught - they were covered at the end of Geometry. Students can reassess these LT's if needed. Section 1.4 then, is the first taught lesson.
LT 1.4.1: Solve absolute value equations
LT 1.5.1: Solve and graph 1-variable inequalites (& interval notation)
LT 1.6.1: Solve and graph compound inequalities
LT 1.6.2: Solve and graph 1-variable absolute value inequalities

Then we repeated this for Chapter 2 - and that's as far as we got today :)

It's possible that doing it this way, we may end up wth way too many LT's and that's okay - we recognize this is a work in progress :)

So method wise, we have discussed both Kate's "2 quizzes per goal" method as well as small non-graded assessments, with a traditional quiz after every 2-4 sections with the only difference between this year and last year being the grading breakdown. I see pros and cons in both, especially considering we are doing a "hybrid" model, where we will still have traditional tests at the end of each chapter that are summative.

Ideas we are sold on
• We both definitely like the idea that students cannot get tutoring and re-assess on the same day. We both agree this feeds into the short term memory issue.
• We do want kids to have to schedule an appointment for reassessment so we can make sure and have one ready for them - this planning will be necessary so we don't feel so frazzled
• We both like the idea of some kind of notebook where the kids keep their checklist of skills as well as their scores (I think this is either from Kate or Jason)
• We do agree that we do not want to give our students permission to forget, so as LT's come up in our previous knowledge sections, student grades can go down (but they can still come in and reassess if that happens)
Issues and questions we still have
• We aren't sure which rubric we want to use - probably will be 5 pt, simply b/c I like multiples of 5 in my gradebook :)
• If we do 2 assessments and add them together like some people do, then the student comes in to reassess, which two scores then get added? Like say I got a 3 the first time, a 2 the second time, then reassessed and got a 4 - which ones go into the gradebook?
• What happens when a student is absent? Our quizzes right now are fairly traditional - and I forsee them staying that way with only big change being at the top where each LT is listed. If a kid is absent on quiz day, do they take it the next day? Take zeros on that quiz and have to do the reassessments for those LTs? Take a makeup quiz? Right now, we give 2 versions of the quiz and we show it to them, but they don't get to keep until everyone has taken it, but that won't work if we are trying to provide the quiz as a study guide.
• How much proof do we need to require in order to reassess? Obviously for the first reassessment, they have to show they have attempted the assigned practice problems for that LT, but what about after that? Tutoring with a teacher or our peer tutoring lab would work as well.
• For those that do a hybrid model, what is your percentage breakdown for grading categories?
• We are thinking of doing away with our warmups - they have ended up more punitive than we meant for them to - what do you guys do at the beginning of the hour instead?
• AN IMPORTANT ISSUE: How do you grade a problem that addresses multiple LTs?
• ANOTHER IMPORTANT ISSUE: What do you do with something that is important, but maybe not enough to get it's own LT? Like for example: Function evaluation in function notation - F(3) = ? - This is something the kids need to know but I'm not sure that it's a big enough topic for it's own LT, especially when often it fits under evaluating expressions.

I need to send a HUGE thank you to all of my twitter PLN that have patiently answered TONS of questions, listened to me brainstorm, provided feedback, asked questions to make me think things through, and just in general for being there :) I can never tell you guys how much I appreciate you!

Suggestions and comments welcomed, as always :)

## Sunday, June 27, 2010

### My foray into SBG

Over the past week, there have been lots of discussions on twitter about implementing Standards Based Grading (SBG). Here is a braindump of my ideas on how to use SBG in my classroom. Feel free to rip it apart, that's the best way for me to learn :)

Main Motivation
I know the current model is broken. I had a situation this year with a student that worked his/her tail off when test day was coming, but that's it. He/She did pass my class, but throughout it all, I just felt slimy. I knew his/her test grade did not reflect his/her knowledge and that really bothered me. Some students "rent" the knowledge until test day, but never "own" the information. I want kids to "own" it. Every year, I struggle with this. I think overall I'm a pretty good teacher and I try to get better every year. I am always thinking of ways that I can be more effective in the classroom and how to better help my students.

Some minor issues:
I am convinced that SBG is the way to go. I want students, parents, and myself to know exactly where students are and what they need to improve on. However, I also have some limitations within my district. We have an online gradebook that we are required to use and we must enter at least one grade per week. Horizontally, we give common finals and benchmark exams. We have a district guide for order of topics and overall pacing and we are supposed to be within a couple of days of the other teachers of the course. To add to this, every year the district surprises us in August with new mandates, so I can't totally go SBG or otherwise, I would just end up extremely pissed in August when the rug is pulled out from under me :)

My plan:
With the above limitations, I have decided a hybrid model based on converstaions with my twitter PLN. Also, I only plan to try this in my Alg2 class for this year. Basically, for this first year, I will be pretty traditional, but more detailed. I will still give an assignment sheet for the chapter, although I will probably break it down a bit more, so that instead of just the lesson title and assignment, I will have the lesson title, then the learning targets (standards) for that lesson and the practice problems for that learning target (LT). As Kate Nowak says "Then, I teach". After a few lessons, I would give a quiz, similar to traditional quizzes, but instead of giving a total grade (13 points earned out of 15), it would be separated by LTs (order of operations, whatever) and a kid would get 3 or 4 different grades for the quiz (one for each LT). Rinse, repeat... Then it comes time for the chapter test. I will probably keep the chapter tests like normal (we will be more than likely moving to common tests there anyway).

Issues I'm still pondering
• I'm not sure yet how often I will reassess a LT in class - some people do 2 times in class on 2 different quizzes, but time may be an issue, dunno yet
• I'm not sure how to format my paper gradebook - I use the Whaley 3-line gradebook, but may have to go to a self-created gradebook since quiz grades will now take up 3-4 columns rather than 1
• I've not discussed this idea with my admin and so I'm not sure how this will go over. I have awesome admin, but we'll see how it goes :)
• Each LT will receive a grade on a 4 or 5 point scale (not sure yet, I've seen both and still mulling over the idea)
• I would really like to integrate more application and writing skills into these quizzes rather than just skills based
• I've seen others comment that kids have a limit on how many LTs they can reassess per day, not sure what I think about that, definitely agree on the "can't reassess on same day as you got help on the LT"
• I'm worried that with the reassessments, some kids will still "rent" for their low skills, trying to get their grades further up that A/B/C scale
• The time committment does stress me out a bit. I have 3 preps plus teach at a Div I university - I already spend way too many hours grading and planning. The idea of creating multiple assessments freaks me out.
• Currently I do "Quick Checks" which are similar to what others call "Homework Quizzes", except I give them the problem rather than saying "write #3 on your paper". I'm thinking these Quick Checks could be part of my quizzing system & can be put on the Promethean, thus helping the copy paper/budget situation
Final Thoughts As you can see, I still have way more questions than answers. I don't know how to fix some of the issues above yet - but I'm working on it. I have my PLN, books by Marzano, Reeves, and other assessment gurus. I will be ready when August arrives :)

## Thursday, June 24, 2010

### The End is Here :)

I've come to the end of my Literacy book - what I thought would be a fast read (< 100 pages) has taken me a week to read. Of course, taking the time to annotate the book (my AVID buddies would be SO proud of me), blogging about what I've earned, and of course spending LOTS of time on twitter learning about a multitude of things have slowed me down a bit. And while I can easily burn through a lengthy novel in a day or two, professional literature just doesn't flow at that same level :) However, I am eager to move on to my other books (especially those about assessment & Standards Based Grading), so I'm trying to get this one finished up. As such, this post will not be as lengthy as the previous posts (which is probably a good thing!)

Make a Picture! Make a Picture! Make a Picture!
Chapter 4 was about Graphic Representations in the math classroom. While this chapter was an enjoyable read, with several vignettes, I really didn't learn much. Of course, I am a VERY visual learner, so maybe I already knew this chapter's information from experience.

The main theme of this chapter was that student drawings allowed us to catch a glimpse of student thinking processes, which can be extremely helpful for students who cannot fully explain verbally where their confusion lies. Through the power of a diagram, teachers may find that what makes sense to our more mature thought processes does not make sense to our students based on their prior knowledge. One example in this chapter was about quadrupling a recipe that called for 1 1/4 cups of flour. Without prior knowledge of how "cups" relate, the student answered that they needed 8 total cups of flour in the new recipe - 4 big ones and 4 small ones. I'm not much of a cook, and as a kid, I rarely spent time watching my parents cook, so I could have easily had this same misconception when I was younger. As teachers, we have to be careful that we don't assume that students have prior knowledge about everyday things and having the students draw a picture can help us pinpoint these problems.

As math teachers, we often tell our students (particulary with a "word problem") to draw a picture. Using graphics helps with teacher assessment, but more importantly it allows students to make connections between the words and the concepts. For visual and hands-on learners, making a picture may be vital to the learning process because it forces them to slow down and process. For me personally, I am not auditory at all - I struggle in traditional classrooms, in meetings, listening to NPR, because I have to focus so much on what is being said that I can't keep up. :)

Talk it up!
The last literacy strategy of the book is discourse, which is what Chapter 5 is devoted to. This strategy comes easier to me in Stats than in Algebra, mainly due to the nature of the course. Even so, I still came away with some useful jewels of knowledge.

One of the first statements in this chapter says that "discussion and argumentation improve conceptual understanding." Personally, that statement shows itself to me all of the time via my twitter PLN. For example, this morning, I tweeted a question about standards based grading, which lead to a lengthy conversation with several colleagues, a few new blogs to read, and in the end, way more questions than I had started with. This discourse with my peers truly improved my understanding of SBG and allowed me to put the puzzle pieces together in my head of how to implement SBG in the classroom. The free-flowing idea stream that came out of today's discussion was simply amazing, although in the classroom, I could definitely see where this "non-controlled" environment could stress some teachers out. I had no idea where my question would lead me and in the classroom, that can be a scary thought (especially depending on your clientele!)

I have always tried to keep my classroom open for discussion, often asking students "why" in order to get them to explain their thinking. However, I may change that. One teacher that is used as an example in this book uses the word "More?" as a way to keep kids talking about an idea and appending previous student comments. I like that idea because it opens up the discussion to more than just an explanation - it could be any comment about the idea at hand.

The other big idea that I got from this chapter that will impact my classroom is this: "Rich, deep, and argumentative discussions occur when students display their work and present their strategies". I really need to have students tackling more application-rich problems and presenting their findings to the class. Of course, while I know that I need to do it and I really think I would enjoy doing it, I have no earthy idea of where to start, so obviously some research will be required there. I'll get back to you on that :)

A couple of other tidbits I got from this chapter:
- Don't rush to save kids too quickly. Often they will discover and correct errors on their own as they think and explain their reasoning.
- Have students share their methods, esp non-traditional, as it help everyone grow mathematically (I had this happen this year as a student noticed a pattern w/ perpendicular slopes when the equations were written in standard form - love when kids come up with their own algorithms!)
- Don't have kids just memorize vocabulary - they need to process the concept before the vocab word makes any sense to them
- Graphic organizers are great tools, but in order for students to truly expand learning w/ these tools, they need to discuss and share with others in order to clarify thinking

The big ideas...
Overall, I really enjoyed this book. I came away with a lot of ideas on integrating reading, writing, graphical representations, and discussion in my classroom. I know that not all of those ideas will make it into my classroom this year, but that's part of the purpose of this blog - to act as my "holding place" for my "mindful mediation" :) Having these thoughts written down here will help me throughout the years as I reflect back on previous ideas and things I want to change. Now I get to dig through my treasure trove of books from last week to find my next mind-bending adventure....

## Wednesday, June 23, 2010

### Writing in Math

Chapter 3 of Literacy Strategies is about writing in the math classroom. I was particulary interested in this chapter because the topic of writing (journals, learning logs, etc) has come up several times recently in discussions with my twitter PLN. While I got some great ideas from this chapter, I'm ultimately left with more questions than answers about how to integrate writing effectively.

We all know writing has great benefits. For the student, they are provided a canvas in which to develop their communication and thinking skills, and for the teacher, an avenue in which to assess how well the student understands and processes a concept. The author of this chapter relates writing as "mindful meditation" and the page as a "holding place for our thoughts". To me, that idea is the basis behind a journal or a blog. I've never been much of a writer, but even I find writing on this blog to be very useful for my personal and professional growth/reflection (aka mindful mediation) and I've often used my blog as a minddump of ideas that I haven't fleshed out, but that I don't want to forget. However, I had never quite put that idea into the classroom.

In the classroom, I would guess most of us rely on verbal communication, whether that comes from lecture, student responses, etc, yet all of us would like for all students to be engaged in the classroom. The author points out that only one student at a time is able to speak, but if we ask them to write instead, this encourage more participation because the entire class can be involved at the same time. Again, a simple idea, but one that I had never quite thought of. Ultimately, I would like to get to the place of presenting a problem, having students think and write individually, then work with a peer group to refine and edit, but worry about issues like student buy-in and wondering if kids will take it seriously or just jot down random things and not really grasp the benefit of the writing.

One point that the author made that I struggle with is that the thinking involved in writing/explaining is different than the thinking needed for solving a problem. All of us have experienced this issue. Students can find the answer to the problem, but struggle with explaining the how and why of their work. You may have even had a situation where a student could explain a topic (such as multiplication), but has very little computational fluency. There must be a balance between these two types of thinking and I'm not sure where that balance lies. We want students to be successful in both conceptual and computational learning, but how do we find that balance?

Writing in the classroom should allow us to open a dialouge with our students. When presenting them with a task that requires them to explain their thinking, we should take advantage of that opportunity to assess their thought process and any gaps or misconceptions. The teacher taking the time to read and respond to student writing on a regular basis is important in order to help students develop clarity in mathematical thinking and communication. However, that poses another question - where do we find the time? Obviously reading and responding to written responses will take a lot more time than grading a traditional math assignment. Also, many writing assignments may just be an informal assessment, gauging where students are conceptually and are never meant to be entered into a gradebook.

This chapter also provided insight on how writing can help ELD and SPED students develop mathematically. One point the author makes is that for both of these subgroups, there is a need for teacher assistance in organizing their thoughts through structured-response prompts. As confidence grows, the teacher can provide less and less structure until the student is performing independently. In my opinion, all students, not just ELD and SPED, could benefit from this structure as they are learning how to write in the math classroom.

Overall, I leave this chapter feeling convinced of the power of the written word in helping a student learn math and to reflect on their learning. I still struggle with some of the practical questions that come with this idea, such as the time issue, needed balance, etc. I feel like this post is more of a jumble of random thoughts instead of a cohesive review, but that may be appropriate considering that I feel quite lost and jumbled in how to effectively apply this strategy to my classroom. :)

## Sunday, June 20, 2010

Chapter 2 of Literacy Strategies (which, btw, is freely available for you to read at the ASCD website), really made me squirm in my seat. When I was a kid, our pastor used to (and still does) get up on Sunday mornings and preach his heart out. More sermons than I can remember had him saying that when he was praying about and researching for that week's message, that he felt convicted, that God had "really stepped on his (the pastors) toes" that week. After reading this chapter, I knew exactly the feeling that Pastor meant. This book really stepped on my teacher toes this weekend and I feel very convicted as a result.

This book is a collection of essays from a group of teachers, and as such, this chapter was much smoother to read, but very deep in content. The big idea of this chapter is this: Ultimiately, the responsibility in teaching a student to read a math textbook lies with us, the math teachers. Granted, we have not had formal instruction on how to teach reading, but their reading teachers probably haven't had formal instruction on technical texts either. Here's a list of ideas from this chapter and my reaction...

Book: Traditional math instruction is training, not education. Students can perform procedures on cue like a trained animal, but have not really learned the mathematics until they can apply it.
Me: OUCH!! If that didn't step on toes, I don't know what will. This idea really knocked me on my rear and I had to step away from the book for awhile to process. I felt very convicted by this statement. How often do we train them for a standardized test, train them how to use an algorithm, without teaching them the true concept beind the computations? I can think of many examples in Algebra 2 this year where, after feeling beat down by pacing, snow days, family issues, lack of sleep, etc, that I resorted to "here's how you do this problem" rather than the WHY of doing the problem. This statement still has the power to knock the wind right out of me :(

Book: Math texts contain more concepts per sentence and paragraph than any other type of test. The text contains words, numbers, and symbols that must be decoded. The eye must travel in a variety of ways that is unnatural to reading (both left/right, up/down, graphs, charts). While reading, some information is extra and must be discarded by the brain, yet still distracts the reader.
Me: I paraphrased the above of course, but I had never sat down and really analyzed the difficulty in reading a math book. Because, as math teachers, we are (hopefully) math literate, our brains ignore all of the issues that are listed above, but as a young reader, can you imagine trying to tackle that? How overwhelming! This section hit home so much that I had to read part of it to my husband because I had never thought of a math book this way. Another issue that I would add to their analysis is the weight of books - holy moly! Those suckers are HUGE!!! Definitely not the book I'm going to sprawl out beside the pool reading :)

Book: "If we are really trying to help students read and understand for themselves, we must ask them questions instead of explicitly telling them what the text means"
Me: Another big OUCH here. How many of us, when a kid comes up and says "I don't get it", just tell the student what to do, rather than asking questions to lead to understanding? Questions like, "Can you read the instructions to me?" "What does this word mean?" "What is the problem asking you to find?". I try to be good at asking questions, often to the frustration of some students, but there are times, when I'm feeling rushed, or multi-tasking, or whatever that instead of asking questions about what they've read, that I give them too much information. Asking questions is also important because it helps me figure out where a student's misconception lies.

Random other tidbits that I picked up from this chapter:
The language itself poses a huge problem. The same word in Math-speak and in English do not mean the same thing. In addition, small words make a big difference (percent of vs percent off). To further compound the issue, clarity in written and spoken language can create complications for students as well. Vocabulary (or lack thereof) can be a huge issue and graphic organizers can be very useful for students to clarify and organize the information.

Final thoughts:
Like with everything in the classroom, kids learn by modeling. As teachers, we need to model the processes we use to read and decode text. We need to "think aloud" while working through problems so that kids have a working example of how to tackle problems on their own. We need to break down the text into manageable "bite-sized" pieces and ask questions along the way to demonstrate the thinking process.

Gosh, after this chapter, I may have to find something more light-hearted to read... my toes *still* hurt!!!

## Friday, June 18, 2010

### Literacy Strategies

Okay, so as previously mentioned, I am going to be spending some time in professional reading (but my new novels look awesome too!), and sharing some insight here. The first book I'm reading (about 100 pages, hence why it's #1 on the list) is Literacy Strategies for Improving Mathematics Instruction.

So far, I've tackled Chapter 1. I have to admit that I kept getting distracted and this isn't an easy read for me - I'm really not one for "goobly-gook speech patterns", I'm really a pretty simple-minded person at heart. I tend to like books that are more of a "say what ya gotta say and hush" type of book :) Edu-speak typically irritates me quicker than anything because most of the time I feel like they are either trying to impress me with their vast amounts of knowledge OR they want me to feel bad for not understanding a word they are saying. However, there was one part of Chapter 1 that really stood out to me....

In Chapter 1, the authors really spend time related Mathematics to other languages. It has its "nouns" (numbers, shapes, functions) and "verbs" (modeling, communicating, transforming) and as a "foreign language", we really should approach it more with ELL type-strategies. The authors shared experiences of "use it or lose it" with both mathematics and traditional foreign languages. For myself, I took 2 years of Spanish in HS, yet retained none of it long term. As the author points out, some of that is of course that lack of usage, but could also be attributed to the way I "learned" Spanish. In Spanish 1, we spent a lot of time on nouns and verbs - my teacher had a table at the front with all kinds of stuff - toys, household items, etc and she would hold up an item and name it, we would repeat it, etc. She also taught us verbs - toss, pet, touch, point, etc. This memorization was useful, but ultimately it was just memorization, not a true understanding of the language. (With that said, I *loved* my Spanish teacher - she was amazing at making it fun to learn). Another point made was regarding decoding the language of math, both symbols and words. For example, the same symbol horizontally (=) and vertically (||) means totally different things in math. Food for thought... especially in how to relate to those students learning BOTH the language of english AND the language of math at the same time.

Overall, I think I'm going to enjoy this book. The next chapters delve into the strategies, but I know that I personally have given lip-service to "math is its own language", without really understanding what that meant. They've definitely opened my eyes to issues I hadn't thought about.

Til next time... :)

### A New Beginning :)

Yeah, I know - I suck at keeping this blog up to date. This year was CRAZY busy for me, and as far as priorities went, this wasn't one. However, every day, I log in and read the updated blogs on my blogroll, so if I have time to do that, I can jot down a few ideas, right? :)

As with every summer, I have time to rest, relax, and mostly rejuvenate myself. I have found that Twitter is an amazing way to re-engerize my batteries and follow 100 of the most amazing math teachers in the world. After an awesome discussion on the value of homework, I was raring to go learn more about how to be a better teacher. Today was hubby's birthday, so he took the day off and we went trolling the town for books (our favorite thing to spend money on) and I came home with about 8 novels and about a dozen professional books. My plan is to read them and post reviews on here.

The first one up is Literacy STrategies for Improving Mathematics Instruction, so I'm off to read!!! Wish me luck! :)