Crickets and Chaos

It seems as I venture into the common core and mathematical practices I am running up against moments that I call crickets and others that are chaos. These are probably obvious names, and probably things many of you have experienced in your own classrooms. Crickets, those times when you pose a question and the room is so silent you can hear your own heart beating. And chaos, those times when the room is so boisterous you can't hear your own thoughts.

Now, I'm not promoting either of these as negatives, per se. I'm merely noticing and wondering more about my own teaching practice as I ask students to notice and wonder about math. Crickets can be uncomfortable. For me I find them a little challenging, particularly because I'm a talker... and I don't like awkward silences. I am running into crickets more often now because when asking students to think deeper about the math a number of things happen.

First, it takes time to think critically. It takes effort, energy and at least a brief moment to synthesize new information (and maybe more than a brief moment). But it is necessary, so the pause is necessary. You cannot expect students to be critical thinkers without allowing them time to think. This is where I struggle. I must maintain a closed mouth position and give students the time they need to process what I've asked, because I am asking "meatier" questions than I have in years past.

Second, the students have been accustomed to waiting for the answer. For some it is a waiting game in which they know if they hold out long enough the answer will be provided. You may even get the "can't you just tell us?". They were trained that the teacher knows everything and they must wait, mouths agape, to take in the knowledge that is being imparted. As the common core has highlighted, this is not the way learning happens. There is some retraining that must take place. This takes patience. Patience on the part of the teacher, as I wait for the students to realize a question still lingers unanswered in the ether of my room. We must wait for students to snap out of the Stepford behaviors of years past, and learn to engage with the material in a new and often challenging way.

As for the chaos, I have come to realize that learning is loud. This is not always the case, but it takes discussion. Sometimes students have quiet "a-ha" moments. But in a group setting there is bound to be noise. When you ask students to work together, wonder, notice and share these things don't happen quietly. I'd like to believe I have a controlled chaos occurring in my classroom, but is the nature of chaos, it is unpredictable. It goes in places I can't anticipate and classroom management becomes a challenge. I struggle to improve my management skills to prevent a full blown classroom breakdown (of course, I'm exaggerating). However, there is a new set of skills that must be learned on the part of the teacher and the student in order to have the chaos be controlled.

I must be able to plan and set up an activity in a way that the flow and tasks are engaging. But as any classroom teacher knows, engaging activities only gets you so far. You can lead a horse to water but you cannot make him drink is an old expression but an apt one. At some point students must also learn that they have to engage with the material and not just expect to be entertained every 90 minutes. There is a give and take in learning that they have yet to experience in quite the same way. I am not looking for compliance in my classroom in terms of sitting up straight, facing the board and taking notes. I am looking for willingness to be a part of a learning experience

Confusion Endurance

At my school we have advisory, in which we have a chosen anchor text to guide instruction. The text we chose for 9th grade advisories is How to Think Like Leonardo da Vinci by Michael J. Gelb. The concept that has struck me the most in "confusion endurance". This is the idea that in order to be truly creative you must be able to stay in the confusion and ride it out. This concept seems particularly relevant to the mathematics classroom.

Students struggle with Algebra and its abstract nature, it is confusing and (holding off on the argument that they are not developmentally ready for Algebra this early) often feels unattainable. Geometry, and especially proofs, seem beyond their reach. Even getting started can be difficult. Not knowing where to begin is unsettling and often results in the abandonment of the task altogether.

I have come to realize more than any other concept I teach, confusion endurance is the one that will be most relevant to their lives now and in the future. They must be able to face a problem and not back down. Whether than problem is mathematical, scientific, literary, or personal, they must know how to persevere through the confusion. They must be able to walk through the tunnel even when no light is visible at the other end. We must give them the courage to persist at something, not give in to the overly popular "It's too hard" mentality.

One caveat that I must add is students have become overly dependent on being fed the answer. This is not completely their fault, as many would argue. Our former (referring to the CCSS as the current) standards, did little to prepare our students to face down confusion and win. We have made them dependent upon their teacher to feed them "pre-chewed" content and regurgitate it on command. We have outlined procedures for skills, not strategies for thinking critically, essentially cutting off their ability to be self-sufficient academically. I will admit, I was this teacher.

I am excited as I look around my room and see the confusion on the students' faces. I know that if I allow the right amount of time, the answers will come. If I am patient they will venture forth. It will not be easy. The old saying "Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime." says nothing about the patience it takes to fill your basket with the catch of the day. Hopefully, as I present situations that may leave students confused and wondering, they will see the joy in the experience just as the fisherman gets joy from fishing even if his basket is empty.

A Year of Living Common Core

This summer I begin my journey deep into the Common Core. I have decided to recommit myself to blogging, with a focus on implementing the Common Core in my classroom. And so I hit my first road bump. I have a lovely set of Common Core standards, like a shiny new car waiting to be driven. However, it came with no GPS and my school district has yet to provide me a map.

I will be honest, I mumbled and cursed the slow to act district and wondered how they expect me (and other teachers like me) to plan for such a radical shift in pedagogy and instruction without providing us at least a rough outline of units. I have never been one for a rigid pacing plan mapping my every move, but I have always tried to follow the unit outline provided by my district to help me sequence the content to match the quarterly assessments I am required to administer.

Let me stop here to insert a point of clarification. Although testing is suspended in California this year, with a few exceptions, it has been made clear by my district that we will still be mandated to give the district's Periodic Assessments each quarter. What is unclear is whether they will be making new assessments or keeping the old ones. There have been no unit outlines released as of today, so I am at a loss for where they expect me to begin. How can I plan for their quarterly assessments if I don't know how they want me to chunk the standards? Basically, what do I do in the absence of guidance?

After much deliberation, I decided to go rogue. Really, it is what comes most naturally to me. I started my teaching career afloat in rough sees in nothing more than a dinghy. Why not approach this change in teaching in the same survivalist sort of way?

It's not to say I am totally alone. The math blogosphere is quite rich with resources, knowledgeable teachers and support networks. I am definitely more prepared for the journey this time around. I have years of experience, successes and failures, to help me map my course. I have a supportive administration. What does all this amount to? As I set out on my journey into the uncharted waters that are Common Core, I have upgraded my dinghy to a skiff. And so, I set sail...

I am Sisyphus

Why is it I always plan to do so much work over the break, but never actually accomplish it? I have grand plans of how I will spend the time, for which I pack up the necessary materials from my classroom and haul them to my car. My husband watches as I drag it all into the house, filling the formerly empty spaces of my small dining room-turned office. My once easy to move about work space becomes a maze of books, binders, bags and crates holding all the materials I could possibly need (but never realistically get to in the time I will have at home).

This is the curse of the teacher. We roll our boulders uphill, planning (or preparing to plan), only to see the end of the break arrive and watch as our good intentions roll down hill. 

I am alone, in my plight? I doubt it... although I think others may get more done than I do. Generally hard working teachers see these breaks as a time to catch up, get ahead, plan better, and improve our craft. It is a small window of opportunity when we do not have to teach, grade, make parent phone calls, address student concerns, or attend meetings. We can focus on the one singular goal of preparation uninterrupted by normal workday demands.

Unfortunately, this is when I tend to get lost in the high-level ideas and get little of the practical day-to-day work done. I think to myself "Now I have the time to rethink things, improve or change since I do not have a lesson to teach tomorrow." So instead of focusing and getting things done that will get me ahead for the semester, I think of how I can make changes to the fundamental methods of my teaching practices.

Perfection is one of my character defects. I fear to begin a task until I have all the details settled. This is particularly true of teaching. I know there are things I could be doing better, so instead of wasting time preparing lessons in accordance with my previous (lesser) methods, it seems better to decide how I would like to change and plan to that end. The issue is, there is always something to be improved... and there are so many ways to approach the task how can I be sure I have chosen the one right way?

As I read the above paragraph I realize how silly it sounds. There cannot possibly be one right way because the variety of students we serve changes not only from year to year, but from class to class during the day. All I can do is strive to be the best I can with the information I have at the moment. So I find myself at the end of winter break. Second semester starts tomorrow, and with it the papers to grade, lessons to teach and school business to handle. That being said, I guess I'd better get to work!

Thinking Outloud

I have been combing a vast amount of information related to SBG (standards-based grading), mostly from blogs I follow, and have decided to try to put my thoughts on "paper" to see if I can generate some amalgam of the information I've gathered into my own uniquely plagiarized system. (BTW, this is what I love about teachers... we are equally willing to share what we are doing and let others use it, and plagiarize others work and make it our own). So here are some things I've come up with:

4-Point Grading Scale
I have used a 4-point grading scale for years, but have never been completely satisfied with the descriptions associated with each level. I pulled the main idea from misscalcul8, who not only has great descriptions from a teacher perspective but also descriptions of what the student is likely thinking at each level. I also found Kate Nowak's descriptions really helpful although, I will admit, I don't know if the descriptions are what she uses with her students or what she keeps in mind while grading. Finally, I found Always Formative to be helpful. All three of these posts were useful for the specific topic at hand, but I encourage you to browse around their other posts for more information on grading, instruction and assessment... I have found them extremely useful.

Here is what I've come up with:

I will admit, it feels wordy... I considered eliminating the right column to solve the problem. But I realized I couldn't part with it because I think this is the one part of the chart that will resonate most strongly with the students. I may post the above table with the first to columns only in class but offer the complete table on my web page for parents and students.

Retests
I absolutely love misscalcul8's retest form, which can be found on her post discussing SBG. It appears my experience with retests is very similar to hers, and probably countless other math teachers out there, so the idea of requiring them to show evidence of reviewing their errors, watching online videos for additional instruction, and showing evidence of this two days before coming in for the retest is genius! I will probably adjust the form somewhat, because that's just the kind of girl I am, but the ideas behind it will remain intact.

I have played around with the deadlines for completing a retest, most recently having allowed students to retest on any quiz all the way up to the end of the semester. The philosophy behind this I still agree with, students do not learn according to the schedule I dictate, so affording them the maximum time possible to learn a concept seems like the right thing to do. However, for reasons both of practicality and reality, I have decided to set each 5-week grading period as a cut off for retests.

The reality is that students will often perform to the deadline given... so if I allow them until the end of the semester, they will put it off until then. In terms of practicality, there are only so many retests I can grade in the final days before semester's end. For this reason, I must cut things off so my workload is reduced to a more manageable size.

Grading
Ugh! This is the part I struggle with the most. Many posts I've read talk of percents and points. Again I am confronted with reality: I must enter my grades into an online system visible to students and parents. Initially my grading system wasn't as confusing to students and parents because I was the wizard making the grade program do what I needed it to without having to worry anyone would be peeking behind the curtain. Now, there is no curtain. Let me explain with specifics.

I use a 4-point rubric to grade assessments and projects. Every graded assessment is given a score of 0-4. All scores earned are averaged together to produce a GPA. The benefits of this are students are fully aware of how GPA's work, therefore additional explanation is often unnecessary. The downside is I have yet to find a grade program that allows me to average instead of calculate a percentage.

My initial solution was to determine a GPA-percentage conversion. I did not need to reveal this conversion to anyone except my administrator as part of my official gradebook submitted at the end of the semester. So I never got the question "What percentage do I have?". I even had a great score sheet that allowed students to do a quick "visual average", so I could deflect questions about grades and required students to calculate them for themselves (what a relief!).

Now that my grade program is visible to the students and parents, the percentage is visible as well. Can I just advertise the percentages I've used all along? Sure. But I worry that the appearance is I'm giving away grades (compared to a traditional percentage scale). Here's a chart that shows the conversion:

To me, the GPA's look fair... but in a percentage world all but the A breaks the norm. Don't get me wrong, one of the main reasons I switched to a GPA system was because the grade distribution seemed so much more reasonable than a percent system in which almost 60% of the scores you can earn give you a fail. But when non-believers look at this it may seem like I'm an "easy" grader.

An Afterthought to Grading
As I write this, I realize I don't care what they think. Traditional graders are who they are, and I am who I am. I have researched, read, attended conferences and workshops, discussed, and thought long and hard about how I grade. I will not apologize for developing a system that breaks the mold, but that I feel is a better reflection of student learning than the way I did it when I first started teaching.

It will be an adjustment to get students, parents and my peers to see the value in the system I've developed. As far as I know, no other teacher at my school uses a system like mine. However, change begins with one. So, here I am!

What Now?
Now that I have sorted that out, it is time for me to spend some time developing my topics and pacing for 2nd semester. I am behind the 8-ball already, but am feeling energized and enthused. I will keep you posted (pun intended) on how this develops!

The Weakest Link

I just came across a concept that was foreign to me, but has totally rocked my world... conjunctive grading. The idea is a student cannot compensate for the lack of one skill by doing really well in another skill (basically, preventing a student from averaging an F and A to earn a final grade of C). The logic behind this is based on the idea that grades communicate content mastery, and averaging scores in the traditional way masks the student's true level of mastery.

To be honest, I am not sure how I feel about this yet. There is part of me that says, "Wow, that's awesome!" and there's part of me that says, "Um, is that reasonable?" The part that appeals to me the most is the idea that each major concept is considered separately. If I am working toward proficiency in a subject, say geometry, I want to ensure each student has proficiency in every major concept within geometry. I also appreciate the idea that a student cannot hide failure in one area by being proficient in another. Each main idea or concept is viewed independently, which gives a much more complete view of a student's true content mastery.

The part I struggle with is what happens to conjunctive grading when you use it within our current system of grading. We work in an education system that requires a student's content mastery to be boiled down to a single letter grade (not a system I totally agree with, but not one that is not likely to change any time soon). Because of this, conjunctive grading still must be consolidated into a single mark, the weakest link. In order to determine a student's overall grade in the course, the concept on which he/she performs the worst is the one that dictates his/her overall grade. In other words, your overall grade is only as strong as your weakest concept grade. Something about that doesn't sit well with me. 

In an attempt to reconcile this uneasy feeling, I tried to think of real-world examples that either supported or refuted this type of evaluation. For example, if I am a painter (as in artist, not house) do I fail in painting if I can do everything well except mix colors? Does this ruin the overall painting? Possibly. But maybe that's not a good example. Maybe it is more along the lines of being able to paint in the style of the impressionists but not as a surrealist. Does this mean I have no talent as an artist? I would think not. Let's forget art and consider a different example, such as carpentry. If I can use a screwdriver, hammer, tape measure, etc. but not a level, do I fail as a carpenter? I would think so, for who wants a crooked house? Examples from both sides come to mind, leaving me no clearer on the conclusion.

After all that I am no closer to reconciling my feelings about conjunctive grading. However, I would contend this issue is not with the conjunctive grading itself, but the system in which it is being utilized. If we were allowed to keep our concept grades separate, never having to combine them into a single overall letter grade, I would be much more at ease with the idea. But until then, I am not sure I can wholeheartedly endorse a conjunctive grading system.

Alternatives in the Meanwhile

1. Break my subject into major concepts, providing each concept an overall grade. Check out this blog for some more about this idea.
2. Average the concept grades to produce a final grade, thereby giving each concept equal weight and showing students and parents areas that need more work and areas in which the student is excelling.

Just to provide a little more information for those wanting to delve deeper into the grading dilemma, here is a great post about standards-based grading, a 4-point grading system and how that can be converted to the traditional percentage system. This is more along the lines of how I grade, and the post has some excellent and thought-provoking questions to consider.

Grade Robots

I have spent many, many hours trying to develop the perfect grading system. In all my research I have broken the issue down to a few key questions. I have wrestled with these questions, losing some rounds and winning others, for years. I cannot say I have successfully addressed them, nor have I come up with the perfect solution to my dilemma, but I am choosing to share them with you now so that we may ponder together as a community of math educators in a world of math-phobes.


What should be "counted" toward a student's letter grade?
This covers a number of issues commonly discussed by teachers such as whether to give points for participation/attendance, grading homework for correctness vs. effort/completion, and whether to give points for homework at all. Before addressing this issue, I have decided it is most important to address the larger issue of the letter grade itself.

What does your letter grade represent?
Most teachers, I assume, would quickly respond with something along the lines of "the student's degree of content mastery" (and might even add the flippant, "duh") . But when you consider the types of extras that are added into a student's grade that are not reflective of content mastery (participation, attendance, effort, etc.) it begs the question, what is your letter grade really saying? Does it say the goal is learning? Or does it simply say if it looks like you're trying hard enough, that's good enough for me?

The Cynic vs. the Optimist
We all have that story of the student who tried with all his/her might to pass, and just barely squeaked by. Maybe this student received effort points because their determination was so strong it was hard to see them fail in spite of it all. Is it fair this student fail after having given it 110%? What will it do to the child? Will they give up because no amount of trying produced success? Feeling responsible for the future success (or lack thereof) of a student is a huge burden to bear... then multiply that by five or ten per semester (just to be conservative). I have an ulcer just thinking about it.

On the flip side, there are those students who make the hair on the backs of our necks stand up at the mere idea they will not only pass, but get a C when they did "nothing" all semester long. For some, the issue is the student clearly is not living up to his/her full potential... but for others it is the fact that we have had to put up with the obnoxious and rude behaviors of the intelli-lazy (brilliant but lazy, in case my word play was distasteful). These behaviors include talking or sleeping during class, using electronics, not taking notes or doing homework, and doodling/drawing, among others. Does this student deserve a C when they put no effort into earning that grade?

"Please, sir, may I have some extra credit?"
Most students fall somewhere in between the above extremes. We all know the way students try to game the system. It's only natural. We humans are built to constantly conduct cost-benefit analyses all the time. Why would I retake that test if I could simply turn in some missing homework I copied off my friend? They understand enough about the points and percentage system to know when to try more and when we have created the mathematical necessity for them to give up (but that is a topic for another post). By the time I see them in high school, they have had 10+ years of training to become the grade robots I meet. You know what I'm talking about. For example, [using your best robot voice, read the following questions] "Will that be on the test?", "How many points is it worth?", "What grade do I have?", "Can I turn that in late?", "Is there any extra credit?".... and on and on.

A Grading Manifesto
With as much time, energy and discussion as I have invested in the topic, I have decided it is time to write a grading manifesto. I must take a stand on how I feel about each of these issues and what I plan to do about them. But where do I stand? For now, I have one simple philosophy: Your grade reflects how much you know. Notice I did not say how much you learned. That was intentional. How, when and where you acquired that knowledge is irrelevant to me. Your letter grade should tell everyone that sees it how much _______ (fill in Algebra II, Geometry, Algebra I, etc.) you know. If you don't know it, I cannot give you a grade that says you do. If you don't need me to teach it to you, that gives me time to go help someone else. And why don't you help someone, too! If you are somewhere in between, I will not negotiate your grade for Kleenex (I have been offered this before). However, I also understand you may not be able to demonstrate your learning at the time I give the assessment, so I will let you show me in your own time.

So what does this look like? Here are my rules:

1. You may retest any quiz to improve your grade.
2. I do not offer extra credit. (see #1)
3. Homework is practice, which is helpful for learning. It doesn't count toward your grade. If you do not see the need or benefit of doing it, it may show itself on your next quiz.
4. Grades are calculated as a GPA. Graded work (quizzes and projects, if I give any) are given a 0-4 score. These are averaged to produce your letter grade just like the GPA on their transcripts is, with a slight variation in the scale.

Am I right to grade the way I do? I don't think there are absolutes when it comes to grading, so no one can answer that question with certainty. This is what best matches my philosophy on grading. It may not match yours, which I understand. Feel free, if you're out there and still reading, to post a response. I'm curious to hear what your philosophy is!