# Are you a 1, 2, 3, or a 4? What’s numbers got to do with it?!?

I, along with a couple of other teachers, are piloting a grading strategy that is generating some interesting conversations on a DAILY basis with our students!

We’ve all read that grades do not improve or motivate learning. In fact, once a grade is given, the student assumes that idea is ‘done’ and drops it, moving on to acquire the next grade.

What I am about to share with you has MY KIDS talking about how THEY can improve their learning…

First, I have to give credit for the base of this idea to an amazing educator that I work with every day: Rebecca K. She, of course, credits it to an idea she learned in a workshop some years back. Anyway, she started the year off with a cool bulletin board, that looks something like the image above, which I used to create a powerful way to motivate my babies to take more responsibility for their own learning!

The students I am talking about are your average 9th grade (yes, FRESHMAN!!) students, that run the gamut of every freshman stereotype you’ve ever met. Really. (This includes students with personal learning plans and students whose first language is not English!) AND  we’ve got them talking about growth – THEIR growth – as learners. When we hand back a paper, instead of the ‘crumple it up and put it in the bookbag or the trash’ mentality, the comments are varying forms of, “..tell me what these results mean!”

Here’s how it works:

Four numbers, four learner identities:  1. Novice, 2. Apprentice, 3. Practitioner, 4. Expert

Novice: I’m just starting to learn this and I don’t really understand it yet.

I explain to the students that this is where everybody in class starts out. Algebra I will have lots of things that are new to them, and we expect that they won’t be familiar with the material! We don’t expect them to know it all before we teach it. Sounds obvious, right? Sometimes you have to be explicit with Freshmen. I think that’s where the name originates!

Apprentice:  I’m starting to get it, but I still need someone to coach me through it.

The apprentice is the beginning of the learning phase. When a student gets a 2 on a problem or a whole assignment, they are in the initial learning stages. As a teacher, I’ve just told them (by marking it a 2) that I know they still need help with the concept, and that I will be supporting their learning. This also tells them that they are not there YET – and that they have room to continue learning. Sometimes we have to give kids permission to not know things YET!

Practitioner: I can mostly do it myself, but I sometimes mess up or get stuck.

This is a proud moment for most of my students. That little 3 next to a problem or on a paper, tells them so much more than a traditional grade. This sends them the message that I get it that they’ve got it! This affirms their learning. This affirms their work. This is personal. Better than that, this motivates them to keep going, to keep learning. They ALL want to be….

Expert: I understand it well, and I could thoroughly teach it to someone else.

Isn’t this where we want our babies to be? You know that if they know it well enough to teach it – THEY KNOW IT!! That peer tutoring thing is for real! Please notice that there are TWO parts of this level: knowing and teaching.

How does this work?

My (totally awesome) co-teacher, Stephanie W.,  and I, use the following grading process. Feel free to modify it to fit your students, and what is happening in your classroom. We know that what we are doing is working for our kids – you may want to start with this, and then modify as you see what is working for you.

We give an assignment or quiz. We grade each problem with a 1, 2, 3, or 4. We add up all the grades and divide by the number of items. That gives us a number between 1 and 4. Many times that will generate a decimal, say 1.8 or 2.5, or even 3.8. Here is an important point: we DON’T ROUND UP! We DO EXPLAIN the process to our students. It is important for them to understand that this is not arbitrary. They must own the process for this to work. These conversations happen EVERY time we return an assignment. That’s a GOOD thing!

Our goal for our students is mastery, so unless the resulting average is an actual 2 for example, the child is still a NOVICE (1, 1.2, 1.8, 1.9 – doesn’t matter. They are still a 1). Same with 2 point anything – they are still a 2, same with 3 point whatever – still a 3. The ONLY exception is 3.8 and above. If the student has one or more 4+ answers, with clear justification statements, then, and only then, will we round up to a 4. See below for the PLUS explanation!

Our evaluation goes something like this:

a) Answer that is incorrect, No work shown, or No answer at all: give it a 1.

b) Answer with some work shown (they attempted a solution) but it is incorrect in major ways and answer is incorrect or incomplete; give it a 2 (remember they are still learning and need more help!)

c) Answer given is incorrect, but work is also shown. (OR answer is correct, but NO work shown to support the answer). Student did pretty good, but minor errors and/or mistakes caused the incorrect answer; give it a 3. This student is obviously getting it, but he/she is letting errors get in the way. Maybe they are lazy, maybe in a hurry. The 3 tells them that they are getting it – but they NEED TO BE MORE CAREFUL! (The 3 for NO work shown is to allow us to ensure students are not ‘borrowing’ answers from another student! We are giving them the benefit of the doubt until further notice.)

d) Answer and work is shown and is completely correct. This baby gets the 4!  The student can feel the glow of being an expert. But wait, there’s more! This only satisfies HALF of the description. What about the ‘teaching’ part?

Four “+”? What is Four Plus???

‘Four +’ is that special designation for the child who not only knows the material, but can prove to us that they are able to teach the material to another student. Time dictates that we don’t have the opportunity for EVERY student to demonstrate teaching ability (although we do try to build in those opportunities!). We have explained to our students that the way to demonstrate this ability is to justify the work they’ve shown, with brief written explanations.

Written Justification sets the student up for PROOFS in Geometry

Algebra I is a class of foundations. It is important to teach with an eye to the future courses our kids will encounter, and proofs are some of the most difficult lessons for students. One of the Algebra I standards is to be able to justify the steps taken to solve simple one step equations. This is an important step to understanding that there is a mathematical reason for being ABLE to take that step – and not just because the teacher said so! By building this into the idea of EXPERT, we are modeling the concept that understanding – that is, the realization that there are solid REASONS for why math ‘works’ – is a valuable part of the learning process.

What WORDS do you use to tell a parent how their child is doing in your class?

I know this is just a brief overview of this process, but I wanted to share because I feel it is the first solid step in moving towards talking about GROWTH and LEARNING, instead of grades. I believe it is important that we take the focus off of grades, for students and parents. To do that, we, as teachers, have to stop using GRADES as the unit of measure in communicating with our students and parents. Unfortunately, our grading systems, and I’m talking the actual computer systems we have to use, are not set up to show mastery – they are set up to show GRADES!

I already changed my conversations, my wording, my language,  with my students. It will happen with my conversations with parents in my next phone call/email home, as well. Will YOU?

What’s the downside?

My school still uses a grading system built on averaging traditional grading numbers. That means I can’t just put in 1, 2, 3, 4, or 4+. I have to turn these numbers into a grade between 0 and 100 that will accurately translate and describe my students’ mastery of the curriculum.

My solution is two-fold. The grades in my gradebook are tied to one of the required standards, and each of the above levels is tied to a number that has already been given meaning by how it is used as a grade. While the first is fairly easy to accomplish, the second is based on how parents and students interpret grades. A 100, for example is the ideal. That sends the message that the student has mastery of the assignment, or the course. In fact, anything above 93, in my County school system, is an A, and as such, denotes pretty much the same thing as a 100. Same for a B, or a grade in the 80 range. Those two grades are obviously acceptable to most parents and students. The grade of C is a little more ambiguous. The C denotes that the student is somehow less than perfect, but still passing.  While a student may be GLAD to have a C – it does denote that the student is doing the work and IS mastering the concept – it doesn’t have the same cache’ as the A and B grades.

So how do I reconcile the grades with the numbers?

A novice receives a grade of 65. The Apprentice receives a 70. The Practitioner has earned an 80, and the Expert, a 90. The 4+ student will earn a 100, as long as all problems on the assignment or quiz show justification, evidence that they have not only mastered the concepts, but have gone above and beyond to be able to communicate their knowledge with others.

The final issue I will address here: What happens when a student makes no effort at all. Our students never do that, do they??? In that instance, the student has given us no information on which to base a grade. Effectively, they have NOT TURNED ANYTHING IN. The grade in the book becomes an NTI, and we are made aware that we need to step up our efforts with that student. An NTI is a zero, until the student completes an assignment on that material, and we can assess mastery. From there, the averaging work of the gradebook takes over, and the grade reflects the whole course mastery. Grades in this context are fluid, and can be changed by future mastery as evidenced by quizzes or testing situations.

The system is not perfect, but the teachers with whom this is working believe that we have created a system that truly tells us where our kids are with the curriculum, and allows us to modify our teaching darn near immediately, so that we can address the areas in which they need further help – which is the actual point of all this grading, isn’t it?

Here is the poster we use in our classroom to explain the levels. Our students get their own mini copy for their notebooks. We utilize a small chart of “I can” statements for each unit – no more than 3 – 5 statements – that allow the students to chart their progress. Here is the chart for our Unit 1 standards. The kids get this, too. You can use any “I can” statements you need for your particular units.

At the beginning of each unit, the STUDENTS determine their pre-assess level, the quizzes give them the mid-assess levels, and then the unit tests are the post-assess level. The students keep track of these themselves. We incorporate a running conversation DAILY of what their goals are, where they think they are with these goals, and how they are going to get to the 3 and 4 levels. I have personally found this is a great way to have the students tell me where they are at the end of instructional and practice periods throughout class. I simply ask them where they think they are – 1, 2, 3 or 4. The majority of students are incredibly honest, because we are all speaking the same language. The ability to quickly assess and modify my teaching is been made incredibly easy! Grading has become a process of assessing growth, not despairing over what they don’t know. I LOOK FORWARD to grading the work, knowing most of my students WANT to have a conversation about where they are, and what they need to do to get to the next level. Let me know if you would like the rest of the “I can” levels we are using with this course. I’ll be glad to share!

# Sonata in C, and Fluency: there is a price to be paid….

I found myself grading mounds of worksheets, and a couple of quizzes (remediations, really), and I began to wonder if I’d turned into one of those worksheet, algorithmic, obsessed teachers that focus on skill and drill over understanding. And I was beginning to despair, just a little.

I thought about my students, and what allows them to experience success, because it is the successes that motivate each one of them to keep going, to persevere in the “icky, sticky, I don’t get this” parts where they struggle. Part of the reason my students struggle is the lack of fluency. Each concept, each set of steps, each decision they make to solve or simplify, takes a huge cognitive load. They exhaust themselves just remembering what they need to do to factor a number (“Mrs. M., what is a factor again?”)

These children are not fluent. Not in multiplication tables, not in knowing the difference between base and exponent – more than half of them will tell you, “a negative plus a negative is a positive, because two positives make a negative.” I remind them they are adding, not multiplying, and they bravely leap back in, “oh yeah, -11 plus -3 is 8.” And this is after they have laboriously put the computation in the calculator… And I draw another number line on the board, or we play the game where they move their token up and down a number line to the tune of positive and negative numbers.

These babies of mine are not fluent! But they will get there. And therein is my saving grace with the worksheet thing. You see, I learned to play the piano, and I took ballet lessons, and I was on the swim team. And I was good at them in that order. But each of those activities required PRACTICE! I knew what it took to swim 50 meters fast enough to claim the silver, the red, and the blue ( third, second, and first, respectively), but I was better at collecting the silver than the red or blue, because, well, practice was held in the cool early summer mornings – when I’d rather be sleeping, or reading, or doing anything else than getting wet and cold over and over and over…. Well, you get the picture! I never got “fluent” at the swimming thing.

Ballet was a little better – no water! But I wasn’t slender or limber, and I couldn’t lift my leg to the bar without a pulley! I loved the plié, and the costumes and the recitals, but my heart wasn’t in it, (probably because my body wouldn’t cooperate by being tiny and graceful – one can only take so much of that feeling like a cow among graceful swans!)

Then there was the piano. We had an old upright; beautiful and rich sounding tones would pour forth when my mother played. She could play everything! And if she couldn’t play it, she could sight read the music. I soon learned to love the sounds I could produce. I wanted to play the classics – Mozart and Tchaikovsky, and Bach and Beethoven. I wanted to play the rich beautiful pieces mom could play. I had heard them, I could read the notes, but I had to become fluent in the patterns. I would play the pieces haltingly, getting a feel for the notes, but then, to really learn the piece, I would have to practice small sections   – bar by beastly bar, until my fingers would traipse the keys of their own accord, and the piano would yield up its beautiful tones for me, the way it did for my mom.

So, back to the piles of worksheets. I look at them: logarithms and exponentials; growth and decay word problems; breaking down the formula, picking out the beginning value, the ending value, calculating the rate factor from the rate; understanding the idea of 100% being expressed as one. My babies are practicing their fluency with the notation, even as we put details to the numbers on the page. While I teach for understanding, I really want to show them the beauty and the majesty of math’s rich and beautiful notes. I want them to want to produce the beauty that comes as they practice; as they practice the changing from exponential to logarithmic so that they can spot what they need to do when they have to calculate for time, instead of finding an ending balance; as they practice because fluency takes a lot of that cognitive, heavy, exhausting work and turns it into a beautiful smile when the light clicks on and the child yells, “Mrs. M, I got it, let me come up to the board and write the answer!” And so I will keep on with the practice, worksheet by beautiful worksheet. Success breeds confidence. Confidence breeds courage – the kind you need when you tackle something new, or when you persevere because you believe you can find a solution.

To cut down on the paper (and the grading) I’ll keep varying the tasks:  physical practice, verbal practice, mental math practice, practice through competition, things like Jeopardy or Kahoot, because practice builds fluency, fluency builds success, and success is what keeps us trying.

I did finally learn to play a pretty mean Sonata in C, but there was a price I paid to gain the fluency I needed. And, while I am not as good as I used to be, when my fingers find a piano, they slip into the gracefulness that eluded me in ballet, and the speed my body lacked in swimming competition, and they can “fluently” find the notes that will make the piano, and my heart, sing!

# Why do we teach math? This teacher’s honest answer.

A math teacher friend has been questioning his value in his classroom. In his honesty, he asks “why do we teach what we teach?” His plaint comes as children ask him “why do we need this stuff, why prove something you have told us to be true, when will we ever use this?”
His desire is to answer honestly, but brilliantly; to give an answer that will make the child stop, gaze at him in awe, and return to his/her studies with renewed vigor and purpose. I suspect he is not alone in his thinking. For him, and for all teachers who go to this place of doubt and fatigue and, perhaps, even frustration, I offer these words:

Children need the discipline of effort, of struggle. They need to try something new, to push themselves beyond their comfort zone. As all of us know, that comfort zone is, well, it’s comfortable!

Teachers push, encourage, cheer, exhort, challenge, and free students to step into the unknown and the new. It’s like the first taste of vegetables for a baby. Oh, that face! But we know it is good for them. We know what they do not– that there is a wider world out there for them, and that they will need ways of dealing with it. Math has a logical, beautiful order to it. There is a discipline of thought that is rich and worth learning. And that is the first part of my answer. The noble part.

Here is the second:
I teach for totally generous and totally selfish reasons: I generously want children to find the wonder and excitement of knowing something beautiful. I want them to feel and own discovery of patterns and trails that numbers make; how they loop back upon themselves; how they start at one place and end up in another. I want them to see the magic of numbers. I want them to feel the satisfaction of revealing the secrets behind the magic – the elated rush of struggling with and conquering a numerical puzzle. It is Alice finding a key to a door and then choosing the correct potion to become the right size to fit through the door. (And for many children, math is as confusing as wonderland was to Alice!)
And selfishly: to see that most elusive of creatures – the excited spark when a student makes that connection to something learned. That spark is my adrenaline, my satisfaction. It creates a pride in me about that student that is like no other feeling in the world.

There are many comments about how students don’t care; how testing is killing the learning; how teachers’ hands are tied by administration. Still we teach. We teach because we know in our hearts that it is right and important. We want to be in the classroom. We want a better future for our students than they can possibly envision. We hope, eternally. We hope. That’s why we teach.

Our hope is stubborn and sure. Our hope does not back down. Our hope transcends the newest strategy, policy, or curriculum. Our hope spurs us to persevere with every child.

We must not, cannot assume that we have no impact. No one comes up at the end of each period with a trophy or a plaque. Children rarely write thank you notes (or parents for that matter). As teachers we may never see any result, we may feel we are simply parroting what other, greater teachers have already said. We cannot let that stop us. It is persevering into the dark, shadowy night, not knowing what we will meet along the way, with people telling us to go back, to beware, calling us foolish. Hope. What a powerful thing. Our students are the beneficiaries of this conviction, this hope. They may neither appreciate nor value it, now. But someday, ahhh someday, we know they will. There will be that moment, although we won’t be there to see it, when a child will silently thank a teacher for not giving up. And since we don’t know which child in our care that will be, we must place that unopened hope with each child we teach. And we will, because we must teach as surely as we must breathe. No matter what.