# 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!

# How do you tell parents to expect less from their children?

A recent article on the upcoming Common Core assessments that will be administered in 39 states this spring (2015) predicts that student scores will suffer. The writer cites the experiences of Kentucky and New York, where the new testing took place this past Fall (2014), two very different places and two very different results. The difference? Continue reading “How do you tell parents to expect less from their children?”

I want to know how to use this particular beastie to my and my students’ advantage. What do I know about it?

(I sent out some tweets. #SBG and #MTBoS to find out more!)

It is based on the common core standards for my subject/grade level.
I’ve seen these as sets of “I can…” Statements- is there a list somewhere, or does each teacher create his/her own?

(I sent out more tweets: @TarheelMommy95 @algebrainiac1 @JustinAion @WHSRowe were a few of those who generously shared what resources, including two references I definitely want to read: Marzano’ Formative Assessment and Standards Based Grading and Designing and Teaching Learning Goals & Objectives.

A score is given for each “I Can…” that reflects the student’s level of achievement of the standard, usually 0 to 4 or 5, depending on the teacher.
There are some great rubrics in the CCSS materials that could help me here- maybe there are teachers who have also simplified the rubrics for their students and parents – to help them begin the process of steering their own learning. (I feel another tweet coming on! I also remember a blog…. Mrs. Aitoro’s that might help me here. I will ask her to share…

I will want to have some kind of tracking system. That means that I will need to connect each task to the appropriate standard/skill. I will need to be able to identify what mastery is for that skill (oh yeah, the “I can…” statements and the rubric statements will help me there!)

How does the student exhibit improvement? I’ve seen a blog that explains the grade book set up – one grade per standard, it gets changed if the student exhibits improvement, but doesn’t get lowered. I like the idea of two tests with 100% success allows the student to not have to test that standard again. Can I assume mastery after two times? Will the rubric for mastery be clear enough? Will I run the risk of the student forgetting? Does mastery indicate memory or true conceptual understanding?

Thankfully, because of Task #2 and #MTBoS (thanks Justin @j_lanier and the rest of the MTBoS team!) I know I am not the only one out here asking these questions and I don’t have to re-create the wheel for my particular hamster cage! I really want to do this. And now I know I can!

# Do You Speak Words of Life or Death?

“Thoughts become words, and words have the power of life and death. Think to speak life giving words to yourself and others.” Joseph Prince

These words put me in mind of how we as teachers have the power to create hope or plant failure in the minds of our students. Our students believe us. For good or ill, we hold all the answers (even when we don’t).

We can use that belief to inspire our students, to enable them to reach beyond anything they might be willing to do on their own. Here is one way:

Fixed vs Growth Mindset

Do your students have a Fixed Mindset or a Growth Mindset? Do they eagerly tackle problems, curiously start investigating the challenge placed before them, generate ideas for possible solutions?
If you give students a choice of assignments, do they pick the easy ones or the hard ones?
Do your best students want class discussion, or do they just want you to show them how to work the problem, so they can do their work and keep their A?

It breaks my heart when a student walks into class and says ‘I’m not good at math. Don’t expect much from me.’
Or the kid who told me, ‘whenever I’ve done enough to pass, I’ve been told that I usually quit trying.’ Or the A student who is afraid to try the problem until you have shown them how they are supposed to think about it. These students are exhibiting Fixed Mindsets. They have been given the idea, by teachers or parents or grouping or grades that they are dumb or smart or not good at math, or science, or too smart to fail at math, or science, or any other subject. Girls, especially, tend to get the message: math is not your ‘thing’; children are grouped by what teachers believe they can do: advanced, remedial or in-between – all a form of ‘silent’ stereotyping, as deadly as anything we say out loud. What message am I sending when I too quickly provide an answer, instead of asking good thought-provoking questions? How can I encourage a growth mindset?

What is a growth mindset, and how does it benefit our kids?

A growth mindset is the ability to see possibilities. It is a confidence in one’s ability. It is the MacGyver in all of us, to use a modern example. And it can be taught!!!

Teachers can encourage a growth mindset by changing the messages they give to their students:

“I believe in you”

Don’t let grades define your student. Instead of a grade, give specific feedback on problem areas. Tell them – put it in writing – that you are giving them the feedback because you believe in their ability to fix their mistakes.

Celebrate mistakes!

Your students are scared to death of making a mistake, getting it wrong, so they sit on their hands in class. Am I right? How frustrating is it to ask a question about the material and be greeted with blank stares?

It is time to celebrate (maybe even reward) mistakes. Sounds crazy, I know, but hear me out…

Tell the kids that every time they make a mistake and struggle with fixing it, their brain gets smarter. (Don’t worry, it’s true, check out this link: Brainology)

Reinforce the message:
Give them a picture of their head in profile with a brain drawn in it. Make sure the brain has lots of little empty spaces in it, like the one I’ve posted below (or break out the projector and let the kids make their own personal profiles on blank paper).

Tell them that each time they find a mistake, they get to color in a section of their brain. Celebrate the fact that their brain has grown! (Younger students like stickers; older students may want stickers, too! It doesn’t have to be anything huge.) I would even keep a big poster of a brain on the wall- on a really tough day, where the kids have made it through with lots of effort, color in a space on the class brain- they have become collectively smarter! This is also a great community builder. It’s like those scaling a wall, walking on ropes exercises where you can’t make it without everybody pulling together – without the parental permission forms!

And for those of you who aren’t sure whether you have a fixed mindset or a growth mindset, here’s a link to a great article, with a short mindset assessment at the end. Growth Mindset

And don’t worry if it tells you that you have a Fixed Mindset- it is only temporary!!

What did my results say? What do you think? Am I a Fixed or Growth mindset kind of person? I can’t wait to hear what you think!

# A Lesson Starter: Unraveling the Vocabulary

“You’ll know kids mastered a subject if they have the vocabulary to talk about it intelligently.”

This comment was part of a recent post “It’s Building Kids’ Vocabulary, Stupid” published by Educationnews.org.

Vocabulary is critical, especially in math. Look at the language used in the Common Core standards – you have to be a mathematician to understand what each one means. To clarify the purposely brief standards, teachers in Tennessee are being provided with EU’s, essential understandings. EU’s are great, but when I tried to translate one recently, in order to write it in a way a student could understand as the goal for the day’s lesson, the vocabulary was still too dense.

A Lesson Starter: Unraveling the Vocabulary

Let’s say you have told your students that the goal for the day is factoring polynomials. You have given your students a key task designed to give them conceptual understanding about the topic. You have asked them to think about the problem and decide what they think they will need to do to work toward a solution. Then you realize that they don’t recognize the words factor (don’t scoff- my 10th graders didn’t) and they have no clue what a polynomial is.

Instead of defining the words for them, or having them copy some useless definitions out of the back of the text, let them spend some time defining what they think the problem is asking them to do.

Next, have them share in small groups and agree on the actions/terminology the problem requires. Then bring it into a whole group discussion. Have the students agree as a group on the terminology they are going to use as they work their way through the assignment. Use clarifying and summarizing questions as necessary to allow the students to come up with a common vocabulary.

Don’t worry if the students don’t use the formal math vocabulary for the assignment. It’s okay not to. In fact, allowing them to use familiar vocabulary will boost their confidence for when they need to tackle other, less familiar projects.

Once the assignment comes to a close, draw the students back to the formal math vocabulary. Ask them to decide how what they just did matches up with the formal definition. Let them come up with valid connections and understandings.

Then have them explain it to another student. Listen during this process. Ask some students to share their understandings with the class. If there are different ways of explaining, (which there usually are!) have students indicate which way they understand best. It is not a contest, it is a chance to show children that there are lots if different ways to come to understandings.

Finally give the students another problem with instructions in the same formal vocabulary that they just defined. This will allow an even stronger connection to the newly learned term.

(I like word walls, so the new term would definitely be added at this point.)

Dear reader, I would love to know if you were able to use this idea in your classroom.

# Join The Math Revolution!

Check out this exciting website!
Jo Boaler is giving teachers and their students the tools and information we will need to begin loving math.

We all want to see Key Task lessons, what they look like, how students react, what it means when students start conceptualizing math. There are videos, lesson ideas, and links to publications and research.

The site is called YouCubed,
“a nonprofit providing free and affordable K-12 mathematics resources and professional development for educators and parents.”

Be among the first in your block:

I invite you to Join The Revolution!

www.youcubed.org/

# A Reply to Why Johnny Can’t Tell Us Why

The author writes: “Johnny (a.k.a. Mary, Bobby, Dashawn, Jaynaya, etc.) can’t think.  He doesn’t have the basic mathematical understanding of how the operations work, the nature of numbers, and the fundamental “rules” of the game of math.  She doesn’t have the “self talk” skills to decide what to do when she doesn’t know what to do.  He doesn’t have the confidence to just read the problem, take it one step at a time, and TRY. She doesn’t have any tools in her problem solving toolkit aside from learned helplessness and the response, “I don’t know” when posed a question.” http://www.rimwe.com/the-solver-blog/41.html

The link I’ve posted is the author’s full blog post on this topic. From my own experience, I believe it describes what is happening in high school classrooms across our country. The author asks the question, “What strategies or techniques have you found that are helpful in trying to turn the tide? Well, I’ve spent my summer trying to find some of the answers this author is asking. Here is my response.

You were in my class last year, weren’t you?!! Same background, different ethnicity. These students required that I fed them everything and when I didn’t, they fired me as their teacher. I have spent my summer looking for answers to your questions. I believe I have found some powerful answers. I even started a blog to talk about some of these solutions:

Mathematical thinking;
Visualization;
Number sense practice as part of every class;
Encouraging growth through mistakes;
Small group discussion;
Questioning that encourages students explain what they are thinking.

Oh, wait, you wanted something to deal with the anger and the apathy. That is a much tougher question.
I think students have gotten the message that they are not good enough – at math, at English, at any class. I think the response is frustration, after all, wasn’t school supposed to give them these skills? They showed up for class, they did homework or reports or worksheets. Why is it now not good enough? I’d be angry, too.

We could spend years blaming, wishing, and wringing our hands, but let’s not.

You and me and the teachers (and the parents of these children who are frustrated and unhappy with school) who are faced with this scenario are going to have to work with what we’ve been given. As for me, I am going to meet the kids where they are, use number sense puzzles and practice (as simple as I need to go, first grade level if necessary) and begin teaching these kids a new way to think about math.

Will I have to re-earn their trust? YES! It won’t be easy, but for ANY of this talk to be of any more use to our children than anything else the education community has done, for our kids to make it through these new assessments (which we really need to rethink, but that’s for another post); for our kids to make it into colleges, to have good lives, to be good citizens, we are going to have to change the message we are sending our children. They are good enough! They are clever enough to learn ANYTHING! School can be enjoyable and rich and kids can like math and literature and science and history. Anyone who tells you not to expect it, is damaging what the experience is supposed to be. Will it be struggle and hard work? Yes. And that is perhaps where we have let them down the most.

We are afraid to let our children struggle.

Did you know that every time you have to solve a puzzle, work out a problem, or struggle to master a skill, your brain grows? Research shows that synapses fire every time this happens. Mistakes, failures, do-0vers are NOT BAD! These are things that have to happen for us to learn. For me, that means giving my math students rich, complex questions to think about, to examine, and discuss. And maybe solve.

The methods listed above are a start: Belief in our kids, funding schools, giving teachers the knowledge, as I have gained this summer, to teach kids through problem solving – not rote memory and regurgitation – and stopping the insanity of using test scores (we can look at student’s faces and observe their behavior – a focused, well-behaved student, eagerly digging into a lesson because they are interested!) to see if they’ve learned anything is what will ultimately make a difference for our children’s education.

I hope to address some of the topics I’ve touched on here in future posts. I welcome any comments, experiences, resource/research links, lesson ideas, etc. that will expand upon these conversations. Thanks for reading.