# 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!

# Knowledge Machines are here; How will you use them?

There was a time when school was about learning the three R’s: reading, writing and ‘rithmatic. Sounds like the beginning of a long ago time story, doesn’t it?

After reading this 1993 article from Wired, I realized that Papert’s ‘Knowledge Machines’ are, in fact, here.

# 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?”

# CCSS: Key Tasks and Scientific Method

Common Core State Standards (CCSS) are lists of things kids are expected to learn in each subject during each school year. They are not the actual lessons. Your child’s teacher and school system will decide what lessons to teach and how to teach them.

Research shows that one of the best ways to teach children is to give them tasks and have them work through the solutions to the tasks. The child is given directions as needed, or small lessons on specific skills, but the child is allowed to figure out what skills they need, or what they need to know, to accomplish or solve the task. These are called Key Tasks.

To be able to participate in the process of Key Tasks, a child needs to have a way to approach and organize the information. In mathematics, this process is going to feel very different than the existing process of “show the child the problem, work the problem with the child, and then let the child practice problems. Without setting up the structure of the process first, students may feel that the teacher has abandoned them, is not really teaching them anything, or worse. It takes time to transfer responsibility for problem solving when a child has never been asked to shoulder the responsibility (except for remembering how to do some practice problems, or work a formula – not really learning, just memorizing and regurgitating information).

The process of approaching and organizing the information is very similar to the scientific method. Any teacher or parent can help a child learn how to approach these new key tasks by teaching them a “mathematical thinking” process. The steps in the process are simple ones:  Read and think about the problem, draw the problem or restate the problem, discuss the ideas about the problem with others or use resources (group discussion), estimate the answer, “mathematize” the problem (a formula or equation), try/refine/rethink, see if the answer makes sense. These steps may need to be used more than once throughout the process. As you can see, the actual answer is only a tiny part of the process.

For teachers, here is a brief lesson for teaching students how to use mathematical thinking in the class. For parents, you can help your child use this pattern with their math homework:

I love the idea of math as a thinking process. Instead of just giving students the list of actions, , I would approach this the same way I like to approach setting up classroom norms. I would start with a sample problem and just have the students think about it. I would tell them not to try and solve it yet. Then I would have them verbalize their thoughts in small group and then whole group- we would write the thoughts/assumptions on a big sheet of paper titled ‘Thinking’ and tape it to the board. I would facilitate with clarifying and summarizing questions.

The next step would involve visualizing. Students would be asked to draw a picture to illustrate what they saw happening in the problem. Again in small groups, they would create a picture/illustration, titling the poster ‘visualize’. The posters would go up around the room. At this point, I would ask all students to move around the room ( in groups) and visit the posters to see if the illustrations made sense, and if they suggested any mathematical way to look at the problem.

Returning to their seats, each group would create another poster titled ‘mathematics’ showing the calculations / solutions that they came up with. Those would go up on the wall. Each student would then be instructed to visit each mathematics poster and decide if those mathematics/answers made sense in light of the problems. This might be a good place for the students to use sticky notes and place comments or questions onto the posters.

The groups would then go back to their posters, check out the comments (as would I, so that I could come up with more questions) and we would come back to a whole class discussion to examine the various mathematics and reasonableness of answers. I might put up an empty poster titled ‘revisions’ so that students could add ways that they will need to revise their own thinking to solve this and future problems.

The summing up of the lesson will not be right or wrong answers, but a summary of the process itself. The students will be asked to discuss with one other person what steps they went through to solve the problem, and then write a brief paragraph in their math journal about what steps they took to solve the problem.

The final poster, and the one that will remain on the wall for future work, will be the steps the students noticed were common to the process- maybe have each group list a step (different colors, handwriting?). This will give them a roadmap to solving future problems- and as the teacher, I will give them the time to use the steps as we move through the learning process.

Parents can help by giving your children the time to verbalize problems to you or draw what they think the problem represents. You don’t always have to know how to do the math to help your child think through the process. Even if they don’t come up with a “right” answer, or maybe all they have come up with is questions, the thought process is going to give them a way to get in on the next conversation in class.