# Asking the right questions of ourselves…

We question our students to elicit and engage, to push their sensemaking, to activate prior knowledge, and to get them thinking about their thinking. But do we question ourselves and our pedagogy with the same focus?

Table taken from National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.

In the rush to use new ideas, incorporate technology, or just ensure our students are doing math things from the minute they walk through the door, are we giving enough thought to why we are choosing an activity? What is that activity suppose to achieve? Has it earned the time it will take, not only for the students to complete, but for the grading and feedback? In other words, will it move these students further towards the goal?

Learning Targets are Not Just For Kids

My colleagues and I have been asked to share learning targets with our students; to write the daily lesson or goal on the board and go over it, so students know what successful learning looks like.

As you think about what your students will be doing, do you ask yourself just how the activity will provide the experience you want for the student? What will it tell you or your student about their learning? How will it move them closer to understanding? How will it engage the learner to produce the desired result? What will the failure of this activity tell you? Tell your student?

For the math classroom, skill builds upon skill. Knowledge is formed by understanding how the old can be reshaped or used to fit into the new. It’s like reading, but with numbers. In learning to read, we begin to decode shapes that are letters, that make sounds, that can be arranged into words (patterns of letters), that are then arranged into larger groups of sentences to convey information.

In mathematics, we learn our numbers, which instead of sounds convey amounts. At first, these amounts are concrete, as we count fingers or toes or toys or blocks or cheerios. At some point the numbers begin to represent the amount. We put these numbers together into groups that define patterns, and we put these patterns into sentences that convey information. Every time we learn a new concept, we can place that building block in context and do more than we could. A concept in math means we’ve identified a relationship, a cause and effect, a reasoning about how one action effects an outcome. When we understand the connection, we can extrapolate, interpret, compare, contrast, synthesize, and create. All of those things that we say we want our students to be able to do, no matter the subject.

Is this what your materials and lessons are teaching?

Every teacher reading this has bemoaned the lack of time we have in the classroom. How we spend that time often forces us to cut our activities, explorations, and conversations about the material. We have to hit the ‘most important’ standards, or the ‘big ideas’. Yet we know that knowledge is built by exploration, by focusing on a problem or situation, by playing with ideas. But how often have you asked ‘how will this activity increase understanding of the concept?’ ‘What is it teaching?’ ‘How does it allow showing the learning, or mastery?’ ‘Will it allow for connections to what has already been done, or to what is to come?

Is the idea or activity sticky?

By sticky I mean will this be something the student will think about longer than the activity itself. Will a student come in a day or a week or a month later and say, ‘I’ve been puzzling about this idea and I think I finally get it.’ And yes… I believe all of our ideas can be sticky – not necessarily for everybody at the same time. If we are truly giving each part and moment of our lesson thoughtful care, there will be more sticky moments than not. Those moments are what build interest, knowledge, and understanding. One of the best examples of this is the Four Fours activity. My students worked on that for over a week!

How do we get there?

1. Put yourself in your students’ shoes.

Think about what is happening to them daily. When they walk into your class, where are they coming from? Have they had time to process their last class? (Probably not.) Are they looking forward to math or dreading it? Did they do their homework – or even understand it? Is your class a relief, a chore, or an interesting, thought provoking space in their day? As I write this, I see the faces of my students, and can easily see the few that truly look forward to this class – but there are occasions where my lessons have let them down, too!

What do they need from you in that moment, to get their mind off of what has happened up to the moment they walk through your door?

For a start, pretend you are a student and walk into your classroom. Pick up that starter. Take it to a desk and try your own lesson. Where is your student brain? How does it make you feel? Does it do you want it to do? Loosen them up? Assess yesterday’s lesson? Review a skill they need in the main lesson? How will you check the outcome? This shouldn’t be a ‘take up and grade’ – it’s very name implies short, sweet, and to the point. What you want to accomplish must guide what you do. What you do sets the tone for the rest of the class. If the starter isn’t working for you, it isn’t working for them. Stop. Just stop doing what doesn’t work.

One teacher I know

has a great routine. She has trained the kids to pick up a starter (half page, every day) on their way in. Some fill it out. Some don’t. She goes over each problem, quickly working it on the board. She asks a few questions about the numbers or the process. Usually she has to get the class’ attention, many are off task. The kids who knew how to do this are already zoned out. The ones who don’t know how either copy her work down exactly, or don’t write anything. She does this quickly, and in her mind this is circling back around as a review for weak skills or concepts. She is practicing good classroom management by getting kids in their seats and working. She has trained them that math is boring.

During one week, she gave the same material as a starter and as a quiz to check for Learning. To her frustration, it did not result in increased knowledge for those who hadn’t already learned it (and I suspect it was extremely boring for the handful who did!) This is a 15-20 minute activity every day. How could she change this activity to get the desired outcome, i.e. strengthening this skill?

A process is a pattern of activity. A concept is the explanation or reasoning for why we do the process. Teaching a concept should lead to the process. In the interest of time, students often learn the process. Then it’s practice, homework, and a test. Are you teaching process or concept? Are you reviewing process or concept? Are you practicing process or concept? Concept is harder, takes more time and doesn’t work well on a worksheet. It is much more interesting, however. Concept is sticky.

You do not have to reinvent the wheel!

No time to write those magnificent lessons? Have I got a tip for you! You do not have to do this alone! Lessons and resources are out there and so many are FREE. Check out these links (courtesy of Matt Vaudrey and the #MTBoS:

Not only will you find good lessons, you will find teachers who are constantly looking for better ways to share this wonderful world of mathematics!

Here are a few more questions for you to consider, (and which I will be grappling with while planning my next classes):

3. What is my lesson intended to do? How do my materials (problem set, delivery, class activity and structure, timeframe, sensemaking, etc) support this goal?

4. Where are my kids likely to fail? What can I do beforehand to support the weak spots (Starter idea!)?

5. What does the learning of the concept look like? What do I do for those that ‘get it?’ What do I do for those that need more? How will I know (formative assessment). If they don’t start, WHY not? If they don’t finish, WHY not? Do they really know how to do it? Is homework appropriate- i.e. will this truly extend the learning?

6. Does my lesson connect this idea to what they already know? Does it give them a peek into a future idea?

7. When/how will I give them time to process what they’ve done?

8. When will I revisit? How will I revisit? (Yes! Plan for this!)

I leave you with this:

The moment you can really know a student has internalized a concept/learning target is the moment you hear/see them sharing what they’ve learned with another student. Plan for that, too.

# Change the mindset from ‘finished’ to ‘learning’….

In this continuing exploration of Academy high school practices and their unique position to affect change, the idea of changing classes every day, every hour or more, is examined.

Currently, the Academy school model is some type of block schedule. Students take an assortment of courses in order to meet a specified list of credits towards graduation. Throughout the day, students get an hour to 90 minutes of a subject, bells ring, brains shift, and the activity is repeated over and over, until the final bell. Is this really the best way to learn? Is it the way we learn to tie our shoes? Did mom give us an hour of this and an hour of that as we learned to make cookies, or learn that different sized pans would only hold so much, before spilling the contents across the floor? Did a timer go off somewhere as mom yelled that it was time to go learn something else?

I believe there is a better way. We learn by experiences: examination of a situation, trying a solution, evaluating the result, trying again, evaluating, reflecting, etc. and throughout the process, storing the experience for future reference. There is also an element of sharing, talking over results with another person who has experienced, or is experiencing the same thing. With my students, however, I usually get one offering a solution and the other copying it down, in order to simply get finished. No learning, because the goal isn’t to learn. The goal we’ve set is for them to get ‘finished.’

Change the mindset from ‘finished’ to ‘learned’ or ‘learning’ and time becomes irrelevant. The goal is learning, so students don’t leave (or they return each day) until they’ve mastered the concept.

The idea that students are given a list of items to accomplish at the beginning of their high school career, and that they can finish them in any order, and in whatever time frame they are able, is a concept whose time may have come.

What if high school were as exciting and looked forward to as coming of age? Shouldn’t this be a time of discovery and promise, instead of dreaded and scary? To give our students the responsibility of their own learning, I believe they also need to know what that learning entails, so they are properly equipped to run with the responsibility!

I think it is time we return to trusting our kids with more, sooner. The movement to protect kids has pushed personal responsibility to the back burner. We are so afraid of letting kids fail, we do things for them, which creates a child that doesn’t need to step up and take responsibility. In addition, it creates a child that views failure as a disgrace, meaning that child will do everything in their power to avoid failure. I’ve observed students who work harder to avoid failing – often by cheating or straight up avoidance – than they would to engage in the learning! In their defense, the classroom can be a real snoozer if there is nothing engaging or relevant going on.

‘I believe every child can learn’ is the new mantra.

What I don’t see is the belief that every child can take control of their learning; that we can trust natural curiosity to take them places our planned lectures never could or will. There has to be a freedom on the part of the teacher to ‘hang on for the ride’, as the student forges ahead.

It’s a little like taking a horseback ride.

Every student has a mentor, advisor, or adult that holds them accountable. The entry to high school is planned in a community of parent, student, teachers. The goals for the learning are spelled out. The reins are placed in the child’s hands, with guidance. The adults are the spotters, close in the first few rides, backing off as the student gets more familiar with the process and expectations. The student isn’t being pulled along the path to the destination; the student is choosing the way, enjoying the ride, the pace, the view. The destination arrives naturally, and perhaps a little differently than first envisioned.

This idea does require a bit of a structural change. Instead of a class schedule, a school could end up with every student starting in the same place! Big room needed! The solutions could involve everything from an orientation style of instruction with starting points, to letting students come up with possible solutions that would allow them to get in the knowledge- and learning time- they need.

The Checklist

So what does this checklist look like?   Is it the same for every student? Is it modifiable, like college programs? What’s required? What’s negotiable?

Is it a list of standards, or more a list of abilities, attitudes, or problem solving? Is it a bit of both? How do we assess the learning? Who assesses the learning and levels of achievement?

This process requires collaboration among student, parent, and faculty… but it also requires a commitment on the part of teachers and school leaders to stick by the rules: student choice, student struggle (a critical component), and a plan to reward  success AND failure, because there will be both, if we’ve done it right. It’s time to do this right, and to return a love and excitement for learning back to our children!

# Academy schools are uniquely positioned for changing the landscape of education.

The first day of 9th grade. DaiCrede is very nervous. He’s heard about this high school, just rumors of course, that they let you choose what you want to learn about, there are no regular classes; you work with teachers in each area as you need the information to complete your project. There aren’t grades, just levels of achievement for learning targets. He’s not sure if he can make it in this environment. He is excited about the robotics lab, though. That would be cool…

Shelly can’t wait for the bus to get her to school today. She fingers her Advances in Analytical Chemistry magazine. Finally, a school that will let her pursue her dream of becoming a medical researcher! Just think, a whole day devoted to learning how to run a research program. No breaking the day into language, math, history! She can grab those things as she needs them for her project. She loved meeting with her teacher mentor during the summer to set up her project parameters. She’s nervous and ready.

Ned is nervous, too. He rides his bike, slowly circling the parking lot. High school. He’s not sure how having no classes is gonna work. How will he know what to do?

First Week: Orientation

This Academy High School has a Ninth Grade Academy for incoming freshmen. They will be going through a series of workshops this first week to learn how to navigate the process. By the end of week two, they’ll have chosen an initial Academy. During the third week, they’ll have chosen a project and have begun breaking their project into tasks – and identifying the various areas of knowledge they’ll need to access. They won’t go it alone, however. All students have been assigned two mentors: a teacher, and a student from a higher grade, (Mentoring is a learning target for all students, more on those later) who will help them navigate the project system and hold them accountable for task goals and deadlines. While this may not feel like a structured environment, there is a definite structure and protocols. The flexibility comes in as each student is allowed to follow his or her interests, change from one Academy to another as they explore, and begin to search out what they need to know as they need it. There is a framework for that!

That first week will see new students rotate through a series of workshops and learning sessions on the School’s Academies. These new-to-high schoolers get information on the various fields of study available to them. (Students may have chosen to come here- if their zoned high school is not an academy school, or if they were not doing well in a traditional school setting).  Returning students share their experiences with the process about to be undertaken; what worked, what they liked, what they found most challenging, what they would do differently. They testify to the powerful learning that takes place when they were able to choose topics for study that they wanted:

“Math becomes relevant when I had to figure out what was happening in my chemistry experiment. I went into the math room, laid out my work, and asked for help. Once we started, I realized I didn’t know the basics. I spent two weeks in the math lab, working through background knowledge, then learning how to apply it to my research. Whenever I got stuck, I would go back and get help.”

“I had to write up a report on my project. The requirement that it be a formal paper, with citations and everything was overwhelming. I didn’t know how to do that. I had to spend that last month in the English lab. I wish I’d started there first!  Everything I had done was in this big pile of notes. I had to learn how to write, how to make coherent paragraphs that made sense to others. I must have rewritten my summary statement a million times before I wrote my first draft. It was hard work, but I wanted to submit it to the robotics journal. I didn’t want to be embarrassed.”

“I have always wanted to go into nursing. I got to plan each of my 9 week projects around a different area of nursing. At first, it was hard to stay on task. I didn’t have to do anything but show up. I would log in to the electronic attendance monitor and consult my task plan. That plan kept me on track with assignments. If I didn’t know how to do something, I would go to a lab and get help from the teachers. It’s really different; me asking them what I need to know, instead of them telling me what I was going to learn that day.”

“The projects seem really hard. There is so much to do, it’s overwhelming. That first project is really where you learn how to do everything. The first few weeks of high school, you learn about the academies and you are encouraged to pick your project. There are lessons on how to break down your project by tasks. I took a quiz to find out what I was interested in for my first project. Some kids come in knowing what they want to do. I wish I had gone to the summer workshop. I could have started my project so much sooner!”

“My mentor teacher was a big help. He ran one of the math labs, but he always had time for my questions. When I felt like quitting, or when I would hit a wall in my project, he would let me talk it out. He listened, really listened, to me. As a sophomore, I’ll be completing two projects, instead of four. I’ll need a team of students to meet the advanced requirements. I’ve made some new friends on this last project that are in my Academy. I think we’ll work well together.”

“The best part of my project, water resources for our community, was presenting what I had found out to the local water board. I had some suggestions for making our water supply healthier, with the project costs and a timeline for implementation. My next project will be on finding a new way to deliver water to neighborhoods. Seems to me there has got to be a more resourceful way than digging and burying pipes in the ground!”

“I graduate tomorrow. I’ve already got a starting job in a large engineering firm. I was able to intern with them as a result of a project I chose during my freshman year. That led to another project during my sophomore year. My junior year, I got a small grant to research affordable housing – after I learned about writing grant proposals in the English lab. One of my projects was on making presentations to community developers, which I used to apply for the job I’ll be going to after high school. They were impressed with the amount of experience I’d gained in researching and development of my projects, they liked my presentation skills, and they will help me pay for my engineering degree while I work for them!”

Learning Targets are the New Standards for Career, College Readiness

Teamwork, innovation, self-motivation, serious work ethic, honesty, integrity, and getting paid for something we love doing are some serious life/work goals. The Learning Targets replace standards by giving students real, usable skills for life. Critical thinking is absolutely necessary for making sound decisions. Being able to communicate through written, visual, or verbal methods is a must. These, and more Learning Targets, are imbedded in every project outline. Each year, the project should add appropriate learning targets, building on prior years. And who says a student must take four years? An Academy school has the ability to let a student move more quickly towards a goal, be it work or college. In addition to the projects, which can increase in complexity for those pursuing two, four, or six year collegiate or technical degrees, there are technical and apprenticeship projects and programs that would fit cleanly into this model, allowing our students to investigate different types of jobs through projects, and interact with the community during their research, giving them an authentic audience – the best way to incorporate honest evaluation, and spur our kids’ interests in their futures.

I work in an Academy school. I believe in this scenario, and I believe our students would be more than willing to embrace – and benefit – from this new way of looking at their education and preparation for life.

I see a couple of things (and will probably think of more!) that would need to be done:

1. Start with the 9th grade, move up with them. Don’t try to change all four grades at once. Set reasonable learning targets for them, understanding that this replaces the 9th grade standards. Build in what they need to know in each project. These won’t be lightweight! Each project must take each child through the four core fields of history, science, language arts, and math, incorporate electives such as art, physical activity, technical (computer) or programming…. but it’s OKAY if some projects are heavier in one area than another. They will be completing four projects across the year. I think this mindshift on the leadership will be the hardest!

2. Train the teachers. Take two-three weeks to train your teachers in the Learning Targets and what mastery of these Targets should look like. Teach them how to facilitate the labs, because they won’t be teaching specific, planned lessons! Teach them the framework tasks of the project- so that no matter what the child chooses to learn about, all tasks from the framework are applied. For example, a child wants to learn about yo-yos: there would be tasks to learn the history, find the financial impact of the toy, write their findings in an essay with citations, consider the making of the toy, the science behind the motion of the toy, the aesthetics, or traditional design and decoration of the various models,perhaps the value in an exercise program, and how it could benefit the user. This is a do-able 9 week project for a 9th grader.

3. Inform the parents. Teach them what is changing. Tell them what we are looking for in terms of benefits. Give them the long view. Give them the questions we want them to be asking through the process, so they can feel, and see, their child growing and learning through the process. Create parent buy-in at the start.

4. Tell the kids, in middle school, what is happening, what we want for their future, what will be required of them. Give them a chance to go to a summer workshop, where they can investigate what their interests are, a short survey, some simple practice on picking topics, a brief look at the project tasks framework, what the labs will look and feel like, how to approach teachers and ask for help.

There is more, but I think this is a big enough chunk to chew on for today. Your constructive thoughts are welcome!

# 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!

# Gwinnett County Public Schools is hiring…

They are looking for math, science, and special education teachers.

I work with absolutely excellent educators! We need teachers who teach students the subject matter, not the subject matter to students. There is a difference, and it matters.

Our county has been the recipient of the Broad Prize for excellence, not once, but twice. We excel. We are Gwinnett. It’s what we do.

Please put my name in the comments of your resume to let them know you heard it from me!

http://publish.gwinnett.k12.ga.us/gcps/home/public/employment

Good Hunting! Your next job is out there.

# 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.

# New Year’s will be in August, this year.

If you are a teacher, that is.

On August 8, hallways and rooms will fill with the wriggling eager bodies of their parents’ best! I can hardly wait! During the summer, I’ve been loading up on great ideas, reading about effective teachers, discovering new tech and new resources, and creating learning plans that will put them into practice!

I am teaching my students Algebra I this year; 9th graders, some returning 10th, and I want them to feel the excitement, the sizzle that I feel with math. This is a new year, a new crop of children, a new chance for me to share what I love- math – with children who never fail to delight me (and challenge me, worry me, turn my hair gray, and, well, you get the idea- but that’s another post!)

The year I have planned, this year, will be different. This will be the year that every student tests proficient on the EOC, aka Georgia Milestones. My lessons will start with Wonder/notice, there will be lots of student conversation, with roles for small group work, and conversation starter posters on the wall! My class will be fully engaged, will actually complete their assignments, will receive thoughtful feedback, and grades that really show how well they’ve mastered standards. I’ll make all the calls, on time, to the parents.

My IEPs will have clear goals, my re-evals will be works of art! I’ll handle my discipline issues with skill and compassion. This year, I’ll have strong closure routines, include literacy in every lesson, hold awesome number talks, and have nimble responses to my formative instruction.

This year, my room will be organized. I’ll have study centers, whiteboard walls, standing desks, and engaged, curious students! This year – well, this year will be everything I was hoping last year would be…
So, you see, teachers really do celebrate New Year’s in August!

# Reflections that push me towards next year.

As I rest and recharge myself this summer, I am like one of those little chipmunks- stuffing my cheeks with ideas, thoughts, and nubbins of lessons.

I start a list of those items that MUST go into my lessons next year: good starters, exit strategies, literacy activities… You, too?!?

At some point, I need to actually plan! And I will. But not today. Today I am going to read a book. Not a ‘teacher’ book! This one is purely for pleasure: a new mystery novel. But first, let me check out this new email from Edutopia…

# What do you mean, it “…can’t be solved?!?”

I came across an Algebra I review problem the other day on Classworks. The challenge was to solve a quadratic using the Quadratic Formula. One of the answer choices was “can’t be solved.” Which I did not notice.

I was working with three students who did not understand what to do. Once I wrote out the quadratic formula, (actually, all I had to write was the negative b plus or minus!) they began to remember. One boy immediately told the other two how to find a, b, and c. That required a discussion about standard form, so we had to do a little rearranging of the problem given on the screen. Once we got the formula equal to zero, the second student plugged the numbers into the correct places! The third began offering solutions to various parts. I thought we were doing pretty good! Until we came up with a negative under the radical.

Like the music in Jaws… Dum, de dum, dum… They looked at me, dumbstruck.

“What do we do, Ms. Maxcy?”

I asked them if they had learned about imaginary numbers. (Of course they hadn’t – yet. This was only Algebra I! But sometimes I forget which level I am teaching… Which is another story altogether!!!)

Still not checking the given answer choices, I blithely proceeded to give them a brief ‘reminder’ lesson on real and imaginary numbers. They continued to look at me blankly.

As I magically (to them) unraveled the answer as 2 plus/minus 2i sqrt 11 divided by 3, they stared at me. Then they stared at their answer choices. They looked back at me.

“It’s not there, Ms. Maxcy.”

At this point, admit it, we teachers think, “it’s got to be there, that’s the right answer; why is it not there? Gosh, did I do it wrong?” And then we doublecheck our answer. And then it hit me. This was Algebra I. We don’t teach imaginary numbers. Yet. It was then that I finally looked at the answer choices…

The correct answer was there, but it wasn’t the correct answer at all!

Right there in front of me, there was the answer that the students were supposed to choose: choice “D) Can’t be solved.”

Right there in front of me, there was the answer that the students were supposed to choose: choice “D) Can’t be solved.” This is a terrible choice! It’s not the right answer! It’s not a good answer! Okay, so we don’t teach them imaginary numbers in Algebra I, why don’t we just list the result with a negative under the radical as the answer?!?

The kids get used to seeing the beast (negative radical) and we teach them how to simplify in Algebra II or geometry, depending on your school system. But, please, NOT “can’t be solved”!

That is just setting them up for trouble ahead! Lay the foundations, don’t build a wall that will have to be torn down later. Please!

Rant finished. Thank you for listening.

# Murder Mystery Solved with Trig!

Dateline: April 14, 2016

The murder of Maria, whose body was conveniently found at right angles to Leg Streets A and B, has been solved! Investigators found the weapon across the river, apparently thrown there by her assailant while he was running down Leg Street A in an attempt to escape. A quick thinking officer (who had majored in math at the police academy) was able to calculate an angle measure for the angle made by the throw from the perp and the street leading to the victim.  Another savvy investigator was able to determine the distance from the suspect to the location of the attack.

With the mathematical evidence in hand, investigators were able to triangulate a conviction. Math teachers everywhere weighed in, saying it has the proportionate ability to change the way investigators do business!

Dimensions of the prisoner’s defense will be released at a later date. Film at eleven.

Okay, so I don’t really have film (we forgot to assign the job of reporter!) What I do have are a room full of kids who can now set up the proper proportions for trig problems!

Here’s how the crime went down:

Scene 1: Before the murder, I handed six students a few props:

Each student had to use the prop to arrange themselves into a triangle. The other students watching were, um, helping. (that’s what they called it!)

A short q&a followed:

Me: Okay leg A, are you opposite or adjacent to angle b?

Hapless Student holding Leg A sign: “I’m opposite, um, no, I’m right next to him (indicating student holding the angle b sign)! What does adjacent mean, again?”

We were able to sort out the definitions, and the students holding the leg signs got pretty good at determining whether they were “opposite” legs or “adjacent”  legs. A big moment came as students noticed that they could be opposite OR adjacent. More importantly, they were able to articulate WHY the status would change.

More importantly, they were able to articulate WHY the status would change.

Scene 2: The next six students were given the cards. This time, I stood back and let the first group help position the players. A little skirmish ensued as Leg A and Leg B were being positioned. After a brief discussion about whether or not leg locations could be interchangeable (did Leg A have to go in the same place as the first triangle?), it was decided that as long as a leg were placed on each side of the 90 degree angle, it didn’t matter what we called them.

The opposite and adjacent discussion began again. It was fun watching students correct these new players, or making them guess by giving them tantalizing clues!

(If you ever want to know what you look like teaching, give your students the reins. Mimicry is not dead!)

Scene 3: With everyone up to speed on definitions, the murder could now commence! Maria was positioned. Ryan was immediately suspect, as we put the crime scene tape in his hand and instructed him to escape a bit down the hall. The “weapon” was given another piece of crime scene tape and told to take off in the opposite direction. The “hypotenuse” was asked how far the “perp” had thrown the weapon. We stretched the crime scene tape from the suspect to the weapon location. It was at this moment that I heard several students say “Hey, we made a triangle.”

It was at this moment that I heard several students say “Hey, we made a triangle.”

(Scary, I know, right?)

After a bit more discussion, the students determined that we needed an angle and we needed the distance from the body to the suspect to set up a proportion to solve for the distance. Two students were dispatched with the piece of crime scene tape that had been held between the victim and the suspect (Leg A, for those of you following along). Twelve inch square floor tiles assisted in the crime scene measurement. I used my oversized protractor to come up with the angle measure, and we were ready to set up some proportions!

Back inside the room, our eager detectives checked their trig proportion info sheet (yes! They used their NOTES!) and settled on cosine, adjacent and hypotenuse. I stood back and watched them argue over who was going to set up the problem, exactly how to set it up, and how to enter the information into the calculator. Then I watched them convince one another which answer was correct.

Concrete to representational to modeling AND peer tutoring…I love it! I would say that a murder wasn’t the only thing that got solved today!