Variable Credit and Standards Based Grading

I’ve been soaking up a lot of information about standards-based grading (SBG), and today came across this in my twitter feed:

I am already very focused on encouraging growth mindsets, so the idea of assessing it was very much something I wanted to know more about. With some follow-up tweets, I got a link to the presentation, which included a SBG rubric template that I’m excited to look at more closely.

The school where I teach, Mid-Peninsula High School, has a lot of things that make it different from other schools where I’ve taught, observed, or attended. One thing stands out that may be unique to Mid-Pen, though. We have a variable credit system, rather than a standard all or nothing system. The VCS (because we need another acronym in education lingo) was the most confusing system that I encountered, although in retrospect it is because it was such a foreign concept.  Each semester class is typically worth 5.0 credits, but students receive 0.5 increment credits throughout the semester based on the amount of satisfactory work that they turn in. This allows for differentiation between two students that may look the same on paper in a traditional system.

Suppose you have two students, Alicia and Benjamin. Alicia finds Geometry class very easy, and halfway through the semester has an A in the class without too much effort on her part. She then decides to blow off the rest of the semester because she has x, y, and z priorities that are more important to her. She doesn’t turn in homework, doesn’t study, fails most of her quizzes and tests, and bombs the final. When all the grades are averaged out, in a traditional grading and credit system, she has a C and 5.0 credits.

Benjamin has always had a tough time in his math classes, but works persistently and diligently, and always completes his work on time, even if he usually gets mediocre grades. Throughout the semester, he maintains a consistent C average in the class, and at the end of the semester, in a traditional grading and credit system, he also has a C and 5.0 credits.

On their transcripts, these two students look identical, but there are very different stories behind those grades. In our VCS, Alicia may end the semester with an A, but only 2.5 credits. Benjamin would still have a C and 5.0 credits. This means that there are two meaningful measurements on the transcript. The credits reflect the amount of work that has been satisfactorily completed, and the grades reflect the quality of that work.

So, what does this have to do with standards-based grading (SBG)? For several years before I arrived at Mid-Pen, I was interested in implementing some sort of SBG but wasn’t sure how to do it. Halfway through my first semester teaching at Mid-Pen, I realized that basically what I was doing was SBG. I determined, in 0.5 credit increments, what amount and type of work qualified for those credits. Inevitably, each unit was either 0.5 credits or 1.0 credit, but it was mostly based on what had been covered by the end of each grading period. We have grading periods after 1.5, 2.5, 4.0, and 5.0 credits. Students are able to make up missing credit at the discretion of each teacher, but generally it’s encouraged, and even expected, for students to make up missing credit during the semester. Otherwise, it gets pushed to an independent study or summer school, both of which can be a huge pain for both students and teachers.

During that first semester, I took a few weeks off for paternity leave, so I was a bit preoccupied and didn’t put in the necessary time to formalize each half credit. I’ve had three more semesters at this point, but no other excuses, so my big summer project (besides deciding on an Algebra 1 text) is formalizing SBG for our VCS. More on my progress (and credit given to whomever I steal from) later in the summer.



Brainstorming a Penalty Kick 3 Act Task

I came across the following video in my twitter feed, and think it would make a great 3 act task for my Trig/Precalculus class, and maybe could work something out with my geometry class as well, although probably without the algebraic equations. Maybe something we could hash out nicely in Geogebra.

The biggest question is how much information to give. My initial answer is usually none, but especially at the beginning of the year, as students are just getting used to my style of making them work for the information they need, is it necessary to give them a bit more to go on? I think a lot will depend on the students that I have in the classes, their cultural and mathematical backgrounds.

I’m thinking about finding a couple students from the soccer team at the beginning of the year to practice penalty kicks while I record it. Not sure exactly where this really fits, though conic sections seems to be a good bet. I tend to do conics later in the year, and have generally had students in four groups lead the lessons on each of the conics. It’s a nice setup for the unit that I’ve found really successful, but sometimes it’s worth trying something new, just because. Plus, I’ve had a number of my students on the soccer team, so maybe this is just a good way to help them score some more points, win some more games, and answer for themselves, “When am I going to use this?”2015 Mid Pen Coed Soccer 0017.jpg

It would also pair nicely with Henri Picciotto’s Soccer Angles problem that I was already planning to add to my toolbox for next year, so putting together a combination of tasks related to soccer, even across different classes (Trig/Precalculus and Geometry), would be a lot of fun. Plus, hopefully it will help us maybe win the league championship that we’ve been close to the past couple of years. Go Dragons!



I Can’t, Shouldn’t Be the First to Believe

There is a comment I’ve gotten frequently from students, and it’s an absolute compliment, but one that tears me apart.

“You’re the first teacher who believed I could do math.”

In one way or another, that’s one of the most common responses I get in my end of year report card from students each year, or in cards or emails from students. I am thrilled on one hand that they felt I believed in them, because that is one of my biggest goals. I absolutely believe that everyone can learn math, that everyone can always learn new and more challenging math. I’ve held this belief for just about all of my teaching career, and it’s driven so much of my approach to my classes. So, I’m glad that that got through to students.

And yet…

Am I really the first teacher that believed in these students? Some of these students were in 9th grade, some were in 12th grade, some in between, but am I to really believe that each of them had teachers all the way through elementary/middle school that gave up on them? In fact, I know for a fact that many of the students did have other teachers that saw their potential and did believe in them, but somehow they did not get that message. Why is that?

Sometimes, the words of a single teacher can have such an impact that they color the words of every teacher that comes after. A 3rd grade teacher who tells a student that maybe she’ll never be any good at math because she can’t memorize her times tables. A 5th grade teacher who tells a student who struggles with fractions that at least he is good at other things like reading and art. An 8th grade teacher who tells a student that maybe Algebra just may be too hard for her, but at least she’s cute and can get help from boys on her homework. These are all stories I’ve heard from students, and their impact can be life changing. The words of a teacher, at the right time and in the right context, can dramatically change the perception that a student has about his or her abilities – for better or for worse.

It is easy to throw elementary school teachers (and to a lesser degree middle school teachers) under the bus. After all, they’re the ones who did all this damage, right? And they aren’t even really math teachers. Most of them don’t like math, and have a phobia about it, and shouldn’t be teaching. It is so tempting to complain about their inadequacies, which is what I often did early in my career. I even had anecdotal evidence – when I’d attend a math education conference, high school teachers were there because they wanted to go, and elementary school teachers were there because their administrators made them go. It was such a tempting mindset, until I realized that I was doing nothing to improve things, just complaining and making a case for why my job was so hard and why I couldn’t succeed with every student. This isn’t uncommon. As Kaneka Turner pointed out during ShadowCon16 at NCTM this year, how many of us as high school teachers at math education conferences ignore the elementary school teachers sitting nearby?

We are part of the problem! We need to be inviting elementary school and middle school teachers to our world. We need to be reaching out to all of them, and asking them to join us in showing all students that every single one of them is a mathematician.

On a related note, one of my Trig/PreCalculus students said a few weeks ago that she and her classmates weren’t mathematicians, that I was the only mathematician in the room. It was in the context of a debate, and I think she felt my glare and knew what she had said, but I didn’t address it until earlier this week.

“In English class, when you write, what are you?”

“A writer.”

“In art class, when you make art, what are you?”

“An artist.”

“In music class, when you make music, what are you?”

“A musician.”

“Then in math class, when you do math, what are you?”

“Math students.”

And then it sank in for them, and for me. There’s more that I need to be doing, because despite all the success I think I have sometimes, at the end of the day, my most advanced math students don’t see themselves as mathematicians. I need to send them better invitations.


Always Becoming a Better Teacher

I just read a nice post this morning, Zack Cresswell’s How 10 minutes on Twitter reminds you that you’re awful and not trying hard enough. It really spoke to me a lot about how easy it can be for those of us who care about our work as teachers to feel like we never really measure up. And it’s absolutely true. After fifteen years, I’ve had a lot of success with students, and that is usually the public face that goes out on social media, but it’s my failures with students that keep me up at night. The student who doesn’t do their work, who doesn’t study, who isn’t excited by my class, often makes me wonder what I’m doing wrong. The student who does their work, asks lots of good questions, really pushes to do their best, but still doesn’t get it on a test – that student ALWAYS makes me question my methods.

At the end of each day, though, I try to reflect back on what worked, and what didn’t, and more importantly, ask myself if I did more good or more harm that day. What does success mean, and is it an endpoint or a starting point? For the student who comes to my classroom at the beginning of the year saying that they hate math and have never been any good at it – am I making efforts each day to show them something exciting and wondrous and awe-inspiring? Am I assuming that they can learn something new? Am I meeting them where they are at, and trying to find a way for them to feel successful at something in my class? If none of those efforts worked, do I try again the next day, with a combination of the same approaches and different approaches? At the end of the year, does that student feel better or worse about the world of math, and does that student feel better or worse about their place in that world? For some students, success may not be an A, or even a B. For some students, success may be passing a class that they thought was going to be impossible, and feeling like they have a place at the mathematician’s banquet, that there’s something there for them to eat.

Then, what is failure? Have I made a student feel worse about their ability to do math? Have I kicked them out of the banquet hall, and uninvited them? Hopefully that hasn’t happened, but I’m sure if I were to go back and interview the hundreds of students I’ve had over the years, some of them may well have gotten that impression.

It’s important to remember that in a society where people proudly proclaim that they aren’t math people, where parents post angry rants about Common Core assignments (that have nothing to do with Common Core standards, but that’s another issue), where students regularly question why they have to take math in a way that doesn’t seem to come up in other subject areas, where pop culture is constantly talking about how math is hard and nobody likes it, that we as math teachers are facing an uphill battle. I still get upset when someone that I normally like and respect (John Oliver), makes such a terribly math-phobic comment:


For some students, success may be holding our ground and not making things worse. For some students, maybe there are so many other things going on in their lives that are beyond our control that all we can do is push forward in the smallest increments, in the hopes that when they are ready, either we or the next teacher they get will be ready to help move them forward.

I realize I’ve stealing some metaphors directly from some inspiring people that I’ve recently been introduced to, and want to acknowledge before I forget their contributions to my thinking- Kaneka Turner, whose NCTM 2016 ShadowCon presentation on inviting students to the math table clearly impacted me, and John Stevens and Matt Vaudrey, whose book Classroom Chef has whet my appetite for some exciting updates to my lessons for next year.

Success With Minimalist Homework

Over my career, I’ve been trimming homework more and more – at least required homework. I allow unlimited redoing of homework assignments, my grading has focused on completion far more than perfection. I’m looking at making even more changes for next year – assigning even less, not grading it, and further emphasizing process over final answers. But I’d like to share a story of a student who found success through some dedicated work outside of class.

Ben came to my Trigonometry/Pre-Calculus class this year as a senior who has never felt like he was any good at math. He’d made his way through, but never completed his work on time, didn’t show his work, and when it came to math tests and quizzes, always seemed to fall apart. Even if he felt like he understood something in class, nothing made sense when the test came, so he figured he really didn’t understand things in the first place, and just wasn’t a math person.

Much of this year wasn’t too different. Ben’s assignments were frequently late, and he sometimes missed class for various reasons (often on test and quiz days, which may have been a coincidence). On those days when he did take a test or quiz, he did not perform well at all. I’ve had students like these over the years, and refuse to believe that they aren’t “math people”, although maybe they haven’t been “math class people”. But just because a student hasn’t been any good at math class doesn’t mean they aren’t good at math. It’s not to say that I’ve seen every student of mine turn into a complete success in my math classes, but there may be a variety of reasons for that – maybe I (despite my best efforts) just didn’t find a way to click with a student, maybe the student wasn’t ready to put in the necessary effort and I wasn’t able to help motivate them to do that, and maybe there has been a decade of math phobia and anxiety that is difficult to undo in just a year or two.

Quite frankly, I thought that perhaps that would be the case again with Ben, but for a variety of reasons (support from home, from his other teachers here, and some strategies that I suggested), little by little, he started to turn things around. It seemed to start with him showing his work, absolutely beautiful, creative, and organized work for his homework assignments. This helped him to follow his own thinking better, and helped me to give him better feedback, which he started to read and work to absorb. He redid assignments to correct his mistakes, and was able to describe them to me. But he still wasn’t really retaining what he was doing between the assignment and a test or quiz.

Recently, we went over his study strategies, which were somewhat typical among traditionally “good” students – read notes, practice lots of problems, and get math fatigue before each test, a total overload of information that he was having trouble organizing in his head. I suggested a new strategy. Instead of doing a whole bunch of problems, do 1-3 problems every night, but do them slowly and thoroughly. Get to know each problem, every detail of the problem, different approaches to that problem, things that seem to work and things that seem to lead to dead ends or circles. At the end of a week, he would have gotten to know about 10-20 problems very well, and started to see similarities and differences.

The end of the semester came, and Ben had one previous test he had to make up because he hadn’t passed it the first time, one previous test he just had not taken, and the final test of the semester. Over the course of less than a week, he took all three tests, and not only did he pass them all, he scored 87%, 91%, and 92%. What an amazing achievement, and one that really confirmed for me the benefits of reducing the number of problems, but focusing on each one, going deeply into the math more than going as wide as possible.

More than anything, I’m really proud of Ben, who I hope will realize that he has every ability to be successful in further math classes. He’s off to college next year, and even though I wish I had another year to work with him and help him continue to develop these great study habits, as well as his confidence, I have faith in his future. Ben may not always be a great math student (though he’s developed a lot of skills that should help), but he’s definitely a math person.