The 5 W’s and an H of grading Part 1- Who?

Having just completed my first semester of Standards Based Grading (SBG), I have been doing a great deal of reflecting about what worked and didn’t work and also just thinking about the whole process of grading in general.  I have come up with more questions than answers.  But that is how we learn, right?  So I am going to write down my questions and my reflections and invite feedback from my wonderful colleagues out there in the MBToS.  After a brain wave I got while lying in bed this morning (I love sleeping in!) I decided to frame my thoughts using the traditional Who, What, When, Where, Why, and How questions.

Who is most responsible for the grade that is earned, the student or the teacher? (You may be surprised. Or not.)

What criteria should be used to determine the student’s grade? (A big debate is always raging about this one.)

When should grades be given? (Another very interesting question.)

Where does grading take place?  (For me, preferably in my comfy chair at home with a cup of hot tea and maybe a familiar movie playing in the background to keep me awake. Smile. . . . Actually, there may be more to this question.  Stay tuned.)

Why do we give students grades?   (O0-00, this should be a good one.)

How do I implement what I consider to be best practices in grading?  (Ay, there’s the rub.)

This post (and hopefully I will have time to go through all of these) will concentrate on Who.  Who is responsible for the grade that is earned?

All teachers with any sense realize that both the student and the teacher contribute to the grade, but we like to think, especially as math teachers, that our grading system is a reasonably objective reflection of what students actually know–their mastery of the standards of our class.  Ideally, if a student is willing to put in the time and effort, he should be able to master the standards and earn a good grade.  I switched to SBG this year in part because my previous system of grading was flawed in this area and I wanted something better.  However, who sets the standards? The teacher (OK, the state and the district and the school, too, but certainly not the student).  Who is responsible for creating or procuring lessons, resources, and practice activities to help students master the standards?  The teacher.  Who decides how to measure the mastery of those standards? The teacher.  What I choose to measure and how and when I choose to measure it, along with how well I teach, has a huge effect on student grades.

And how objective am I in my assessments?  I have trouble being totally consistent from student to student on a single quiz, so how consistent am I from unit to unit or from year to year?  I know that I cover fewer topics and different topics than I did 10 years ago or even 5 years ago and I wonder if I am grading more strictly or more leniently from year to year.  Does an A in my class vary from year to year?  Do I sometimes give the benefit of the doubt to my good students but not to my poor students when deciding between two grades?  I will not answer those questions because I know the answer.  Guilty as charged.

We all know those extremists in the teaching profession:

  • The teachers who never give A’s and who delight in failing everybody, nobly clinging to their “high standards” while their colleagues “slide down the slippery slopes of academic mediocrity”.  Any failure on the student’s part is solely blamed on the student, of course.
  • The teachers who ensure the “success” of their students by giving generous test curves and copious amounts of extra credit, giving high grades for learning almost nothing.  (There are various reasons for this behavior:  Feeling sorry for the students, lack of time or effort to fix the real problem, compensating or covering up for inept teaching or grading practices, and/or bowing to administrative or parental pressure to bring up grades are the ones that occur to me.)

Although I am not either of these, I have sometimes leaned one way and sometimes the other in my grading mentality, even compensating for one by doing the other.  (Am I the only one?  I think not.)

The point I am trying to make in all of this rambling reflection is that not matter how hard we try to be objective, assigning grades is very subjective.  I wish–oh, do I wish–that I could just teach without giving grades.  (Am I the only one?  I think not.)

What brought on all of this agonizing self-reflection, you ask?  My final exam.  After a semester of SBG quizzes with multiple chances to retake, I gave a cumulative, mostly multiple-choice final exam with no retake, worth 20% of the semester grade.  My reasons for giving a one shot cumulative final:  College-bound juniors and seniors need to learn how to take these types of tests, students review and relearn material they would otherwise completely forget while studying for the final, part of mastery is retaining material and being able to recall more than a few isolated skills at a time.  I stand by these reasons for giving the test.  I even had several students finally figure out some concepts for the first time while reviewing for the final.  My reason for the 20%?  I wanted it to affect their grade.  An A student who couldn’t get at least a B- on the final was not an A student in my mind.  Yet 20% allowed a student to get even a low F without lowering their grade more than one letter grade, so it wouldn’t destroy all of their hard work over the semester.  I have always had a wide spread of grades on the final, from perfect scores all the way down to the 30% range.  But I didn’t expect the grades I got this year.  After a semester of SBG, with multiple retakes, I anticipated a higher level of mastery than previous years.  Instead, I got 6 A’s, 19 B’s, 3 C’s, 4 D’s, and 22 F’s.  I believe that my test and my grading of it was comparable to previous years.  I have always had more low grades on the final than on other tests, but the number of F’s and the huge gap between the A’s and B’s (about half my students) and the C’s , D’s, and F’s was more pronounced.  I know that some of the F’s were due lack of study and effort.  I also anticipated F’s from some students who had struggled all year long.  But it doesn’t seem that allowing multiple retakes on concepts all year really helped my lower students retain concepts any better than they did before SBG.  However, the almost total absence of C’s indicates that my average students did seem to benefit and achieve higher mastery then previously (I think).

I know that grading policies are only part of teaching, but how did my grading policies affect student learning?  I’m not sure.  I was definitely hoping for better results.  Everybody ended up passing the class (without any tweaking on my part) and I only had a few D’s, but 14 of my 54 students had lower grades (1/2 to 1 letter grade lower) as a result of failing the exam.  It seems a fair assessment of their mastery (retaining concepts), but perhaps is also an indictment of my teaching and grading methods.  I’d love to know what you think.


MTBoS Mission #5

Did my first Twitter Chat last Thursday.  It was a good experience, but not my favorite way to spend an hour and a half on a school night.  I felt like it took a lot of time to say very little, although I did glean a few useful ideas on which to follow up.  The best part was discovering some more like-minded Precalc teachers to follow on Twitter and possibly exchange ideas with later.  I’m not sure if I’ll do it again, but I am definitely finding Twitter to be a wealth of wonderful people and enough ideas and resources to make my head spin.  I think I tend to be more of a blog person.

MTBoS Mission #4

I listened to a podcast, the one “that started it all.”  I enjoyed listening to the discussion between Ashli Black and Daniel McMatherson, two teachers who are as passionate as I am about trying new things and who also struggle as I do with those new things they are trying!  Daniel switched to SBG cold turkey, just as I did, because he wanted to force himself to really think about what he was teaching and why, saying it has been hard but definitely worth it.  I switched to SBG because it offered more authentic grades, but soon found myself forced to plan much more carefully and deliberately than I ever have before,so I understood exactly what he was talking about.  Hearing him talk about how hard it has been for him makes me feel better about my implementation of SBG.    The two of them also talked at length about those days when they ended up apologizing to their students after teaching a lesson that no one really understood.  I’ve been there, too.  Listening to them validated my efforts this year to keep trying new things even if they don’t work the first time around.  And I loved Daniel’s “gift” at the end–wishing that all teachers could have another like-minded teacher with whom to “talk math teaching.”  I was beginning to despair of finding such a person outside of the occasional conference until I stumbled across MTBoS.  I’d love to listen to some more of the podcasts, but they are so long.  An hour is a lot of time for a busy teacher.

Fun with Daily Desmos

My Desmos solution

My Mission #3 assignment with MTBoS was to explore one, only ONE of several excellent websites and write a blog about my experiences.  Since I just commented in my previous entry that I didn’t know anything about Desmos (and everyone who is anyone on MTBoS seems to use it) I decided that now was the time to learn it.  So I did a couple of the basic challenges on Daily Desmos and I was pleased with my trigonometric transformational approach.  I wonder if anybody else tried that.  The online Desmos graphing calculator is user friendly and the Desmos Challenge problems (matching graphs) complements my Precalculus curriculum very nicely, so I hope to incorporate it in my classroom.  I will have to Twitter some questions first…

Of course, I had to check out some of the other interesting websites:

Estimation 180:  Teaching estimation skills with pictures (similar to the visual approach of Dan Meyer’s Three Act problems)  I like the idea of using my own pictures to do some interesting warm-up problems.

VisualPatterns:  I can use definitely use these in the classroom (functions, sequences) and with math club.  Saves me a lot of work!  Woo-hoo!

Math Mistakes:  What a novel idea–posting student mistakes and then reflecting on the conceptual misunderstandings and implications for teaching.  I read some very insightful posts.  Here was a great one:

Mistakes, Radicals, Rational Exponents, and Partitioning?

One Good Thing: A forum for teachers to post something GOOD that happened in their classroom.  Very uplifting 🙂

And …. I just figured out how to embed the links to all of these in my post!  Another Woo-Hoo!


I just tweeted a few people and read some tweets. Nobody has tweeted back yet, but I have already found some amazing blogs and downloaded some great resources that I found on Twitter feeds. I can tell that my biggest problem will be managing my time and knowing when to stop.  I hope that I can cultivate a few like-minded Twitter pals to share ideas with.  I guess that the best thing I have learned is that all of these wonderful teachers who know how to use Desmos (I don’t) and attach links to Twitter feeds that have “bitly” in them (I don’t know how to do that either) and who use these amazing activities that I want to learn how to use still struggle with the same classroom issues and feelings of inadequacy that I have.  And they share the same joy when they try something new and it actually works!!  

An Experienced Amateur starts to blog

I am a 16 year veteran of teaching high school math.  I teach in a private Christian high school with supportive families, generally good kids who care about school, and high expectations for academic rigor. Like many teachers, I started out teaching pre-algebra and first year algebra, was “promoted” to second year algebra, and am now teaching Precalculus and AP Statistics.  (Somewhere along the line, I skipped geometry entirely, and I have found that to be a detriment to my math background at times.)  I have started this blog because I want to be part of the MathTwitterBlogoSphere (MTBoS) with all of its resources and teacherly camaraderie.

I consider myself “an experienced amateur” because I am an experienced teacher with strong content knowledge and classroom management skills and, I think, excellent rapport with my students.  I have developed much of my own curriculum over the years and my students are challenged and learn a lot in my class, but, BUT, I am always looking for better ways to motivate my students and communicate the beauty of mathematics.  I recognize that I am holding myself to an unattainable standard of perfection, but I can’t seem to help it.  I want to be an amazing math teacher, not just a good one, and I am not there yet.

Maybe this blog will help.  Help me to improve.  Help me to realize that I am not the only crazy perfectionist out there.  Help to realize that it is OK to strive and fall short of perfection and remain joyful and optimistic while doing so.