The 5 W’s and an H of grading — Part 2 What, When, and Where

What are the criteria we use to grade students?

  1. Mastery of content
  2. Good study habits and organizational skills
  3. Classroom behavior unrelated to academics

Starting with #3:  I used to have a behavior/extra credit/participation grade in which students were awarded 10 point per 9 weeks. They all started out with 10/10 points and then would lose points for being tardy or for excessive talking (off topic). With SBG, I dropped that grade because I wanted grades to reflect only mastery of content.  Unfortunately, now I have no incentive for discouraging tardies, because we are all expected to deal with tardies within our own classrooms.  So I understand why teachers include behavior as part of their classroom grade.  It is hard not to.

#2:  I think that when we teachers intend to measure mastery of content we are really grading how well students know how to “play the school game”.  Well-organized students with planners and neat notebooks full of resources, who turn their homework in on time and are prepared for tests, of course tend to get better grades.  Teachers often assume that those students also work harder and care more about their academic success than the students who lose their homework, don’t follow directions, and forget that the test is today.  But that is not necessarily true.  Disorganized students usually care very much and are very frustrated by their own disorganization.  Such students might work hard on an assignment and then not remember where they put it or study hard for a test, but study the wrong things.  Or maybe they want to study but lose their notes or leave their textbook at school.  Giving second chances and multiple ways to demonstrate knowledge and skills helps these students to truly demonstrate what they know. I agree that life skills such as responsibility, organizational skills, and punctuality are important, but if we claim to be grading mastery of content, then our grading system should not punish a kid just for being more disorganized or less mature than another student.

#3:  Accurately measuring mastery of content is an art, one that I have yet to master.  It is fairly easy to measure skills and even conceptual understanding, but I need to work on how to measure creative thinking and problem solving.

When should we grade?

 If we want to grade mastery of content, then when we grade is very important.  We should grade in the formative sense as often as possible, with immediate feedback, so students do not reinforce bad habits.  I need to do more of this.  Students who want to learn always are eager to know if their answers are correct.  Hopefully I can help all of my students to develop that eagerness.

We should grade in the summative sense when students clearly understand what the standards are and how we expect them to be able to demonstrate their knowledge, and after they have had adequate time to practice.   This is a nice ideal but hard to achieve with limited time and a diverse group of students who learn at different rates.  Once again, it is important to give specific feedback and to allow students a chance to improve and retest.

Also, we should grade and return all work and assessments as soon as possible.  Feedback is most helpful when the work is fresh in the students’ minds.

Where should we grade?

 I mentioned in my previous post that I like to grade in my comfy chair at home with a hot cup of tea.  Also, if you are like me, you have graded papers almost everywhere and probably have a red pen in your car or purse.  However, I did have a more insightful thought.  Grading in class in front of students can be really helpful.  This could be done with sample student work, with anonymous answers collected from the class, or one-on-one with students.  Being able to discuss what work is good, what needs to be improved, what I am looking for when I grade, what common mistakes are, etc., is really helpful to students.  Grading can also could be done with video or by email to give students more personalized feedback.


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.

Feeling very “amateur, but experienced” today

I had one of those days which probably went OK for the kids but didn’t seem to flow at all well for me.  Here is what happened.  Yesterday the students took a learning target quiz.  Since students would be finishing at different times, but there was still a lot of time left in the period, I gave them the assignment to connect to the internet and watch a video after the quiz that went over some introductory notes about logarithms and converting between exponential and log form, a topic they had previously covered in Algebra 2.  That went smoothly, amazingly enough.  Internet access worked and everybody watched the video and got the notes done.  Today I used my Navigator system to check for understanding.  The problem was that we had to update calculator operating systems, remember how to all log in, etc. etc, which was a necessary evil, but it ate up some class time.  Meanwhile my SBG trained kids just started working on the two worksheets they had picked up, before and during the Navigator review, so some students were far ahead of others, but that, I guess, was OK, too.  The formative assessment (FA) showed about 75% mastery of concepts, which was not bad for the first day of reviewing something from Alg 2, so that was OK.  I did a bit of reteaching as we went through the FA, spent a few minutes introducing a couple of log properties, and then did the first problem with them on another worksheet about exponential growth, leaving them to finish up both worksheets and check keys online.  As I look back on it, nothing was really negative, but I felt like I was jumping all over the place with not coherent plan to my lesson and the kids were all doing their own thing, some paying attention, some just working on their own, so I wasn’t sure if students were getting the point of what I was saying, especially my weaker students.  And coming from 16 years of structured lecture, followed by practice, the whole thing just seemed sort of loosey goosey to me and I felt like I had blown it–very amateurish when it comes to the whole SBG flipped classroom experience.

Guess what?  After writing this, one of my weakest students popped into my room to ask a question.  I asked her how class had gone for her today–was it too chaotic, hard to follow, etc.  She said very nonchalantly, “It was fine. I understood everything.”  She had already done most of the worksheet and just needed to clear up a few details she had questions on.  Eureka!  I am not a failure.

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.

Sad, but glad

Two day ago, I used the cricket chirp/temperature relationship and had students come up with a linear equation to describe the relationship as an introductory activity to mathematical modeling.  The sad thing:  Some students still had to be reminded how to find a linear equation from two points–in Precalculus!   Students were thrown by the context of the problem.  Too often, they only see:  “Here are two points (3,5) and (-2,8).  Write an equation of the line containing those points.”  But two points in real life context just messes up their neat math world and they don’t know what to do.  In fact, one student told me that he never before realized that you could actually use  the equation of a line to figure out something in real life.  How sad that he is first encountering this in Precalculus!  But how glad I am that I get to help open their eyes to a little bit of what math is all about!

SBG Trials and Triumphs

Continuing my Precalculus journey…

So I decided to try Standards Based grading this year.  I forgot to mention that we are also  moving to Bring Your Own Device next year and maybe going paperless? (The contract on our copiers runs out after this year and our principal has asked us to move to a paperless environment–another issue that the math department needs to deal with and probably the subject of another post.) I am the department head, so I think it is important for me to be the first one to try new things so I can help others in the department with the nuts and bolts of the transition.  So I have invested a lot of time in exploring online resources, checking out apps and various devices, and making videos of lectures and posting all of my notes and handouts and lots of extra resources on my website, in addition to changing to Standards Based Grading.  So how is it all going?  Amazingly well, considering the enormity of the undertaking.

I will start by explaining what SBG looks like in my classroom, since SBG is a broad concept whose details look different from school or school or from teacher to teacher.

1.  I don’t grade homework at all.  Students can do as much or as little as they need to do to learn a concept.  Complete answer keys for all assignments, with work shown, are posted online, along with all worksheets, notes, and other online resources.  (I use Google Drive, a Google site, and YouTube)  Here is the link to my most recent unit on my website.  After trying various ways to organize my resources, I like this one the best so far.  You are welcome to use my stuff, but my videos are not high quality–strictly amateurish.

2.  Videos explaining all concepts (mostly made by me) are posted online.  Some are repeats of lectures given in class. Some are assigned to view outside of class (partial flipped classroom).

3.  Students are given a list of learning targets (standards to master) for each unit.  Here is an example.

4.  Students are quizzed twice in class on each learning target (LT). There might be several LTs on each quiz, but each LT is scored separately as a 10, 9, 8, 7, or 5, (I also use 7.5, 8.5, or 9.5), which correspond to A, B, C, D, and F in our grading scale. (The reason that I give a 5 instead of a 0 is because I realize that this is a grade in progress and I don’t want students to lose their eligibility to play sports, for example, until they have had a second try.) The score for each LT on the second quiz replaces the first.  However, if the second grade is lower, I will only lower the first grade by one point. (I may change this to averaging the two scores. A student who gets an A and then an F on a standard doesn’t deserve a B, in my mind.  I want them to retain the information.) Two 5’s in a row becomes a 0 in the gradebook, because if a student doesn’t show any improvement at all, then their grade needs to take a hit at that point, to force the student to do something about it.
Students can then retest on any individual LT outside of class.  After the third try (2 times in class and one outside of class), the maximum score a student can get is a 9.

5.  Class time is spent in a mixture of whole group instruction, collaborative work, individual practice, and quizzing.  I don’t spend time in class going over quizzes or assignments, except to comment on certain questions missed by nearly everyone or to work with individuals or small groups on questions.


1.  Students are actually doing assignments to learn instead of just to get a grade.  It took a few bad quizzes for some of them to realize that they still needed to do the work, even though it isn’t graded, but they soon realized that the effort they put in actually resulted in learning.  Some students who can master the concepts without doing much practice are not doing unnecessary (for them) busy work.  Students are even requesting additional problems so they can practice more.

2.  Students are becoming self-directed learners.  Because I do not grade homework, I can post answer keys and even videos explaining how to do some of the more difficult problems and encourage kids to use those resources to help them when they are stuck on something at home.  I have some students who watch videos multiple times and who reprint worksheets to do again for extra practice.  I have also recruited peer tutors and have paired them up with some of the students who struggle and now they are helping each other.   They are figuring out how to teach themselves and what works best for them and it is awesome to see.

3.  A clearly defined list of LTs helps the students to know exactly what they need to know and what they have mastered already and which areas they need to work on.  When students get back a quiz, the individual scores on each LT allow them to self-diagnose their strengths and weaknesses.  Clearly defined LTs also help me to identify the core concepts that require mastery and focus my teaching in those areas.

4. Grading is vastly streamlined and more informative.  I don’t waste time checking homework that may or may not reflect the student’s own effort and knowledge.  I can give harder problems and grade more strictly on assessments, not padding the grade with partial credit, because students can try again, if necessary.  I also have time to give more detailed feedback on assessments because that is the only grading I am doing.  Here is how I show scoring on a quiz.  Often multiple problems will contribute to a score and I grade holistically.


5.  Test anxiety is no longer an issue.  Prior to SBG, when students did badly on a test, a significant proportion of them would say that “I knew how to do the problem, but I always freeze up and go blank on tests.”  Sometimes that was true and more often it was lack of understanding or failure to prepare adequately.  But that is what they said.  Amazingly enough, no one says that to me anymore.  If students do badly now, they say things like, “I didn’t have time to study that” or “I wasn’t prepared” or “I need to get some help with that” and then say that they will be ready on the second quiz, and they usually are.  Test anxiety is not even mentioned.  Knowing they can improve their score seems to have taken off the pressure.

6.  A higher proportion of students are mastering the concepts, including my weaker students.  That is the bottom line.


1.  Coming up with the list of learning targets is difficult and time-consuming.  If they are too broad, students don’t know how to prepare.  If they are too detailed, grading is tedious and you lose the big picture and the inter-connection of the concepts.  It is hard to strike the right balance, but it does seem to be getting better as I gain experience.  It is always a hard call to determine what is essential and what is not as essential for students to know.  I’m sure I will do some revising next year.

2.  I am spending a large percentage of my time in class quizzing.  Some of that has gotten better as I have streamlined my learning targets, but it is still taking a big share of classroom time, to the extent that I am not going to be able to cover as much as I did last year.  Maybe that will get better with practice, as well.  I was flying by the seat of my pants at the beginning of the year and we have had some internet issues at school, both of which have contributed to wasted time in class, as well, so maybe that was part of the problem.  Having each LT on two different quizzes in class is more time-consuming, but gives me much better information on what students really know and retain, so I am not ready to give that up at this point.  Maybe my learning targets are still too numerous and need to be even broader.

3.  My best students need more to challenge them.  I started adding in bonus opportunities for those students who master all of the LTs quickly on the first try and don’t need as much practice to master concepts.  They still have to take both quizzes, to demonstrate mastery and retention, but they usually finish so quickly that they have time to do a bonus topic or a challenge problem.  There is a cap to extra credit, but just having the opportunity to meet a challenge is an incentive for many students.  I also have been giving some extra credit assignments (no key posted) for students who are not necessarily fast on the quizzes but are willing to do extra work outside of class.

4.  How do I incorporate open-ended problems?  I want to do some projects or open-ended collaborative work but how do I assess those types of activities using SBG?  I’d love some feedback on that.

I’d love some comments from other SBG users.