Standards-Based Grading: Math (1 of 7)

This is the first in a series on the implementation of standards-based grading in specific disciplines. A lot has already been written on this subject that I hope to expand on.  A bit of motivation before moving on: Ask yourself, “Does my gradebook mean anything to anyone other than myself? How can I use assessment tools to better communicate with  students about their progress?” Finally, can we use assessment to empower students to control their own formative behavior in the classroom?

Alright Math, you’re up first. I teach predominantly math, and use standards-based grading in all of my courses. My math classes used to be fairly conventional. A lot of me talking, students asking questions while I was talking, and then students practicing from a book. Then we had little benchmark quizzes. Once in a while we’d have big ol’ tests that would cover many chapters of material. The problem was that students weren’t breaking ideas up into their logical pieces. They’d see a grade in the gradebook like: “Quiz 5 – 23/30,” and think to themselves, “Oh man, I better step it up on the next quiz.”

Aye, there’s the rub. The NEXT quiz? What about the material you don’t know from this quiz? What about that? Huh?! To a student, a conventional quiz is just an opportunity to gain some more points. They don’t see it as a chance to demonstrate a specific skill set. Until now!

Standards-Based Grading!

Here’s the list of things I changed. I will explain the reasoning and logistics of the changes, and then I’ll run you through my typical experiences as students interact with the new system.

  1. Fracture Your Gradebook: I had to break my gradebook into much smaller pieces. Now there are entries for every single learning target (standard, concept, whatever), and they are all worth the same amount of points (10). The entries in your gradebook must now be super clear as to what they represent. These are formative and can be changed during the semester. There are also summative (traditional) entries, including tests, or anything else I want turned in on time (responsibility credit, more on this later).Here’s a screen shot of a part of my gradebook:
    Grade Booke Screenshot

    I have yet to give a summative assessment (test), mostly because we’re only a few weeks into the quarter. All of the grades represent specific items on a quiz (Q means Quiz and I means Item). The standards are clearly written for students and parents to understand in the description of each grade.

  2. Allow for the formative: I now have to give more opportunities for kids to demonstrate skills (yay!). This has really opened my classroom. I give quizzes about every 8 days that usually cover 1-5 standards. By listing quiz items separately we do not destroy any information by adding scores and reporting a block score for one quiz. Kids see a string of scores out of 10 (sometimes more or less depending on the importance of the standard), instead of one score out of a total. There are many other ways to assess a standard: class work, group work, talking with students, anything that you feel genuinely expresses their understanding counts. It is your discretion as to what counts as an assessment and what doesn’t.
  3. Allow for re-demonstration: Now comes the tricky part. This is the piece that will test whether you buy into this system or not. You now have to allow kids to show you that they’ve made progress. In my classes I allows students to come in no more than once per day to attempt one standard in any way I see fit. Sometimes I grill them interrogation style. Sometimes I just write a problem on the board. Sometimes I ask them to create a situation where the standard would apply in the real world and make them solve the issue. Many times I just put a question similar to one from a previous assessment on a more current quiz; that way I keep getting data about their understanding as we move away from a topic. All of these demonstrations are taken as a measurement of the student’s understanding, and the grades fluctuate in the gradebook, not new grades mind you. We no longer care what cryptically numbered quiz this is, we only care about what content each question is assessing.
  4. Less frequent Summative Assessments (Tests): I now am free to create true ‘Midterms’ and ‘Finals.’ These tests are now more trustworthy, because students have been informed all semester about the true status of their progress. These tests now represent a chance for a student to do many things that do not have to do with specific content standards: They can practice the skill of studying as needed for college, they can practice self-assessment, and they can develop a healthy confidence for an exam that they know can’t be reattempted. Those of you who are traditionalists will love this. Kids see the midterm and final as a kind of monster to prepare for, and they happily do it, explicitly checking off understandings as they move towards the battle.


What does this actually look like? Let me give you a narrative of a day in my life as a Calculus teacher:

  1. Today, I showed up before school and kids followed me up to my room. After some greetings and mild cajoling, students began to ask if they could “make up a problem.” Which is how they see it: getting points back for screwing up. Not the way I would hope they think about it, but students rarely fit your theory.
  2. I then decide how I will accept each student’s re-attempt. Some I give another problem to on the board, some I just talk to, and some I make write their own problem (depends on the kid).
  3. The first-block bell rings, and I’m left to grade a bunch of re-attempts. I alter scores in the gradebook based on new performances, and the day begins.
  4. I teach a few classes, presenting ground-breaking and highly-engaging lessons that are both rigorous and relevant. Hopefully.
  5. Students come in over the lunch hour to re-attempt questions. (See 2)
  6. I teach a few more classes.
  7. Students come in after school (See 2)

It’s all in how you do step 2. Are you hard-nosed? Do you coax? Do you prod? Are you aloof? Do I change my behavior based on the particular student? Yes, yes, yes, maybe, and uh-huh. The best part is when a kid says something like this:

Cherub: “Mr. Cornally, I was looking at my grades, and I see that I don’t really understand how to draw the graph of a function’s derivative, I have a 5/10.”

Cornally: “Did you review the concept with your notes, the book, and or try some by yourself?”

Cherub: “Yes, I tried a few from the book, and I think I get it now. Can I show you?”

Cornally: “Sure.” The student draws a function (simple parabola) and then draw its derivative fairly accurately.

Cherub: “Is this correct?”

Cornally: “Yes, but I need you to show me with a function that may not have already been in your head.” Cornally draws complicated function. Student draws derivative fairly well. “Ok, you didn’t quite get this part . . . but you’ve definitely shown improvement on some of the basic ideas behind this standard, I will change your score to a 7.5/10, a ‘C.'”

Cherub: “OK, thanks. I’ll be in tomorrow morning to try again.”

This. Actually. Happened.

  1. Standards-Based Grading: Math (1 of 7)
  2. Standards-Based Grading: LA – English (2 of 7)
  3. Standards-Based Grading: Science – Qualitative (3 of 7)