On Twitter last week, Kristen asked, “What are your grading categories and what percent of the students’ final grade comes from each?” Kristen is a 7^{th} grade math teacher and was looking for suggestions because she wants to change her approach.

When I was in the classroom full time, I used a grading system that I had revised and honed over several years, that worked for me and my students. Before I describe its details and justifications, let me first say that each school and classroom has its own considerations, so every teacher should do what works for your situation. Also, I mostly taught high school math, so some of this would be different for middle school and 9^{th} grade.¹

**POINTS NOT PERCENTAGES:**

In my math classes, every test, quiz, lab activity, or hand-in assignment was worth a certain amount of points. Quizzes were usually 10–40 points, Tests 50–100, Labs/Hand-ins were 20–50. To find a student’s average, __add up all the points and divide__.

Students need to __show the mathematical thinking__ (“show your work”) in order to get full credit. If they show good work, but have the wrong answer, they might earn 4 out of 5 points. If they have the right answer but without supporting work, they only earned 1–2 points. Any mistake that is carried through to later parts of a problem without making new errors does not get new deductions (akin to the AP exam free response question grading).

Each question on a test or quiz is worth whatever the mathematics warrants, from 1 to 10 points. Thus every similar question throughout the marking period has similar weighting, it doesn’t matter if it is on a “test” or a “quiz”. This is one reason I changed from “Tests 50%, Quizzes 30%” type system; in that setup, the same question on a test can be worth much more than on a quiz. Also, I sometimes only had two tests in a marking period, which didn’t seem worthy of half of the student’s grade.

Lab activities and hand-in assignments meant that a student’s grade did not just depend on timed “higher-stakes” assessments. Students with test anxiety could demonstrate their knowledge in another way, with less stress and time pressure. I usually had one of these every week or two throughout the marking period.

**HOMEWORK:**

I checked homework daily, for completeness (not accuracy). During the few minutes I took to get around the room, students were discussing the homework with partners or small groups, checking answers from a key, and resolving misunderstandings. I marked down if homework was complete, incomplete, or not done.

The student’s homework results moved their grade up or down from their class average in a range from +2 to –5 percentage points. My reasoning was that doing homework consistently helped their class average be as good as it could be, and homework was essential to success. If a student did their homework all the time, their grade was increased by 2 percentage points; if they missed many assignments, they were penalized by losing up to 5 points. Many students counted on those two added points and worked hard to earn them.

I had felt that other systems for grading homework weren’t equitable. For example, if the homework was worth 100 points (perhaps 3 points per night), students who had been running a 90% might have their grade go up 3 points, but students with a 70% might get a 10 point boost. With the +2 to –5 range, **every student got the same impact** for doing (or not doing) their homework.

**OTHER CATEGORIES:**

As for Class Participation or Notebooks, these seemed to be hard to capture with a grade, and often created extra record-keeping work for me. Students might have viewed them as easy ways to bring their grades up, but I generally did not attach any grades to them. If I valued notebooks or taking notes for a particular class, I might grade it as a lab, especially in middle school or 9^{th} grade when I was trying to build habits for success for the rest of high school. In some classes, we did a quarterly portfolio as a way to summarize, consolidate, and reflect upon the learning.²

Other commentators in the twitter discussion pointed out that a teacher might value engagement in discussion, or seeking help, or collaboration with other students. Consider using a rubric (shared in advance with your students) to **promote the student habits you desire**. Here is one on “Class Participation” along with a record sheet for students to analyze their contributions (thanks to Carmel Schettino @SchettinoPBL) and here is one on “Student Work Habits”.

Other types of Formative Assessment don’t fall into my grading scheme, because they are formative… the information being gathered helps steer my teaching and gives the student feedback on their learning progress. Nearly everything that happens in the classroom is part of formative assessment, helping all of us calibrate where we are on the learning journey.³

The decision whether to do Test Corrections or Retakes is a much larger discussion, but basically I did not give retakes or give points back for corrections. My experience while teaching high school was that if students expected a guaranteed option for a retake, they didn’t always take responsibility for being prepared in the first place.

There were some times when everyone bombed an assessment, and usually that means I didn’t do the job as the teacher. We would reteach, review, reflect, and then take a second version of the test that was averaged with the first. I wanted to send the message that the first (poorer) grade doesn’t go away.

**EXTRA CREDIT/BONUS QUESTIONS:**

When a good opportunity arose, I would put a bonus question on an assessment or give extra credit for an optional part of a lab activity. The points earned for these things accumulated as a separate “bonus quiz” for each student, rewarding them for doing more math extensions on our current work.

If a bonus was worth 5, you got 5/5 in your bonus quiz. By the end of the quarter, students had bonus quizzes worth anywhere from 1/1 to 35/35, and some had none. The bonus quiz didn’t fill holes of points lost elsewhere, but helped boost your average on the margins.

I’ve seen teachers who have successfully added ON bonus points (or included a grade such as 5/0). This method allows bonus knowledge to make up for mistakes, which I have tried when coursework is very difficult and/or class averages are very low. But if class averages are doing well, the 5/0 method results in averages greater than 100%. It also might imply that you can make up for not knowing/doing some math last month by doing an extra project this month, and I wanted to make the point that all our work is important and students can’t avoid some work while still earning top grades.

**MISCELLANEOUS:**

I did NOT give pop quizzes, because I felt that to be a punitive practice (kind of like, “Gotcha! You’re not prepared”) that could be used by teachers to combat other issues, such as poor behavior or not doing homework. Students always knew in advance what a test or quiz would cover, and most classes had designated review time in the day(s) prior.

Whatever your school’s grade scheme (letter grades, numerical grades up to 100%, 4.0 GPA, etc.) decide in advance what your cut-offs and rounding routines will be. I had a firm “.50 and higher rounds up, .49 and lower rounds down” policy, which meant that a student with an 89.48 did not get the A– for the quarter. If this feels unfair to you, decide in advance what you would do; options are to “borrow” the .02 from the coming quarter or to be lenient if you feel that particular student has earned the higher grade level.

**MOST IMPORTANT REMINDERS:**

Whatever your grading system is, perhaps the most critical thing is to __be prompt returning graded items with feedback__. The learning process is a partnership between me and my students, and if I delay or deny feedback, I’m not doing my half of the job. When students wait days before getting a quiz back, they cannot learn from mistakes on concepts that are the foundation for new material. Often, the same topics will be on the upcoming test, and I want my students to benefit from having the quiz to study from.

Be transparent about your grading system and __keep students informed of their current grade and progress__. This gives students agency over their performance and the grade they have earned. Back in the day (before online grading portals), I would print grade slips from my spreadsheet or grading software and hand them out several times during the marking period. I had a physical piece of paper to hand to the student so there was no grade mystery and no surprises at the end of the quarter, and I could give them a verbal or written comment if something specific needed to be addressed.

If you decide to change your grading system part way through the year, be honest with students about the changes and your rationale for making them. Discuss with them the incentives you want your system to provide. Linda Wilson wrote a 1994 Mathematics Teacher article, “**What Gets Graded is What Gets Valued**” and that is true to a large extent, for better or worse. I found that if I didn’t check or grade homework, my students wouldn’t do it; so if I valued that practice, I needed to include it in my grading structure.

Ralph Pantozzi (@mathillustrated) notes that whenever people are given a metric that they will be judged upon, they behave so that they perform well against *that standard*. His advice is to “__make your system revolve around students doing the math you value__” so that they will work to achieve those goals. Well said.

Notes:

¹For younger students, I used +3 for homework (which I also did for HS when material was very difficult). I required test corrections in some middle school classes as a homework assignment, to place clear value on understanding what went wrong and what can be done differently to avoid errors in the future.

²Portfolios took some time, but were worthwhile in both Algebra 2 and PreCalculus. A good resource for portfolios is Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions edited by Jean Kerr Stenmark (NCTM, 1991). These same classes also did writing in Math Journals with a few prompts each marking period. A nice summary of how to use writing is Marilyn Burns’ article “Writing In Math” in Educational Leadership (ASCD, October 2004).

³Thanks to Steve Phelps @giohio and Martin Joyce @martinsean for these points about Formative Assessment. I have also found the book Mathematics Formative Assessment by Page Keeley & Cheryl Rose Tobey (Corwin, 2011) to be helpful.

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