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Making Math About More than Numbers: A Case for Evaluation-Based Grading

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This post is by Sarah Strong, Ninth Grade Math Teacher, High Tech High, and Carlee Hollenbeck, 12th Grade Math Teacher, High Tech High North County

A lively group of 11th grade students is sitting on a bus to the US/Mexico border to interview Border Angels as part of a Humanities and Spanish project. The previous day they had taken a test in math class and were waiting in anticipation for the grades to be uploaded into the online gradebook. Though there was some nervous anticipation, the students were largely positive and energetic. About halfway through the trip, one student announced "Grades are posted!" There was a pause in the activity as students checked scores on their phones. "I got 65/60," one girl exclaimed. "I knew I got that extra credit one right." Another student at the front of the bus stood up and danced over his perfect score. Some students talked quietly to their neighbor, and many students sat silently. A few even moved to different areas of the bus, tears in their eyes. The posting of the scores changed the atmosphere on the bus from one of lively and social students, to a group ranking and comparing themselves. The students' academic identities had either been elevated, affirmed, or dashed, all with the posting of one score.

Systems of ranking and sorting are not uncommon everywhere in today's educational setting. In high school, where we teach, it is very common to hear students asking questions like, "How many points is this worth?" or "Is there any extra credit to improve my grade?" These questions have always left us feeling like the educational experience we are giving our students is cheap and reductionist. As we worked through this dilemma, we agreed upon a short set of hopes for our students for the coming year:

 

Reality of the Present:

  • Students "learn" exclusively for a grade
  • Students complete work because it is worth 10 or 20 or 150 points
  • Students view teachers as authoritarians who judge students' rote content knowledge with scores
  • Students form their identity exclusively around grades, particularly quizzes and tests

Hopes for the Future:

  • Students learn for gain in knowledge, skills and self-improvement
  • Students create extremely high quality work because the work they do tells a story of who they are
  • Students are viewed as collaborators within their learning journey
  • Students have a broader scope through which to form their academic identity

 

In the summer of 2015, Jo Boaler, a world-renowned math education researcher, offered a conference in Oceanside, California, and invited participants to thoughtfully evaluate their math pedagogy and the collective student experience. She shared that current brain research shows that students learn better and are more productive in math courses when standard grading systems are altered to allow students to focus on their growth and shape their mathematical identity instead of a grade. While reflecting on how students form this identity, Jo states, "Our performance and testing culture harms students and the continual assessment of students through tests, grades, and homework is part of why so many students have a negative relationship with mathematics." It is disheartening to have students with a predefined self-worth as a math student based solely upon previous grades. Additionally, in a description about the identity-harming in math, Boaler claims, "Mathematics teachers feel the need to test regularly, more than any other subject, because they have come to believe that mathematics is about performance, and they usually don't consider the role that tests play in shaping students' views of mathematics and themselves." Finding a way to help students have a positive view of their potential to be successful in mathematics is critical and without altering the way they experience math assessment, we cannot expect their mathematical identity to change.

To make this shift happen in our classrooms, we needed to be willing to forego some control of the classroom and view students as collaborators.  It was necessary to invite students into the creation of expectations and most importantly to provide space for them to reflect and evaluate their own work and understanding. We kicked off the school year by sharing with students that we would not be assigning numeric grades on assignments throughout the school year. Alternatively, for every assignment, task, or assessment, students would be given our specific expectations, collaboratively set some of their own, and receive feedback in person and in PowerSchool (Figure 1). At the end of the semester, students would use evidence to propose a final letter grade through a mini-conference with us, so that colleges could evaluate their level of work in the class (Figure 2).

 

Sample Student-generated Scoring Rubric for Group Work Problems

EE (exceeds expectations)

Student mathematical voice is evident

The assignment has an idea about ALL questions (and an answer when necessary)

Student explains ideas thoroughly AND makes connections

Student asks questions

Student goes above in one way or another

ME (meets expectations)

Paper is complete

Some thought process/work is present

Some answers aren't thorough (just numbers)

NY (not yet)

Only partially complete (some work done)

Some answers present but lacks explanations

No work shown

I (incomplete)

Not turned in at all

 

Figure 1: (sample co-created rubric for assignments)

 

Guidelines for Grade Proposals

A range: Mostly ME, with a significant number of EEs

B range: All MEs (no I's, no NY's)

C range: Some ME's, Some NY's, Few I's

D range: A significant number of NY or I

 

Figure 2: General Guidelines for grade proposals lifted from our syllabi





 

We finished the year with our students by having one-on-ones with each of them for them to propose letter grades that would reflect their effort and growth from the year. In these meetings, the students reflected on their strengths and areas of growth, and then we were able to share some observations with them. In contrast to a number score on a test as a simple indicator of mathematical worth, the students' identities were formed by opportunities that they took to use feedback to refine their work and persist through challenging problems.

We continue to strive for this new student experience in our classrooms and hope that our students, instead of saying, "what is my grade?" will have reflections like this student from Carlee's class: "Overall I always strived to exceed expectations in math because I would learn more and become more confident in myself and my abilities. Rather than doing math for a grade I did it for my own growth and curiosity!" We invite others to join the conversation about how small gradebook and scoring shifts can open up opportunities to assess students more deeply around what truly matters in our classes.


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