Throughout my first years of teaching, I was often bothered by the thought that my traditional grading system didn't accurately communicate the level of knowledge my students possessed. Why were those students with poor behavior and indifferent work habits consistently getting

*C*s,*D*s, or*F*s when they had demonstrated a level of knowledge equivalent to an*A*or*B*on assessments? How come some of my "good students" received*A*s or*B*s as course grades when they performed at*C*level or below on assessments? It became clear to me that my grades didn't accurately reflect student knowledge.Recent research has pointed to standards-based grading systems as a valuable way to support learning and meet individual students' needs. In a standards-based grading system, teachers clearly define learning objectives that frame their assessments and guide differentiation.

Several years ago, as I became aware of possibilities for standards-based grading, I began overhauling the traditional grading system I had used. Every year since, I've increased how much I differentiate my teaching, and my students have shown increased learning growth.

Let me walk you through the grading methods I use now, which more clearly reflect learners' knowledge level and help more learners master math.

## Pretests Set the Stage

In my upper elementary math classes, after I complete the essential step of defining student learning objectives for a unit, I pretest students. Before every unit begins, students answer two or three questions for each objective. When I review these pretests, I use colored markers to indicate the level of understanding each student shows for each objective. Red indicates little or no understanding of that objective, orange indicates the student shows some understanding of the concept in question, and green indicates mastery.

I use these results to differentiate class time. Students who demonstrate a solid understanding of a learning objective on the pretest are excused from the lesson on that objective to participate in alternative enrichment activities, often taken from the enrichment options included in the packaged curriculum I'm using or from outside resources, including free activities available through the Internet. Students work on enrichment individually or with partners in a set-aside area while the rest of the class participates in the main lesson.

Students who demonstrate a partial understanding of a learning objective participate in part or all of our classroom activities, depending on the topic. Sometimes students participate in the "meat and potatoes" portion of the lesson, and then pursue alternative activities. Students who demonstrate little or no understanding participate in the entire lesson.

For example, here's how three groups of students worked during a lesson on the order of operations. I gave students who demonstrated an above-proficient level of understanding on the pretest guidelines so they could work independently in a different part of the room. Together they practiced using the correct order of operations to simplify expressions that contain more complex operations, such as nested parentheses and brackets. After checking their practice work themselves, students used a teacher-created set of cards that contained a variety of numbers and mathematical symbols to create algebraic expressions that simplify to a given number.

Students who demonstrated a partial understanding of the order of operations stayed in the classroom for the teacher-led portion of the lesson and participated in a guided practice activity. (I usually include such an activity after whole-group instruction.) These students then worked on the enrichment activities listed above.

Students who had shown little understanding of this concept participated in the whole-group lesson, watching and listening as I used a think-aloud to model the correct order of operations. They then added notes to their interactive notebook, including examples, and worked through a cooperative learning activity. I gave small groups of these learners cards of practice problems. After a student chose a card, the entire group simplified the problem on individual whiteboards; when everyone was done, students compared their boards. The last part of class time was dedicated to independent work with order of operations. As students worked, I helped as needed and checked in with the groups of students working on enrichment activities.

## Further Assessments Flag Students' Needs

In a standards-based classroom, after students complete the learning activities in a unit, another assessment covering the objectives is in order. I score these tests and record the results. But because my aim is formative, students see their results not as letter grades, but as feedback about progress on each of the learning objectives (Chappuis & Chappuis, 2007).

**Figure 1. Grade for an End-of-Unit Assessment**

How I Overhauled Grading as Usual-table

Learning Objective: | Problem # | Points possible | Points earned | Proficient score |
---|---|---|---|---|

Order of operations | 1-5 | 5 | 3.5 | |

Mental math | 6-9 | 4 | 2.5 | |

Evaluating expressions | 10-13 | 6 | 4.5 | |

Translating expressions | 14-16 | 7 | 5.5 | |

Writing expressions | 17-21 | 7 | 5 |

To manage this much formative data for all my students, I use a sheet that shows each learner's raw score for each learning objective assessed. As shown in Figure 1, this sheet indicates which math problems measure that objective, the highest number of points one can earn on those problems, and what score on the problem set is considered proficient. The number of problems or level of points allocated to that particular objective shows its importance in the unit. Organizing assessments according to objectives helps me maintain a reasonable time frame for grading. To keep my own detailed record of progress, I enter each student's score for each learning objective separately into my grade book (see fig. 2).

**Figure 2. Partial Snapshot of a Standards-Based Grade Book for a Unit on Algebraic Expressions**

How I Overhauled Grading as Usual-table2

Overall Grade | Order of Operations | Mental Math | Evaluating Expressions | |||||
---|---|---|---|---|---|---|---|---|

5.0 | 4.0 | 6.0 | ||||||

Kris | 80 | B- | 4.5 | 90.0 A- | 37.5 F | 100.0 A | ||

Nora | 83.3 | B | 4 | 80.0 B- | 4 | 100.0 A | 4.5 | 75.0 C |

Aiden | 70 | C- | 3.5 | 70.0 C- | 2.5 | 62.5 D- | 4.5 | 75.0 C |

Craig | 86.7 | B | 4.5 | 90.0 A- | 3 | 75.0 C | 5.5 | 91.7 A- |

Jenny | 93.3 | A | 5 | 100.0 A | 3.5 | 87.5 B+ | 5.5 | 91.7 A- |

Paul | 60 | D- | 4 | 80.0 B- | 1.5 | 37.5 F | 3.5 | 58.3 F |

Brian | 86.7 | B | 4.5 | 90.0 A- | 3.5 | 87.5 B+ | 5 | 83.3 B |

Alecia | 96.7 | A | 5 | 100.0 A | 4 | 100.0 A | 5.5 | 91.7 A- |

Jonathan | 53.3 | F | 2 | 40.0 F | 3.5 | 87.5 B+ | 2.5 | 41.7 F |

Kyle | 100 | A | 5 | 100.0 A | 4 | 100.0 A | 6 | 100.0 A |

Changing to a standards-based assessment and grading system can be difficult for students. Many are anxious; they miss the comfort and familiarity of overall scores and letter grades on assessments. Before returning the first assessment, I discuss with students my assessment system and the reasons behind it. This helps us focus on learning and deemphasizes the importance of a grade. I explain that students won't receive an overall grade on any assessment because it's their progress on learning objectives that's important.

Students and parents often need help to maintain this perspective, particularly in the beginning of the year. One week before each assessment I send parents an e-mail to inform them of the assessment and share some details. I usually include the kind of information shown in Figure 1 and provide problems from the textbook that correlate with each learning objective. After an assessment, I make affirming calls to the homes of students who demonstrated proficiency on every learning objective or those who have struggled but have finally met proficiency on certain objectives. If a student didn't show proficiency on at least two learning objectives, I talk with that student to make a plan and communicate the situation to the parents.

I give students a learning record (see fig. 3) to record their progress. After receiving results of each end-of-unit assessment, students write down each objective, the score they earned, and the proficiency score. (This is usually a point value that equates to 70 percent of the possible points, but it varies depending on the objective and the level of mastery of a skill that I believe students need to prepare them for future educational experiences.)

**Figure 3. Student Learning Record**

**My Learning Record**

How I Overhauled Grading as Usual-table3

Learning Objective | My score | Proficient score | Intervention needed? | Dates I've worked on it | My new score | |
---|---|---|---|---|---|---|

Yes | No | |||||

Order of operations | /5 | 3.5 | ||||

Mental math | /4 | 2.5 | ||||

Evaluating expressions | /6 | 4.5 | ||||

Translating expressions | /7 | 5.5 | ||||

Writing Expressions | /7 | 5 |

At this point, my end-of-unit assessments show their formative side. Students compare their scores with the required level of proficiency and determine whether any intervention is needed. They note on their record what interventions they will take on, and I provide the means. Following the return of an assessment, I allocate one or two days of class time for work on interventions or enrichment.

## Interventions, Retakes, and Results

Printed materials and videotaped tutorials connected to the course curriculum provide practice for learners who need it. For each of the objectives, I point learners to reteaching and practice pages as well as links on the classroom website to online video lessons and interactive activities. I require students who haven't yet demonstrated proficiency to complete additional practice in the key areas, attend reteaching sessions with me during lunch or recess, and arrange for a retest. Students who need to complete additional interventions do so outside of class time. Enrichment activities typically involve problem solving or logical thinking.

After a student completes the practice for any learning objective for which they have not yet demonstrated proficiency, I briefly discuss with that learner what he or she now understands about the objective. This gives me an opportunity to assess whether a student has cleared up any misconceptions and now understands the material better. Students must have completed every relevant practice assignment to earn the opportunity to take a retest. If the student and I both feel that student is ready, I allow him or her to take a retest on the learning objective. To improve the reliability of the results, I make students wait a minimum of one day after receiving approval to take the test.

My retests typically consist of four or five questions, and students' scores replace their previous scores on that objective. On the rare occasions when a student does not show growth on the retest, I offer that student additional practice and support, but I don't allow a second retest. Usually, we have a conversation about how the student can better assess his or her own knowledge. Students who score at proficiency or higher may also retest once on any given learning objective if they want.

My quest to ensure accurate grading has led to changes in the format of my grade book. Generally, tests—broken down by objective—account for 80–90 percent of a student's grade; the remaining portion is based on project work. I evaluate homework and follow up with students who are missing assignments, but I weight homework at 0 percent.

Some educators raise the concern that allowing students to retest and replacing old scores with new scores will result in inappropriate grade inflation. Although grade inflation is a legitimate concern, the grading system I've described does not contribute to it. Students must consistently exceed proficiency on each learning objective to earn an overall grade of

*A*, and they must meet and exceed nearly all objectives to earn a*B*. At times, this has resulted in hard-working, organized students earning a grade other than*A*. I've found that it's helpful to find ways to recognize students' effort, for example, by writing comments, sending complimentary postcards, or making phone calls home.My standards-based classrooms have received positive feedback from students and parents. Students take more ownership and can reflect on the concepts and skills they understand well and those they have yet to learn (Brookhart, Moss, & Long, 2008). The infamous student question, "What's my grade?" becomes obsolete after students several weeks of my typical response, "How did you do on each of our learning objectives?" Even grade-focused parents appreciate the de-emphasis on cumulative grades and the increased focus on learning.

Many students who have previously struggled with test anxiety feel more comfortable during assessments, knowing a system of interventions is in place. Students with learning difficulties are more successful.

Assessments in a standards-based classroom provide valuable feedback to students, teachers, and families about students' growth. I've found that using this assessment system helps me answer the toughest question posed by learning community leaders Richard and Rebecca DuFour: How do we respond when students do—or don't—learn? (DuFour, DuFour, Eaker, & Many, 2006).