Our assessment journey began at the purpose of a grade: to somehow represent how well a student understands the content, or more precisely, how well they have mastered the grade level standards. Since that is the purpose, then all summative assessments must actually assess the standards. However, teachers have been misusing formative and summative assessments for a long time, so we reviewed the purpose of each.
Formative assessment is assessment "for" learning. They should help us diagnose student readiness or issues with content standards. Formative assessments are meant to be used by teachers (and students) to guide them in the learning process. They are not reflections on mastery of content, but rather roadmaps of how to get to that mastery.
Summative assessment is assessment "of" learning. They should tell us how well a student has understood the content. These assessments are what should actually make up a student's final grade because they should reflect mastery.
We quickly realized that many common grades that teachers take are actually formative and should not be used in a summative fashion. For example, class participation, extra credit, effort, homework completion, and even homework accuracy don't reflect mastery of a topic. A student could put forth tons of effort, participate lots, earn extra credit by bringing in Kleenex boxes, complete all homework, and even get the right answers on homework through legitimate parental, peer, or teacher guidance and still not actually understand the content. We had to eliminate those things that didn't show mastery from the summative list.
We also needed to be careful to not go to the other extreme. If we really wanted to know what students know "in sum" for the year, we'd simply give one huge test at the end of the year and that would be the student's final grade. We wanted to have multiple summative measures to provide a preponderance of evidence of the level of student understanding. Thus we finally settled on the following categories that we use as needed:
Possible Formative Assessment Categories - all worth 0% in a weighted category percent grading system
- Computation - This measures below grade level computation skills with natural numbers, integers, decimals and fractions. Since it is below grade level standards, it is formative. During the 12-13 school year, we did not use this category.
- Homework Completion - This gives a measure of effort, which we all know is crucial to success in any area of life, but does not show mastery of content. When parents see this formative score, they also get a good idea of the general effort a student is putting into class.
- Homework Accuracy - Since homework is meant to be practice and a learning tool, it does not show mastery. Students learn better when given the chance to make mistakes and correct those mistakes. This score can also inform parents how well students are using the resource of the answer key to learn from their mistakes.
- Mastery Task - After we can reasonably expect mastery on a specific skill, we do a short warm-up activity at the beginning of class consisting of 2 to 4 questions on that specific skill. The score from this is recorded as a formative grade to give us an idea of how much we need to review and how prepared student's are for upcoming summative assessments. When communicated to parents, this score let's parents and students know where to concentrate their study time at time.
- Pre-Test - For each unit we give a pre-test to determine what students already know. This guides our lesson planning for the unit and allows opportunity for differentiation.
- Remediation - When helping a student fill in gaps in learning from previous years, we are working on below grade level standards. Therefore, these cannot be included as a summative grade. This category may also be useful as progress monitoring during the RtI process if it is based on a single skill.
- Enrichment - Likewise, if a student is working at above grade level standards, how well they do on those topics has no bearing at all on how well they do on the actual grade level standards.
Summative Assessments - all count towards a student's final grade
- Problem Solving (10%) - This is an application and multi-step problem that demands a written justification. Some of these we actual use as formative and only count them as summative grades when we could reasonably expect mastery of the content.
- Weekly Quiz (30%) - Each week we give a short quiz over what we expect students to have mastered during that week.
- Post-Test (30%) - At the end of each unit we give a post-test much like the pre-test. This not only gives us a summative look at learning, but provides a growth model by comparing scores to pre-test scores.
- Quarter Exam (15%) - A 25 question multiple choice test (the only multiple choice test we give) mainly designed to prep students for comprehensive finals at the high school and college level.
- Quarter Project (15%) - Each project is meant to be a large application of multiple topics students have learned throughout the Quarter.
Note: There is nothing magical about the percents we assigned to each category. Since we have two post-tests and usually five quizzes each quarter, this gave us what we thought were nice ratios of value. We would not impose these percents on any other teacher, but we would suggest that each course should use the same grading method (weights and scale). It should not be true that a student's grade is dependent on which teacher they get, but the same performance should earn nearly the same grade with a different teacher if we are truly assessing the standards. With this in mind, we tackled a few other issues:
Other Grading Issues
- Extra Credit - This inflates grades and does not assess the standard. Hence, we don't use it. If it does assess the standard, then it's regular credit, not extra credit.
- Partial Credit - If a student misses an algebra question because of a computation error, they still have demonstrated that they understand inverse operations. We give partial credit on questions like this. In fact, we have defined on every question on every test and quiz how students can earn partial credit.
- Late Work - Since all of our summative assessments are done in class, there is no chance for students to have late grades (except on the quarter project). We have eliminated the need for a late work policy.
- Curving Scores - Curves by definition change how well students did. Rather than curve something, if we found our assessment was not valid, we simply give a better assessment. We do not distort grades by curving.
- Zeros - We don't need the faking of grades by only giving students a minimum score of 50%. If a student knows 0% on a summative assessment, that is the best representation of their level of understanding. The reason some educators wanted to eliminate zeros was because many teachers used formative assessments in a summative way. We don't have gradebooks filled with zeros because our summatives are given in class.
- Test Retakes - Since we are trying to determine mastery of content, test retakes make sense if a student has gained mastery of a previous objective. However, we offer one chance at a retake and only after the student has demonstrated that they have gained new levels of mastery on the content through remediation work with the teacher.
- Calculators - We allow calculator use throughout most of the year since we are generally not doing computation. If we do teach computation processes, such as the rules for exponents, we don't allow a calculator because the point is to determine if students understand how and why the rules work.
Points vs. Percents
Finally we realized that grading using total points or using category percents is exactly the same mathematically at the end of a grading period. There are differences between the two grading methods within a grading period, but at any point where the fraction of assessments completed in each category is the same, the two systems line up. While total points is generally more aesthetically pleasing, it takes much more long term planning and locks in the number of summative assessment you can have. It also leads to odd point values for assessments that are difficult to work with. By using weighted categories we eliminate those problems and can have 0% categories for our gradebook program to help us track and analyze formative assessments.
For more detailed information on grading policies you can check out this Power Point Presentation by Mr. Bright who would be happy to discuss assessment policies in your school with you and your staff. Please contact him at firstname.lastname@example.org with questions. (Mr. Eric Bright is the author of the CMS 8th Grade Math Curriculum, and while he has moved to Georgia and is teaching there, he has given permission to share his email here in case you have questions.)
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