Formative Assessment
Formative assessments are important checkpoints for both me and my scholars. Whereas summative assessments tend to measure students' holistic progress toward mastering a given set of standards, formative assessments offer the opportunity to identify strengths and misconceptions at a much more granular level. As such, it is essential to maintain balance between formative and summative assessments and to create a classroom culture in which both students and teachers view formative assessments as helpful indicators of where more work is needed rather than as high-stakes referendums on student abilities.
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I attempt to employ a miniature version of the full assessment cycle—design, administer, grade, analyze, and adjust—for every lesson that I teach. Before each class period, I design or select an exit ticket aligned to the day’s standards-based goal and then plan a lesson intended to enable students to succeed on the exit ticket. At the end of class, I administer the exit ticket to all of my students as an opportunity for them to show me what they have learned. I grade the exit tickets and sort them into categories based on patterns in misconceptions and learning gaps. These categories, informed by other data I have collected about students’ mastery of the standard, delineate small-group assignments for the next lesson. I discuss remediation strategies in collaboration with other educators—I have multiple weekly meetings with instructional leaders and colleagues devoted to analyzing students’ formative assessment scores and adjusting instruction accordingly—and prepare small-group instructional plans for correcting the misconceptions I have observed. Finally, once I have worked through the concept again within small groups, I reassess it using the next exit ticket or another short formative assessment.
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Based on this cycle, there is often significant overlap among my exit tickets from day to day. The three exit tickets below come from the section of a unit that dealt with Common Core State Standard 8.EE.A.1: know and apply the properties of integer exponents to generate equivalent numerical expressions.
First exit ticket assessing standard 8.EE.A.1. This exit ticket assesses basic comprehension of exponential notation with questions 1 and 2. Then, with question 3, it previews the material for subsequent lessons and identifies students with enough background knowledge of the topic that they may benefit from extension activities instead of regular instruction.
Second (top) and third (bottom) exit tickets addressing standard 8.EE.A.1. These subsequent exit tickets probe for deeper mastery of the topic and are intentionally very similar to one another. This allows me to compare the mastery gains that students experienced as a result of the remediation I provided during the second ad
Heat map of formative and summative assessment scores for standard 8.EE.A.1. I record and analyze my assessment data in Microsoft Excel so that I can use color-coding to observe patterns in scholar growth and challenges quickly and easily.
My re-teaching strategies based on formative assessment data are generally inspired by the specific misconceptions that I observe. For the topic featured above, misconceptions generally (and predictably) stemmed from computational errors or misunderstanding of exponent properties. However, during a recent unit with my sixth graders, I encountered a common error that I had not anticipated: students confusing division with subtraction in word problems. During my weekly data analysis meeting with one instructional leader, we discussed this problem and decided that a categorization activity might help struggling scholars.
Sixth grade re-teaching activity. Students found it much easier to write their own division story problems once they had spent time distinguishing them from subtraction problems and observing patterns in the two types of stories. Student mastery of the concept improved more than 100% as a result of this activity. Note also the detailed feedback, encouragement, and support that I have written on each exit ticket. My note on the second page is in Spanish because that scholar finds it easier to read comments in Spanish.
Formative assessments are not limited to exit tickets. Indeed, I periodically use individual and group projects as formative assessments during class. For example, I recently asked my seventh graders to create a scale drawing of their “dream classroom” rather than giving them a formal exit ticket. Many scholars produced very thoughtful work on this assignment. Significantly, some of the best drawings I received came from students who often struggle in the more formal assessment settings of a traditional exit ticket, quiz, or test. This is a powerful reminder of the importance of designing assessment tools that gather data in a wide range of ways so that students have ample opportunity to demonstrate mastery of a given topic.
A sample of students' "dream classroom" formative assessments. Project-based assessments give students the chance to demonstrate mastery in a variety of different ways. The three top drawings demonstrate strong mastery of the content; these students can put their theoretical knowledge of scale drawings into practice and are ready to move on to more advanced applications of the concept. The two drawings on the bottom come from scholars whose prior exit ticket scores about scale factors have been very low. However, whereas the scholar who drew the image on the left appears to have very little understanding of scale and perspective, the scholar who drew the image on the right seems to understand the basic concept of scale drawings despite some continuing confusion about perspective. Thus, these two scholars merited (and received) different forms of remediation during subsequent lessons based on their unique levels of understanding.
Regardless of the type of formative assessment I am using, I always turn it back to students with detailed feedback, encouragement, and support. My handwritten notes to students are based on the work they submit and my personal relationships with them. My goal with these notes is always to push scholars to examine their own thinking and learning in a way that guides them toward increased mastery of the material. Even students who understand the mathematical concepts well need frequent reinforcement to produce the sort of quality work that demonstrates the tremendous progress they are making.
Feedback on a seventh-grade exit ticket. Note that scholars receive positive reinforcement for excellent work (p. 2), specific math tips (p. 5), and even personal check-ins (p. 13) through my handwritten notes.
When I began teaching, I thought of exit tickets and formative assessment as one and the same. Now, although exit tickets are still a fixture within my classroom, I realize that there are myriad sources of formative data available during every class period. This understanding leads not only to more variation in assessment types (as exemplified above) but also more data collection during daily activities. For example, I frequently poll students by having them raise fingers or a dry-erase board to indicate their solution to a problem. Quickly noting which students have solved the problem correctly and which have matching incorrect answers is a great way to figure out which scholars will need extra support from me for the rest of the lesson. Once students are working with me at a station—sometimes on the basis of the answers they gave using their fingers or boards—I can further assess their progress by asking them to solve a problem with a new approach or strategy. I frequently pick one problem from a worksheet as a miniature exit ticket of sorts and ask students to solve it during the last few minutes of a rotation to demonstrate what they have just learned. I also treat homework and classwork similarly. I usually grade it for completion rather than correctness, but I track which students are struggling with it so that I can provide them with additional support in subsequent classes. High-quality assessment is all about gathering data, and expanding the pool of resources from which data can be collected gives teachers more tools with which to do their jobs effectively.