Friday, April 29, 2011

Exit Tickets

As math educators, we must make broad judgments daily about whether the class understood the day’s lesson before we move on with instruction the next day. The pulse of the class is taken easily because of the level of student interaction and discussion during the questioning segment of the lesson, but it’s harder to get a clear picture of what individual students have mastered and are able to do independently. Though whole group instruction may move forward the next day, it is our responsibility to ensure that all students are reaching mastery. We need to know specifically students who need small group reteaching or more support for success. Because, at CCE we are aware that retention rates for students are highest when they teach others (90%), practice by doing (75%), and partake in discussion groups (50%), many days my students are working in pairs or small groups in math. There is not always the opportunity to collect independent student work, so we needed another teaching strategy to accomplish the goal of knowing whether every student was at mastery on the day’s work.

Exit Tickets have become our answer. An Exit Ticket is a formative teaching strategy given immediately after the Math Workshop concludes which focuses students on the core content of a lesson and promotes a quick and independent assessment check. Each student answers a question or two that targets the big idea for the day. The checkpoint, taking only a few minutes, offers teachers the immediate opportunity to check students’ independent mastery of the day’s content.

Exit Tickets are simple and time efficient to create and analyze. When preparing for a lesson the teacher has to think, “If I teach this math concept or skill effectively, which question should students be able to answer at the end of the lesson?” This question or two should align with the big idea.

Typically, we create an Exit Ticket on a ½ sheet of paper for easy distribution and collection. Having it on a ½ sheet of paper makes it effortless to sort students’ work into piles once the task is complete and collected. Within minutes, you can have several stacks of student work. One stack of student work proves independent mastery of the lesson, the second stack contains student’s work where mastery is not clear and more information is needed, and the third stack demonstrates work with misconceptions or lack of understanding. Students whose work is in the first pile need no additional instruction; Students whose work is in the second pile need a teacher to confer with them so they can explain or justify their answer because the written work did not prove mastery. With this quick conferring session, the teacher can tell whether or not additional instruction is needed. If additional instruction is needed, the teacher can pull the student into a small group during the next day’s Work Session. Students whose work is in the third pile need small group reteaching to acquire more knowledge on the concept or skill. In addition, they may need more strategic questioning during whole group instruction and more feedback during the Work Session as the concept or skill is developed.

As a rule, the whole process of Exit Tickets takes little time and provides great benefit. Teachers don’t have to wait for a summative check on a math quiz or assessment, they have the formative Exit Tickets that help them prescribe instruction along the way and help prevent misconceptions or gaps in knowledge.

Third Grade Exit Ticket Example:

During a unit of study on developing and understanding fractions and fraction equivalence, students needed to be able to use models to represent equivalent fractions and identify representations of equivalence. To get started, we had students work with pattern blocks. They identified the yellow hexagon as one whole, a red trapezoid as ½, a blue rhombus as 1/3, and a green triangle as 1/6. They created equations like ½ + ½ = 1, 1/3 + 1/3 + 1/3 = 1, and 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1.

Additionally, we taught students to find ways to make one whole using combinations of halves, thirds, and sixths with pattern blocks as their tool and write equations. For example, ½ + 1/3 + 1/6 = 1.

Students quickly began to find equivalent fractions like ½=3/6, 1/3 = 2/6, and 2/3 = 4/6, and make generalizations like, all fractions that contain denominators twice as large as the numerator are equivalent to ½.

After several lessons, we played a game in which students received a recording sheet of yellow hexagons. Students rolled a fraction die and had to add that fractional piece to one of the yellow hexagon pieces. The object of the game was to fill in all their yellow hexagons.

During the two days of lessons using the pattern block manipulatives much of our discussion was in student pairs. We weren’t confident that every student had transferred our classroom conversation to independent mastery, so we used an Exit Ticket at the end of Math Workshop on Day 2 to formatively assess students. The students were given three minutes to complete the task and then we collected their work. In the first problem, students had to write an equivalent fraction for 3/3, 3/6, and 2/6, and in question number two they had to answer the following question, William had a fraction cookie with the equation ½ + 1/6 + 1/6 + 1/6. Sebatian told William that he could just write ½ + 3/6 or ½ + ½. Is Sebastian right? Explain.
Within minutes, we had sorted the students’ work. Some students easily, accurately, and articulately answered the questions and needed no further instruction. Some students answered the questions correctly but their explanation of the equivalencies was not articulate enough to know whether they fully understood the concept. These students would need a quick conference to identify whether they fully mastered the concepts. In some cases, we found that no further instruction was needed, but in other cases, we found that there is a gap in knowledge and small group instruction is needed for mastery. The third group of students could not accurately answer the questions and we formed a small instructional group to offer more instruction and practice.

When I first heard the idea of an Exit Ticket, I jumped too quickly to the conclusion that I would gain the same information from a quiz or assessment. But, after implementing them on a trial basis consistently for several weeks, I realized that they had tremendous value for gathering data and giving immediate and consistent feedback to students. It was the difference between assessing with a summative (a quiz or test) and a formative which helps guides the next day’s lesson. I would recommend the use of Exit Tickets to any math teacher who is serious about offering differentiated math instruction to meet the needs of each of their students.