Classrooms that have moved toward a problem-based model often wrestle with the idea of individual accountability. If we offer tasks that are worked on collaboratively, we need to make sure we learn more about how each individual student is thinking. To do this, one common practice is providing our students with exit cards at the end of the lesson.
However, I wonder when we talk about terms like “exit cards” are we envisioning the same thing? Take a look at the following headings, and some sample exit card prompts. Which of the 4 purposes do your exit cards typically fulfill?
Questions designed for meta-cognitive reflection / connection:
- How does today’s problem remind you of a problem you have solved before?
- Explain one of the strategies discussed in class that was different than yours. How was it different than yours? How was it similar?
- What do you believe was the purpose of today’s problem? What did you learn?
- What area gave you the most difficulty today?
- Something that really helped me in my learning today was ….
- What connection did you make today that made you say, “AHA! I get it!”
- Describe how you solved a problem today.
- Something I still don’t understand is …
- Write a question you’d like to ask or something you’d like to know more about.
- Did working with a partner make your work easier or harder. Please explain.
Questions targeted towards concepts:
- Use a diagram to help explain how to compare 2 fractions with different denominators.
- Create 2 addition questions, one that is easy to solve mentally and one that is harder. Use a number line to explain how to answer both. What makes one of the questions harder?
- When would you ever need to know the area of a rectangle? Pose a math problem using this information with an appropriate context and find the answer.
- 1/2 + 1/3 = 5/6 When would you need to know this? Pose a math problem using this information with an appropriate context.
- When 2 even numbers are multiplied together we get an answer (product) that is even. Is this always true? Give examples to explain your thinking.
- Draw a picture to explain why 2/3rds divided by 4/5ths is 10/12ths.
- Two rectangles have the same area but very different perimeters. What could the dimensions of the rectangles be? Explain why you picked these rectangles
Questions targeted towards procedures:
- Two fractions are added together. Their sum is between 1/2 and 3/4 . Show 2 fractions that could possibly work.
- Explain to someone unfamiliar with multiplying how to solve a 2-digit by 2-digit question. Give an example. Solve it in 2 different ways.
- How many ways can you solve 68 + 18? Explain each way. Which was the most efficient for you?
Questions focused on clarifying misconceptions:
- Susan and Jamie are arguing over which answer is correct to 12.1 + 25.25. Susan believes the answer is 26.46. Jamie thinks the answer is 37.35. Explain how both got their answers. Who is right? What misconceptions led to the incorrect answer?
- Phillip explained that 100cm2 is the same as 1m2. Explain why he is correct/incorrect.
- Explain one of the disagreements we had today during our congress. What did we learn from our initial misconceptions?
- Is 2/4 larger or smaller than 2/6? How do you know?
- Tracy says you can reduce 8/10 to 4/5. Dan says they are the same, but Tracy says that 8/10 is larger. Who is right? How do you know?
When we are asking our students to provide us with information individually, I think the type of information we want to collect from them tells us a lot about our own beliefs about what is important!
Let’s take a quick look again at the 4 types…
Questions designed for meta-cognitive reflection / connection
Providing students with these types of prompts tells our students that we want them to be monitoring their own thinking, and that we value their thoughts and care about their identity with mathematics.
Questions targeted towards concepts
Providing students with these prompts tells our students we care about the big ideas in mathematics, and that we want our students to deeply understand the concepts we are learning about. Asking questions like these asks our students to really pay attention to the thinking and reasoning of others in class discussions.
Questions targeted towards procedures
Providing questions like these asks our students to think flexibly and make decisions. Although they ask for our students to show they understand procedures, we still keep the prompts open to help reach all of the students in our class.
Questions focused on clarifying misconceptions
Providing questions like these might take a bit more thought on our end, but it tells our students that mathematics is about constructing constructing and critiquing mathematical arguements. See SMP 3 – Construct viable arguments and critique the reasoning of others.
I also want you to notice what kind of exit card I didn’t mention. I didn’t provide room for closed tasks, ones where there is 1 right answer, where the answer doesn’t require thought or reasoning… Maybe this shows my bias!
What is your balance?
Here is a printable version of my Exit Card Types document. Share it, use it for ideas, use it to reflect on our own decision making…