Welcome back! This is part five of my seven part summer blog series focused on formative assessments. So far, we’ve talked about three of the five techniques that are introduced in the book, The Formative 5. The first technique was observations. The second technique was interviews, and the third technique was a show-me response. (Missed the first four blog posts? See them here!)
Today, I want to introduce the fourth technique called a hinge question. “A hinge question provides a check for understanding or proficiency at a particular hinge point in a lesson” (p.85). We might think about using a hinge question at that place in the lesson where, in order for students to be successful or show mastery of the skill, students have to understand a particular point or piece of information. We can think of a hinge question as the point where success really “hinges” on them being able to successfully respond to a question that illustrates their thinking about and understanding of a topic or skill.
Hinge questions can be used in a variety of places in your lesson depending on how the responses will be used:
• Hinge questions can use used at the end of the lesson to help a teacher decide, “Where do I go tomorrow? In what direction do I move my next lesson?”
• A hinge question could be used in the middle of the lesson to determine whether or not to continue with the current trajectory or if a new trajectory is needed.
• You may use a hinge question at the beginning of the lesson to decide whether some additional interventions are needed, the lesson can continue as planned, or if a more challenging lesson or activity is needed.
Hinge questions can be used with the whole class as a diagnostic tool to gain a better understanding of what students know and understand about a topic or with a small group to assess where students are in the learning cycle and whether further interventions or challenge and extensions are warranted.
How do we get started with hinge questions? That’s right– we’re going to plan for it. Just like with observations, interviews, and Show Me tasks, the first thing we’re going to do is make a plan for how to use this particular technique as a formative assessment tool in the classroom.
- How will you use hinge questions to assess student understanding? This is where we think about whether the hinge question will be used at the beginning, in the middle, or at the end of the lesson. We also want to consider what type of question we will ask, i.e. a multiple choice formatted question or an open-ended question. Lastly, we’ll consider whether the question will be used with the whole class or a small group.
- How will you use the responses you receive? This is where we think about what to do with the information we receive from the students’ responses, such as using it to decide on tomorrow’s lesson, whether or not review work is needed, pull a small group, or decide to provide more practice for that particular component of the lesson.
- How will students respond to the hinge question? This is where we want to decide whether students will respond with a response card, where they display an A, B, C, or D, to indicate their answer or if they will indicate their response with a whiteboard.
- What type of hinge question will you use? This is where we want to think about the type of question we’re asking. The National Council of Teachers of Mathematics’, NCTM’s, Principles to Action: Ensuring Mathematical Success for All, identifies four different types of questions.
a. The first type of question is one where we’re just trying to gather information to see if students can recall something.
b. The second type of question is to probe student thinking and investigate how they’re thinking about something. We listen to their responses to gain a better understanding of the processes and thinking patterns they’re using.
c. The third type is a question that makes mathematics visible. These questions make connections to ideas and highlight relationships between mathematical content and skills.
d. The fourth type of question is one that encourages reflection and justification. They’re those follow-up questions that encourage students to think about their reasoning, actions, and processes.
5. How might students respond to the hinge question? This is where we want to think about what we might hear from and see in a student’s response. Thinking about and processing this question in advance will help us decide how we’re going to respond and follow-up on the information we receive from students.
Let’s look at an example (see below). I’ve used a hinge question planning tool to help illustrate how to plan for a hinge question within the same lesson highlighted in the previous three parts of the series.
From the planning sheet, you can see:
- This is going to be a middle-of-the-lesson hinge question because it is important to know whether students can match an expression to the story problem. If a student is unable to determine the dividend and the divisor in the story problem, the student will not be able to successfully move forward.
- The hinge question will be posed to the class as a whole.
- Because the hinge question states that students should write an expression, the question a short-answer type of question.
- The students’ responses will be used to determine whether the class is ready to move forward with the lesson, using a visual model to illustrate the answer, or if more time needs to be spent practicing how to decide which quantity is the dividend and which quantity is the divisor. There is even an activity idea noted.
- Students will respond to the hinge question using a whiteboard to record their expression. Then a sampling of the students will be probed further to ensure their thinking matches their expression.
- This hinge question represents a making math visible question because students are taking that story problem and translating the words into an expression to illustrate the action of the problem.
- The planning guide indicates students may respond in one of four ways:
- Students will have the correct expression.
- Students will reverse the two quantities.
- Some students’ oral responses will not match what is recorded on the whiteboard.
- Some students may pull out the four which indicates they’re not even sure which quantities they need to represent the problem.
Once we’ve made a plan for how to use a hinge question to gain a better understanding of what our students know and understand, the next step is to insert the hinge question into a lesson and take action based on the students’ responses.
Sound Off! How might you use a hinge question to formatively assess your students?
- Fennell, F., Kobett, B. M., Wray, J. A. (2017). The formative 5: Everyday assessment techniques for every math classroom. Thousand Oaks, California: Corwin.
- National Council of Teachers of Mathematics. (2014). Principles to actions: Mathematical success for all. Reston, Virgina: The National Council of Teachers of Mathematics.