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Insights Into Algebra 1 - Teaching For Learning
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Workshop 8 Mathematical Modeling Teaching Strategies
Teaching Strategies:

Listening to Students

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NCTM Standards


Listening to Students

Effective Questioning and Listening
The Classroom Environment

According to veteran teacher Steve Reinhart, students can sometimes be the best instructors. In an April 2000 article in Mathematics Teaching in the Middle School titled "Never Say Anything a Kid Can Say," he wrote the following:

When I was in front of the class demonstrating and explaining, I was learning a great deal, but many of my students were not! Eventually, I concluded that if my students were to ever really learn mathematics, they would have to do the explaining, and I, the listening.
Listening to students, and using their responses to guide instruction, is a difficult, yet necessary, skill to acquire. It is impossible to promote learning without hearing what students have to say. The National Council of Teachers of Mathematics (NCTM) promotes active classrooms in which teachers gather information about students through questioning.

To ensure deep, high-quality learning for all students, assessment and instruction must be integrated so that assessment becomes a routine part of the ongoing classroom activity ... In addition to formal assessments, such as tests and quizzes, teachers should be continually gathering information about their students' progress through informal means, such as asking questions during the course of a lesson, conducting interviews with individual students, and giving writing prompts (Principles and Standards for School Mathematics, NCTM, 2000: p. 22)
Listening to student responses in class and during interviews helps teachers make informed instructional decisions based on what the students know and do not know. Listening also enables you to formulate questions that can help students develop deeper understanding.

Read what Orlando Pajon says about listening as a tool for assessment:

Read transcript from teacher Orlando Pajon
The purpose of the presentation, first of all, is that we want the students to tell us what they found out or what they learned... Read More

Effective Questioning and Listening

In order to use student responses to inform instruction, you must establish an environment in which students feel safe to respond. Ask questions that will encourage students to answer. Then, listen carefully to the student discourse so that you can frame additional questions that will bring a deeper understanding of the concepts and allow students to correct any misconceptions that they may have.

The following list of reminders for listening well and asking good questions is paraphrased from Steve Reinhart's "Never Say Anything a Kid Can Say."

Never say anything a kid can say!
This one goal will help to keep you focused. It requires you to develop and improve your questioning skills.

Read what Carol Malloy has to say about how Sarah Wallick uses student responses to guide a lesson:

Read transcript from teacher educator Carol Malloy
The [transmission factor lesson] was brilliant... Read More

Ask good questions.
Good questions require more than recalling a fact or reproducing a skill. A student should learn by answering your questions, and you should learn about your students' level of understanding based on their responses.
Listen to what Carol Malloy has to say about Sarah Wallick's questions:

Listen to audio clip of teacher educator
Carol Malloy
Sarah has a talent for asking students questions and allowing them to say exactly what they mean, but also explain why they feel that particular way... Read More

Use more process than product questions.
Product questions - those that require short answers or a yes or no response, or those that rely almost completely on memory - provide little information about what a student knows. A process question asks the student to reflect, analyze, and explain her thinking.

Instead of giving a lecture, ask a series of questions.
Use student responses to disseminate the information that they need to know. If you think that a lecture might be a better format, ask yourself the humbling question, "How many of my students will actually be listening?"
Read what Sarah Wallick has to say about using questions to guide instruction:

Read transcript from teacher Sarah Wallick
One of the advantages of using this exploration model rather than direct instruction is that it allows students to be able to develop the ideas on their own... Read More

Read what David C. Webb has to say about Orlando Pajon's use of questions:

Read transcript from teacher educator David C. Webb
You'll notice that Orlando continues to draw from students' informal ideas... Read More

Be patient.
Wait time is important. Most students need to time to process their thoughts and to gain the courage to raise their hands. By always calling on those who raise their hands first, you cheat those students who need more time to generate a response to your questions. When you show students that you are willing to wait and let them think about a question before they respond, you will be rewarded with more thoughtful responses.
Reflection:
In addition to the suggestions given above, list at least two other strategies you use to ensure that you ask effective questions during a lesson.

record your thoughts in your journal



The Classroom Environment

A prerequisite to listening to students is encouraging them to share their thoughts. A supportive classroom environment, in which students believe that their opinions are valued, develops over time. Interaction will likely not happen on the first day of the school year, but with careful planning, students will grow more comfortable sharing their mathematical thoughts.

A corollary to the "be patient" rule is "be uncompromising." While it is important to give students enough time to think about an answer, it is equally important to require students to express their thoughts. Allowing students to remain quiet during classroom discussions sends the message that their thoughts are not important and, more generally, that classroom interactions are not necessary for learning.

Listen to what Sarah Wallick has to say about promoting classroom interaction:

Listen to audio clip of teacher
Sarah Wallick
At the beginning of the year, my students were not as forthcoming ... Read More

Once students begin to express themselves in the classroom, they will continue to do so only if they can see that the teacher values their responses. It is a teacher's responsibility to provide an environment in which students feel safe to share ideas.

In addition, students must understand that everyone in the classroom has a responsibility to listen carefully to every speaker. For successful interactions, students must listen to the teacher, and students need to listen to one another, too. Often, in the course of discussion with a classmate, a student will recognize an error in their thinking. And many times, an explanation from a peer will be far more effective than a lecture from a teacher.

Read what Sarah Wallick has to say about students listening to one another:

Read transcript from teacher Sarah Wallick
When a student comes out with a really good point and nobody else is listening except me, then nobody else learns anything... Read More

Read what Carol Malloy has to say about students speaking with one another about mathematics:

Read transcript from teacher educator Carol Malloy
There was a conversation going on about, "Well, how do you know how many times this [pulley] goes around? How do you figure it out in the very beginning of the problem?"... Read More

To promote classroom interaction and foster a safe environment, teacher and peer reactions to a student response should be nonjudgmental. Most teachers understand that negative reactions are hurtful - an unsatisfactory answer from a student does not require a harsh critique, especially in front of the rest of the class. But it is important to remember that a positive reaction can also have a deleterious effect on class participation. Imagine being a student in a math class, and the teacher says to a classmate, "Wow! What a fantastic answer! That's tremendous! Okay, who's next?" How likely would you be to raise your hand and attempt to follow that? Even the most confident student wouldn't want to have to go next, let alone the shy teenager who lacks self-confidence.

Read what David C. Webb has to say about developing an effective classroom environment:

Read transcript from teacher educator David C. Webb
Such a classroom is not developed overnight, and students don't necessarily come into a teacher's classroom ready to engage in these types of lessons... Read More

Reflection:
Explain how you might implement one of the strategies discussed above to increase the potential for learning in your classroom.

record your thoughts in your journal

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