This is the third in a series of instructional articles to support teachers in implementing the 8 Effective Teaching Practices outlined in the book Principles to Actions: Ensuring Mathematical Success for All. This article discusses teaching practice 5: Pose Purposeful Questions.
“Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.” (Principles to Actions, 2014, p. 35) It is through questioning that teachers are able to determine the level of student understanding. The type and pattern of questioning plays a major role in collecting the evidence of the level of student s’ understanding.
Principles to Actions identifies four types of questions teachers often use in instruction: gathering information, probing thinking, making the mathematics visible, and encouraging reflection and justification. It is best to include a mix of question types in your classroom instruction. One would use gathering information questions for lower level responses from students. These responses would be the recall of facts, definitions, or procedures. Probing thinking questions would require students to explain, elaborate, or clarify their thinking. Making mathematics visible questions would be a way to support and foster mathematical discourse as these types of questions require students to discuss mathematical structures and make connections among ideas and relationships. The final question type, encouraging reflection and justification help to reveal deeper understanding of reasoning and supports students in engaging in mathematical arguments. As you can see, the four types offer a variety of cognitive demands to engage students as they respond.
In addition to the types of questions, we must be asking our students the pattern we use while asking questions which will also have a great impact in gathering evidence of student thinking. There are two pattern types that have been identified: funneling and focusing. The funneling pattern does just what its name suggests. Teachers use this pattern of questioning to guide/control the direction of the discussion and the learning, leaving very little room for students to draw their own conclusions about the topic. All four types of questions may be used in the funneling pattern, but the end result of the discussion is predetermined by the teacher. The focusing pattern allows the students to guide/direct the discussion. While using the focusing pattern, the teacher encourages and supports students to explain their thinking and to justify their decisions. This does not mean there is no end goal for the discussion, just that there is flexibility in the pathway that is taken and that pathway is student-led rather than teacher-directed. Just as the funneling pattern uses all four question types, so does the focusing pattern.
It is important to note that one type or one pattern of questioning is not better than another type or pattern. It is the use of all types and all patterns of questioning that is most powerful.
Some additional resources teachers may find helpful in fine tuning their questioning techniques are:
Mentoring Minds offers Critical Thinking Question Wheels that provide question stems for various levels of cognitive demand, NCTM Principles to Actions toolkit has resources available to NCTM members to support teachers in understanding and implementing the 8 teaching practices, Ontario’s Capacity Building Series resource, Asking Effective Questions provides tips and strategies for provoking student thinking through the use of questioning in the mathematics classroom, and Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement describes 10 instructional shifts, the associated research, and a summary of what one should expect to see in an effective mathematics classroom. Three of the ten shifts are particularly supportive of posing purposeful questions. Educators across the state can support posing purposeful questions by making the three shifts below a routine part of their instructional practice:
- Create language-rich classroom routines
- Tie the math to such questions as: “How big?” “How much?” “How far?” to increase the natural use of measurement throughout the curriculum
- Make “Why?” “How do you know?” “Can you explain?” classroom mantras