Posing purposeful questions involves asking questions that deepen students' understanding of mathematics while providing information about their mathematical thinking.
National Council of Teachers of Mathematics, 2014
When teachers ask students questions, this is an opportunity to encourage them to think deeply about the mathematics they are working on. To ask purposeful questions you need to understand the mathematical content and to plan in advance what questions will best engage students in deep mathematical thinking.
Purposeful questioning can be scary to students—questioning can generate cognitive disequilibrium when it pushes students beyond their existing understanding, causing confusion and discomfort. But when you use questioning purposefully, you give students chance to grapple with unfamiliar mathematical ideas and new insights emerge. Cognitive reorganisation of the student’s current mathematical understandings occurs, and these new connections are added, and new understandings emerge.
reSolve tasks use questioning in a number of different ways and for different purposes throughout the Explore and Connect phases of a task. The only question posed in the Launch phase is the one which sets students on task. During the Summarise phase the students may be asked to reflect on what they have learnt during the lesson.
Questioning in the Explore phase
Assessing questions are intended to make a student’s current thinking visible, ensuring that the teacher understands what the student did and why he or she did it. Advancing questions are intended to move students beyond where they currently are, toward the goals of the lesson.
Smith & Stein 2018, p.44
As students explore a task, you can use assessing questions to…
- gather information.
- probe students’ understanding.
- make the mathematics more visible.
- get students to reflect on and justify their reasoning.
Assessing questions focus on the mathematics that students have produced, as well as what they understand about that mathematics. It is important that teachers actively listen to the student’s ideas, to establish what they actually understand and to help them advance this understanding.
An advancing question is a question you ask before you walk away from a student. It focuses and extends students’ existing mathematical thinking towards the mathematical goal of the lesson.
Questioning in the Connect phase
In the Connect phase your questions should be crafted around student solutions, to make the mathematics visible to students during the whole class discussion. Teachers intentionally select student solutions which are central to the key mathematical learning goals of the lesson, then use targeted, purposeful questioning to help steer the class’s attention towards seeing explicit connections between the student solutions and the lesson’s mathematical goals.
Questions in the Connect phase can…
- ask students why they used a specific strategy, rather than asking what they did.
- emphasise specific connections between student solutions and the lesson’s mathematical goals.
- make the mathematics visible to the presenter and the listeners.
Discuss with your colleagues:
- What questioning strategies do you use?
- How is your use of questioning similar to and different from the questioning described here?
References
Huinker, D., & Bill, V. (2017). Taking action: Implementing effective mathematics teaching practices in K-grade 5. Reston, Virginia: National Council of Teachers of Mathematics.
Imm, K. L., Fosnot, C. T., Dolk, M., Jacob, B., & Stylianou, D. (2012). Learning to support young mathematicians at work: An early algebra resource for professional development. Heinemann.
National Council of Teachers of Mathematics (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: National Council of Teachers of Mathematics.
Smith, M. S., Bill, V., & Sherin, M. G. (2020). The five practices in practice: Successfully orchestrating mathematics discussions in your elementary classroom. Reston, VA: National Council of Teachers of Mathematics.
Smith, M. S. & Stein, M.K. (2018). 5 Practices for Orchestrating Productive Mathematics Discussions. National Council of Teachers of Mathematics.