Asking Questions and Promoting Discourse
Read more on how to implement these tips:
Observe another teacher. Pay particular attention to the questions the teacher asks the class and also individual students. Were the questions effective? How can you tell? Did the questions result in single answers or explanations from the students? Were you able to tell if the students had a true understanding of the mathematical topics? What kind of questions would you suggest to the teacher? When observing another teacher, consider how they are encouraging participation from all students. Are they using wait time effectively? Are they providing different ways for students to demonstrate their understanding?
Reflect on the questions that you pose in your own classroom. When reflecting on your teaching practice, use the Question-Listen-Question technique to evaluate the effectiveness of your questions. Record yourself teaching, then review the conversation to focus on the interaction after posing a question. Ask yourself: Do your questions prompt students to develop deeper understanding or guide them to a desired answer? Do they encourage critical thinking and discussion or quick responses? Are students learning from the series of questions or simply recalling facts? By reflecting on these questions, you can refine your practice to promote deeper mathematical thinking and understanding in your students. Utilize a variety of open-ended- techniques to engage students in active observation, thinking, and learning. Try these techniques:
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Use "
Notice and Wonder" prompts to engage students in active observation and inquiry. This technique encourages students to observe mathematical patterns, make connections, and generate questions about what they see. This approach is particularly effective in promoting identity development, as students' observations and questions become an integral part of the learning process. By giving students the space to notice and wonder, we are acknowledging their agency as mathematicians and mathematicians-in-the-making, empowering them to drive their own learning and develop a sense of pride in their abilities.
- Utilize the "
5 Practices of Productive Discourse" framework to structure effective classroom discussions. This framework includes anticipating student responses, monitoring understanding, selecting strategic questions, sequencing discussions logically, and connecting ideas to deepen understanding. To further enhance this process, incorporate advancing questions that challenge students' thinking and deepen their understanding. For example, after a student responds, follow up with questions that prompt the class to explore connections and implications further. This combined approach ensures that classroom discourse is both structured and thought-provoking, fostering a richer learning experience.
Respect diverse perspectives and model active listening. Imagine a classroom where every student is empowered to reach their full potential. As educators, you hold the key to unlocking this kind of learning environment. By creating engaging, thought-provoking lessons and fostering a culture of inclusivity, empathy, and mutual respect, you can encourage students to connect with their peers and with you. Respect diverse perspectives and model active listening to promote thoughtful, respectful discourse and participation. Embrace a growth mindset where students feel comfortable taking risks, asking questions, and learning from their mistakes.
Students are responsible for their own engagement through active listening and participation. They should communicate their thoughts and disagreements respectfully, using phrases like, "I got a different answer, I wonder if..." or "I respectfully disagree because it does not follow the rules of mathematics. I approached it another way, I wonder if...". By providing a variety of tools and creating opportunities for students to share their perspectives and learn from each other, you can establish a collaborative environment. This approach empowers students to take charge of their own learning and growth, creating a classroom where everyone feels seen, heard, and valued.
Use a variety of question types to gauge students’ understanding. When gauging students' learning in math class, it's essential to ask a variety of questions that encourage critical thinking, communication, and reflection. Open-ended questions can help you understand students' thought processes and identify areas where they may need additional support. Probing questions can uncover students' thought patterns and help you diagnose misconceptions. Higher-order thinking questions can assess students' ability to apply mathematical concepts to real-life scenarios and make connections to broader mathematical ideas. Self-reflection questions can help students identify their own strengths and weaknesses and develop a growth mindset. Modeling and visualizing questions can encourage students to think creatively and develop their spatial reasoning skills. Finally, discussion and connection questions can foster a sense of community and help students see the relevance of math to their everyday lives. By mixing up the types of questions you ask, you can get a more comprehensive picture of your students' understanding and provide targeted support to help them deepen their learning.
Identify, in advance, the big ideas that your lesson examines and the mathematical outcomes that students should achieve. Before teaching, identify the key concepts and mathematical outcomes that your lesson will cover, and anticipate various approaches students may take to solve problems. Prepare questions that address these different approaches and common misconceptions, encouraging discussion about when each approach is most effective and why certain misconceptions are flawed. Additionally, consider incorporating real-world data sets or problems that resonate with students' diverse backgrounds and experiences. By doing so, you'll create a lesson that is engaging, relevant, and effective in promoting deeper understanding and critical thinking.
Use Fermi questions in your classroom to encourage multiple approaches, emphasize process rather than product, and promote non-traditional problem-solving strategies. Fermi questions are unexpected questions about the natural world whose answers are rough quantitative estimations. When asking
Fermi questions, it's essential to use examples that reflect the experiences and backgrounds of students from different cultures and communities. This can help create a sense of relevance and connection to the math and can also help to promote diversity and inclusivity in the classroom. For example, instead of asking "How many drops of water are in Lake Erie?", you could ask "How many gallons of water does a family in a drought-affected area need to conserve each month?" or "How many pounds of food does a refugee family need to collect each month to survive?" By using examples that reflect the diverse experiences and backgrounds of your students, you can help to create a more inclusive and supportive learning environment.
Boost participation & gauge understanding with tech-enhanced questions. Offer students the choice to respond to closed-ended questions using traditional thumbs-up/thumbs-down gestures, or leverage technology with online polls or interactive whiteboards. Embrace technology and use online polls or interactive whiteboards to encourage participation in closed-ended questions. This allows everyone to respond anonymously, fostering inclusivity and reducing student anxiety. Bonus: Real-time data visualization on these platforms can give you immediate feedback on student understanding, allowing you to adjust your lesson plan as needed.
Make math fun and reflective.
Games and activities are a fantastic way to engage students in math. But to maximize learning, take it a step further! After the game, incorporate a "thinking reflection" activity. Ask powerful questions that prompt students to explain their reasoning and problem-solving strategies. For example, instead of just asking if they won, ask:
- "What strategies did you use to be successful?"
By encouraging metacognition (thinking about their thinking), students solidify their understanding and develop stronger problem-solving skills. This approach transforms a fun game into a valuable learning experience.
Use students' questions to evaluate your own progress. Student questions are a goldmine for gauging your teaching effectiveness. Are you fostering a culture of curiosity where students ask questions that spark deeper exploration and lead them towards discovering new mathematical relationships? Go beyond procedural questions: Pay attention to the types of questions students ask. Are they focused on completing tasks ("Will you work number six?") or on bigger ideas ("What would happen if we changed this parameter?")? Strive for the latter! By encouraging questions that delve into "what ifs" and explore the "why" behind the math, you can transform your classroom into a space where students actively participate in the discovery process and develop a deeper understanding of mathematical concepts.
Pose an unanswered question to challenge your students. Pose open-ended questions that challenge your students to think critically and creatively, without providing a clear answer or solution. Allow them to explore, research, and develop their own theories, and be prepared to reveal the complexity or uncertainty of the problem later. By doing so, you're preparing students for real-world mathematics, where answers are not always clear-cut. Use real data sets to ask open-ended questions that encourage students to think critically and make their own conclusions, such as "What insights can you gain from this data set?" or "Which graphical representation is most effective for illustrating this data and why?
Emphasize engagement and productive struggle in learning. Base the success of your lessons on the extent of students' engagement with ideas rather than their immediate happiness. Encourage your students to embrace and navigate the struggle inherent in the learning process. Present them with challenges that require deep thinking and problem-solving, rather than always offering questions with obvious solutions. When students are uncertain about where to start, guide them with prompts like, "Is there something you can try that might work?" and "Are there any mathematics tools (technology or manipulatives) that could help?" Incorporate modern teaching practices such as collaborative learning, inquiry-based approaches, and the integration of digital tools to enhance their problem-solving experiences. This approach not only builds resilience and critical thinking skills but also prepares students for real-world applications of mathematical concepts.
Enhance student learning through collaborative quizzes. Periodically incorporate partner or group quizzes allowing each pair or group to ask the teacher just one question. This practice encourages students to ask thoughtful questions and promotes student-student discourse. Because they are limited to one question, students will be more inclined to discuss and justify their reasoning with each other. Ensure that the questions for the collaborative quiz are more complex than those for individual assessments to encourage meaningful collaboration. Allow them to ask for anything except the answer, and you'll often find that groups turn in their work without needing to ask a question. This method fosters deeper understanding, teamwork, and communication skills among students.
Use reverse engineering in problem solving. Use the strategy of providing students with an answer and asking them to create the question. Tailor this approach to fit the needs and abilities of your students. For younger children, be specific: for example, "Write a story problem that has an answer of 20 cookies," specifying the units to guide their thinking. You can further refine this by adding conditions, such as requiring the problem to involve subtraction. For older students, have them create problems and then exchange papers with a peer, without providing the answer. Follow up with a discussion focused on identifying problem-solving hints, extraneous information, and the challenges encountered. This method encourages creative thinking, deepens understanding, and enhances students' problem-solving skills through peer collaboration and analysis.
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