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How To Be Responsive Ifa Student Solves It One Way And Cant Think O

How to Be Responsive if… · A student solves it one way and can’t think of any other way: · Ask if they can draw a picture that shows the answer. · Ask if they can invent a new way to solve it. · Show them a method that they haven’t used and ask if they can figure out how it works and why. · A student solves the problem multiple ways easily: · Ask why they did what they did. Why do their methods work? Be specific about what you want to know. · See if they can come up with another method that isn’t as easy to find. · Ask the interviewee how their methods are similar and different. Be as specific as possible. · A student solves the problem incorrectly: · Remain neutral. · Ask the interviewee why they did what they did. Why do their methods work? · See if they can solve it a different way. Compare solutions. · Say, “I saw someone else solve it like this….and they got 90.†What would you say to that person? General Strategies for Being Responsive · Ask, “Why?†Why did they do …(be specific about what you want to know)? How do they know it’s mathematically correct? · Be patient. Use lots of wait time, and don’t answer your own questions. · Focus on understanding what they are thinking. · Ask them to make connections. · How is this the same as what you did in the first solution? · How is this different then what you did in the standard algorithm? · Ask them to generalize their strategy. · Will it always work to …? · What if it was … instead?

Solution Strategies and Chart for Students Strategy Example Probing Questions Direct Modeling Equal groups Array · How does this represent the problem? · Could you represent it in a different way? · 18 groups of 5 instead of 5 groups of 18 Traditional Algorithm · Why did you put a little 4 on top of the 1? · Why didn’t you put the little 4 on top of the 8? · What does the little 4 represent? Partial Products · How is the 40 represented in the traditional algorithm? · Why is it 50 instead of 5? · How did you know how to line up the 40 and the 50? · Can you apply this method to 32 x 9? Box Method · How did you know where to put the numbers and what to write in the boxes? · Why did you add 50 and 40? Distributive Property a(b+c) = ab + ac 5 x ( 10 + + OR 5 x (5 + 5 + + 25 + OR 5 x (11 + + OR 5 x ( · Why did you decide to break 18 into 10 and 8? · You broke the 18 into 10 and 8. If you broke it up differently, would your method still work? · Does the distributive property work with subtraction? Doubling/Halving 5 x 18 Double 5 → 10 Halve 18 → x 9 = 90 · Why does this strategy work? What is happening here? Repeated Addition 18 + 18 + 18 + 18 + 18 = 90 OR 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 18 · Is adding 18 five times the same as adding 5 eighteen times? Why? Associative Property 5 x 18 5 x (6 x x 6) x 3 30 x 3 90 · Why does this work? · Why did you choose to factor 18 into 6 and 3? image1.png image2.png image3.png image4.png image5.png Template for the Responsive Listening Interview Performance-Based Assessment #2 Due October 18 11:59 AM Who did you interview? How long did the interview last? Write a paragraph describing how the interview went in general. Responsive Listening Responsive Listening 1 Timestamp from your recording. Transcribe an interaction between you and the interviewee in which you demonstrated responsive listening. Why was this responsive listening? How did this interaction support and/or extend the interviewee’s thinking? Responsive Listening 2 Timestamp from your recording. Transcribe another interaction between you and the interviewee in which you demonstrated responsive listening. Why was this responsive listening? How did this interaction support and/or extend the interviewee’s thinking? Responsive Listening 3 Timestamp from your recording. Transcribe another interaction between you and the interviewee in which you demonstrated responsive listening. Why was this responsive listening? How did this interaction support and/or extend the interviewee’s thinking? Observational or Directive Listening In this part of the assignment, you need to provide three examples, each example can be either observational or directive. So, you might have 1 observational example and two directive examples. Observational or Directive Listening 1 Timestamp from your recording. Transcribe an interaction between you and the interviewee in which you demonstrated observational or directive listening. What type of listening was this? Why? If you could redo this interaction, would you do/say anything differently? If so, what? If not, why not? Observational or Directive Listening 2 Timestamp from your recording. Transcribe another interaction between you and the interviewee in which you demonstrated observational or directive listening. What type of listening was this? Why? If you could redo this interaction, would you do/say anything differently? If so, what? If not, why not? Observational or Directive Listening 3 Timestamp from your recording. Transcribe another interaction between you and the interviewee in which you demonstrated observational or directive listening. What type of listening was this? Why? If you could redo this interaction, would you do/say anything differently? If so, what? If not, why not? Reflection: Complete the Reflection by answering the following questions. · How did you feel during and after the interview? · What are your strengths related to responsive listening? · What areas do you want to keep working on? · What challenges do you expect to face related to implementing responsive listening when you are a teacher? Self-Assessment: · After you have completed your interview and the prompts above, reread your work, and then assess yourself using the rubric below. · Show your rating by changing the shading in the section to indicate a score of (initial, emerging, or proficient) that you have found your work falls under. · Write an explanation for why you gave yourself that rating. · Note: You do not need to turn in your recording of the interview. Keep it in case you need to go back and revise your work. Student Work Example Identifying Responsive Listening : Below is an excerpt from a student’s assessment. Notice that this student transcribes more than a single sentence. The back and forth between the student and their interviewee provides context that helps demonstrate that the student is listening responsively.

Paper For Above instruction

The importance of responsive listening in educational settings cannot be overstated, especially when engaging with students in mathematical problem-solving contexts. Responsive listening fosters a deeper understanding of student thinking, encourages critical reflection, and supports the development of mathematical reasoning skills. This paper explores various strategies and practices for effectively implementing responsive listening, particularly when working with students to solve math problems such as multiplication, and discusses how educators can extend and support student thinking through purposeful interactions.

Effective responsive listening begins with a mindset of openness and neutrality. Teachers must be patient, allowing students to express their ideas fully without interruption or premature judgment. This patience ensures a safe environment where students feel valued and understood. For example, when a student solves a multiplication problem differently from the standard method, a responsive listener might ask, “Can you draw a picture that shows how you arrived at your answer?” or “Can you invent a new way to solve this?” These prompts not only affirm the student’s effort but also invite them to explore their thinking further and consider alternative approaches.

One critical aspect of responsive listening involves asking targeted questions that probe the student's reasoning. For instance, after a student uses the distributive property to solve 5 x 18, a teacher might ask, “Why did you decide to break 18 into 10 and 8?” or “Does this method always work?” Such questions help clarify the student’s conceptual understanding and reveal their mathematical intuition. Additionally, encouraging students to compare their methods fosters meta-cognition—thinking about their own thinking—which reinforces their mathematical discourse skills.

Strategies such as drawing, inventing new methods, and analyzing different solution pathways serve as powerful tools for extending student thinking. For example, if a student solves 5 x 18 by repeated addition, a teacher might prompt, “Is adding 18 five times the same as adding 5 eighteen times?” This encourages students to reflect on their strategies and understand the underlying mathematical principles. Similarly, when students use properties like doubling/halving or the associative property, educators can deepen understanding by asking, “Why does this strategy work?” or “What is happening here?” These questions guide students toward recognizing mathematical patterns and relationships.

Implementing responsive listening also involves recognizing various types of listener responses. Responsive listening frequently includes asking clarifying questions, extending explanations, and encouraging students to generalize their strategies. For instance, after a student explains factoring 18 as 6 and 3, a teacher might ask, “If you broke the 18 into 12 and 6, would your method still work?” or “Can you apply this approach to a different multiplication problem?” Such interactions promote flexible thinking and transfer of knowledge across contexts.

Furthermore, teachers must be attentive to their own listening style—distinguishing between responsive, observational, and directive listening. Responsive listening involves actively engaging with students’ ideas without giving solutions prematurely, whereas observational listening might involve simply noting what the student says, and directive listening could involve leading the student to a specific answer or method. Understanding these distinctions helps teachers tailor their interactions to maximize student learning and engagement.

In practice, effective responsive listening requires ongoing self-awareness and reflection. Teachers should regularly assess their listening behaviors, identify moments of successful responsive listening, and recognize areas for improvement. This reflective practice enables educators to refine their questioning techniques and better support student reasoning. Ultimately, fostering a classroom environment rooted in responsive listening not only enhances individual student understanding but also cultivates a culture of thoughtful mathematical discourse, critical thinking, and lifelong learning.

References

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