Association of Teachers of Mathematics in Maine
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Chapter 3: Response Choice 1

07 Jan 2019 8:24 AM | Anonymous member

Make notes of the questions you typically ask in your math lessons. Think about them in terms of the focusing and funneling questions framework discussed in this chapter.


1. Which way does your questioning sequence lean?

2. How can you make focusing questions a stronger presence in your mathematics classroom?

Comments

  • 08 Jan 2019 10:00 AM | Colin Bacon
    Thinking back over the last couple weeks and the types of questions I've asked my students, I think I lean more into funneling that focusing. That being said, there are definitely examples of both. I think the clientele of students is super important when it comes to what kind of questions are asked to move forward. I also think that the type of learning that's occurring is super important when deciding how to drive the lesson with questions. For instance, when the topic is mostly surface learning, such as introduction of a new concept, focusing questions can be very helpful for engaging students in the material and peaking their curiousity. "OK, when I throw this ball in the air, what is going to happen? Have we seen examples of the ball's movement so far in our learning? How might we predict where the ball will land?" Focusing questions are also great when students are struggling, and you don't want to "force" them to an answer. I use focusing questions often when going over a student's incorrect answers on assessments. "OK, so what strategies do we have to approach the zeroes of a polynomial? Given this problem, which approach seems like it would make sense to you? Why?"

    I think there's a place for both varieties of questioning in a math classroom. The reality is, we often fall too quickly into funneling questions, because we want lessons to keep moving forward and we don't want to be bogged down in those awkward moments, where the only thing that can be heard during a lesson are the crickets outside the window. HOWEVER, trying to stick entirely with focusing questions can definitely leave a class floundering, when their understanding isn't where it needs to be. Trying to convert to focusing questions is great for opening student engagement and increasing buy-in. It's also great for encouraging problem-solving and critical thinking. But focusing questions will only work if the student has at least a decent understanding of what's going on. When playing "catch-up" with a student, I do find that funneled questions streamline the process, and students do get to where they need to be.

    I felt as though the chapter definitely tried to make a point that we should always strive for focusing questions. And I understand the philosophy, but disagree with the practicality. I think there's a time and place for both.
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    • 22 Jan 2019 8:47 AM | Anonymous member
      Colin, I do see your point about there being a time and place for both to avoid awkward moments but those could be times when the focusing questions need to be rephrased differently or students could ask clarifying questions. This is also a great time where students can work on persevering and teachers can help support productive struggle. This can be difficult when learning new material and students do not have much prior knowledge to use when trying to answer focusing questions.

      Focusing questions really puts the cognitive demand on the students unlike funneling which seems like the teacher is doing more work than the students. I have seen this several cases where teachers have used funneling questions and the students just wait for the teacher to guide and eventually give the answer. The focusing questions really do allow more thought from the students. Funneling questions also put more emphasis on the answer than the strategy used.
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  • 09 Jan 2019 5:02 PM | Anonymous member
    Recently, I've tried to work on using more focusing questions in my instruction. I realized that with my middle level students I was sometimes falling into the trap of using too many funneling questions in groups where students didn't want to speak up and offer any input into problem-solving. Based on areas where my students have struggled in problem-solving, I tried to create similar situations where I've done a think aloud with solving based on a mathematical concept, and then I've asked students to struggle through something similar in order to better understand the concept. For example, I asked students to complete a question with exponents where there was a 4 number pattern in the units digit. I asked students if they noticed any patterns, and when they knew where to stop based on the patterns in order to help find the answer of 7^2018 power, and to find the units digit of the number. I found than when I am teaching concepts where students have less prior knowledge understanding, that I sometimes revert to funneling questions, and that I need to have a balance of the two questions, but that students will better understand a concept if they do progressive struggle with focusing questions. To continue working on using focusing questions, I need to be intentional with the questions that I give students. If I give them an open task to work on, it is easier to come up with focusing questions to solve the problems. One source I sometimes use for this purpose is the Illustrative Math website. I have found that the tasks on this website are aligned to curriculum standards, are worth the time to visit deeper with my students, and generally have a variety of cognitive demand including some deeper thinking opportunities.
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    • 22 Jan 2019 8:50 AM | Anonymous member
      Carolyn, I am happy to hear you have tried to use more focusing questions during instruction. You mentioned that you need to be intentional with the questions you give students. Do you ever write questions prior to the lesson based on what you think students will struggle with, have misconceptions around or need their thinking pushed? Sometimes thinking about how your students are going to solve the problem ahead of time helps you have focusing questions pre-developed going into the lesson.
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  • 12 Jan 2019 9:16 AM | Kim L.
    Do you have the kids who immediately ask for help when given a math task to work on independently? I sure do! I’m working on getting them to start thinking through the problems themselves, but I definitely use a mix of focusing and funneling questions.

    My first response to kids who ask for help is to ask them what they are thinking about a problem, and/or what they have tried so far. I ask what they think they should do next, and I tell them to try whatever strategy they have and see how it works. Those are focusing questions. If students come up with strategies that are somewhat random (like adding denominators and adding numerators), I ask them “why do you think that would work?” and/or “why does that make sense?” I’ll have kids diagram their thinking rather than just use numbers and then (hopefully) get them to talk about why their answer does or doesn’t make sense.

    I definitely also rely on funneling questions and cues, especially with struggling students, such as “if you multiply the denominator by 2, what do you have to do to the numerator?” I do try to ask why that make sense so they begin to practice explaining math thinking. The book mentions that “funneling questions can create the illusion of deep student learning but really, they only require the student to know how to respond to a teacher’s questioning pattern,” (p 90). My struggling students definitely do this, but my hope is that with practice they will start asking themselves the funneling questions. I also work hard on my facial expressions - in their quest to just “get the answer,” kids look for cues from my face when they ask a question rather than struggling with their own thinking. I’ve pointed out to kids that that’s what their doing - it usually makes them giggle.

    I need to try more questioning to activate background knowledge. Figure 3.5 gives prompts “Think about what you remember about …” and “What do you recall about …” which would be good starters for me. These might help my struggling students more than cueing them to the next step in a problem.

    I also sometimes rely on volunteers during class discussions, which gives the impression that more kids understand than they realistically do - in a 45 minute math class, time feels precious and sometimes I want the pace to be faster than it should be. I use popsicle sticks to choose groups sometimes, and I could use them during class discussions to keep more kids focused.
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    • 22 Jan 2019 8:56 AM | Anonymous member
      Kim, it can definitely be struggle using focusing questions when you know students are not quite ready for them. The idea that students will start asking themself the funneling questions would make sense if this is a practice you continually use. Once they can start asking themselves those questions then you can start asking those students focusing questions over time. There really needs to be a classroom culture of mathematical discourse and the safety of it being okay to be wrong. Those things come over time but as it happens students become more used to the focusing questions.
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  • 13 Jan 2019 6:52 PM | Anonymous member
    "How did you get that answer?"
    "Can you explain your reasoning?"
    "Do we agree/disagree? Why?"
    "Can you tell me more ..."

    1. Which way does your questioning sequence lean?
    I feel that my questioning sequence is lean when I stick strictly to the program and the scripts provided by the program that I teach. While some of the program allows for deeper thinking and questioning, I feel that the time constraints placed upon the learning impacts the questioning sequence. I feel that my questioning becomes more "surface" questioning that is looking for the answer the less time that I have on the subject. When I worry less about "fitting it all in". I feel that I have richer discourse that takes place in the classroom.

    Also, I have found that when we focus less on the "Correct" answer, and more on the process, I have more students that are willing to participate in the discussion, because they are less worried about the accuracy of the answer, and more focused on how they got their answer.

    I find that some of the program that I teach can be very much funneling questions, guiding students to think and answer using a specific strategy. And they are introduced to a variety of strategies, and then asked to use specific strategies when answering questions on assessments. Instead on focusing on a strategy that works for the individual, they are expected to apply all the strategies to gain an appropriate response to the question.

    2. How can you make focusing questions a stronger presence in your mathematics classroom?

    In my experience, students are more likely to engage when they don't know the "right" or "wrong" answer. When reviewing Chapter 3, I found that I use focusing questions frequently in the classroom, as my goal is for students to "do the heavy lifting." By asking focusing questions , students guide the lesson based on their background knowledge. This allows for more student engagement, encouraging them to think about their answers and provide a reason they got their answer. Eventually the students get there by sharing their thinking and reasoning with others, which helps guide them, rather than depending on the guidance from the teacher.

    Sometimes we need to let go of the reigns, and let the students do the heavy lifting.
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    • 22 Jan 2019 9:10 AM | Anonymous member
      Holly,
      "Sometimes we need to let go of the reigns, and let the students do the heavy lifting." Absolutely! I keep finding that when teachers let go of the reigns their students surprise them. I have seen this happen several times this school year being in and out of classrooms. Without giving students a chance to open their wings and soar on their own, as teachers, we will never know what they are truly capable of. It sounds like the program you are using does not necessarily allow for that, are you in a situation where you have scripted conversations with your students based on the program you use?
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      • 19 Feb 2019 1:28 PM | Anonymous member
        The past two years that I have been teaching primarily math, I have had "scripted" programs, which allow for little flexibility with questioning. I do "go rogue" occasionally, and have students really try to dig deeper and explain their thinking and reasoning in order to better understand the concept. Whenever I can jump on the opportunity to allow them to "think deeper", such as review days or flex days, I feel that the lessons are more valuable and meaningful to them.
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  • 15 Jan 2019 7:23 PM | Deleted user
    First, I found this chapter very interesting because it really made me think about the kinds of questions I ask. Over time, I think I use both focusing and funneling questions. As others have stated, sometimes I feel constrained by time and tend to ask those to-the-point funneling questions to lead students to get to the correct answer or to demonstrate a particular strategy or simply to have a reluctant mathematician participate in a discussion. However, I am really trying to focus on having students understand concepts and become independent problem solvers. I am taking part in a professional learning group on teaching math at the third grade level this year so I am spending less time on "exercises" and more time having kids solve more complex problems and having them share strategies. When I am working with individuals or partners on these problems, I tend to ask more questions such as "What are you doing to get started on this?' or "Does the modeling you are doing fit the problem? If so, show me!" "Does the answer you have check? Does it fit with what you knew at the beginning?" As Holly stated, I want kids "to do more of the heavy lifting."
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    • 22 Jan 2019 9:21 AM | Anonymous member
      Pat, the time constraint is definitely hard and makes it difficult to be able to build in the focusing questions. Having tasks that promote reasoning and problem solving really does help open up more opportunities for using focusing questions. I like the question "Does the modeling you are doing fit the problem?" and asking students to show you. That does not tell students whether they are correct or not it is just asking them to justify the strategy they used.
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  • 21 Jan 2019 8:55 PM | Anonymous member
    This is something I have used more and more since working with Kelly Adams at Whittier! She is very good at this (hopefully she will chime in!) I find that I have to use focusing questions not only to get students to think deeper and look for understanding, but as a talk moves strategy in order to get students to listen to one another and participate even if they aren't raising their hand. I spent some time studying talk moves with the NGSX program through Next Gen Science, and I really find that these apply in Math as well. So, even if I start with a funneling question, like "What is my next step here?" I then will switch over to a focusing question, "Can someone explain why ___ said ___? How can that help us?" Middle School students are so trained for back and forth teacher talk which involves "right" and "wrong" answers. It takes months to get them to answer questions in a different way. Another strategy I use is to give the answer right away. I know the answer is ___. I don't care as much about the answer as how to get there. Can you back up and tell me what strategy you used to get that?
    Of courseI am never satisfied with my questions and always look for ways to improve. I would like to spend more time on questions and be able to pause and discuss longer, I tend to move on too quickly. Also, I use questions for teaching more than I use them for assessing. I would like to be able to use these strategies to tease out what students know more often.
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    • 22 Jan 2019 9:40 AM | Anonymous member
      Heidi, I appreciate you mentioning how well focusing questions go along with talk moves and helping students listen to one another and participate in the conversation. This is a part I feel is so important when it comes to mathematical discourse and focusing questions are directly tied to it. I am interested in hearing some more about the NGSX program and what you are learning in relation to talk moves. I think the focusing questions really are good formative assessments, if you ask the right questions, it will definitely help inform your instruction, jot down notes on student responses and then plan from there.
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  • 22 Jan 2019 8:27 AM | Anonymous member
    I would say that I lean heavily in the focusing direction, that has always fit with my teaching style. With that being said as I begin my new semester I'm going to try to be mindful if what I think is happening really is happening. I will admit that when we are pressed for time or I am doing a review I tend to move to the funneling questions. I think especially during review, whether at the end of the chapter or when going back over previous learned material, funneling questions can be appropriate. I don't think it should be done all the time and I certainly agree that focusing questions are a much more effective learning tool, but I think there is a place for both in the classroom.
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    • 22 Jan 2019 9:42 AM | Anonymous member
      Tennille, I had not thought about using funneling questions as part of review. I understand that students would have already learned the strategies and skills and are just doing a quick review but when doing so, are you turning to focusing questions when students are truly stuck and need to really think more deeply and call on their prior knowledge?
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      • 20 Mar 2019 9:27 PM | Anonymous member
        I would definitely turn to focusing questions if students needed the help, but if that behavior is being displayed when the students should already know the material it may be time for one-on-one time, as that shouldn't be the norm in a review setting.
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  • 22 Jan 2019 4:48 PM | Anonymous member
    Initially, discussions in my classes start with a few questions that would fall into the funneling questions category. My goal is to make sure the students all share an understanding of the vocabulary needed for discussion as well as any needed surface learning concepts. The questions will then move to prompt the students to discuss the reasoning behind their problem-solving. What I need to develop are questions that direct the students to greater depth and complexity of thought. “Good questions are seldom spontaneous.” (page 93) Planning for lessons requires thought about where the students are in their understanding and then preparing questions to move them from surface learning to deep learning. I am looking forward to the next couple of chapters that I hope will give suggestions for this.
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    • 30 Jan 2019 3:11 PM | Anonymous member
      Mary, I agree that questions really need to be prepared ahead of time to ensure that deep learning is taking place. You have to predict what your students are going to be thinking ahead of time, then prepare focusing questions to ask and when to ask them.
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  • 23 Jan 2019 10:13 AM | Jenny Jorgensen
    I think there's a time for both types of questions, funneling and focusing. I was reminded about the teaching practice, Pose Purposeful Questions, on pg. 86 and that's how I should be thinking about the types of questions that I ask.
    Like many of the responses, I find that I can slip into the funneling questions if I'm not paying close attention. I think that "time" tends to sometimes influence the type of question that I ask, if I see that we are almost to the end of our work time, I tend to slip into funneling and know that's not a good thing. With the students that I'm teaching, a no credit community college math class, it's important that students learn to problem solve and funneling questions do not help them with this. I need to ask them: What do you know already? What are you trying to solve? Have you talked with someone else? What have you done so far and what does your work represent in relation to the problem?
    I like that questions should be an "invitation" (pg. 89) for students to think and respond. My questions need to push "students to do the cognitive work of learning" (p. 89) and not make the problem easily solved without understanding.
    I liked the description of the two types of questions in that funneling might be thought of assessing what the student knows, whereas focusing questions should help advance student learning.
    I think my questioning leans toward focusing but think that I can work to make it even a greater percentage of my questioning technique. Keeping the goal for the students in mind will help with this - it's not all about the answer, it's much more about helping students become problem solvers. If I keep this in mind, I think I am less likely to jump to a funneling question.
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    • 30 Jan 2019 3:16 PM | Anonymous member
      Jenny, I think it is so easy to slip into the funneling questions. Knowing you only have so much time and need to get through a lesson can make it challenging to really focus on focusing questions. I think you have a great perspective coming from high education and would be interested to see how student learning advances when asked focusing questions. Thinking back on my own education prior to college I know I was always asked funneling questions so when I started getting asked why and having to share my thinking was terrifying to start.
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  • 26 Jan 2019 7:18 AM | Cynthia Snow
    As part of my Math Worshop routine, I conference with each student weekly, which gives me information about how they are doing on the standards we are working on presently. My questioning sequence is always the same..."What are you working on as a mathematician? "What are you doing well?"Once I ask these questions and look at the work the student is doing I can decide how I'm going to work with the student and what further questions I'm going to ask. This interviewing and information gathering helps me to decide what support to give the student and many times after a little coaching I leave a post it note behind with simple graphics and words to serve as reminders. I would say this routine would be more of a focusing question routine. After reading chapter 3 the useful questions on p. 92 will be added to my routine because I think they will give me more information so I can improve my instruction.
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    • 30 Jan 2019 3:21 PM | Anonymous member
      Cynthia, the idea of conference with each student weekly sounds great. I can definitely see the questions on page 92 working well during conference time with your students. If a student shares a spot where they may be having some challenges, I think the questions on 92 should really help get to the deeper understanding the student has or does not have.
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  • 27 Jan 2019 3:54 PM | Anonymous member
    Since reading this book and Principles to Actions, I have been leaning more toward focusing questions, but I do not feel I am as comfortable or as skilled at these types of questions as compared to funneling questions, which I feel I have used more of in the past. Having possible questions prepared prior to each lesson would help me to use more of these types of questions until I am more comfortable and able to ask them more readily, or I become more practiced with these types of questions.
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    • 30 Jan 2019 3:24 PM | Anonymous member
      Kristin, it is definitely easier to use focusing questions when you plan them out ahead of time. Trying to predict what your students know on already or may have for strategies can help you plan out those questions. I could also see have the questions from page 92 on a small chart in my classroom to refer back to. This could help me remember my questioning but students could also use it to question each other during discussions.
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  • 28 Jan 2019 6:05 AM | Anonymous member
    I tend to start out with focus questions and when I feel like we are getting nowhere, I tend to switch to funneling questions. I also find that with my low level class, there is more funneling questions than focus questions. I am trying to get the students to ask themselves the same questions. I really need to work on thinking about what focusing questions I am going to ask ahead of time and to have perseverance. When the students have no response to my focusing questions I need to think of other ways to ask the same focusing question and try to push their struggle instead of giving up and falling back on funneling questions.
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    • 30 Jan 2019 3:28 PM | Anonymous member
      Renee, I like that you mentioned perseverance and struggle in your post. When using focusing questions students really need to persevere when it comes to sharing what they know and as a teacher you have to support productive struggle. That being said you also don't want them floundering so I see where the focus questions would come in. Sometimes I question myself when I see students getting to frustrated and starting to flounder, do they have the prior knowledge needed to do and share what I am asking of them?
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  • 24 Feb 2019 10:26 AM | Pam Coulling
    Hello,

    It is interesting, at the beginning of the chapter, when they talk about time as a consideration and not timing or rushing students. I would love to give the students all the time that they need, but at the upper levels (whether it be a quarter, trimester, or year-long class) time is always a factor. Given a certain number of units, with a certain number of concepts w/in a unit, and ‘x’ many days for teaching, monitoring progress, and assessing, time seems to be the make or break issue for students (and their proficiency).

    In regard to questioning techniques, I use a combination of funneling and focusing, especially at the beginning of a unit when I am trying to get students to make connections to prior learning. I will sometimes do a quick all class discussion (using diagrams or skill processes). At other times, I have developed a set of questions for the students to answer individually to the best of their ability (to pre-assess their knowledge retention). In geometry class, this can help them review vocabulary, algorithm, or concepts (e.g. angle relationships).

    Units like Trigonometry and Measurement more readily lend themselves to applications of mathematical processes. As I help students with the Circles unit, the central, inscribed and exterior angles portion is much different learning the equations of circles. The application Geogebra can be used to allow students to dynamically explore relationships and answer questions (or develop a hypothesis). I use the Pythagorean Theorem to make connections to the equations of circles, but haven’t yet come up with a way for students to lead themselves into creating the equations. On the higher level end, giving them a center and a point on the circle and asking them to determine a radius (without prompting) promotes more “student” cognitive work.

    Pam
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    • 25 Feb 2019 10:08 AM | Anonymous member
      Pam, I completely agree with you about time. As much as we would like to say that we are not "timing" or rushing students, in the current educational system we do have time constraints. By the end of the school year or course, all work needs to be completed. It seems to be that there are definitely times when funneling and focusing questions would be appropriate. Finding out what prior knowledge students have would definitely help you understand if you can do more focusing and less funneling. If students really have no prior knowledge then funneling may be more appropriate to start.
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  • 10 Mar 2019 9:52 PM | Anonymous member
    After reading this chapter I realized that I have been using more funneling questions with one of my remedial math classes and more focused questions with a geometry class. I need to increase the use of focused questions in my remedial math class.
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    • 11 Mar 2019 3:13 PM | Anonymous member
      Allicia, That is an interesting realization you had. Do you think there is a reason why you may have been using more funneling questions with your remedial and class and focusing with your geometry?
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