yTaking Action Book Study: Chapter 5

Chapter 5

Pose Purposeful Questions

Reflect:

After reading Chapter 5, please reflect on the questions below and post your response by Tuesday. Feel free to respond to any of the questions provided or share something else that you intentionally did differently in regards to posing purposeful questions.

Please note: the prompts below are to help you reflect. There is not an expectation for you to respond to all {or even any} of the provided questions!

Respond:

Option 1:

Analyzing Your Questions for a Lesson

Teach a math lesson using a high-level task. Video or audio-record the lesson. Consider the extent to which the questions you asked -

revealed students' current understandings;
probed students' decisions by asking them to explain, elaborate, or clarify their thinking;
made the mathematics more visible and accessible for student examination and discussion; and
engages students with the reasoning of each other.

Then consider the discussion from an equity perspective:

Did historically marginalized students have equal opportunities to answer questions that probed their mathematical decisions and made their mathematical ideas visible, accessible, and valid for examination by other students?
Did some students only get asked information retrieval questions?

or Option 2:

Posing Assessing and Advancing Questions for a Lesson

Select an upcoming lesson that uses a high-level task. Identify the mathematics learning goal and anticipate student solution paths, including both productive and unproductive ways that students might approach the task.

Formulate both assessing and advancing questions aligned to your goals and the anticipated solution paths to ask students as they work independently or in small groups.
Teach the lesson and reflect on the ways the assessing questions gave you greater insights into student thinking and how the advancing questions moved student learning forward.

Interact:

On Tuesday, read your colleagues' reflections and respond to at least one other post by sharing a comment, insight, or interesting possibility by Friday.

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shawnseeleydotcom 44p · 271 weeks ago

While I was reading Chapter 5, I was making connections between my own teaching experience, my experience as a student, and the example teachers in the text. Much of my experience as a student matched the "funneling" teaching in the text, and if I'm honest, my first two years of teaching mathematics were similar as well. Last year, after attending NCTM in Seattle, I started to make a change in the way I teach math, and this year, I feel like I've changed even more. Although I still catch myself asking funneling questions now and then, I've become more intentional at using assessing and advancing questions most of the time. I found myself agreeing with the benefits of "focusing" questions, reflecting on times I had the most success with students in my classroom and tutoring over the summer.

The biggest takeaways for me from this chapter were to prioritize the quality of questions I ask students, to increase wait time (this is SO hard for me), and to anticipate student solution pathways so I can predetermine possible assessing and advancing questions for those scenarios. While I know we can never predict with absolute certainty just which strategies students will use in every situation, I believe that most often, if we reflect on learning trajectories/pathways and previous experience with former students, we can anticipate the most common student strategies and misconceptions we might encounter. When we have anticipated these strategies and misconceptions, we can better assist students in advancing in their understanding and scaffold appropriately, while still requiring students to "engage in high levels of thinking and reasoning" (p. 115). This anticipation phase of planning takes a lot of time; however, if we work as grade-level teams or even across grade-level teams, such as 3-5, this process can be expedited and enhanced as many minds make light work.

2 replies · active 270 weeks ago

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Stephanie Clement · 271 weeks ago

Shawn,

Wait time is really challenging for me as well! One time I waited 3 minutes for a student to respond...it felt like forever! I don't recommend that, but it is definitely something that I work on as well. I'm always feeling so rushed through my lessons and really need to slow down. I like your idea of anticipating student pathways. This will really help us prepare good questions to guide them.

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shawnseeleydotcom 44p · 270 weeks ago

Stephanie,
Three minutes is a lifetime! I can hardly wait 15-30 seconds without feeling like I'm going to have a heart attack.

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Stephanie Clement · 271 weeks ago

Last week, I taught a lesson using a practice performance task. We set up wipebooks on tables and I had random groups of no more than 3. All students had their own color pen and were able to participate on the wipebook. Looking back on the lesson I think that students revealed their current understanding by not only showing their work on the wipebook, but by also explaining how they got their answer to the class. I did walk around and probe students by asking them to explain, elaborate, or clarify their thinking. Students walked around the room, asked other groups questions about their strategies, and also shared their own strategies.
An area I need to work on is asking assessing and advancing questions intentionally. I tend to ask questions that guide them to the right answer, but I would like to try more advancing questions that really gets them thinking. I think that they will better understand the concept in the long run, by truly doing the thinking themselves. I think that a good variety of purposeful question (both assessing and advancing) can really benefit the students and their thinking. It will create engagement, and participation.

2 replies · active 263 weeks ago

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Caty · 271 weeks ago

Stephanie,

I feel like I am in the same boat as you :) I totally need to work on asking those questions without scaffolding them too much. I feel like I do it half the time and the other time I want them to be able to get to the right answer. I also think that the advancing and assessing questions can help with any type of learner. It can push those higher level thinkers and it can also help those who need a bit more support.

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Susan Heater · 263 weeks ago

I agree with you, Stephanie! I think that both the assessing and advancing questions can benefit student thinking. Explaining, elaborating, and clarifying their answers are definitely great ways to assess their knowledge on a concept. I feel that advancing questions can be more about giving them a challenge or getting them started, if they are stuck, without actually leading them too much. For me the advancing questions are more challenging for me to come up with when they are struggling because I do not want to overscaffold. It is much easier for me to ask advancing questions when kids are ready for a challenge.

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Julie Rodriquez · 271 weeks ago

Posing purposeful questions is the most challenging component for me. I think because it requires me to think on my feet and I am a planner. I love that the author provided a set of questions with the idea of recording the questions on notecards and keeping them handy until I become better at using advancing and assessing questions. I am planning to do this!

Today with our division unit, I was deliberate in considering how I worded my questions and math conversation. We started with two number talks (38 divided by 7; 285 divided by 5). I gave the students plenty of wait time to mentally think through the answer and their strategy. Then we had between 5 and 7 students share their strategies out loud. I tried to focus on having students identify similarities and differences between the strategies and between their own strategies. I asked students if they would consider using one of the shared strategies when they solved the next problem. Then we moved onto a partner problem where students worked together to model a division problem and then solve it using a strategy of their choice. Reflecting on how I shared the models, I realize I did too much of the talking rather than asking students to discuss what they noticed or wondered. I think this was because modeling a division problem appeared hard for many of my students (they wanted to go straight to solving with numbers) and so I started trying to explain the two models that were shared with some explanation from the students who created the models. I did notice when we moved onto the next problem that more students were using models/pictures to make sense of the division but I could have allowed for more student ownership. At the end of the lesson, I had one set of students solve the division problem 528 divided by 6 in a very creative way and we spent a lot of time as a class discussing how the strategy worked and how we could make sense of the math. Several students saw and communicated the information in a way different than I expected which was a positive thing and led to further discussion; however, I also caught myself trying to ask a purposeful question and then giving too much information, which then dumbed-down the conversation and the rich level of thinking. I know I am better at creating purposeful questions and building rich conversation into my math lessons than I used to be, but I also recognize there is still room for lots of growth.

2 replies · active 270 weeks ago

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shawnseeleydotcom 44p · 270 weeks ago

Julie,

I hear you on being a planner. A book that I read over the (5 Practices for Orchestrating Productive Math Discussions) summer really made me think about how I could plan for most of the questions I'd ask ahead of time. Thinking more on it, my wife likes to joke that I have to plan spontaneous, fun outings. This takes a bit of time up front, but the idea is that your learning goals would be spread over multiple lessons, all related to a rich task. I found success with this in our multi-digit multiplication and division units this year and know that I'll get better at it over time.

The basic idea of the five practices is below:

1. Anticipating
• Do the problem yourself
• What are students likely to produce?
• Which problems will most likely be the most useful in addressing the
mathematics?
2. Monitoring
• Listen, observe, identify key strategies
• Keep track of approaches
• Ask questions of students to get them back on track or to think more
deeply
3. Selecting
• CRUCIAL STEP – what do you want to highlight?
• Purposefully select those that will advance mathematical ideas
4. Sequencing
• In what order do you want to present the student work samples?
• Do you want the most common? Present misconceptions first?
• How will students share their work? Draw on board? Put under doc cam?
5. Connecting
• Craft questions to make the mathematics visible.
• Compare and contrast 2 or 3 students’ work – what are the mathematical
relationships?
• What do parts of student’s work represent in the original problem? The
solution? Work done in the past?

5 Practices for Orchestrating Productive Mathematics Discussions
by Amazon.com
Learn more: https://www.amazon.com/dp/1680540165/ref=cm_sw_em...

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Julie Rodriquez · 270 weeks ago

Shawn,

This is so helpful! Thank you for the resource and detailed information. I love the idea of solving the problem on my own and anticipating future student responses. I will definitely apply this set of steps to future lessons.

Julie

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Caty · 271 weeks ago

Just this week I did a rich task with wipe-books. I used one of the differentiated cards from unit 3 where students had to create a division word problem. In the beginning of the lesson I had them do a warm up, which in my opinion, is a high level task on its own. Then I started the lesson with a discussion about remainders and word problems. I could tell from our discussion that as a whole they did not have a solid grasp on what exactly a remainder can mean when applied to different types of word problems. The activity on the wipe books had groups of 2-3 create a division word problem, one group used the remainder as their answer and the other group used the quotient as their answer and ignored the remainder. I assigned each group randomly and as students were working on it I could not tell which group was which. Many students were unsure of how to incorporate the remainder as the answer. At the end I had students evaluate each others work and decided if there problem is where the remainder is the answer or is ignored.

As an area of weakness, I really want to work on asking more assessing and advancing questions. I feel like I am always guiding them with questions to help them achieve an answer rather than challenge their thinking. I will say I am good at walking away after asking a question because I do want them to think about what I said.

1 reply · active 270 weeks ago

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Julie Rodriquez · 270 weeks ago

Caty,

I love this approach of having the students create a problem. We are just starting our lesson on interpreting remainders and it is one of my favorite lessons but also one that challenges the students. I tend to give them lots of extra problems to solve with a variety of ways to interpret the remainder, but I love the idea of giving the students the task of creating their own problems. Renae shared this strategy last week in our training, too, so I am excited to apply it later this week! Maybe we should have our students or classes create a set of problems for each other and see if they can interpret which situation is happening??? Could be a good challenge for our fourth and fifth graders! And then we could practice on our advancing and assessing questions together. :)

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Christine Wilson · 271 weeks ago

When I was reading this chapter I really connected to this idea and how we can help student persist by asking the right kind of questions. Also, the type of question that sparks conceptual understanding. When I read "Segment 2" connected to the "Caterpillar Task" I was excited to see the connection between the two equations and thought teacher did a good job of drawing out how they work when asking the right questions. Then looking at the "Brownie Task" I loved Robert's example and thought about how to ask him to share his answer and thinking. One thing I know is that it is difficult to think of the right questions to ask in the moment so I notice in the prompts above it tells you to anticipate student solution paths and possible problem pathways. It seems tough but obliviously the right way to set yourself up for asking good questions. I can't wait to try it.

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Susan Heater · 263 weeks ago

There is a wonderful math challenge in the curriculum that uses tangrams to create quadrilaterals. Its starts with having the students use all of their tangrams to create the rectangle that is displayed. At this point I could ask how we know the shape they have made is a rectangle. This would be an assessing question as I would be asking for evidence. The next step is for them to use those same 7 tangram pieces to create a square. I could use an assessing question and ask how they know this shape is a square, and also to compare the shape they originally made and the square they had just made. Here is where I feel I could ask advancing questions. I could ask," I wonder if a square could be made with less pieces." or " I wonder if a square could still be made if you had more pieces" or "Do you think you could rearrange these tangram pieces into a square if I said that none of them could be in the same place they are right now?" I could also ask them to see if there are any other quadrilaterals they could make using those same 7 pieces. If a student was stuck, I could have them look at a different students' work and ask, "How is your work similar to (student name)? How is it different." This may get them back on track without telling them how to do the work.

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