A Conversation with Jon Star

I am currently part of a cognitive science inquiry group with about ten other math teachers. The goals of the group are to learn more about what cognitive science research says about teaching and learning and also somehow apply this research to our classrooms through some sort of new or revised structure or routine. So far, we have read Make it Stick and Why Don’t Students Like School and  analyzed them through the framework of generating questions that are prompted by our reading and the relationship of the ideas to our own teaching experience.

I have all sorts of questions, but this week we posed three of our group’s bigger questions with Jon Star, who is an educational psychologist at Harvard who focuses on flexibility in problem-solving and acquisition of algebra. I came away with so much to think about because he was able to give specific suggestions for practice that were very obviously grounded in research.

Question 1: What can we do to support students, many of whom have identified disabilities, whose working memory has a smaller capacity or who have other challenges with working memory?

Answer: Here is a list of strategies, all of which are centered around the principle of modifications/accommodations that do not sacrifice the learning goals. These are strategies that can be considered “good teaching” because they can benefit all students. However, the negative consequences of not using these strategies hurt some students more than others.

Strategies:

• Reduce arithmetic complexity. Harder numbers make problems more complicated, but does not necessarily require a deeper understanding. He suggests making things conceptually harder, not computationally harder.
• Be aware of the amount and type of words in a problem.
• Be smart and organized about how you are using illustrations and board space. Processing everything verbally is extremely taxing on working memory. Board space and other visuals can be used a surrogate working memory for students.
• Reduce the need for dual processing (Ex: Expecting students to read and listen at the same time)

I really appreciated that he also clarified that awareness of when you are/are not doing any of these things is the more important than making sure to use all of these strategies all of the time. There are good reasons for not following each of these strategies when there is a specific purpose.

Question 2: How do we foster a culture where students are motivated to persevere through spaced, varied, and interleaved practice, even though it is harder and the results are not as immediately obvious?

Answer: It is important to complexify what cognitive scientists are saying about practice.

• Nuance #1: Practice should differ in different phases of learning—the first exposure to a concept/procedure vs. solidification after basic mastery. Some blocked practice may be necessary in the initial phase for motivation and initial formation of knowledge.
• Nuance #2: Elaborative recall is the main principle that drives recommendations about effective practice. The more opportunities to reconstruct/apply/elaborate/expand knowledge, the more solidified it becomes. With blocked practice, the concept/procedure gets too automatic and students don’t reap the benefits of the recall. Also, once students automaticity with a procedure, that knowledge is very stable and difficult to reexamine/extend/reconfigure. Thus if students gain automaticity before associating with concepts, it is extremely hard to do this later on. Ideally, we should be building automaticity and connections simultaneously.

Question 3: Ideally, we are building procedural fluency from conceptual understanding. Where does practice fit in this arc and should the practice look different depending on where in the arc you are?

Answer:

• Point #1: It’s a misconception that there is an order to how students should learn concepts and procedures. It is not true that conceptual understanding needs to precede procedural fluency. It is not true that procedural knowledge cannot develop conceptual knowledge. Order is arbitrary—instead it is more important that they are connected and developed iteratively.
• Point #2: There are the same best practices for developing procedural knowledge as conceptual knowledge. We can define conceptual practice as an opportunity recall and reconstruct concepts (just as we would define procedural practice as opportunity to recall and reconstruct procedures).
• Point #3: It’s hard to articulate what it looks like for conceptual understanding and procedural fluency to be intertwined. One possible way to “see” this is through flexibility: students should be able to solve a problem more than one way and identify which strategy is “better” (ex: more elegant) and what the criteria are that decides what makes one solution strategy different than others.

One final gem from Jon Star: 

When you are listening to a performance of a piano concerto, often the performance itself is evidence enough of mastery of the skills and concepts behind the music. You wouldn’t need to ask the soloist to explain why they made the decisions they made. The same should be true for math. A student does not always need to explain in order to demonstrate conceptual and procedural knowledge. Sometimes the work/thinking they do speaks for itself.

On my mind now:

My biggest questions coming out of this conversation are about Star’s points about the (as one of my coworkers put it) commutative nature of developing conceptual understanding and procedural fluency.  My whole teaching framework is built upon the idea of building procedural fluency from conceptual understanding. NCTM’s Principles to Actions articulates this as one of their math teaching practices: “Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.” 

However, based on the challenges that I have experienced when trying to teach this way (When are they ready to move from concepts to procedures? How do I help students actually connect the procedures to what they have built conceptually? How do I encourage students to go back to the conceptual understanding in order to re-build procedures that they have forgotten?), I am definitely in a position where I want to read and think more about Star’s position. I think that a lot of the current emphasis on conceptual understanding is a direct response to a history of teaching procedures with no conceptual understanding. It makes sense to me that the most important part is that we are doing both and connecting them, not that there is an extremely delicate, perfect sequence to have procedural fluency build out of conceptual understanding. Star also stated that understanding a procedure is different than having conceptual knowledge of a procedure, which is something I would like more specifics on. What does understanding of a procedure look like then? So I’m waiting on some recommendations from Star for some further reading in order to help me incorporate (or not) this into my ever-changing math education philosophy.

Adapting Scope and Sequence for Remediation

Like many schools, we have students in every grade who start the grade with unfinished learning/misconceptions/gaps in standards that fall under previous grades. We operate with a general policy of trying to remediate through grade level standards—as an eighth grade teacher I am teaching primarily eighth grade content and always using that as the starting point/end goal of any reteaching of prior-grade-level content. However, we have not done very much work to make sure that this happens in a systematic way. I was really excited when the Standards Institute addressed exactly how necessary and challenging this work was and provided a framework for thinking about how to do this type of Tier 1 intervention.

This slide from the Standards Institute (Day 3 powerpoint for all of the math groups) illustrates how students will fall further behind and never be able to catch up if we spend a significant amount of time filling gaps in isolation from the current grade-level content.

As an alternative, they offered these ideas about where and what to remediate. The idea is to make a strategic plan instead of trying to review everything or only reacting after the fact to what you have learned about students’ foundational knowledge.

While this generally matches how I have been trying to remediate, I really appreciate how clearly and intentionally this process is laid out. As someone who is in a department where we don’t use a curriculum and primarily write our own sequencing and pacing, I think that this work is really our next step in building vertical and horizontal coherence. I am extremely excited to take this framework to my team for when we are doing our big-picture planning.

The Standards Institute also introduced me to two amazing tools that will be essential to this work:

1) Zimba Wiring Diagram: One writer of the common core’s interpretation of how the standards connect to each other both between- and within- grades.

2) Coherence Map: This is an interactive map that allows you to “zoom in” on the wiring map. You can choose a standard to start from and then follow it to a connection of your choice.
3) Content Emphases by Cluster: This designates which clusters are major, supporting, or additional standards. Shockingly, I had never seen this before.

Rigor vs. Cognitive Demand

Between work on creating my school’s instructional vision and attendance at the Standards Institute this week I have been doing a lot of thinking around what makes good instruction at different grain size—lesson, unit, curriculum, sequencing, and overall educational experience. Two concepts, which I would once have used interchangeably, have come up frequently.

Cognitive Demand:

Stein, Smith, Henningsen, and Silver define cognitive demand as “the kind and level of thinking required of students in order to successfully engage with and solve the task.” I have analyzed tasks with their four levels of cognitive demand in many settings. The biggest question that comes up for me is what is the ideal placement and balance between low- and high-cognitive demand tasks? One of the professors in my teacher prep program always suggested  “a steady diet of high cognitive demand tasks” which I found both wise and frustratingly vague.

Rigor:

The idea of rigor as a concept separate from cognitive demand is a newer one for me. In the past nine months, though, it has come up for me in two places—as part of my district’s curriculum review tools and at the Standards Institute. At corestandards.org, they define rigor as “deep, authentic command of mathematical concepts” and clarify that it is “not making math harder or introducing topics at earlier grades.”

Here are the elements of rigor. I’ve also included the definitions from the five strands of mathematical proficiency, because I think they better describe the three elements.

	Corestandards.org	Adding it Up Chapt. 4
Conceptual Understanding	The standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives in order to see math as more than a set of mnemonics or discrete procedures.	Comprehension of mathematical concepts, operations, and relations.
Procedural skills and fluency	The standards call for speed and accuracy in calculation. Students must practice core functions, such as single-digit multiplication, in order to have access to more complex concepts and procedures. Fluency must be addressed in the classroom or through supporting materials, as some students might require more practice than others.	Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.
Application	The standards call for students to use math in situations that require mathematical knowledge. Correctly applying mathematical knowledge depends on students having a solid conceptual understanding and procedural fluency.	Ability to formulate, represent, and solve mathematical problems. (This is called strategic competence, not application, here)

The language of the shift calls for students to pursue the three elements with “equal intensity.” However, this leaves me with questions about how the three elements interact.  One of the tools that my district used in evaluating curriculum starts to further illustrate exactly what balance of rigor looks like. 

The authors of Principles to Actions state “Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.” With this in mind, we were really looking to see whether and how procedural fluency was explicitly built off of conceptual understanding.

And then there’s the question of applications. In my experiences with both the Standards Institute and on the curriculum review team, applications were generally defined as any problem with a “real world” context. I find this interpretation problematic for three reasons.

1. Instead of applications acting as a third leg in the three-legged stool of rigor, all conceptual understanding and procedural fluency problems can be categorized as applications or not
2. There wasn’t a larger conversation around how well the real-world context was executed (See Dan Meyer here on one of my biggest pet peeves).
3. There’s a reason that the phrase “real-world and mathematical problems” occurs in the common core 31 times rather than just “real-world problems.” I think we need to better define what it means to have an application that is in a purely mathematical context, but I don't think we should just drop it.

I am not yet ready to fully develop my ideas around how to better define application, but I think that the strategic competence description in Adding it Up would be a good place to start.

Relationship

Based on these definitions, it is clear to me that I can’t use the terms “rigor” and “cognitive demand” interchangeably. But these are both words that I hear thrown around a lot when trying to evaluate teaching and curricular materials. So what relationship do they have to each other?

In looking at the text of a problem and the execution by both students and teacher, I think it makes sense to identify the foremost element of rigor and the level of cognitive demand separately. However, I would imagine that conceptual and application problems have a higher likelihood of being high cognitive demand, and that procedural fluency problems have a higher likelihood of being low cognitive demand.

I also think that it’s worth trying to push a little bit beyond the concept of “a steady diet”—which I think can be applied both to high cognitive demand tasks as well as tasks of each type of rigor.  In the standards institute we started to look at arcs of the elements of rigor over a particular topic or unit. In general, we seemed to see the sequence of conceptual understanding --> procedural fluency --> application, though of course it was not quite that clear cut. I would also question the placement of application primarily at the end because I think it underestimates students and impedes their learning to say that procedural fluency is required before being able to apply a concept.

This makes me wonder if there is a similar general flow that makes sense for cognitive demand. I would certainly argue against low cognitive demand being a prerequisite for high cognitive demand. I think that there’s a lot of value in starting with high cognitive demand tasks because they are an ideal place to surface student reasoning and build upon the foundation that students already have. But I wonder if it is oversimplified to suggest high cognitive demand --> low cognitive demand --> high cognitive demand as an arc for a unit. It might make more sense to have a unit that is composed of a series of shorter cognitive demand arcs of that nature.

Practice/Review Games

There were two goals for my classroom re-set this January—to make our class more productive and more joyful. An element of this was to make my lessons feel different and more fun than the regular structure I use in about 5 out of the 8 periods a week.  This structure is guided notes that involve a mini-lesson, practice/application, and then discussion. However, the thought of trying to change each lesson so it felt different and fun was overwhelming. Instead, I decided I wanted to have a couple of new practice structures that would meet my goals, but that I could just insert into my regular lessons.

In choosing practice structures, here were the four criteria that were important to me:

a) Easy to Prep

b) Individual Accountability

c) Versatility of Use

c) Didn’t Require a Whole Period

It’s also important to note that I chose these structures  to build fluency with procedures. I don't think they are a good fit to introduce new ideas or to build conceptual understanding.

Practice Games

Climb the Ladder

Description: I first heard of this from my mentor teacher. It involves a series of problems, each with increasing difficulty. Students get each problem checked when they finish (I had three student leaders with answer keys who did the checking) and then they get to “climb the ladder” to the next problem. The worksheet, with directions, is here.

Analysis:

Easy to Prep: It took me a little while to get the formatting to show the ladder on the page, but I can now just modify that sheet whenever. Very easy prep.

Individual Accountability: Students each had their own paper and needed their own answers checked, but they were helping each other out. In general, motivation to get to the next problem was high.

Versatility of Use: I have used it for solving equations and identifying equivalent equations so far, but it could be used for anything. It is especially good if students can build on what they did in the previous rung (ex: Rung 1 is solving x +4 = 10, Rung 2 is solving 2x+4=10)

Didn’t Require a Whole Period: 20 minutes seemed about the ideal amount of time, with about 8 problems. Everyone finished the first ladder (4 problems), and fast finishers got to all of the problems.

Other Notes: I find it is extra fun if you excitedly say "Climb the ladder" every time a student gets a problem correct.

Solve-Crumple-Toss

Description: Students get a half sheet with a problem on it. It is checked for accuracy (I had three students with answer keys to do this in my bigger classes, I personally checked all of them in my smaller class). If it is incorrect, the student revises their work. If it is correct, the student crumples the paper and gets to toss it into a basket to earn their team a point. The directions I projected for students is here. Also read Kate Nowak’s description here.

Analysis:

Easy to Prep: I had to cut up all of the half sheets, but they were extremely easy to make. In the future, I will make fewer of the later sheets because not all students get to all of the sheets.

Individual Accountability: Students each had to put work on their own paper, but were generally helping each other. I saw a handful of students more engaged than I have seen them in a long time because they really wanted to toss their paper. This desire also led to several students just copying their friends’ work so they could throw sooner.

Versatility of Use: Could be used for any type of problem! The problems should be a little bit meaty so that the time spent doing the problems vs. crumpling/tossing is heavily weighted towards doing the problems.

Didn’t Require a Whole Period: I think a minimum of 15 minutes, maximum of 40 is probably appropriate here. I want to make sure that students who are taking their time/checking their notes/explaining to a partner still get the reward of getting to crumple and toss their paper.

Other Notes: I was worried about too many people finishing at the same time and the checking/tossing part being overwhelming for me. Having 3 students checking, each of whom was in charge of a group of about 9, was really helpful. And they didn’t finish as quickly as I anticipated—the line to toss the paper was never over 4 students in a class of 27. I also had one student who was pretty distressed about crumpling her papers up when she finished. I had decided that this was ok because they already had a sample in their notes that they could look back at and I just wanted them to get more practice.

Speed Dating

Description: Students each get their own problem that they have some time to work on individually and become experts at. Then they pair up and trade problems, each person helping their partner if they need it. Every 5 minutes or so, the partners shift. There are more detailed descriptions from  Kate Nowak, Elizabeth Stratmore, Meg Craig, MaryAnn Moore, and Amy Gruen.

Analysis:

Easy to Prep: Pretty easy to prep. You need a different problem for each student (though when I do this with my larger classes, I will split them into 3 groups and then only have 9 different problems rather than 27). Also, whiteboards and dry erase markers are helpful to have for each student (though they could just do all of the problems on a separate piece of paper). This has been the limiting factor for me, so I have only done this with my class of 11 so far.

Individual Accountability: Speed dating is excellent for this! Students get exposed to a ton of problems where they have their own personal helper. They also have to be able to explain really well one particular problem. It’s also good for differentiation in the difficulty level of the problem each student initially gets.

Versatility of Use: Could be used for any type of problem!

Didn’t Require a Whole Period: This one is a little bit longer. 5 to 10 minutes to become an expert at your own problem. Probably about 2 minutes to get set up into the rotating columns. Then 3-7 minutes of work time for each pairing.

Other Notes: I loved how uninvolved I was as students were doing the speed dating. It was amazing to see the amount of math talk going on and how they were really explaining to each other.

Content Auction

Description: Teams get $1000 and an “auction catalog” (read: worksheet with practice problems). They are told what they want to buy (in my case equations with one solution) and given 10 minutes to work on the worksheet in order to plan what they will bid on.  Then the auction begins! Teams bid on the problems, and the problem goes to the highest bidder. After each item is won, we go over the problem to decide whether it was a wise buy. Here's the powerpoint that I used. Further description here and here from Sarah Hagan.

Analysis:

Easy to Prep: Extremely easy to prep. You need a worksheet with some practice problems on it. I also made bidding paddles (a notecard with the table number stuck to a popsicle stick) and a powerpoint with the problems, but those were extras and not required.

Individual Accountability: There wasn’t great individual accountability when teams were working on deciding what to bid on. I did, however, require students to copy down the answer as we went over each problem.

Versatility of Use: There needs to be some way of distinguishing which problems students need to buy and this distinguishing element is where the doing the practicing the math comes in. For example students might want to only buy true true statements (as opposed to false) or functions (as opposed to non-functions).

Didn’t Require a Whole Period: You definitely need a whole period for this one.

Other Notes: I felt like this one was the least successful out of all of the games that I tried because there was a high ratio of unproductive chaos to productive math practice. Students didn’t do that many problems before the auction started and then once the auction started the bidding was a lot of time without math thinking. Then reigning the kids back in to go over the problems after they had been bought was hard. However, I think some tweaks in the future would help. I would probably start with 5-10 minutes of individual work time. I would then have the teams split up their $1000 dollars however they wanted over all of the problems. I would collect this info some way (electronically?). Then we would have volunteers to explain each problem and then reveal which team had the highest bid and thus won it. I think this would be more focused on doing the math, but still have the fun bidding and competition elements.

Student Responses

After we had done Climb the Ladder, Solve-Crumple-Toss, and the Content Auction at least once, I asked my two larger classes for feedback on which game was their favorite and why. Here were the votes:

• 1^st Place: Climb the Ladder (15 votes)
• 2^nd Place: Auction (9 votes)
• 3^rd Place: Solve-Crumple-Toss: (8 votes)

There were enough votes for each one that I let the class know we would be doing all of them again.

Here were some of the best reasons that kids gave for their top choice:

 

Other Practice/Review Games

These are games that I haven’t tried yet because I didn’t want to introduce too many new structures at once and/or they didn’t seem as good a fit for my specific criteria. They may however be useful for others!

War: Descriptions from Denise Gaskins and Kate Nowak

I Have, Who Has: Sarah Hagan and Sarah Hagan again

Ghosts in The Graveyard: Kim Hughey

A couple other compilations of review games:

Tina Cardone, Sarah Hagan, Global Math Department

Celebrating the Victories

At the beginning of January, I did a re-set with my class because I felt like students weren’t learning and neither the students nor I were enjoying being in class. 5 weeks later, it’s the end of a tough week and I am feeling discouraged again.

However, I wanted to take some time today to focus on the positive changes that both the students and I have seen since the re-set. A week ago, we had a class meeting to celebrate the positives that have come out of the work we have done as a class to make a more productive and learning environment. Here's the student feedback that I got during that meeting.

Survey

Directions: Here is a list of new things that we have tried. Rate each one with a symbol:

+ Has really helped the class improve

✓ Has kind of helped the class improve

— Has not helped the class improve

Results:

What we have tried	+	✓	—	Weighted Total +: 3 points ✓: 1 point -: 0 points
New math games (Climb the ladder,  solve-crumple-toss, auction)	27	10	1	91
Seats in tables instead of rows	27	8	2	89
Not using the warning/lunch  reflection system	26	11	1	89
New bulletin boards with space for  you to decorate how you want	27	7	3	88
More group work	24	14	0	86
Do Now questions to help us get to  know each other	23	11	4	80
Team captains handing out smiley/sad faces during the Do Now	19	12	3	69
Team captains helping us stay  focused during class	13	21	4	60

 

Student Responses:

In your opinion, do you think class is better than it was before winter break?

 

8C:

• Maybe because I’m starting to get use to this and it is more comfortable and nice
• YES. Because I feel like it really helps me focus
• It was ok because things got better
• Yes a lot because we are now learning more before we were learning a lot even though we aren’t perfect right now we will continue to get better
• Yes because everyone is being more and more focused and they are working harder and better than before
• Yes
• I think yes because we settled down after we got the seats but I still think its not working well that much so we should switch seats every month
• Yes because before we did we couldn’t do no project and we never paying attention and we always got a minus on clipboard. But now we get more work done and learn more in math class and it more fun now.
• Yes
• Yes I do because before I was bored with the lesson but now there more fun and I think people pay more attention
• Yes because most people are working more and I now understand more of the math and am able to help more people understand it too. And I getting to participate more in class!! I love it! But can we step it up like the math to improve 8^th grade math a little harder
• Yes because class is going much better

8B:

• Yes, because now everyone listens to her but before the break everything was a mess
•  I think it’s ok. I feel like it was better when it was no group.
• Yes, I think class has been better before winter break because we have improved as a whole class
• Yes, I think it has been better now than before winter break because now it’s more focus, and engaged people and it’s less chatty than before
• Yes because more people are concentrating than before and also because a lot people are getting their grades up
• Yes because we got more work done and less people getting in trouble and helped me understand more classwork and helped me stay on task more
• It was better because before we didn’t let you talk and we made all this noise
• I think class wasn’t better before winter break because people keep getting into trouble. I think that the class is way better than it was before.
• Yes
• Sure, because we are better than before
• No
• Yes because everyone is participating more
• Yes because some rules that we made are working out
• I think it’s better than ever!

Shout-out Certificates:

The kids also did a great job recognizing each other. This is just one example of the certificates that they filled out.

Productive Struggle

Here is part of the quiz I gave on Friday:

The first time you go to the gym, there is a fee you have to pay to sign up.  You also have to pay every time you use the gym.  If you use the gym 5 times, you will have paid $70.  If you use the gym 10 times, you will have paid $110.

a) What is the cost per time you use the gym?

b) What is the sign up fee? 

To give a little bit of context, we have been working with linear functions for the last five weeks or so.  I have completely overhauled the unit from last year in order to (hopefully) have students develop significant conceptual understanding and then leverage that as we work towards fluency. In order to reach this goal, part of what I am doing is giving students more tasks where there is not a set procedure for them to follow and supporting them through productive struggle.

With this quiz question, about 1/3 of the students aced it, and 2/3 had no idea. There was very little middle ground. The majority of students who were able to solve this problem are also the ones who have been persevering through problems all week-talking through them with their partners, asking questions, and sharing ideas with the class.

I was frustrated that despite spending significant time on this type of problem in class, 2/3 of the students were not able to answer this question. My solution was to do more of these problems with more scaffolding.

But then I went to talk to one of my co-workers and asked for his advice. He had two pieces of advice for when the class is so starkly split in understanding of a concept.
1) Raise the level of demand/difficulty, at least for part of the task. This evens the playing field and doesn't leave 1/3 of the students frustrated because they already get it.
2) Take a break and come back. Use the break time to come at the concept from a different angle or do something totally different. It should be different enough that it's not only the same kids feeling successful.

This was exactly the advice I needed to help me keep on this path of students as sense-makers, productive struggle, and building conceptual understanding.

Introducing Student-Generated Questions

On Thursday, I am going to be introducing the idea of student-generated questions to my classes.

Inspired by Mary Bourassa and Alex Overwijk, we will start class by projecting the picture below. Students will write three questions that they have based on this picture. After having a couple students share out their questions, I will pose the question of why I am asking them to generate questions. Some of my reasons are that asking questions is part of what mathematicians do, in generating questions students connect natural curiosity to math class, students may be more invested in answering their own or their peers’ questions, making space for student-generated questions gives students power and voice in the classroom, and being able to ask good questions is an increasingly important skills. However, I am interested in hearing what reasons students will give.

 

Once we are done with that discussion, I will introduce the kids to number bracelets. They will do a couple examples in order to understand how they work. Then, we will go through a modified version of the Question Formulation Technique, which was developed by the people at the Right Question Institute.

Here are the steps in the Question Formulation Technique:

1. Question Focus (jumping off statement most often set by the teacher)
2. Produce Questions (four rules: ask as many questions as you can; do not stop to discuss, judge or answer the questions; write down every question exactly as it is stated; change any statement into a question)
3. Improve Your Questions (categorize questions into closed and open, and then re-write at least one in each category so it would be in the other category)
4. Selection of Priority Questions (groups choose their top 3)
5. Next Steps (teacher and/or students decide what to do next with the questions)
6. Reflection Activity (debrief the process)

For the first day, we will only be doing steps 1, 2, 4, and 5. In pairs, students will generate questions about number bracelets following the rules. They will then choose their three favorite questions and investigate (at least) one of them. My hope is that this will serve as enough of an introduction to the process and then the next time we do a student-generated questions task we will follow the whole protocol.

Thoughts or suggestions for supporting kids in generating interesting questions?

(Cross-posted at BetterQs)