Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 21: Three Techniques to Engage your Students and Hook them into Learning › Lesson 21 Discussion

Lesson 21 Discussion
Posted by Jon on May 1, 2019 at 11:42 amPlease post your thoughts and questions on the 4 techniques you learned about in lesson 21: “How you see these fitting into your lessons this week.”
Victoria Murphy replied 2 weeks, 6 days ago 60 Members · 97 Replies 
97 Replies

As you guys know, this was one of the biggest takeaways from your workshop for me, and doing one small thing–withholding information–made a huge difference in the way I taught this past year. I didn’t always have cool tasks for the kids, but even when we were learning how to multiply polynomials, I let them play with the blocks and notice and wonder until they started seeing patterns for themselves. Not preteaching them everything but instead withholding some information was a fabulous beginning to a major shift in my teaching.

Couldn’t agree more! So glad this was a takeaway for you. Really does put the thinking into the hands of the learner.


Some really great strategies were shared in this lesson. I have definitely tried to spark curiosity in my math lessons before and have used Notice and Wonder, but now I’m thinking that I probably didn’t spend enough time building the culture of noticing and wondering early on. Some students would always share while others were more reluctant to engage.
I have also encouraged estimation, both with ‘regular’ math problems, and also through using tasks such as Steve Wyborney’s Estimation Clipboard and Estimysteries, which my 5th grade students have loved. However, I do see students skipping that step when it’s expected as part of their problem set.
So far, I’ve used Notice and Wonder and Estimation type tasks as more of a warmup, before moving on to the Eureka lesson of the day and trying to plough through all the requirements that go along with that. I’m excited to see how I can take these techniques and weave them into the content, so that the engagement lasts throughout the math lesson and not just for the beginning. That task feels very daunting right now, but very worthwhile.

At first, it definitely feels daunting! However in time, it’ll flow naturally. Something to consider is potentially skipping some of the warm ups that are disconnected from your lessons and build using these ideas around the lesson to have a built in warm up. Ie: sparking curiosity could be the warm up.


Last wednesday I introduced my functions lesson doing a kind of performance. I told them that we will infect us with coronavirus. We settle the velocity of infection at 1 and then I give a piece of paper to the first infected that he had to give an infection paper to one student, this new infected did the same, and so one. One student secretary was counting and writing on the board the number of the new infections and the accumulation of them.
Then we did the same with velociti 1,5 so the first infected gave one paper to one student and a half of paper to another one. The students who had one paper or half and half could infect the others. And finally we did the same with a velocity of 0,5. We take the data and we make the plots.
Now I think that to make this activity more interesting, and with more curiosity I could make them stand up and take datas without saying that we are making an experiment about coronavirus infections. And after that use the notice and wonder strategy. I think they could have more curiosity.

I think that would certainly leave them with a memory of the learning that they could lean on when experiencing this idea in the future.
One thing worth considering is that the challenge we have when we use context is that certain contexts can affect students in different ways. So while I’m sure you approached this particular context with care and concern, it is possible that covid has affected students in different ways. Just something to be cognizant as @jon and I are only now realizing that some of the things we’ve done in the past may not have been ideal for all students.
Keep up the great work!


The biggest takeaway for me in this lesson is “withholding information.” As a resource specialist, I am always prompting, using scaffolds, preteaching, using mnemonic devices. This is something I need to work on. Currently, in my parallel math class, my students don’t know what do when left to think on their own. I get silence most of the time. This is one reason, I don’t advocate for classes that are are leveled. My students need to work with their general education peers and see how others think and then begin to feel confident in themselves and their ideas.

Great reflection and inspection here @helen.calaway We find that students generally would rather think less. We need to put them in situations where they think regularly. This will build their confidence as long as we’re there to support that thinking.


I use some Notice and Wonders, but I have been doing them in online learning, so I haven’t been able to really see the benefits. I have been using pictures, but will try to incorporate videos in the future. I like starting with a notice and wonder because it ignites some thinking and gets the students brains working. I really liked the candle burning example. I am curious about the 3act math tasks. I am not familiar with them.

Hi Dawn!
Yes, online learning introduces even larger barriers to engagement including determining how engaged an entire group is. It is clear that this learning environment is not anywhere near as interactive or engaging as being face to face (and even that was hard enough!)
Despite the challenges, problem based lessons are still the way to go rather than straight direct instruction. Here’s some problem based units you might want to check out to help you along;
learn.makemathmoments.com/tasks


I have a few students who just “want to get on with it” and a few who check out as soon as they walk in the door. When I tried with holding some info and having them notice/ wonder the kids who don’t normally say anything were suddenly participating, and those who are impatient to “just do the math” had to wait, but they did not seem upset about it. I tried it with some work we are doing with financial literacy, using pictures of homes and asking them to notice/wonder about them.

I have had a go at designing a few lessons of my own based on your model and some kids are now finding Exploration day (Mondays) their favourite lesson. They like Notice and Wonder – they like the “success for all” aspect of that part of the task, but also some definitely compete to come up with what they see as the most sophisticated mathematical questions. I am also enjoying trialling “withholding info” and seeing good results of higher engagement and more leaning in.

This is fantastic to hear! If you utilize a problem based approach (like we do in our units learn.makemathmoments.com/tasks) then every new problem based lesson day will be an exploration! Glad to hear it is impacting your practice! Give it a go!


PS what software did you use to make the “Maya flower bed” video?

We use Apple Keynote for animations, but PowerPoint is really powerful, too!


Love all this so far and need to be more intentional about withholding information and taking more time when needed!
My biggest question is…how do you start the school year off? Do you start day 1 with some random notice and wonder task to get kids excited? I know in high school common first days are here is the syllabus…
I’ve done Jo Boaler’s week of inspirational math, but curious how you all would start?

Great question! We have a whole mini course in the Academy about how to start the school year off right which you should definitely check out.
The key upfront is building a community of math learners which can happen in a number of different ways. I tend to start with getting to know you type activities and then dive into some mathematics – I try not to hold off on math too long because I want students to quickly see / experience what math class is going to be like vs maybe what they might know / have been exposed to.


After watching this video I used a Notice and Wonder in my lesson on Volume of a cylinder. I really liked it as a questioning strategy and was suprised about how much prior knowledge it activated and student interest it sparked. I also made it a point to have students estimate answers and again was very pleased with how effective this was. Students were regularly able to identify if a solution was reasonable/unreasonable based on their estimates.
Witholding information seems like a great way to build conceptualization, but it is new to me and I will need more practice before implementing. I am looking forward to learning more about it.
Lastly, I loved the idea of “cranking up the math dial”. What a great way to keep students engaged and also develop their math stamina!

I have used notice and wonder in my classroom in my ELA and Science and Social Studies lessons usually with pictures and vocabulary. I have used it occasionally in math with geometry and patterns. I try to encourage and accept all comments when children share.
I really like the idea of withholding information I am interested in learning more about this. When teaching problem solving at the beginning of the year I will share a problem 1 sentence at a time and encourage students to draw the problem as I read each sentence. This has helped to get students to think about what the problem is asking. Sometimes after sharing each part of the problem and encouraging them to draw I will ask them what they think the question might be or what we might be solving for based on their picture.

@gerilynstolberg We agree! Unfolding the problem in stages allows students to think about strategies and adjust those strategies as they get more information. Great for their problem solving skills.


I laughed through the section where you talked about the inappropriate and unrelated comments. One key to building relationships with my students is to value their voice, even when it’s not related to the content. They just want to be heard. There are so many times that students (especially high school students) just want to be noticed and get attention. Let them have their moment, don’t give it any power, and move on.
Regarding the transformation of textbook questions into notice and wonder style questions… My brain is really starting to work thinking of ways I can change these boring textbook questions, omit information, and create anticipation by changing it to bare bones style. I’m also very thankful that you two have done a lot of the video creation for us. My video skills, while getting better, aren’t quite as good as yours!!

I used the “put your arms around it” task from Mindset Mathematics book in several Gr 24 Elementary Math classes. Students explore perimeter by going around the room with a string (students get all different sizes) and they have a chart – objects that are too small and objects that are too large and they write them down on their clipboard. They draw the object in the room that the string wraps around perfectly on the back of their page. What I am realizing about this task is that it works because there is alot of estimation going on as Ss try to predict which objects in the room it could fit around. There is not much information given to them and there is lots of noticing and wondering going on. They get to explore objects that are of interest to them. Will my string wrap around my waist? Around this globe? Around this recycle bin, water bottle… etc. It’s also a nice visual and physical model / manipulative to refer to later. How the teacher presents the students with their string and starts the questioning would be important to “withhold info, create anticipation, get noticing and wondering and then estimation…” Knowing what I know now, I think I’d do a better job with this lesson next time I try it.

Discuss prior findings from a prior lesson, discuss why they were doing the steps they needed to in order to solve the problem, withhold information because it leads to the students wondering what if questions and activate their own discovery for finding how they need to solve various problems, have the students notice and wonder different patterns on their own rather than immediately sharing what the patterns are for various problems.

It all makes sense to me and you demonstrated how it works in module one. I am a believer because those 4 techniques worked on me. The scary part is starting and figuring it out with the curriculum in my class. That’s why I am here, to learn how to go about it. I’m interested in trying some of the videos you have made with my current curriculum. I think the videos are definitely a way to grab students attention as long as you have the other parts built in to make the learning successful.

This can certainly be scary at first. As you make these changes, be sure to document/journal where things aren’t feeling right or aren’t going as you had originally thought. Bring them here to the community and let’s all try to work away at them!


I have yet to do this module, but already got so excited from Module 1 that I found and am incorporating your 3Act ‘maximizing the area of a rectangle’ task into my lessons this week. I know students have been craving for some more handson curiositysparking tasks as our school returns from virtual into hybrid learning and this would be the perfect way to get some more energy and excitement flowing. Thanks for the great work you do!

Awesome stuff! Tarini! Great job implementing the ideas so quickly.


Really great concrete tips to orient us as we plan these tasks. I totally agree with the anticipation part and planning the progression to spark curiosity. We are curious beings and child or adult, get more invested when there’s something we are actually trying to solve. Kind of coincidental, but after Module 1 I just happened to look up more of your tasks since I wanted something for quadratics and found one very similar to the maximizing area of rectangle. Going to do it end of this week so let’s see how it goes. One technique you briefly mentioned that intrigued me was ‘lowering the math dial’ too. Particularly for honors courses, they tend to be super fluent and quick with the skills, but stepping back and contextualizing it has been a huge goal of mine this year – making it more about problemsolving (and yes fluency helps, but it’s the big connections that we can hone in on). My one worry in the standard classes I teach is student frustration from those that normally struggle at not having the information and sort of giving up early. But like you mention this might be to do with the culture from the beginning and making it part of a routine. Insightful tips all over.

Fantastic to hear that you’re finding the lessons helpful and are ready to dig right in! There are so many factors that affect the implementation of an effective lesson, but it sounds like you are considering the common challenges and will have a great go at it. Let us know how the lesson unfolds!


This lesson was a great reminder. I’m going to look through some of my lessons this week and see where I can withhold information, and add some notice/wonder, questioning, and estimation to them. Sometimes kids don’t realize they need a piece of information and they start doing the problem anyway, and the moment they realize and ask for that info is always one of the highlights of my day.

This video really maps out how to create an engaging and effective math lesson. As a district math coach, I find this fascinating, but being out of the classroom makes it hard to implement. I am looking to partner up with some teachers to try these strategies, but I fear it will be a oneoff and make it hard to encourage the classroom teacher to continue with it if it’s not an immediate success.
My next step is to connect with a trusted teacher and work together to plan out some lessons and teach them together during a few weeks period.

Since I started listening to the Podcast and I took the transform your textbook course, I have been trying to use Notice and Wonder a lot with my high school classes. It really does help students to have a voice when they typically don’t speak up in math class and it definitely helps build that culture. I gave them a problem the other day and I was not anticipating or planning for them to do Notice and Wonder but they all started doing it! I also tried withholding information on a problem involving inverse variation in my class with juniors and seniors using a video clip form “Father of the Bride” and they did a really nice job with thinking about what I might ask. I really like using these types of activities because I really want to get the students thinking and talking in class. They do sometimes say things that are “unimportant” or mildly inappropriate but it still gets them into the work.

I am a relatively new primary school teacher (in my fifth year) teaching in a remote area where my kids are about three years behind provincial expectations in mathematics. I am excited about implementing anticipatory activities to spark notice and wonder in my math lessons, however, since your examples are high school level mathematics I will have to be a little more creative to create scenarios to engage students. I myself am not learned in mathematics and find the high school examples difficult to generalize to my .students’ experience. I am working to rectify the situation by upgrading my skills through courses. I understand the concepts generally but think I need some concrete support by way of examples to consolidate my learning. Could you suggest some resources that would be helpful to me? My students are just completing a unit on multiplication and I will be teaching them division in the coming weeks.

Hi my friend! Actually, much of what we share typically are in the middle grades but if you look at our problem based math units we have tons from upper elementary and middle years. So use those for inspiration as you continue your learning!


I love notice and wonder because it helps students move from being solution oriented to process oriented. Often in trying to work out the right answer, students don’t really engage with problems, even when there is a real world context. They look for key words, similarities with previous problems etc. Like your economics example, students are thinking about systems of equations rather than observing that supply and demand are starting in different places and moving in different directions (that’s even more noticeable in the dots example). Noticing and wondering about the movement of the elements make the seemingly arbitrary question of when will they be equal more relevant and intuitive. It also promotes further questions – is it your starting point or how fast you move that matters more, etc.
Relatedly, I’m also removing information more in my class to promote students asking questions.

This is great to hear and once this approach “hits you”, you’ll never go back!


I really liked these practical suggestions, and that you dispelled the notion that changing the person’s name in the problem is a sufficient motivator.
Withholding information seems to have another benefit; students think more about the problem rather than rushing in and calculating. In Geometry, for instance, showing a figure with congruence (or parallelism) annotations (and no numbers or variables) encourages students to think about and discuss relationships. “Which angles or sides are congruent?” “Should the measure of this angle be greater than, less than, or equal to this other one?” As soon as the numbers and variables are shown, students will rush into, “SET THEM EQUAL!” or “ADD THEM TO GET 180!” One the problem is solved, students will also have a frame of reference to determine if their answer is reasonable. I need to do this more consistently.

Stephen, that’s a great benefit of withholding information. I often wonder: how can I promote careful thinking in this lesson?


Sparking curiosity is so valuable. It also makes teaching the lesson so much more fun and rewarding. Other than “3 Act lessons,” I like to include a “what do you notice?” almost daily and even multiple times a lesson. Especially when introducing new concepts. I also think that estimating is such a critical skill and that it should also be part of the culture of daily lessons.

I really like the idea of sparking curiosity, as it seems my students hardly ever have any curiosity when it comes to math. And I think withholding information is a wonderful way to do that. I look forward to the chance to implement this.

Everyone has curiosity – I think we just fail to draw it out in mathematics. Specifically, we often ruin / spoil the curiosity by constantly “giving away the ending” when we preteach so much to students upfront. The curiosity path is designed to help address this common shortcoming.


I love the thorough explanation of why you did what you did. So many times we go to conferences and don’t come with anything super concrete. I love the idea of withholding information as a motivator for interest. I think that’s my biggest takeaway here.

I have always been so bad with spatial reasoning and estimation. My biggest fear is showing these weaknesses to the students. So many students are better thinkers naturally than I am but I’m willing to give it a try. I am a product of here’s the formula, now use it. I never could understand the math behind it, I just knew how to use it. I’m going to be right there in my students shoes with this new type of teaching. I’m excited!

Many of us feel (or felt) the same way! I was certainly a plug and play sort of math student and felt that I had very weak reasoning skills all around. Over time you will build it! Keep up the great work!


My biggest fear with diving in, is anticipating what students will say. I have a hard time looking ahead on what students will struggle with, and what students will give. Like Laura, I have always been “bad” with estimations. I long for the “tool” to just get me to the answer. My favorite part of the chocolate activity was how little I ended up caring to know what the answer was. The process was exciting and that is where I want my students to be. I want to give them the lesson, that they enjoy and think about the process, and the least exciting thing is the answer at the end.

This will definitely take time to flip your own mindset and then be able to model that mindset enough to flip your students mindsets. It sounds like you are on the right track though!


Good techniques to practice in order to get student interest, participation and achievement. I enjoy applying withholding information to my advanced classes as they critically know more info is needed almost right away. My lower level classes could work for a bit until they realize they do need extra info to move on. Estimation is also a great technique, I always try to ask students where the answer should be (could it be negative?, is it a large number? what units should it have? What values would make sense?) and thus try to have them “live” the problem as a personal experience to be better at estimation.
Noticing and wondering is a good way to start a question, so they can wondering what info is provided, what is needed and the overall goal of the task. Finally, anticipation is interesting too, from my point of view, it’s lower in level of importance compared to the others, I think some kids don’t fully need anticipation in order to successfully solve a task and to gain full understanding of it.

With my lessons this week, it was tough for me to think of ideas to get students to notice and wonder and get students interested in learning about trigonometry. Usually at the beginning of lessons, I try to tell students how we can use the concepts to solve realworld problems and of course I told students about how trig has a lot of applications in physics, engineering, etc and showed a simple diagram of what they’d see in physics with a force diagram, so that’s my way of getting students interested in the lesson. I’m excited to learn about notice and wonder activities I could do with my students with trig!
With teaching trig, though, I did promote estimation with thinking about reference angles and which quadrant certain angle measures in both degrees and radians would end up. Before even having them implement the formula for changing from degrees to radians or radians to degrees, I promote thinking about it and estimating about which quadrant it should end up in.

What you did was a great improvement from how we might traditionally dig into trig. Asking students to estimate angles and side lengths… in particular, estimating how big one side is compared to another is helpful too… can they articulate that the opposite side looks like it is 80% (or 0.8 times the length) of the hypotenuse (if a right triangle) for example…
These are all ways for students to sort of get a sense of what they should be coming up with when they do finally use a formula.


The thing that has stuck with me as I start trying to turn regular problems from our text into better problems is the withholding of information. In BTC he talked about the books ruining problems because they give all of the information away at the beginning of the problems.
Figuring out what info to eliminate and still be able to spark curiosity is definitely a skill. I am getting better at it, but figuring out what to cut and what information will still be enough to spark curiosity is a skill.
I love that you mentioned just changing the names…I thought that was enough. Why aren’t the students totally engaging with the problem? Well, if any of them cared because of the name, it would only be that one kid. 🙂

I can not wait to try this with my students! Notice and wonder, anticipation, withholding information, and estimation all to spark curiosity. I am looking forward to a new school year using this method. What math we will learn!

My take away is the power the curiosity path to garner authentic engagement and sense making. I wonder how to extend the engagement if the task is not easily solved using the student’s current strategy toolkit. For example, if students do not have previous experiences with using a table for reasoning or identifying which operations apply for a given situation, how do I keep them in the learning zone?

Consolidation is key here. Using what students have done to reshape the representation can be really helpful. There are times where you may need to be more explicit and that is ok too!


I’m out of school for the summer, so I won’t be using these techniques until August. However, I did get a lot out of this video! I think the technique of withholding information can help students really think critically about what information they need in order to solve a problem. I actually think some of the techniques shown in the video could help level the playing field between my special education math class and the gen ed math class next door – we could provide the same bare minimum information (picture, video, etc.) and see where the students take it, adding information and subbing in levelappropriate numbers as necessary. I think it’s really fascinating to watch how a relatively boring problem can suddenly become interesting when there’s mystery involved.

I also wanted to mention: this type of problem is so much more accessible to students who struggle with reading and language. A student’s ability to do the problem doesn’t hinge on their ability to read and comprehend a paragraph of text.


Thank you for unpacking these techniques! I can read about things all day, but it helps to “see” them visually. I also appreciate hearing “what you were thinking” as the teacher in the background to help me in designing my math course.

I learned that the techniques to spark curiosity are essential. While I tried to integrate 3act math tasks into my classroom this past year, they often failed miserably. Why? Because I failed to spark my students’ curiosity. All of these techniques were used less and less due to student resistance. Don’t want to notice or wonder? Okay, we’ll skip that part … and there goes anticipation and withholding information as well. Some of my students made progress on estimation while most simply went through the motions. For me, my success [or failure] to transition to this type of teaching is the creation of a culture of curiosity and wonder.

Great realizations here regarding how you might shift your approach moving forward to ensure that students don’t see it as an “option”, but rather how we “do” math.


I really like the idea of slowly cranking the math dial. This ties in with the notice/wonder, anticipation, and withholding info. I also want to incorporate more estimating.

The biggest takeaway for me was to withhold information. I am really bad at wanting to rush them to the aha moment because that is the exciting part. I need to take away information and do more notice and wonders to allow them to anticipate what is coming. A question I have is, how often do you do these types of activities?


My favorite technique is estimation. I loved guessing how many jellybeans were in a jar as a kid and would come up with the most ludicrous strategies. I can’t wait to come up with similar tasks for my students. The idea of predicting two border values, a high and low, before doing the actual prediction was new to me and I cannot wait to see how that works in my classroom at improving the reasonableness of my students’ guesses

Their estimations improve pretty quickly once you get in the routine of it. They truly build fluency and flexibility and begin to maximize their use of spatial reasoning skills!


As a special education teacher who will be starting pull out math courses at the high school level I have a lot of thoughts. I like the idea of getting students curious about math. Many of my students who have been in general education classes, but really struggled just do not like math. Often when asked anything about math they will state that they hate math and there is no need for math.
On the other hand, when I was a student I would have hated being asked to wonder and be curious. I wanted (and still do) to always be correct in the most efficient manner, so I would have been that student who boycotted the teacher when asked to notice and wonder.
I am most curious about the Dan Meyer’s math dial and seeing if I can use that not only as a tool for me as a teacher, but a tool for students to measure their growth.
I am excited to create a community that assures safety, curiosity and comfort in math. My concern is that as a special education teacher who has not independently taught math courses in the past 7 years that my comfort level may not be at the level of safely guiding or building that curiosity correctly (I may let them go down the wrong path) or I may not know enough to get them started in the direction I need the students to go.

Thanks for taking baby steps with this. I spent the last year working on eliminating the preteach and increasing the Notice & Wonder, and we had fun with estimation (7th graders). I laughed when you were substituting student names to create relevance and curiosity–I do that only to separate tasks between classes, haha, so I can tell which class the tasks belonged to. But you’re right, we can withhold information to increase the student buyin. I love it, and I plan to work on this aspect of lesson implementation. Lots of great ideas here.
Is it at the Academy level that you talk about the other strategies that you said you won’t go into detail about in this course?
 This reply was modified 5 months, 1 week ago by Erin Beaver.

Glad you found some humour in it!
I’m not sure what you are referring to re; the Academy and strategies we won’t be going deep into here. I’m guessing in the Online Workshop.

I have tried some notice and wonder questions in my classes but not enough to build the culture. My goal for next school year is to set up the culture early on in the year so students are familiar with the thinking process. I also want to work on withholding information. It seems like a simple game changer to provide thinking opportunities with my students. It was mentioned how if students can anticipate what they need to solve a problem they are on their way to problem solving. In the past I have given groups hint cards when working, but after watching the 4Techniques video, I want to try information cards. If they are stuck, what information would help them.

Since I won’t be teaching this week (or until August! Yay! lol) I guess I have a more general reflection rather than response to a prompt. I feel I struggle most with the variety of tasks. I needed to hear that it doesn’t ALWAYS have to be a video and doesn’t ALWAYS have to be a handsonwithmanipulatives task. I think I get stuck and frustrated sometimes when I try to find a handson task for something that a chocolateeating video would suffice! Or vice versa. So bringing this into my classroom will mean having a more open mind in what I search for and also the creative thinking I’l have to do.
I also see myself getting frustrated at the “Jonnie Jokester” and “Olivia Overacheiver” in my room. Like I never know how to react when they don’t take it seriously or refuse to work at all. This past year I gave up right in the middle of the boycotts and went back to fillintheblank notes pages. I know now, after this video, it’s better to validate that than to stress about it!
I’m honestly just so excited to start looking though my lessons again and seeing, “Well I stopped looking for something curious here because I couldn’t find a handson task. Let’s search a little broader, or let’s start with a textbook problem and see how I can alter it.”
I also loved hearing, “You can always add but never subtract.” Which I heard with sore ears because the same ears heard a hundred students complaining about how I wouldn’t just TELL THEM what to do. I can see myself implementing all of your strategies so excitedly and then getting popped like a balloon at the students who refuse to work in the “new” way.

Glad you’re feeling good about what you’ve learned here.
In regards to going back to filling in blanks due to some students not taking it seriously – this stems from a lack of culture having been built yet. It takes time especially since students don’t “get” what you’re trying to do. So being explicit about why you’re doing what you’re doing is so key. You’ve got this!


As a K12 math specialist/coach in our district, I am very interested in the Notice and Wonder activities in class. Our new curriculums already have SOME of these questions in place (both elementary and secondary) but it is not a weekly activity (maybe every 2 to 3 weeks before the next one occurs). I am wondering if teachers would buyin to making this part of their weekly routine and class culture. Since this is year two of our implementation of new curriculum, I am thinking teachers would be more familiar with where they could bring in this type of activity on a weekly basis. My job will be to convince them the time they spend on activities like this will help increase student engagement because students are choosing the direction of their learning.
Here are my “wonderings”: 1) how does a teacher choose which pieces of information to withhold, 2) if students are struggling (because I might have chosen the wrong pieces to withhold), is this the point where I ask students what pieces of information would be helpful in making their thinking move forward?, and lastly, 3) do students choose which “wondering” to use as the question for their inquiry (which would drive my Type A teachers nuts and the majority of my secondary teachers are just this type) or do teachers get to choose the question for students to answer?

Great wonders.
1) there are no rules to which pieces of info to withhold only the goal of leaving enough of a gap where there can be some wondering and discussion.
2) it is always a good idea to ask them what info might be helpful – you don’t need to wait for them to struggle.
3) we always have a question we will be exploring. We can add some student wonders to the list or answer them as we go, but there is always intentionality to the question we will explore to draw out specific strategies and models for a big idea.


I have used “notice” activities alot in my class but have not really gotten to have my kids to the wondering. I feel I can do these notice activity on the fly during my lesson but I do feel I need to set up my lessons better with these 4 techniques. What is your recommendation on how to start this process?

I have done the problem manipulation with names of my students, and problem details that are relevant to them. I agree that helps, but isn’t the same. However, I think it makes an assessment feel more comfortable.
I use notice and wonders a lot, but I think I will use them much more effectively now. I plan on being able to use them midlesson if stuck. I can withhold information, like using “problems without figures” and remember that if they want the information, it is much more powerful than that just immediately given. The key is to have the situation be interesting enough to not just evoke frustration.
I find when kids say, “I don’t know…”, a notice and wonder let’s you push them in whichever way your relationship naturally works. “Are your eyes closed?”, “Everyone can notice something…”, etc. Then validate whatever answer they say and smile. It’s along your “Johnny” example, and we all have at least 1 of him every class.
Funny, when I teach my adult students at night (GED prep), I always make them estimate and think of reasonable answers first. (Predictions). Then I see/hear them when working selfcorrect because where they are going isn’t going to yield a reasonable answer. I need to remember to push my day students (middle schoolers) to do this too.

I was really happy to here your thoughts on making students feel safe and valuing student voice. I teach in an alternative program and students have huge fears and negative feelings about math. There is a lot of thought needed in giving students opportunities to share what they see and know about a situation. Patience is also required. I talked with a student today about not fearing estimation. I went on to talk with them about reasonableness. The high achiever avoidance is really true. I don’t usually have many of these students, but they think there is something about being able to do traditional math that makes them superior to other learners. My students often talk about traditional math and students being told at sometime how smart they are. There is always a point where it becomes hard and some students shut down because they do not know where to go from there. They do not know how to struggle and work their way through the problem.

We all experience many of the same situations and student attitudes, beliefs, and feelings toward math. Now that we recognize these as real we’re in a better position to do better!


I enjoyed learning about the 4 techniques shared to Engage and Hook students. I appreciated hearing about needing a class culture of Notice and Wonder and that you need to do it multiple times for it to become smooth and effective each time. I also wonder if when using this in the past, I had not withheld enough information or created enough anticipation for the notice and wonder to be engaging.
This section had me wondering about Building Thinking Classrooms and I am curious about your thoughts as you have quoted the author a few times so far. I read that book in the spring and it was very specific that in optimizing thinking you can only lead an introduction for 5 minutes or less before sending students to a task. I am curious how you see this framework within that context. That being said, I have done 3 Act Tasks in the past with many elements you have described today with great engagement so I almost wonder if BTC and 3 Act Tasks are just 2 separate fantastic structures to have an engaging math class through? I would love to hear your thoughts about the timing of the introduction of a “challenge” or “task.” Can these hooks be accomplished in less than 5 minutes or is it a separate structure from BTC?

I totally agree with you, Heather. I also have been thinking that much of what has been presented does fall in line with the Building Thinking Classrooms book. I wondered the same as to whether the Notice and Wonder would be considered part of the 5 minute intro or does it become part of the tasks worked at at the VNPS. Looking forward to learning more in the following lessons to clarify this thinking for me.

Great wonders here folks. We’ll be discussing these on our August 16th Live Q & A. We’ll post the replay here afterwards. Join in if you can.



I love the idea of withholding information. When planning a “textbook” lesson plan, you introduce a topic, explain, work together, and slowly release to them. But, when you withhold information, it becomes more intriguing for them. They want to follow along better.

The four steps of sparking curiosity sound great, but I am super overwhelmed at how to do them. I am looking forward to future lessons to clarify how exactly this is done.

I like the idea of withholding information to make the task more open. After listening to your blog I tried a few of your tasks and used notice and wonder. The students participated but it did not seem to spark curiosity. I did have a unique class this past year as I taught Algebra Readiness which was a second math class for student that struggle in math. As most do not like math and did not want to be there I worked hard to build a safe culture. One of my takeaways of this lesson is to realize that it is going to take time. Even if the kids are negative or barely participating I can’t give up. I know that these struggling students need this as much or even more to help them better understand math.
I hope I can better learn how to apply these 4 strategies in my classroom on a daily basis. As I get bored with the “normal” I teach you do way of teaching. But getting past students wanting to stay in the normal zone (even though in reality they do not like and and usually don’t get it) takes a lot more energy. I am praying this year I will be more successful than my attempts in the last school year.

Last year I tried using notice and wonder more in my lessons and the students really did become more engaged in the lessons. I intended to start my year with this, but haven’t yet. I however, didn’t think about the estimation part of the lessons. I will incorporate this into my lessons moving forward.

This is such an easy shift to build into lessons. Make a commitment and let us know how it goes!


I really appreciate the detail that you shared in the presentation.
I’m currently trying to build the culture of notice and wonder in a place where that has not happened in the past. It’s tough and I’ve made the mistake of not persevering enough. I’ve definitely heard the high flyer students getting annoyed and other students wondering when i’m actually going to start “teaching” them how to “do the math”.
Your course is my fuel to keep going down this path and find ways to spark curiosity about math for students who may never have had that spark before. Thank you.

The video really got me thinking about a lesson I use for surface area. The name of the activity is “Dandy Candies”. It is a Dan Meyer lesson. The gist is calculating the surface area of boxes that hold 24 candies (similar to the toothpick perimeter problem). I love the video, I find it mesmerizing. But I don’t think I am doing it correctly after watching your lesson. I do not allow time for any “wonder/notice” nor do I withhold information. We watch the video, usually three times, and then I tell them to find the box with the least amount of surface area and the greatest amount of surface area. This year I will walk the students through the 4step process (especially withholding information). I think it will make a good activity great. I keep coming back to the notion that I need to get out of the way of my students’ learning.
Another reflection is when I do the “Dandy Candies” lesson, I know I have about 45 minutes from start to finish. How often do I design a lesson or activity based on getting it completed within the allotted time? That generally means I am in charge and I will drive the car. I feel like it is a disservice to my students and their learning.

Never think of it as doing it wrong, but rather just not having the awareness of the curiosity path yet! Now that you know, you can try to apply the path to more problem based lessons!


I have done a lot of these techniques in my class but I never really thought about it as a way to spark curiosity. I like thinking of it this way because now I have more of a purpose for doing them and doing them more often.
Currently my class has been working on different angle theorems. As a move on in this chapter I will be more purposeful in sparking that curiosity. I usually think of these lessons as discovery lessons because I don’t just give them the formula, I help them discover it. But thinking of how I can spark the curiosity first rather than discover it, may make students more engaged. Perhaps having them estimate the angle measurement first or not even look at it as a math question but finding real pictures that have angles embedded in them may be a way to start these lessons.

I am not sure how to put these into my lessons this week as I work on operations with rationals. As I write now, I am wondering if I could tie it into statistics more or the stock market and see if I could spark curiosity by showing the decline of the market, but create some data that might encourage multiplying or dividing versus the huge variety of changes that happen naturally. I do see how I could use more of these ideas as we get to geometry and ratios/proportion work.
When I have tried something similar in the past, I do think I gave them the information too soon and so the Notice and Wonder sort of bombed when my kids who were more fluent with mathematical calculations would simply solve the problem.
Finally, I have to say my favorite reminder is that those high fluent calculators are going to be resistive and I appreciate the reminder that they are this way because they just want to solve it. That was a great reminder.

@holly.blahun You’re right! Sequences and series is a great topic to easily withhold information. Show the first two numbers and let them predict the third before showing them the third.
I’m also reminded of this sequence video from Veritasium: https://www.youtube.com/watch?v=vKA4w2O61Xo

I love this! We cover conjectures and counterexamples in Math 202 and this fits perfectly <3

such a cool video and such an interesting take on confirmation bias! Thanks for sharing!

Thanks for wasting the majority of my afternoon watching Veritasium. Now I really want to make a problem based on the 96 million shade balls on top of the reservoire.

There just has to be a problem hidden in there somewhere.