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
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Lesson 21 Discussion
Kyle Pearce updated 2 months ago 77 Members · 137 Posts 
Please 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.”

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.


I have also tried to use the withholding information technique. As your quote from Dan Meyer says “you can always add but you can’t subtract”.
In a more typical lesson on “finding angles in polygons” we discussed our findings from a prior lesson (sum of angles in polygons), students were told there was two steps needed to solve each question and given a worksheet with boxes to fill in each step to find the missing angle. Rather than a demonstration students were left to try the questions on their own, discuss why they were doing each step and we’re only prompted if they had gone off course.

Awesome. Thanks for sharing!
Wondering if there might be a way we could withhold even more information from that activity? Any thoughts or ideas here?


I use notice/wonder a lot in my classroom, and I do agree that kids get much better at it with practice. As a teacher in a sheltered (second language) classroom, It not only helps to spark curiosity, but it’s also a really great way to build and assess the class comprehension of relevant vocabulary. I would really like to try to use the “withholding information” technique a bit more, but it’s not something that comes naturally to me and will take a lot of conscious effort on my behalf to do it well.
Something that jumped out at me was that once you give kids the algorithm, they will always want it. In my educational context, students are trained to use the algorithm from a very early age (I teach grade 2 and grade 3). I have noticed that I can ask students to do problems, for example involving twodigit by twodigit multiplication. They know that the problem is asking them to multiply, and they rush to set up the algorithm, but they don’t know how to deal with the tens place in the second factor. so they just stop. They have said to me “we haven’t learned that yet”, and refuse to draw a picture, or break the numbers down, or think about another way that they could represent the problem. Do you have any strategies for getting kids to BACK UP from the algorithm?? Looking forward to more.

Backing up is so hard when they’ve been trained that they can’t do math without being explicitly shown exactly how to do each type of problem. This is extremely problematic.
An approach we use often is asking students to convince us… the answer doesn’t matter but what we really want is for you to prove to me why something works. This is incredibly difficult for students to do when they haven’t been asked to do this in the past and will likely require backing up to earlier concepts. For example, if they can’t represent an array of 3 groups of 4, then 2 digit multiplication is out of the question.
Students who are only procedural are not proficient in mathematics as there are 5 strands. Give this a shot and let us know how it goes!

What are your 5 strands of math? I’ve heard different models. Thanks!



I use notice and wonders alot already, but this conversation brings in some finer details that I need to attend to, especally the withholding of information. For example, for a recent notice and wonder, I showed a graphed system of inequalities, just 2 linear inequalities shaded on desmos and did a notice and wonder, to hope get kids to see the double shaded area. They had never seen a system before, but they have graphed single linear inequalities. I am wondering if that is to specific for a notice and wonder.

Is say that there are no set rules to a notice and wonder, however withholding information is the beginning.
So MY wonder for you is… what are some things you think students might wonder when you show them that? Is there much meat on the bone or is it pretty obvious as to what you’re “fishing” for? If it is too obvious, then it might not feel “worth it” to the students. Just a thought.


When I think about the 4 techniques shared in this lesson the big takeaway for me was the addition of the estimation or prediction of the answer. It really gets students thinking about what might be realistic. All too often I find students answer questions and have no idea if the answer seems right. They respond when pushed with “I guessed.” This estimation strategy gives them some parameters to work with.
I also appreciated the whole class’ voice in the notice and wonder and estimate and predict. When all answers are solicited and that culture is created that all ideas are valid. You target those reluctant students and give them a voice which is often overlooked in a math class.

Awesome to hear. Apply that to an upcoming lesson and let us know how it goes!


Estimating is something I want to use more. It gives everyone an entry point for the task and helps them get some “skin in the game.” Once they share their best guess, they will want to see if they are right and maybe even try some different strategies to improve that guess. And really, this is what math is for – making more accurate predictions.

I am thinking a lot about the ideo of starting the math dial at 0. I sometimes think about how math is weird to be a “seperate subject” and in an ideal world the class is “life” and we explore all the parts of it – including the mathemaical part. That would allow us to less likely define ourselves as”nonmath people” and more by our strengths because we all come into this class with the “math dial” at 0 and look at the situation from whatever context we are coming in with as people. It is a lot like the Ignatian Pedogogical Paradigm (https://www.google.com/search?rlz=1C1GCEA_enUS910US910&source=univ&tbm=isch&q=ignatian+pedagogical+paradigm&sa=X&ved=2ahUKEwj9mPSD99XuAhVqB50JHeU_CTAQjJkEegQIARAB&biw=1280&bih=578&dpr=1.5). We can start to get involved in the problem (even Johnny the humor guy with his strength).
It also reminds me of slow reveal graphs that Dan Meyer introduced me too (https://slowrevealgraphs.com/). We used this as an anticipatory set last week when we started with a SEL check in on what animal they were feeling like. Then did a slow reveal graph with those same animals eventually leading to a scatter plot analysis of brain weight vs. body weight (using Amplify’s new curriculum field trial). I see a lot more areas for more quesitoning and valuing student voice and estimation than I did last week as I look forward to this week.
Thanks!
This week I will be less afraid to let guys look at data/pictures/graphs without my voice jumping in but instead obselving for the opentings into the math that they will create.

Loving that you have some learning you can put right into practice out the gate!


This was a very interesting lesson to reflect on. Having done various 3 part and 3 Act lessons and trying to create engagement, it was great to learn why with certain lessons engagement intensified and then waned. I could never pinpoint why. I also reflected on when I created my own 3 Act Math lesson with a video, I withheld information which created a great deal of engagement. My problem was that I did not think through all the steps. I still had an engaging math lesson that I did not plan for because students gathered the missing information through a physical model but the different physical models were not what I intended or expected. The math went on a tangent that lead to different concepts being explored which was great and my revealing of withheld information was no longer that important. What these last few lessons have me thinking is how I can reuse my 3 Act math lesson to teach multiple concepts and not just what I originally intended. Next time I use my 3 Act math lesson, I will be much more intentional with the goal in mind and also anticipate how my students my engage with the math.

Great reflection! I feel like you’ve uncovered a game changer for yourself when you can extend a context to explore more than one concept. This will not only save time, but it will also keep students in a state of flow longer.


The bringing the dial down struck me. The belief is that we can apply math to everything we do but is separated from all other school content. (well, except for science, when the science teacher wants to complain that the students do not know how to graph.) But the idea of dialing it down and allowing kids to make those generalizations into other content and real world problems will hook them and enable us to turn the dialup.
The one technique I should work on is the “Withholding Information.” I have used notice and wonder with various success. Still, when there is missing information, students take it as a mystery of what information they will need to solve the problem. Like what was used in the chocolate problem where it was asked, “What information would you need to better solve the problem?” (I do not know what the exact direct quote is for that question) But if the students ask for the information, they would be more invested than if I just gave the information to them.

As I look back at my math learning experiences, I remember feeling annoyed at any mention of estimation. I thought of it as a waste of time, and it was never demonstrated that it could be a means of engaging in a math problem or be a useful skill,. Like Kyle, I didn’t see the point.
These four aspects of sparking curiosity are such a great starting point, and I appreciate seeing the design principle of planning 3, 2, 1, then 4. As a preservice elementary teacher, I am excited to try out these new skills in teaching, and I’m thinking of how these principles apply in other subjects.

My take away is that I need to be better about withholding information from kids. I know how important productive struggle is, but I have such a hard time not hinting and prompting. My new goal is to allow more wait time, withhold more information, and let the productive struggle commence.

So to be honest being new to my standards and not having a curriculum to follow creating tasks seems overwhelming at the moment. I don’t know what is coming in terms of building understanding or how students are going to react to it because it is my first time teaching these topics. I know that I want an engaging classroom and I know I can teach that way due to my science background, but I don’t know which tasks to select or which problems are the standard problems. I like that you broke down the steps based on your experience and can see the importance of building my own experiences, but I am still lost to where to start. I wrote on my notes when you talked about backwards planning my first step is finding the concept or word problem to create the withholding of information from.

This is so common and you aren’t alone especially when new to a curriculum or grade. I’d start with taking a task you’d typically use anyway and how can you hold back some of the information? It could simply be words to start or show an image from Google to get them talking. Of course, it is great to get a really elaborate curiosity sparking task, but in the beginning you need to keep your head above water and simply apply the curiosity path in a meaningful way for you.
Have you checked out our problem based units?
learn.makemathmoments.com/tasks


I have received in service training on these 4 aspects but I don’t think they were presented in any sequence. I see the value in the order, and am excited to try it. I am teaching isolating the variable and balancing equations next week so I will look at the videos you have made to see what fits. If you have any suggestions, I would appreciate it. We will also be writing 1 and 2 variable equations and independent and dependent variables. I teach 6th grade in the US. I am enjoying this course so far. You both speak from real experiences, sharing successes and mistakes.

Hi Teresa!
Glad that you see the value in these ideas and feel like you can put them together in a logical way!
For solving equations, the Shot Put unit is a great one: https://learn.makemathmoments.com/task/shotput


The need to build a classroom culture that encourages questions and curiosity was my biggest take away from this video. It makes so much sense the way you explain it. I’m hoping to learn more about how to promote the “math fights” which lead to this type of classroom culture.

Awesome to hear! Any particular round of math fight you’re hoping to explore first?

I guess I’m wondering if they all follow the same pedagogical approach, and if that is the case then I’m wondering what are the key steps in facilitating these fights. If they are different, then do certain types lend themselves easier to middle schoolers or to high schoolers?

I’d argue those we shared in this lesson apply across the grades. We will be exploring math fights in more depth later in the workshop so hang tight for that 🙂


Creating a vibrant and sustainable culture is not a standalone strategy. I agree with you to build the culture in my classroom and invite collaborators and ambassadors that will ignite the “math fights” and extend it beyond my classroom. Thanks for your post.


Withholding information stood out to me most. I’ve noticed that when I withhold information, students are more engaged in trying to understand the problem or story rather than being the first one to solve it. Offering context right at the beginning with images and videos that are relevant to their lives has also helped spark curiosity and more interest in math. I’m hoping to become better at coming up with context through images and videos that will continue to spark their curiousity.

MB,
I just love the way you weaved the content of the lesson seamlessly. You are a natural. However, the aspect that I couldn’t agree more with was the WITHHOLDING INFO. I am going to need help with that. Thanks for your post.

I have been using notice and wonder activities in some of my other subjects I teach and it is great to see how I could use these in my math classes. I agree that reallife problems don’t necessarily spark curiosity (and in some cases are actually quite boring), so I really enjoyed seeing ways to change these problems to be more engaging. Currently, all of my classes are remote, and I am aware I need to work on withholding information more in this environment. I struggle with the feeling that I need to give students all the information since we aren’t in class together and I can’t physically see many of them working through the problems.

I am eager to change as many of the textbook problems to NoticeWonder type problems as I can. I am certainly someone who has changed the name so the problem is about me, or me and a student with 2 different answers – and it helps a bit, at times, with some kids – but definitely not the ultimate fix.
The ones that really come to mind are Sequences and Series problems – pretty easy to withhold information and let them analyze it one piece of information at a time.
I do really like the area/rectangle and the moving dots for systems of linear equations. I can wait to use them in my grade 10 and 11 math classes!

@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



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

When I introduced NOTICE/WONDER strategy, I noticed that most of the students were solving the math instead of writing about what they noticed. It took a whole month before they gradually bought into it, especially the high achievers. Thanks for your post.


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.

Fantastic task and great reflection / realization about the importance of estimation. As you approach great tasks through the lens of the curiosity path, you’ll start to see more opportunities to leverage purposeful questioning. The result will be an increased level of intentionality all around!


I really connected with the idea that you can always add, but you can’t subtract. I did an activity with my students where they were given a trapezoid and asked to divide it into sections and find the area. It is amazing how many different ways there are to cut up a trapezoid, but sometimes when I do this, some of the students have the formula for the area of a trapezoid memorized and that is all they want to use. I want to subtract that information from their minds, but I can’t.

@marjorie.allred It would be perfect if all students were blank slates! I’m ok if students use the formula but what I would do is push them to demonstrate why the formula works. You could also ask them to solve the problem as if they didn’t know the formula “How would someone who doesn’t have your memory for formulas solve this?” I’d also have a different shape in my “back pocket” for them. Like find the area of this regular hexagon. Can you make a formula for that?


These are the things that I desperately need in my math classroom! I have the lower students, the ones who have already decided that they’re “not good” at math, and have given up. If I can spark their curiosity, then I’m able to introduce math in a very nonthreatening way and get them thinking like mathemeticians…discovering patterns, making sense of things, figuring out next steps, creating math discussions (“Bruh, there’s no way that could be right”). Fantastic! I’m excited to bring this to my classroom.

I have tried the notice and wonder technique, but now realize that I did not create a culture of curiosity. I did inspire students to be curious about that particular demonstration so I got more students involved. After your video I realize that I missed some opportunities to engage more students in the sense building after that. I got them interested because the presentation was different than the typical math lesson, but it fell short because I was coteaching that day with one of my colleagues and we were limited to that one period.
At the time, I realized that it would have been better at the beginning of the unit, but I did it at the end to help students put all the pieces together. I didn’t know how to continue building these types of lessons in the future. It is becoming clearer.

@karynn.faivre Your realization is exactly what Kyle and I did…but it took us a lot longer to realize that we were leaving a lot of curiosity and sense making on the floor. Moving these to the start of the topic will change the atmosphere!


The idea of deliberately determining what information to withhold in order to spark curiosity feels like a real eureka moment for me. Upon reflection, I can think of times when I have done this without a good plan, and how the curiosity leads in a direction that is not intended. I can see how planning around this is essential to the other aspects of sparking curiosity.
During the workshop, Kyle makes the connection between this withholding of information and how it allows students to make sense out of a given scenario. I can see how, when students are able to think critically around problem solving, they are able to develop a better grasp of the mathematical concept. This sense making piece is what is so often missing in our historical math classrooms.
I have definitely already experienced some highachiever avoidance while trying to engage students in some tasks. The need for spending time to build a classroom culture focused on problemsolving, perseverance, and normalization of mistakemaking seems particularly important for providing a space for students who have had prior success in more traditional classrooms as well as those who have struggled historically.
The prospect of the challenge of developing a culture of engagement is invigorating.

@theodore.crum We’re so glad we’ve sparked your eureka moment! While the next steps to create those moments so we can fuel sense making will be tough, the success we see in our students will be worth it.


I am trying to think of how to withhold information for next week’s lesson on stocks & bonds. It feels like the topic is very limited. Any thoughts how to broaden it? There are only 2 weeks left of school and I have 2 classes with a few juniors left (seniors graduated earlier). I know that I will not be able to create the whole culture at this late stage of the game, but would like to dip my toes in the strategy. I would appreciate any thoughts that you have.

Starting with ANTICIPATION will be a game changer. It will give me the hook, and then following it with NOTICE/WONDER, will be bearable. However challenging them to estimate will be brutal because it will take a will power to WITHHOLD INFO.

@azuka.ojini You’re right! Withholding the information is tough especially because our whole careers we thought that to help students we should give them more information!! Stay true to the framework and you’ll see great results in engagement and deep math reasoning.


I think for me the hardest part will also be withholding information, but not just because I have to stop myself from giving the information. I work at a school serving an international community where students have had very different past experiences with math expectations. How do I stop students from sharing the algorithm they’ve learned in other locations? I find that once they’ve shared it (usually in the notice & wonder stage they ask and answer their own question), it is challenging to get other students back to being curious. These are also the students who tend to resist the change in how the material is being taught compared to what they are used to.

My favorite technique is withholding information. I think it is really powerful for students to think about what information they will need or are curious about.
I am finding it challenging to come up with these anticipation problems that with hold information.

It certainly feels difficult at first, but as you continue to think about what can be withheld, it will start to feel natural. You got this!


The 4 techniques are Set up (Notice and Wonder), anticipation, withholding information, and estimation.
I have used Notice and Wonder many times, though not with a video. I’ve used this technique with Algebra and Statistics. I would have the students look for a minute, write, then share with a partner then group (thinkwritepairshare), then whole class (I’d ask each group what they noticed or wonder).
I tried withholding information several years ago with an Algebra 2 class and pretty much got crickets. 🙂 But I, and the students, were new to this technique.
I like the idea of using several techniques together to spark curiousity and will be using more than one to start our lesson or possibly at the end of class as a teaser for the next day’s lesson(?).

@kristina.hill I also would get and still get crickets the first few times I use these techniques with students who have to used them before, especially higher level classes. Keep at it as using them will change the atmosphere of the room.


The quote, “the success of Notice and Wonder hinges on how effectively the task creates the feeling of anticipation through the withholding of information,” was very powerful for me. I definitely related to your stories about lesson flopping because the notice and wonder weren’t set up to spark curiosity and it wasn’t something that I used on a regular basis. I think part of why I didn’t use notice and wonder more was because I wasn’t sure how to use it effectively which caused students to complain about it so I stopped trying it.
I am excited about implementing this 3part framework in my classes next year. I feel that all 4 techniques to spark curiosity are of equal importance, including the estimating or predicting the answer. I know I often tell students to doublecheck their answers to see if they are reasonable and the typical response is, “I used my calculator so it must be right,” indicating they don’t understand what it means for an answer to be reasonable.

Fantastic reflection. I agree that all four are important and really hinge on each other. One thing I’ve really committed to was designing lessons to be low floor where students can reason through problems with friendlyish numbers that can be modelled so they have conviction when they arrive at their answers. Models and strategies are so key for this.


One thing I am looking forward to as I begin planning for next year is how I can take “traditional” problems, like you’ve modeled, and rework them so that they create these moments that spark curiosity. At this point about what a math class might look like taking this three step approach. How does this feed into direct instruction, teaching the procedures, etc. I would love to see a full math class with high school students.
From a technical standpoint, I would love if you guys shared what video editing software (and other tech) you use – for example, how did you make the perimeter/area clip with the sticks moving and rearranging? You mentioned Desmos, but if you have a “Here’s what we use to do this activity/screen shot/video, etc.”, that would be fantastic!

You can check out 30 days in a row from my high school classes (in 30 minutes) so you can see what this could look like https://mrorrisageek.com/30days/
As for editing software we use Apple Keynote to do almost everything. There is a slide transition called Magic Move that works wonders for animation!


I have tried the 3 act math activities with my grade 9 applied classes and always felt I was missing something. I don’t think I spent enough time, letting them wonder, or anticipate… and then when I gave them the information, they had in some cases, lost interest in what we were doing. I know that is what I need to work on, sparking the interest and curiosity at the beginning. This is helpful – Thank you!

We’ve all been there! Purposeful questioning has been a huge help in trying to firm up the process for me… We will be exploring this more throughout the remainder of the workshop!


I appreciate the mention of the resistant “high achievers” math student. Why are we putting a barrier between them and their 90%? Just give the numbers and formulas already and stop waiting their time! I can relate to those comments. Pushback from a student like that would definitely frazzle me when trying this new (to me) technique. Thank you for mentioning this and preparing me for it. Ever get comments or pushback from parents as well?
Setting up the class culture, do you start with shorter, easier, or more obvious problems at the beginning of the year?

Parents can also push back, which is why it is so key to spend the necessary time building the culture of what we are hoping to achieve… resilient problem solvers who use reasoning always.


I need to remember that I can always give more information, but once given, it you can’t take it back! Also, that when building the lesson you want to work backwards… how to build anticipation by deciding what information to hold back in order to successfully “do” the notice and wonder component.

That is a huge take away and so hard to remember and/or hold yourself back from doing… be intentional about this shift and it will become natural.


this lesson converged with what I’m currently learning in a PD about creating a democratic classroom: if I want ALL kids to engage, it seems starting the math dial at 0 is a brilliant way to reduce math anxiety and perhaps get kids talking who don’t see themselves as good at math. Also, the opening problem can provide the “why” for what we’re about to learn. the example in the other PD was to start a unit on food safety by asking “who’s ever had food poisoning?” It led to a really engaging (gross) story that brought home why we’re studying food safety. I could see using that same story in a unit on temperature (I teach 4th grade).

Love it. Showing students that math class is for everyone is so important and can’t be reiterated enough… even if some gross stories come from it 🙂


I need to remember to withhold some information. I can see how this would spark more curiosity.

I appreciate how all of the first three techniques are very much intertwined–by withholding information, you create anticipation, which gives students space and the ability to notice and wonder. I have used estimation in my classes before, but I can see now that on its own, it doesn’t have the same impact.
All of these techniques give students the opportunity to be able to think for themselves, which is a skill that is very much needed. I’m so done with just “spoonfeeding” students information, and am so excited to put these into play in my classes this fall. I teach reading also, and am hoping to use these techniques (with some modifications) to improve my reading instruction as well. Thank you for this course!

So amazing when educators have epiphanies such as the Curiosity Path and what is missing from our usual estimation routines. We are extremely happy that you are here learning and even more so knowing that the learning is resonating! Keep up the great work!


It really shows you all were educators because I was a squirrel trying to crack the effective teaching nut for a while. At one point a flipped classroom was the new educational kid on the block and it was a contest to see who will achieve success with it. Creating videos was going to somehow unlock closed doors. It seems every year there is a new book and the educational community jumps on the wagon because of its popularity. As a teacher, I glean ideas thinking all these little truths over the years will somehow reveal the secret of teaching success.
I say this because my takeaway is the Curiosity Path is an indivisible structure. Removing (or adding) any element in the structure means losing the effectiveness of the proceeding elements. For example, I really want my students to think critically about a problem and find an approach to solving it. This cannot happen until we Notice and Wonder to think about possible methods to attack the problem first. Notice and Wonder can never happen unless there is something to wonder about which is why we need to withhold information and built curiosity through anticipation.
 This reply was modified 3 months, 3 weeks ago by Anthony Waslaske.

So agree with you on this one. There are new ideas – especially technology centred – that seem to show up all the time. They intrigue, but often times still miss the mark on lasting engagement or sense making. Happy to hear that the Curiosity Path is resonating with you and you’re seeing how transformative it can be when put to use in the classroom on a regular basis!
Keep up the great work. You’re crushing the Online Workshop!

I just completed my first year of teaching (5th grade Math and Science) and the ability to withhold information was definitely a challenge for me. (It was so easy to fall into the trap of limiting my students’ struggle time.)
I like how y’all focused on crafting a classroom culture that is willing to slow down and participate in a “notice and wonder” activity. Even though I do have some ideas (and am looking forward to implementing them) on how to spark curiosity with my 1st graders, my question is how is this accomplished when you are required to post and discuss learning targets at the beginning of each lesson?

I have had a lot of success with Notice/Wonder this year, but it was always with material prepared by you guys, or Graham Fletcher, or a Slow Reveal Graph by Jenna Laib. I am eager to try modifying my textbook problems to achieve the same results, but I am also really nervous and I am doubting my ability to bring the creativity and outofthe box thinking to that task. I know, I know, just take the plunge and don’t worry about getting it right.

My quickthinkers want to write 3 words and get moving. I would like to push them to write complete sentences, paying attention to spelling… but I don’t want to slow down the creative process. Any thoughts?

The comment regarding the smart kid who didn’t want to “notice and wonder” resonates with me. This past year, I would use desmos. The number of times I had students say “I prefer you teach” was difficult to ignore. By the end of the course, I asked did you learn and always heard “yes, it made me think”. Acknowledging the student and explaining I have to ensure all students are engaged and learning allowed the student to accept what I was doing. Thank you!
Creating the problems – I have been dabbling with Notice and wonder – this session has given me ideas how to change those textbook examples with all the information.

This week I had the opportunity to try using the too low and too high with estimation and was impressed with where the students’ conversation went. Their higherlevel thinking and explanations led to overall better understanding and willingness to participate. I look forward to incorporating withholding information as I can see how this will benefit and engage the students to anticipate and dig into the notices and wonders of a problem.

I have used all of these strategies at one point or another, but I don’t think I have ever strategically used ALL (or several) of them together. Thinking now that this is why, while I saw some success with each strategy, it was fleeting, and I eventually moved on to try something else. Now I realize the importance of using these elements together. Some of this is so frustrating because I knew about all of these things but never put them together. Seeing this video was like a huge DUH moment, something I should have figured out, but never did. Instead of worrying about what I didn’t do in the past, I can take this insight and move forward with this new way of doing things.

I have noticed that students struggle to identify what information is needed to solve the problem. They often get caught up in information that was included as a distraction. I am sorry excited to see if withholding information can not only spark curiosity but also help them to recognize distractors for what they really are.

It’s interesting that when I saw “Withhold Information” on the 2.2 Curiosity Template that I printed to prepare for this module, I assumed you were going to talk about the use of “numberless word problems,” which is a technique several of us in my building have been trying out or have talked about trying. But I see that you are talking about much more than that.
I paid close attention to the chocolate lesson from both the teacher and student role as you suggested, and while wearing my student hat, I was completely engaged and eager to see the next part of the video. I wanted / needed to see the next part of the video so I could get closer to the answer. I like the way that Anticipating and Estimating go hand in hand. My estimation is tweaked each time I get a little more information. I think it will take practice to know which information is best withheld that will create the most “I gotta’ know the next part!” in students.
I have been taught math for 22 years in grades 2 – 5 at various times. The value of Estimating is often underestimated! I had to chuckle when you said, “The direction to estimate comes up more than the direction to calculate (find, solve, etc.)” It’s so true, and I am also guilty of saying, “Boys and girls, make sure you estimate first so you know if your actual answer is reasonable.” or “Make sure you practice estimating because very often in real life, an estimate is good enough.” I KNOW that a lot of my students found the actual answer first and then went back to satisfy the direction to estimate, after the fact.
In the context of Estimating here, it is much more intentional and I love the question from the first Module “What do you want to know from me to help you improve your prediction?” I can see where this would lead to amazing math conversations.
 This reply was modified 3 months, 2 weeks ago by Terri Bond.

@terri.bond Nice reflection! It looks like you’re making all the connections we were hoping you would!

I really like the idea of using these techniques. I say idea because I have tried to engage, usually grade 7s, and well they are all about how do we use this in real life. I have used some of the videos available for my students this past year and we did some of the N&W. I liked how it played out, but I love the idea of writing down everything. I do think that will help lead the students to see the big picture. I am sure I have used the other techniques but I do think planning to withhold information will be my new favourite for grade sevens. I am thinking about how to teach my next year (6/7) so I can see this working well with that grade.

LOVE the idea of creating something like this during our 5th grade physics unit for graphing motion. Could really get some intriguing ideas for notice & wonder that could really build anticipation as opposed to her is a graph. What is the motion? B O R I N G!
In math, so many kids just want to know what is the formula to use to solve it and what numbers go where. Kids almost feel they don’t have to think anymore. It’s sad that we need to put “thinking” back into “learning”. Let’s do it!!

Love that you’re seeing ways to spark curiosity. You’re right, too… kids will ask for the “steps” to “get it done” if we allow it. Keep those purposeful questions flowing!


In this year of social distancing in the classroom, this kind of task allowed us to work differently as a group. I was able to explore the Notice and Wonder aspect but can see ways I need to improve my planning to make the most of these opportunities. Viewing the lesson both from a student’s engagement and the teacher’s planning, helped me develop a more useful perspective.

The 4 techniques to “Spark” curiosity (aka the Curiositypath) is great. A good order to get the students ready for the math, by having them pretty much wonder about how to solve a problem related to the math for this unit, and to also think about the kinds of problems that can be asked because of the situation presented.
While I was listening to the podcast, I got an idea of doing this path of curiosity for Primary Trig Ratios, and went searching on the internet with the search phrase “Relevance of Primary Trig Ratios” and there were things like Physics, Astrology, Surveyor, and related pictures – so my thought the “Witholding” piece would be to show a picture (relevant to one of those fields) but not tell them what the question is.

@velia.kearns We can totally achieve this with trig ratios. Have a look at an old lesson I did https://mrorrisageek.com/introducingtrigthroughslope/ I’m wondering how you can modify it to fit your class?

Interesting idea connecting it to slope – I didn’t even know there was a connection – when I looked at your lesson, it made sense.
During my research, I thought of the sine wave of a unit circle. I went to you tube and found this video that I liked: https://www.youtube.com/watch?v=Q55T6LeTvsA
So, like yours, I would get them to wonder about a unit circle. Where the height of the right triangle = sine of the angle. Try many angles and see if that is always true.
The connection can then be made that the radius being 1 helps that fact, but if the radius was larger than 1, then height/radius = sine of the angle.
**Researching also talks about Rotational Motion, or Velocity over time. Things to investigate for realtime examples
https://betterexplained.com/articles/intuitiveunderstandingofsinewaves/
 This reply was modified 3 months, 1 week ago by Velia Kearns.

Great connection here! So much to be explored in the unit circle!



I got many things out of this but I will highlight one of the last points of “turn back the math dial.” I often would start right in with the actual math rather than work my way into the math discussion and thinking in a natural way that came from their own curiosity. Instead, I would sometimes try to create or use other materials that had tie ins … but it wasn’t where they were and it wasn’t addressing questions they had.
There were moments when I felt comfortable enough to “slow down” on the fly and address some of where they were.

Great take away. This is something I’m now always thinking about. How do I make this as intuitive as possible – not to avoid students engaging in a productive struggle, but to allow everyone to enter and stay engaged. Glad you’re seeing it as valuable.


I have been incorporating Notice and wonder into my classroom more frequently. However when creating my own notice and wonders, I didn’t withhold enough information nor did I use estimation. It is comforting to know that strategically withholding information allows for estimations and predictions. I am going to edit one of my notice and wonders questions from last year to allow for estimation.
Thank you!

Excited to hear if you start noticing a difference regarding what students come back with. Keep up the great work!


My biggest takeaway has to be that you can always add to the problem, but you can never subtract. I have used numberless problems, but this seems a step further. I always felt like I needed to give the students all of the information (the equations, the steps, or even what they are solving for)at the beginning of the problem in order to be fair. I needed to be the giver of all knowledge, too. That was my job, right? Or at least, I thought! I don’t think it was sparking any bodies curiosity. If I withhold information, I’m engaging them in the task. They can even be the ones to find the equations and steps. This changes the whole idea of my role in the classroom.
 This reply was modified 3 months, 1 week ago by Tracy Arriola.

Tracy – A few years ago, I stumbled upon the idea of numberless word problems while looking for an art lesson. After completing this module, I realize I must modify my approach a bit; however, my purpose in reaching out after reading your post is this…Take the risk! While I do not know the age range of your target audience, my 78 year old students confidently face word problems. They have learned to “read the whole story” and “do the thinking” to determine what information is missing and which strategy they might like to use, rather than looking at the numbers and guessing an operation. It takes time, for sure. Yet, the payoff is satisfying. Over the past four years, several families and receiving teachers have made comments about how excited their student(s) are to be “detectives” and solve the “mystery”(word problem). They are motivated to defend their thinking and love to create their own mysteries. Next fall, I will begin even earlier in the school year, incorporate the other 3 techniques from this module (notice and wonder, anticipation, estimation), and refine which information is withheld. I wish you all the best! Andrea

Things I learned
1) Higher achieving students might take a bit more convincing but power through and the rewards will be great
2) Withholding info is a simple tool and makes a problem way more interesting
3) I was not valuing estimation skills in my class and withholding information is a great way to start building that into my lessons

I learned SO much in this part of the lesson….Inherently we know that kids like to figure things out…I know that my challenge will be “How to create safe and inclusive culture of Notice and Wonder” in my class that is centered around student voice….I am planning to work on this this summer so that I can include these elements in my classroom from day 1 of the 20212022 school year….Indeed I want students “dying” to solve problems and becoming more engaged in “THINKING” about problems while they are in my math class. Also, utilizing the most important tip – withholding information to spark interest and curiosity in carefully selected tasks will be key to implementing this in my classes.

I like the idea of these techniques. My nuerodivergent brain will likely struggle with these in the beginning and need a lot of planning ahead where as I feel real comfortable winging it a little bit sometimes. When I try to plan things out I tend to OVER plan and it creates a lot of anxiety. These techniques seem like they will greatly help me to minimize that overplanning and create more interest in mathematics and how it is all around us. I can see this drawing in students of all types of learning since there are often no right or wrong answers in this discovery process.

As a primary teacher (K2), I notice that many examples are of higher/advanced math concepts and presumably, the potential student audience would have mastered foundational skills such as, counting, cardinality, and conservation of number. I wonder how to use these techniques (1. notice & wonder, 2. anticipation, 3. withholding information, 4. estimation) with students, especially those who have yet to grasp 11 correspondence.
So these are my questions for Jon, Kyle, and/or any of the participants –
*Are there any prerequisite, foundational, math understandings that must be taught explicitly?
*Are there any math concepts that must be understood/mastered prior to following these techniques or the framework, in general?
*When would I use the 4 techniques unpacked in this module? All of the time? Some of the time? When I introduce a new concept? When students are solidifying new learning? When students are extending new learning?
*Is there still a place for direct teaching of concepts, especially in a primary classroom?
I have the advantage of being with my students the majority of the day, except for Music and Physical Education classes. I am confident that the emphasis placed on building relationships, social and emotional learning, and inclusionary practices supports the creation of a “safe space” to notice and wonder. This module has provided some points for reflection regarding the 3, 2, 1, 4 planning sequence. These will serve to increase the effectiveness of our regularly scheduled Notice and Wonder segments woven throughout our day.

@andrea.earle These are great questions to hold close while going through the remaining parts of the workshop. We chatted about these questions in our past live q and a chats. Here’s one you might want to watch/listen to grapple with these ideas. https://learn.makemathmoments.com/modules/march62019isthereatimewhenpreteachingisappropriate/
March 6, 2019: Is there a time when preteaching is appropriate?


I am loving everything about this course so far. I am slated to teach the new destreamed grade 9 math next year and I think all of your ideas and techniques will be wonderful for that class. I was worried about having students of all different abilities on top of the fact that students have been learning online for the better part of a year and a half and I worry about how much math they have learned. However, I think I could work on building this type of inquisitive classroom community by going back to grade 7 and grade 8 curriculum to go over at the start of the year so that they see things that are familiar before we get into the grade 9 curriculum.

I am enjoying this class tremendously, but I also worry that it may be beyond my little grade 2s I’ll be teaching next year. I’m having a hard time seeing how this works concretely in the much younger grades. The Notice and Wonder I can make happen, but I’ll have to spend a bit of time starting the appropriate lesson.
On another note, I teach in French, which isn’t the students’ first language, so I’m excited about the N&W developing beautiful math vocabulary for them to use.

The curiosity path can be huge for lower grades to help build vocab (like you’ve mentioned) and also capitalize on their natural curiosity. You may find it easier to grab that curiosity than teachers of middle/high school.
Even though our examples are geared for a higher grade level the key ideas and concepts will definitely apply to your grade level. We’re excited for you to get to module 4 and 5 where we bring in fuelling sense making!


I love all this. I am wondering though…how are your tasks…that spark curiosity…the same and different than Dan Meyer’s 3 Act Tasks?

Both you and dan Meyer spark curiosity by withholding information in videos. What other platforms do you use?

Hi @mary.Rathlev
I would say that many of our lessons are similar to the approach to a 3 act math task. One big difference is that ours isn’t always a video – it could be an image or even a story problem stated verbally. Also, when you explore our problem based math units in the tasks section (learn.makemathmoments.com/tasks) you’ll notice that we give a full guide to break down the intentionality of the task, student approaches and how to consolidate. This is not common with 3 act math tasks shared out there.


I am very happy to be taking this course. These techniques are exactly what I feel I need to add to my teaching strategies. My school uses the Carnegie Learning curriculum and my math team often feels like we must follow the book exactly as written, but I feel like we can use the content and mix in the curiosity techniques to cut out the dryness of a math curriculum.
The ones that stood out to me most where the “Notice & Wonder” and “Withholding Information”. The math content and problems are there in the book….would just need to make adjustments with the strategies to change up the presentation of the math learning in my classroom.

I think that sparking curiosity will be the key in my classroom. I have a very good relationship with my students, so I usually get pretty good engagement with tasks. But I honestly feel some students are just going through the motions and doing the task because I have asked them too. I am excited to see the difference when they are engaged in a task because they are actually interested in the outcome and how to get there!
I also definitely need to use estimation more in my lessons. I often talk to students about estimating at the end of a solution to see if their answer makes sense. Estimating BEFORE they begin working on a solution makes way more sense!

I will be a first year teacher and I’d like to use Notice and Wonder. I thought the tips about making it part of the classroom culture were very helpful. If students haven’t bought into the idea they won’t participate. The first few times students will be reluctant to participate if they have never been exposed to Notice and Wonder before.

It’ll take time and effort to get started, but the payoff is huge if you stick with it!


I really like the idea of “turning down the math dial”. Sometimes I get so focused and anxious about the end result of kids getting the standards, I miss the whole point of actual long term learning. Curiosity has always worked for me as a learner and it is really cool to ignite that in the Fourth Graders I work with. This is all inspiring and gives me a lot to reflect on and think about!

The dial is such a great metaphor to keep in our minds.


I’ve done withholding information before and really love it. I’m so glad you addressed highachievers reaction to this though because I saw that immediately with my students. They were used to being told exactly what to do, in what order and were very successful with that approach previously so they pushed back with a new format. However, it did yield success later on when one of those same students remarked that one of our endofyear unit lessons was “the best sequence” he had had in a math class and that it made “so much sense” the way I taught it.

I found it very interesting when I also withheld information when students were working on circles. I gave them tools to try and measure them physically and find relationships between them. They told me they really enjoyed the task and everyone was working hard!

Withholding Information in math problems will be most challenging for students, but over time it should certainly help them to strengthen their analytical and problemsolving skills especially if there is a strong sense of Anticipation which is bound to make learning fun and spark curiosity. I think Notice and Wonder is a technique that most students should be familiar with as it is used in other subjects such as Language Arts, Social Studies, and Science in middle school. Weaving this into Math culture might seem out of place to students at first, but it should not be a difficult experience for them. Estimation is a technique that we typically strive for students to use regularly as a first step in problemsolving; I like the idea of incorporating it after Notice and Wonder because it lights the way to a more reasonable guess for a realworld problem.

Totally agree! It seems that somehow math has been looked at as a subject completely unrelated from others when it comes to pedagogical approaches. However, we are now starting to realize that it is actually pretty similar and many approaches can be helpful in math as well. Let us know how you progress!
