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Lesson 1-5: Question & Discussion
How does the lesson style you witnessed in the Lesson 1-5 video compare with traditional math lessons? What are the benefits of this style of lesson? What are your reservations about this style of lesson?
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114 Replies
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In lessons like this, the students are engaged in the problem at the start of the lesson and excited to figure them out, whereas in traditional math lessons it can become mechanical, especially when students are not actively engaged until the practice which typically occurs at the end of the lesson. In the latter the teacher is doing most of the thinking.
Benefits: My students enjoy notice and wonder questions because they are all capable of noticing and wondering. I believe this aids in building the confidence of low performing students. I especially enjoy how problems like the ones in the video have a low floor and many different ways of approaching the problem which make it accessible for all learners. I love how Kyle mentioned coming back to a task that was previously used. I did the post-it note and camera case lesson for slope this year and referred back to it informally last year. Now I am excited to think of questions I can use when re-introducing the problem for writing equations of lines and systems of equations.
Reservations: The challenging part for me is feeling overwhelmed, like I need to scrap everything I used to do and dive into this 150%. I’m not sure if I need to spend a year going fully problem-based (try the illustrative mathematics curriculum), pull problems from all of the resources I’ve found through MMM Podcast, or figure out how to spiral my curriculum.
Thankfully I used the pandemic to test out problem-based lessons and did some exploring and tried many new activities, so I have a place to start.
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Traditional Math Lessons are more “Organized” and Compartmental.
The lesson here was more Organic, and could lead to connections with larger contexts like the math was intended for. Being able to pull the idea from a previous lesson was easier because the “moment” was closer to the memory. It existed in more than just rote copying of an example – but had hands-on, visual, friends talking about it, AND notes.
In this lesson, the notes weren’t the goal – the expansion of the idea was more the goal.
Questions:
When will notes ever be the goal?
I like to show students “Structure” in writing the answer; there is less structure for this lesson – for example in High School writing the x for multiplication wouldn’t be a good thing since it’s a variable – so brackets are advertised/used
After you do this type of learning – for how many days? – does the traditional math class ever come back?
This lesson style is there to spark and fuel, but then part of the connection is the rote copying of notes and examples, isn’t it?
I can use this for the concept, but I also need to “Show” them how to write the answer when dealing with the problem – after they learn how to identify and think through what’s being asked.-
This reply was modified 1 year, 8 months ago by Velia Kearns.
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Great questions here.
In short, the goal is never to copy notes despite the fact that for about 10 years in my classroom, that was pretty much all students did. A question to ask about note taking is what skills are students developing and are those skills what our goal is for students in math class?
The structure can come during / after consolidation as we make connections and summarize our work/ findings. This should be co-constructed by the facilitator and the students (not a copy job).
Check out our problem based units to get a sense of what a 5 to 8 day “unit” would look like / sound like: learn.makemathmoments.com/tasks
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This reply was modified 1 year, 8 months ago by
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Traditional lessons are planned and structured. The lesson starts with the teacher. The teacher tells the students exactly how to do the math for the lessons. Most of the time we are providing them with one way to solve the problem. We provide notes as a roadmap for later. The students copy the work of the teacher. When they get the right answer, we say they have mastered the skill. For students that are below level, they will need some intervention because the lesson started above their level. The enrichment for the students that are successful will happen once they have shown mastery of the lesson content. Most lessons are independent of each other. The traditional lesson seems to take away the student’s ability to think for themselves.
This lesson is also planned but is structured off of the students. The lesson starts with the students. The notice and wonder engages the students. As the teacher presents the problem for the students to solve, it allows students of all levels to start at their level of knowledge. The intervention or enrichment for all students can happen in the lesson. The lessons connect content.
My reservation comes from it feeling like you are giving up control. What if we don’t match up to the pacing guide? How do you build the culture in your classroom, if the students don’t know where to start?
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These are great reflections and wonders.
Pacing guides are always tricky since traditional lessons didn’t help you keep pace either – not unless you were willing to move on without students understanding. The same could be true here: I can keep moving along despite students not being ready or I can meet students where they are and help them progress accordingly.
Building the culture takes time and we will dive into that more throughout the online workshop. When students are stuck, we use purposeful questioning to help get them unstuck.
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An interesting result, of focusing in this direction, is watching the students who are bored because math is so “easy” becoming engaged in stretching their mathematical thinking. Making room for multiple ways to solve problems also validates the different thinking of less traditional learners. A third result is that everyone seems to be more engaged in what is learning. Many students who come in hating math begin calling math their “favourite subject” because their minds are engaged and their confidence has grown. I am on the journey of learning this style of teaching and have already seen these results.
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Instead of the teacher being the one in action, the students are the ones in action. The teacher is a moderator instead of the center of learning. Many different models are used to solve the problem. It is problem based. The students have to think not mimic!
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First of all this one situation can be used in many different ways. It is possible to come back to it later. It is also very visual. It avoids going to numbers and symbols and instead uses pictures and reasoning.
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The benefits is how much the students are doing the thinking. They are the ones making the connections. You don’t have to do that for them. Kids will be way more engaged in these lessons then they ever could be in the traditional type lesson. Students also have multiple entry points in a lesson of this type. I loved it, especially the connection to the derivation of the volume of a sphere formula!
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I feel like this really breaks it down into tactile pieces rather than a lecture style. I think this type of lesson would make it easier to creating grading based on the TEKS rather than trying to rush through a lesson and then fight with students to complete their work. I have seen so many students who have failed classes because they did not connect with the work or format of the lesson even though they completely understood the concept. I feel this could also be completed online with students who may be out sick and need to make up this lesson. We could also utilize feedback sites such as NearPod, Padlet, FlipGrid, and so many others.
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This lesson style is more student guided instead of teacher led. The teacher still has a leadership role, but the students help lead the class as well with their ideas. This would give the students a feeling of control, and pride when their ideas are shared, heard, and encouraged. The reservations of this style of lesson would be the time it takes to get to the final product, as well as the nervousness of the teacher with what can be perceived as lack of control in the classroom while the Sense Making is taking place.
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@vanessa.watt These concerns are definitely valid! Luckily being in this course should help you with both! Looking forward to helping you along the way.
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The lesson gives students a place to start, no matter where they are mathematically. There is less pressure to have the math concepts thrown out right away. It gets students to start thinking and making guesses, whether right or wrong. This usually gets students stuck because they won’t move on unless they feel or are told that they are right. The lesson demonstrates math in its essence…which is what I have loved about the subject. Taking a very simple exploration and show how it can be used to demonstrate very high level of mathematical thinking while giving all students an entry point and now feel as intimidated.
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I am looking for the Chocolate Mania Lesson under Tasks as you directed and I don’t see it. Does it go by another name?
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The lesson style I saw in the 1-5 video feels less structured and not as predictable as what I have traditionally planned for. It feels much more engaging for me as the teacher and for the students in the classroom, I see this as a benefit for all. I also see benefits for my students because they are the ones doing the thinking and sharing their ideas with one another. I like the way all students have access to doing the problem the way they see it. Some reservations I have are about my lack of confidence in trying to carry it out since it is so new for me. I also worry about how one student’s idea may side-track what I think the main goal for the day is. I think that is what the consolidation process will help with.? My other reservation is about other “type A math teacher planners” out there. How can I convince them that this is worth trying?
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Great reflection and great wonder.
You can still be a type A planner – and probably should be – as there is much to think about upfront. See our teacher guides here https://learn.makemathmoments.com/tasks and check the guide tab to see all the thinking and planning that goes into it.
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This lesson is the complete opposite of the way I have been teaching. As per school board directed instructions, I have always posted and discussed the learning goal prior to any lesson. This lesson makes me realize that I have been “robbing” my students of their curiosity path. This lesson also validates what I tell my students. I am always saying that they don’t need to use the method of solving that I show them. My direct teaching method, however, really doesn’t promote that…now wondering how many students are actually thinking “yeah right!”, when I tell them this. I love how we can highlight all the different methods that students may use to come up with the correct answer…maybe now students will believe me:)
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There is much more room for student discussion and for students to approach the problem in different ways.
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This type of lesson is so engaging and fun! I wonder if kids who are typically “good” at math in a traditional classroom would feel more reserved about engaging since there is no memorized formula and kids who struggle would feel more comfortable since they are invited to engage with creativity. Really cool way to open up math to everyone and encourage reflective thought and discussion. Love it!
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We definitely get some of our memorizers or traditionally “strong” students pushing back on this approach as they aren’t comfortable not knowing the answer or the procedure right away. They are put into a productive struggle which is uncomfortable when they’ve never been pushed to truly think in the past. They totally get over it though! 🙂
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It is SO different from the way that I currently teach. I definitely use the traditional model (aka I do, we do, you do) and it becomes so monotonous as the year goes on. This activity invited the students to take ownership of their learning and it make them realize what skills they needed to solve the problem. I loved it!
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Super cool! If you’re loving it, be sure to explore the problem based units which follow the same framework:
Learn.makemathmoments.com/tasks -
The concept of having more students “take ownership of their own learning” is so valuable and often so difficult to obtain. I can see where the 3 part framework/3-act math can make a difference with this!
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I think with this style of lesson it does a lot of beneficial things. It encourages depth of learning over breadth. It connects learning and builds experiences that students can continue to reference. It encourages problem-solving and builds in group work and discourse (and vocab by extension). It is low-floor/high-ceiling so students can enter the task in multiple ways and the discussion style honors individual, creative thinking.
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I love how this type of lesson builds on students questions and offers multiple entryways to a singular problem/ concept!
What I find difficult is being present to help the different students where they may need while also anticipating the extensions needed. I have students who will do all the work/thinking for their peers without letting them attempt the problem(s) at hand.
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The 3-part framework values skills students currently have to solve contextual problems; there is a gradual progression to the instructor sharing the algorithm after students have chosen, shared, and discussed their own path to solve a problem. Everyone can find some success. The traditional math lessons remind me of a recipe that varies very little, and students are expected to follow it in order to get the same outcome.
The non-traditional math lessons provide students with more opportunity to explore different ways to solve problems as they build towards a conceptual understanding of the ‘new’ strategy. I love how there is more freedom for students to use the knowledge they have and then to build on it. Hopefully, fewer students would be left behind in the dust. Additionally, the 3-part framework encourages those students who are very inquisitive to explore outside the box.
My only reservation: Can I get through the curriculum? I usually have at least one class where students are highly motivated to learn and work, so this style of lesson is fantastic to use. The other classes are a mix. It’s there where I worry about progressing too slowly to get to the end point; however, I will definitely give it a shot.😀
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Great reflection here and great question. We often ask educators whether “getting through” means students learned the material? We used to be masters of “getting through”, but often times, our students didn’t make meaning of what they saw. So while there might be a fear/risk of a time crunch, we believe it is worth the risk.
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The interaction with lessons like this, let’s us see how the students were solving the problems. We can hear what strategies they use, their way of thinking and also areas of development.
I think we always say one reservation will be time and the age of students.
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Can you tell us more about the age part?
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I think this lesson style is beneficial if students have confidence already and they are willing to try looking at things another way. They will find it satisfying to defend their answer. Students who are not confident and don’t have strong number sense will still feel lost without adequate support. I, too, worry about getting through the curriculum I have to get through.
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This is an interesting reflection. Have you tried problem based lessons enough to know this is reality or is this an assumption you are making?
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The lesson style enables teachers to utilize more open-ended questions. This heightens the expectation of students having to think and solve problems using their problem-solving skills instead of waiting for the answer. This also does not limit students to think that there is only one way to solve problems. Versus traditional lessons that simply teach students to copy the teacher and not think for themselves.
The reservations about using this style is less structure in the way things are taught, task could take longer than expected and not allow for all task to be met in one day, how to know if students know how to accurately solve the problem, and is this the best way to present new ideas to all levels of learners.
Utilizing this type of style allows students to become more vocal in their understanding, problem solving and communication skills about math specifically. With this style students might be more willing to make mistakes and try again. This type of lesson engages the learners and develop their own style of learning why we solve problems a particular way.-
Thanks for sharing! Great points and some common reservations. These are all ideas that one must grapple with as they begin a problem based lesson journey which will vary from grade to grade, concept to concept.
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This lesson style: Students will become better at problem solving and communicating their ideas mathematically. More focused on engagement and understanding. Sense of discovery from the students.
Fears: Students may get off task. Pacing. Flexibility.
Traditional lessons: lead to more open ended questions. Focuses on what teacher did then students do the same thing.
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This lesson style allows for more exploration into a topic. Instead of a traditional framework where you introduce a topic, walk through it, help them apply a strategy, and then solve problems individually, they will be thinking more conceptually about a situation using prior knowledge.
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This lesson style is different from the typical math lesson in that there is a lot less direction from the teacher and students are exploring and talking. It is giving students a chance to explore and share ideas. This is so important because students need to talk and discuss to learn!
I have noticed that my students this year are less talkative and I have to really coax them into sharing their thoughts in class. I think this is because they got so used to not doing that when learning remotely and it makes me so sad and frustrated! I have tried doing some notice and wonder activities with them and it does seem to get them to share a little bit more.
One thing that makes me nervous about this is time but I think that the benefits outweigh that. I liked how Kyle said you can refer back to the problem to help students remember the math! I think that is so helpful.
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Definitely a shift in approach for most, but love that you remain open to it! Yes that virtual time as made us move back a few steps, however, we can rebuild that culture of sharing / collaboration! You’ve got this!
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First of all the lesson was engaging. It was interesting and it did make me curious. What I loved was helping student to estimate and to help them get riskier by trying to bring estimates to reasonable amounts. That in itself was engaging and then to take off with improve your prediction using math you know. It made is a personal quest for each student to engage it and it was doable for anyone. Traditional lessons usually are just do as I do and we are going to get an answer that you and I really are not invested in.
My reservations is practice in consolidation and understanding the different methods my students may use. I’m also worried that my students that struggle are so not uses to thinking that they won’t know how to start without an idea from me.
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What I really loved about this activity is that it immediately grabs your attention and makes you wonder. Anyone in the room, student or adult, would be intrigued by the “hook” of the video due to its silliness and absurdity. From there, notes are used as a way to organize our thoughts and wonderings into clearer structure. As opposed to traditional lessons, students have the chance to dive into their curiosity here, ask meaningful questions and investigate various avenues. Like you mentioned in the clip, there is room for low floors and high ceilings, and differentiation. The joy and challenge of this type of lesson is its lack of predictability, but that also makes me feel hopeful about it. Good preparation ahead of time might alleviate that. Finally, I’m really a fan of how it can then be used to connect an algebra unit on linear functions to geometry and bring it back full circle. I can see this moment lasting in students’ minds for sure. Hope to use this soon if possible!
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I am excited and overwehlmed by the idea of doing this style of teaching all at the same time. Using the traditional units gave me comfort in know where I was going and that I had curruculum content covered. The hardest part for me is letting go of the comfort of my plan and know exaclty(for the most part) how each class was going to go.
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This can certainly feel a bit scary and that is ok! Note that there is no need to ditch everything you’ve done in the past. Just think of the small ways you can transform what you would have done to follow the framework.
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This style of lessons, students are coming up with their own questions and, as a teacher, you are guiding students through the learning while students explore said questions. In a more traditional lesson, students are given steps to follow, but they might not get their curiosity sparked, get time to discuss with peers, or time to explore in order to get conceptual understanding. In a traditional lesson students will get the “how to” but not necessarily the “why”.
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Great points here! And also note that with a problem based lesson, we aren’t trying to avoid procedural fluency – we are just trying to get there a different way that provides the extra conceptual underpinnings! Thanks for sharing!
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I find that typical lessons leave no space for the students to insert their thoughts; they are typically given all necessary information (and never any extraneous information) and asked to use an algorithm or formula to answer the question.
I also think that using video or images tends to draw students in more effectively than if information were presented solely via text. The same information and prompt could be given as a typical textbook problem, and students would not be as engaged.
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This lesson style is certainly more engaging. It also gives students a sense of agency – I can solve this problem in a way that suits me. This style allow all students access to other students’ ways of thinking. This is important because in traditional lesson students tune out other explanations once they already have a correct answer. Also, since there isn’t a math only restriction on notice and wonder, we can hear what things pop into students’ heads when they see problems – e.g. teacher thinking about math, student wondering how video goes backwards. Rather than dismissing students observations are irrelevant, the class hears it, responds as necessary, and keeps it moving.
My reservation about this style isn’t so much a reservation as something to anticipate and find a work around for. I work with a transient population, so there will be students who transfer after the rest of the class has gotten used process. Also, there will be students who don’t know what we’re talking about when we reference a problem from months ago.
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I’ve been working on implementing problem based lessons for most of the time I’ve been teaching in the classroom, and I’m still working on it. Some thoughts:
1. I struggled with the energy and preparation I need as a teacher to present the task, monitor student work, and consolidate efficiently and meaningfully. This has gotten better with experience, but it’s still a struggle. Peter Liljedahl’s work in Building Thinking Classrooms has recently helped a great deal.
2. When I started, I thought that every single lesson had to be like this. It wore me out, and it wore my students out, and there was no time for consolidation. We had a lot of fun, but it felt very disorganized. There’s still a place for kids doing problem sets in class, and there are still appropriate times for direct instruction. As mentioned in this discussion, we don’t need to throw everything out; this is just another tool to use. For me, it has become the foundation of my classroom practice, but it took awhile to get there.
3. When I was first introduced to 3-act tasks in particular, I didn’t totally buy into the structure (especially the beginning with the notice/wonder, the estimation, etc), but was pretty impressed with how it worked in practice. I don’t do it for every lesson, even lessons that are based around one task, but it’s part of the practice in my classroom. To start out, I found a few tasks that were right for my class, and implemented them in a sort of “by the book” way. The results gave me enough confidence in what I was doing to continue, and eventually develop problem based lessons in a way that was manageable for me. Give it a shot if you haven’t already!
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This reply was modified 1 year, 1 month ago by Jonathan Lind.
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This reply was modified 1 year, 1 month ago by
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1: This lesson differs in traditional lessons in that it rely’s on the students to drive the questions. Furthermore, it relies non the student to draw on their previous knowledge and understanding to solve the problem. Traditional lessons are usually taking a slightly unfamiliar problem and applying the algorithms from their current the unit of study.
2: Students from all levels of knowledge and ability are hooked from the start. All methods of problem solving are welcome and no one person is initially ahead another. It levels the field. Even a new student on that day would be able to enter in the initial debate. Likewise a student with low numeracy skills and little understanding of the unit currently taught could at least be investing from the start of the lesson. All students buy In because they all make predictions that are then published to the class. Everyone has a stake in the problem.
3: I do “3-Act” style questions at least once every unit. Having done them many times, I don’t have many reservations, but I feel like working in groups is a great way to solve the problems once the initial video/intro is shown and the first round of guessing has taken place. I believe, that if possible, discretely grouping students according to their ability helps to avoid one student monopolizing the conversation. The downfall of random grouping, is that the students who need to work on problems solving the most, won’t benefit when the aren’t forced to initiate their own strategies.
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Great points here and in particular, good point as to why a mix of group and individual work is helpful!
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Love the “task with legs” idea. Lay a solid, engaging foundation that can be accessed again and again for deep learning and engagement. Spend the time up front…and it will come back to you. This is also a good reminder to be on solid ground (as a teacher) on the student moves to watch for, so you can be prepared to sensitively and effectively “bump” their thinking/learning to the next stage. Love it.
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Awesome that this resonated with you so well!
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This type of lesson has the ability for students to “learn” more on their own compared with traditional lessons. That will bring more depth to their learning, which will in turn bring about more retention.
I have two concerns in particular about using this type of lesson:
1. It seems overwhelming to me in the amount of time it would take to plan and develop this type of lesson on a regular basis.
2. When I am planning this type of lesson, how will I know that it will accomplish what I want it to accomplish?
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I love the idea of introducing a new topic this way before students have learned a bunch of “rules” about how they “should” solve it. In a real-life situation, writing out a formula or algorithm is probably not how most people would choose to solve a problem and so giving students an opportunity to develop and reflect on some of those more practical strategies and explicitly connect them to the traditional algorithms is so valuable.
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I love the way these lessons help kids think. I am worried about the amount of time they may take up. I feel like my schedule is quick and I am not sure I have time. About how long does a lesson take when you are first starting?
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Having the kids talking, making sense of a question, seeing different ways the answer can be found is AMAZING!! I really am blown away by this. I started using Calc-Medic these past two weeks on finding area and volumes of revolution in AP Calculus. Mind you, I just threw this new type of learning at the kids for the first time. So many students were apprehensive about not being given the notes or fear of getting the problem wrong. If I started the year off with this type of learning, we will have more success. Many of my normal struggling students loved this way because they were interactive the entire time. They were using their creative side that doesn’t get to show up when I give them boring notes. More kids are definitely engaged throughout the lesson. My reservation is fear of change and having enough time to get through the standards. I don’t know how long to let the kids discover the lesson before I swoop in to tell them. I know that is wrong, but I’m still learning.
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So great to hear! We just interviewed one of the writers, Sarah from Calc Medic! Sounds like you’re enjoying the resources!
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Traditional lessons are generally one way where the teacher shares information with little participation from students, often students only participate when asked directly by the teacher.
The 3-part framework is more student-centered: students are asked to think about the problem before hand and to even come up with a possible solution or an idea about the possible ranges of the solution. Then, students explored the question and it was a hands on approach of solving a question. There isn’t a clear structure as often the teacher acts more as a director to help students achieve the answer by themselves, it is a very engaging way to teach, which raises several questions from my side:
– When we apply this method to a Higher Level Course (for example IB Higher Level Mathematics), where there is a huge amount of content to be taught and not really so much time for long activities like this, how could this be effectively implemented (and what periodicity should this take) so that it doesn’t disrupt the dynamics and learning goals of the subject.
– In order to apply this strategy/method, some time is needed to prepare so that the teacher can present significant questions and guide students in the right direction. How much time does it take to prepare an activity like this? Is it compatible with teachers teaching several subjects who also are asked to complete plenty of “bureaucratic” (not directly related to teaching) stuff?
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Great reflections and questions.
For some classes, maybe it looks like starting your lesson with a question and getting right to solving the problem. Maybe it is less contextual or maybe less noticing and wondering. However, starting the learning with a question to solve is so much better than just teaching using only examples.
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I have used 3-act math tasks with my students in math lab, and I use the stats medic lessons for my AP Statistics class. I love how students get “really into” a lesson, and then talk about it for days after. I am a new teacher (in just my second year), so I do not have a lot to compare to, but I definitely notice that my traditional “guided notes” lessons do not have the same impact on students as these. I do believe that practice is necessary, but these math moments have me really excited about where my career as a teacher will take me. I can really see this turning into my teaching style and looking for ways to incorporate these very important math moments a lot more consistently.
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The benefits of this style of lesson is that it creates a spark of curiosity to get them interested in uncovering the concepts of the lesson and also that there’s so much more dialogue and critical thinking involved than just presenting the situation as a word problem. There still definitely needs to be days where students of course just focus on the abstract part of math solving equations using x’s and y’s, but at least those x’s and y’s become a little less abstract when they connect to a problem like the one presented.
My reservations for this type of lesson is that I won’t be able to implement the lesson myself and be as successful with orchestrating productive mathematics discussions, but that’s why I am taking the course so excited to learn about how I can best support my students.
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It will certainly take time to practice (and fail) as you get better over time. You got this!
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To me this is one of the reasons I have been trying to improve my practice. I have spent most of my teaching profession perfecting how to explain difficult concepts and always being the voice and the action. This is not how I want my students to learn, I want to see them take risks and chances themselves to see what thoughts and ideas they can come to. Putting the action on them instead of me is something that really intrigues me and I can’t wait to further this direction.To me this is one of the reasons I have been trying to improve my practice. I have spent most of my teaching profession perfecting how to explain difficult concepts and always being the voice and the action. This is not how I want my students to learn, I want to see them take risks and chances themselves to see what thoughts and ideas they can come to. Putting the action on them instead of me is something that really intrigues me and I can’t wait to further this direction.
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I think most educators (including Jon and I) can relate. We are led to believe that being a good teacher means being the sage in the stage.
As you think and reflect on this more, you’ll find ways to ask more questions and tell less. When you become comfortable with asking the right question which will lead students to the idea of what you’d be saying in that great explanation… then you know you’ve arrived!
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I am a convert. I started using these several years ago. Out text has some 3-act Math videos for us to use. Some were better than others, I have since used them with your notice and wonder framework. I get pushback initially from the high achieving students, who have been able to succeed because they can use algorithms or are good memorizers. Those students sometimes bristle when you don’t give them the answer.
Especially when you just start having them make the three guesses and one of them has to be too low….I know I have them hooked when they evolve from just putting one there and looking at me…daring me to say something about how low it is. When they actually put thought into all three, I know they are invested.
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A few thoughts to ponder…
As I begin using these “tasks” in my classroom, I’m going to have to introduce Kyle and Jon as some “friends” because I cannot recreate all these videos myself!! (is there such an intro video to share with my students?)
Thinking about implementing this, I am a bit nervous about creating challenge/extension questions and about the “pre-planning” or anticipating students thoughts and struggles. I will just have to practice this for myself!
I really like the “Task Placemat” paper for students to get started. I was wondering how/where students would do “bell work” in a classroom that doesn’t use “notes” in a traditional sense.
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@maria-vaikunth Your wonders are natural and common when educators set out on this journey. We’re confident that as you proceed through the course you’ll come to some conclusions for these wonders.
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In traditional math lessons, the teacher owns the math. In this lesson style, the students own the math. I had a professor who always asked “Whose math is it anyway?” and I really want to shift my practice towards having it be student-centered by giving them voice through engaging tasks. My biggest struggle in implementing this kind of lesson is getting my students to understand that there are many ways to arrive at a solution and the only wrong answer is to not try. As such, my biggest reservation is building a math culture that encourages my students to take ownership of their math.
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I love the spark the curiosity moment to get students engaged. I have tried using similar ways and approaches to getting my students engaged. I find it challenging to stop or conclude the concepts because there are just so many other concepts that can be related to the initial concept. “The problem with legs” as Kyle put it. I also want to know how to give practice questions so they can practice the thinking and be able to apply the strategies they discovered in other problems.
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I often struggle to limit what I want to consolidate as there is often so much. You don’t want to try to do everything or the consolidation may go too long and students may not take away what you had originally intended.
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I teach using the (I do, we do, partner share, you do) method and each lesson starts with vocabulary terms, definitions, and the lesson objective. Before we begin most students have disengaged. I think this style of the lesson will be a win-win for the students and myself. Student engagement and thinking should be off the charts! Thank you!
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Amazing to hear! Is there a task / lesson from one of our units that you’re interested in trying this with?
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When I compare this lesson to traditional lessons, the main difference that I noticed was that many strategies show up with this lesson and students will see multiple ways of solving it. As Kyle states in the video, in a traditional lesson students will only see one strategy multiple times. The benefits are that students will be more prone to follow their sense making skills if they believe that there are many ways to get to the answer. Some reservations I have is that it will be challenging to teach this way, but in the long run it will benefit students.
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It’s witnessing and experiencing multiple strategies that will help students with long-lasting problem solving skills, confidence and fluency. Which are some themes folks here outlined as wanting students to recall/remember about math class in the future.
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This lesson style demands engagement from the students. I found myself trying to work out the problem before the instructions were even given! I love that the lesson provides multiple entry and exit points, which is crucial in a special education classroom like mine, where students don’t always have the foundational skills they need to go straight into calculating at grade level. This low floor can also build confidence for students who feel they are “bad at math” – with determination, they may be able to solve it using manipulatives or pictures.
I have provided some lessons in a similar format before, and they have generally been successful – although sometimes I struggle to make sure I still cover everything I need to cover! The need for regular grades in the grade book is a reservation. I may consider providing some kind of exit ticket at the end of a multi-day lesson so I can quantify their understanding. Additionally, in my classroom, there are some students who are so far down the “I’m bad at math” rabbit hole that they refuse to work with others out of fear of looking stupid. I also have certain students with high absentee rates – and it is very hard to “make up” a task-based lesson like this.
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It is completely different and I LOVE IT! This the thinking and mathematical conversations that I long for in all my classes. This lesson makes me excited to teach!
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Compared to the traditional lesson. this helps students build more conceptual understanding rather than just procedural fluency. It also gets students engaged at any ability level rather than everyone working on the exact same problems. It more easily allows for productive group work, productive struggle, and practicing of communication of mathematical ideas.
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As a learning support co-teacher I witness most lessons have a routine of :
homework check with students or teacher at board followed by questions
introduce lesson through examples
teacher led practice
independent practice
At times I have attempted to encourage problem based activities in classrooms. Normally it is only accepted by the content teacher when there is “sufficient time” after lessons are completed. I will acknowledge that the teachers are often surprised at the level of engagement during these activities and will occasionally ask that I identify possible activities for future lessons.
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This is extremely common… how can we better encourage educators to see that the investigations can be used as the lesson with the consolidation being where they can use explicit instruction?
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My only concern is time. But, once the students become familiar with this inquiry-style instructional approach, I think it will be great.
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@reney-mcatee You’re right, you’ll find that at the beginning these tasks may take up more time that you’re used to for a “lesson”. What you’ll also find is that you’ll be able to uncover many more expectations during a lesson like this and may find that you have extra time later.
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This is such a refreshing math lesson. Having gone through a UTeach program and studying inquiry-based lessons through college, I went into my first year with such a lack of support and motivation that I reverted back to traditional teaching and my kids were ALWAYS bored. My lessons forced them to sit in their desks and listen for 50 minutes, but this lesson allows them to be the ones doing the thinking. It’s how I’ve always wanted to teach, but I have such a hard time finding ideas and planning enough in advance to get all of my extension questions done. It’s also hard for me to predict what they’ll say having only taught 1 year. I’m still learning what the common misconceptions are!
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Glad you found this community then! While you’re right that it will take time to more accurately anticipate what approaches students might take, our problem based lessons available in the tasks section of this website have full anticipated student approaches for you to get a sense of what they might do. Have a peek!
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A traditional math lesson also has three parts, in an “I do, We do, You do” pattern, but who is doing the majority of the work? Students tend to watch the teacher do the math and then regurgitate it (some well, others not so well).
The benefits of the type of lesson presented here are that it is student-centered–they are not watching us do the math and then mimicking. We are not owners of this knowledge–we start the students with noticing and wondering and then allow them to play with the math, stemming from a genuine interest and curiosity. Then allowing students to share their strategies and learn from each other, making connections in their learning. This has the potential to completely overhaul classroom culture!
I came to teaching math this last year after 20 years of teaching English (dually-certified, though), and it was mathematical innovators like Make Math Moments who inspired me to make the change so that I could teach math differently (better) than it was taught to me. I enjoyed playing with all the ideas from K Pearce & J Orr, P Liljedahl, A Overwijk, D Meyer, G Fletcher, P Harris, S Singh, and J Boaler this year, and I sure had fun. Turns out the kids did too! I had great feedback from students–lots of boosts in confidence and requests that I continue 3-Act Tasks and problem-solving groups with my classes next year. I loved that spending the most time with Noticing and Wondering helped my students who are not (self-reported) as mathematically inclined make observations and be curious about their world–and reinforced that they brought their valuable mathematical selves to the table.
There is just so much out there that it does become overwhelming to decide what I need to do, but that seems like a good problem to have. I am enrolled here this summer to help me focus and hone in on my practice.
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Wow! Congrats on making the move over to mathematics and for being so open to learning new approaches that might be more effective than what you remember from your own school experience! We have lots of problem based units with full teacher guides to help make that transition easier on you, too!
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This style of lesson totally lends itself to all levels of students. The task provides an entry point for students to be able to problem solve (from special ed students to gifted and talented students). Special ed students can feel successful by solving the problem in a way that makes sense to them while at the same time the more advanced student can challenge himself to solve it in as many ways possible. But the true value of this style of lesson can be found in the discussion taking place when students explain their thinking while others are listening (and at times critiquing) and questioning their classmates about solutions. This critical thinking piece is so important for students to be able to understand and internalize the mathematics they are discovering. This is far better than the sage on the stage approach I started my career with!
My only hesitation for this type of lesson is getting other teachers to see the value of them. As a math specialist and coach, I have some teachers who just want to follow the curriculum they have been handed without thinking through the lesson in terms of how to spark that curiosity in students and fueling that sense making in students. Getting teachers to realize there are moments they can capture for students to do the thinking instead of doing that thinking for them. I realize that part of it is the stress of a new curriculum and teachers doing what they need to survive. But my job is to figure out how to spark curiosity in my teachers and fuel THEIR sense making about math. I have got a lot to think about for teachers 🙂
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This reply was modified 9 months, 1 week ago by Julie Gonzales.
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You’re bang on here in terms of the value of this approach to teaching math as well as some hesitations you might bump into. You’re right that you’ll need to find some ways to inspire educators to want to do this work because it is necessary if we want to engage all learners and provide them all with an entry point into the learning.
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This reply was modified 9 months, 1 week ago by
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I love the “low floor, high ceiling” aspect of a lesson like “Chocolate Mania”, and I love the way the lesson gets kids thinking! I also happened to notice that you’re having teachers stand at vertical white boards to solve problems! I picked up “Building Thinking Classrooms” by Peter Liljedahl and I’m reading it this summer alongside your course. I’m super excited to implement a different pedagogy in my class.
I just started working in a school that uses “Everyday Math” as a program. This is the first school I’ve worked at in some time that follows a program. Prior to this, I’ve been fortunate to work at schools that give teachers the flexibility to create units and lessons pulling from many resources, and I’ve used 3-act tasks, Joe Boaler, Cathy Fosnot etc. and aimed to teach as conceptually as I could using problem-based learning. This past year I taught third grade and really had to follow “Everyday Math” like a script because that is what the 2nd and 4th grade teachers expect. So we did workbook pages! Unfortunately I would hear kids sigh at math class, or declare they didn’t like math. And kids who needed challenge were simply bored. Next year I’m teaching 5th grade and I don’t have to follow “Everyday Math” with fidelity because the 6th grade doesn’t use it anyway. I got permission from my principal to veer off. My biggest concern is successfully preparing the kids for middle school content in a rigorous college prep atmosphere! I’m also concerned that the students I have (and their parents) will have expectations of following the “Everyday Math” program, so I’m wondering how I can marry “Everyday Math” with other pedagogy, and also ensure my pacing keeps up enough to cover all the content necessary and expected. I know kids will be far more engaged if I don’t submit them to completing copious amounts of workbook pages… I want to hear kids saying, “Math class is fun!” again.
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Following a program is great for consistency, but can certainly create a pretty dull experience for students. In our Transforming Textbook Questions lesson coming up (and the full additional course in the Academy) we spend a significant amount of time helping educators to find quick and easy ways to transform a boring lesson into a curious lesson that fuels sense making. Stick with it and you’ll be ready to go!
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Traditional lesson the teacher does most of the talking and explaining. There is alot of I do – you do structure in a traditional lesson. In the present style, it is much more student centered, the students are doing the explaining.
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I feel the benefits are the students because willing problem solvers and not afraid to put themselves out there and try something.
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The 3-part framework is different from traditional math lessons because the students are free to explore and do more of the thinking on their own. Traditional lessons usually start with the teacher model how to do the example problems, instead of allowing students to try their own strategies first. Here students are encouraged to make predictions and create estimates with less emphasis on finding the “right” answer and more time spent on improving their original emphasis using information to help get them closer to the answer. This allows students to try multiple strategies and different methods to show thinking before the teacher consolidates the important points or shares a specific strategy or model. I also think that traditional lessons often completely neglect to spark any curiosity before beginning a new topic or problem. Here students are engaged first and want to know what is actually going on in the situation. They have more time to think about and understand the context before any math is applied. In a traditional lesson, we often model mathematical procedures without given students enough time to understand what the situation is or why it matters. Using multiple strategies allows students to make sense of the problem in different ways, and they can see that there is more than one way to solve a problem. Instead of showing a strategy to the whole class and asking students to replicate a process or procedure, the teacher is guiding the students through a process that they have started on their own, and then connecting the dots for everyone at the end of the lesson. Student voice, collaboration, and discussion are valued in this type of lesson, and it is more likely that students will remain engaged longer.
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We’re glad you’re seeing the benefits. Did you have any wonders or hesitations?
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Yes, I wonder about pacing, which is something I have always struggled with as a middle school math teacher. Even with a very traditional lesson structure, it is difficult to cover all the content.
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I wonder if I will be able to time lessons like this effectively, without pushing them toward the conclusion too often or too quickly when it feels like time is running out.
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This does take time and practice to get better at. After building the culture of curiosity, you will find that you can spend less time at the start of a lesson and more on the middle / consolidation.
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Traditional math is all about teaching a method to get to a correct answer. Math should be a discussion and thinking about different ideas and perspectives. The conclusion is that there are different ways to get to a correct result. If you want to make math meaningful everything that you as a teacher do in a classroom, discussions and questions, lead to challenging students to think for themselves and to reason through problems. They should expect to struggle and understand that mistakes happen and can be corrected. We all need to challenge ourselves and learn to find joy in the process.
This nontraditional style gives students who think differently a chance to bring their perspective into the conversation. Students do not learn the same way or in the same amount of time. We as educators need to understand that we want students to be able to do more and better things than we were taught. Learning to think for themselves is a great start!
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Traditional Lessons have the assumption that teachers need to give a specific strategy or method to the students and then have them copy/practice it multiple times to learn concepts. The lesson we watched with the chocolates has a very different way of helping students. It has them enter the problem with any ideas and all of these ideas are honored. There is no “absolutely correct” way to do the problem. Teachers can show and celebrate the different strategies and push students towards more efficient work when they are ready or even just exposure to that if they are not yet ready. The benefits of this style of lesson is that students are able to use manipulatives and any representations that they need to access and all of these are honored in the classroom. Students also are given a problem that they are not just following what the teacher did and copying the teacher’s strategies. I think this method over time would increase confidence in all students to be able to struggle/persevere through problems when it is not obvious exactly what to do. This seems to much better prepare students for life with honing skills of risk taking, perseverance, struggling, and thinking. My reservations of this style of lesson is just wondering how to make sure to have all students practicing grade level work. For example, if in 4th grade they need to learn the standard algorithm for subtraction but are not there yet, will the consolidation period of seeing examples of this method from their peers actually help them to achieve the standard by the end of the year? I am on board for higher engagement and more thinking in my classroom… I think curiosity will help students be open to learning new concepts, even when it feels tough.
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This type of lesson reminded me of the “Building Thinking Classroom” format that Peter Liljedahl shared in his book of the same name. I loved being able to see it done out from the other side of things. I have implemented several of these lessons over the course of the previous year but it was great to be in the “student’s” seat so to speak to truly see how it is from their perspective. The benefits to this type of learning are limitless as students gain more ownership over their learning and it means more to them. It was absolutely amazing to see the students shine and work through challenging problems without have been “taught” the material first. This is a stark difference to the traditional style of lesson and one that I have always believed was better for student learning. For most of my career, I have been trying to incorporate this type of lesson without having a name or plan for it. I am so grateful for having read the aforementioned book and for choosing to participate in this conference as they are solidifying for me what I have always known was a great way to work with students. The only reservations I have are that I get so into the kids and their solutions that I run over time and consolidation ends up being rushed. I have to work better on my pacing after I get the kids into the groove. My students LOVED board work last year and would do any and all work at the boards in groups if given the opportunity, even if it wasn’t a “task” situation. This made me smile as they eagerly got up to discuss math!
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Glad you’re seeing value in this learning! Have you checked out any of the problem based units in our tasks area? This can also help you with transforming your lessons on a regular basis: https://makemathmoments.com/tasks
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No, I have not, but I certainly will!
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It seems to be very student driven. I try to do this, but I feel like it peaks then I go back to leading. I also feel very rushed in stuff like this. Like I’m thinking about “the next thing”.
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You’re not alone. I think we rush with the belief that we can eventually “cover it all” if we move fast enough, however what if it is the approach altogether? Give this a go and let us know how it goes!
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Traditional lessons always start with the teacher explaining and demonstrating how to do the math that is being introduced. But this lesson style leaves it a lot more open for students to discover truths found in math. Students can discover the math.
I have tried a few of your lessons. I looked for easier intro type lessons as I am now teaching Algebra Readiness which is for students that are struggling in their regular math class. So my class is a second class in math for them for the semester. Some of the classes really tried to get into solving a given problem, others really resisted diving in. All of the students wanted to be spoon fed….like the traditional math class. They were easily frustrated and after a few tries I gave up. I actually started the semester out with growth mindset videos from youCubed which I showed one daily for the first 7-8 days of classes. I wanted to break down the negative stereo types and negative self talk and have students understand that everyone can do math. Because all my students struggle in math I have very few students that can be encouragers, and/or leaders.
I truly believe my students can benefit from this type of teaching but the energy to help them overcome their negative attitude and beliefs often drains me. Also even though they have learned some of the tools that could help them solve a problem they don’t know when using them could be helpful.
I don’t know how to reconcile this with traditional teaching. When do students learn how to write equations or how to show proper work for multi-step equations etc.. How do they learn this without being taught? I took this course hoping it would help to answer the questions I had when I tried to do this, this past school year. I want to teach this way and help my students to discover their ability to problem solve. I just need more tools and better understanding so that I can figure out how to work through the inevitable bumps in the road as I pursue this way of teaching.
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Building a positive classroom culture for math class can be challenging in the best of circumstances so when you’re working with students who have a damaged relationship with math it can be even more so. Stick with it and be sure to stop often to help them notice and name frustration to try and help them turn it into productive struggle.
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This type of lessons cause students to think about the concepts, to understand where answers come from and how they are created. Traditional lessons require more memorizing and lots of practice.
The majority of my students won’t memorize or will only memorize long enough to pass the test. How much better it would be if they understood how to think through a problem.
My reservation is my ability to create lessons like this, and I always struggle to know how to solve problems in different ways, because I didn’t learn that way.
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I think it is very clear from the learning so far that this style of learning involves making the students actually do most of the thinking. So often in traditional lessons I feel like I am the only one doing any thinking and students are either mimicking (the “good at math” ones) me or are just tuned out (the “not good at math” ones).
I think one of my reservations here is still how do you teach students truly fundamental skills (that they ideally should have learned in an earlier grade, but clearly have not grasped) through this method? I currently teach Grade 6 and I have multiple students whose basic ability to even add/subtract/multiply with single digits is very weak, let alone be able to identify what strategies would be most appropriate to use in a given context.
This is still something that I haven’t quite settled in my mind and I often wonder if it is just be defaulting back to what is “familiar” when it comes to teaching math/excuse making or if it’s a legitimate reservation, but these are my thoughts as they currently stand!
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Glad you’re seeing the merit in the approach! Yes, many are concerned about whether they can “get through the material” or build fluency, however, with solid intentional consolidations, this becomes a non issue. Check out our problem based units to help get started with this 🙂
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This type of math lesson has some similarities with a literacy workshop style, but with some key differences in sequence. Typically, literacy workshop (or a traditional math lesson) would run something like I do, We do, You do. Whereas this type of math workshop lesson runs the opposite… You Do (see, think, wonder), We do (work with a small group), I do (consolidation).
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Exactly! We call it “the real flipped classroom!”
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I love it! I left my undergrad work with a constructivist mindset. Put the students in the driver’s seat. Over the years, it became easy to slip into the “teacher is the holder of all knowledge” paradigm. How often do I say to myself, “if they just did what I told them to do they would get the right answer.” Too often we (math teachers) see the world in black and white – meaning there is one way to answer a problem, more than likely the most efficient way. It just isn’t the case.
I actually introduced a Dan Meyer problem today with one of my 7th-grade classes using the “what do you notice/wonder” model. I wouldn’t say it went awesome, however, we had great discussions and they seemed to enjoy the process. I still led too often but it will take time and effort for my students to see themselves as mathematicians with something to offer me and their peers.
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It takes time to build it into a habit, but keep reflecting on it and you’ll eventually overcome the want / need to lead / guide too much!
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This is an ongoing lesson that the class can go back to over weeks. As you said at the beginning, you may spend a class period doing this at the beginning of the year do it this to set up norms and to show how students are expected to think in this class. Eventually this may be expanded to be part of an opener to look at another concept that can be found in it, such as geometry rather than rate.
Another difference is that it can be differentiated to the level of the student. Student who struggle may be asked to show one thing whereas students who need to move further can be handed a card or asked to extend their thinking by being asked a follow up question.
Students are also asked to visually represent their answer in different ways on white boards so that the entire class can see different ways to come at the problem.
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The 3 part framework is different from a traditional math lesson in that it involves a lot more mathematical reasoning for students. They have to predict an answer and then use math to almost prove or disprove their initial prediction. In a more traditional setting, students will use the formula or steps to come up with an answer and then use a prediction or estimate to validate their math work.
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The students who are learning mathematics with reality will understand more than the traditional method.
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Hi there!
The lesson is modelled through this lesson in the online workshop and a breakdown / summary can be found here:While we do not have that particular lesson crafted into a full unit like we have been building out in our PBL lesson area (https://learn.makemathmoments.com/tasks) checking out the flow of our 30+ problem based units and the teacher guides will help you put the curiosity path into play with those units as well as build the confidence / skills to apply them to other lessons as well.
Have a look and let us know where you are struggling.
