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Lesson 6-4: Questions
Share any comments or questions you have on the five misconceptions about long range planning here.
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76 Replies
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The colorful graphics at the end of the video helped me understand the ideas better. I was glad to see that most of the lessons start with problem-solving but not all. I was always wondering how a topic so abstract as Solving Systems of Equations by Elimination could be derived by students themselves. I have been able to find tasks and activities where students could intuitively derive the graphing method and the substitution method to solve systems of equations but I had trouble with the elimination method. Now I know that I could mix-match lesson structures but always keep in mind the curiosity path framework to try to incorporate it in my lessons as much as I can.
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This reply was modified 2 years, 11 months ago by Claudia Sever.
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This reply was modified 2 years, 11 months ago by
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I used to teach linearly with definitions, examples and non-examples, theorems, worked examples, class work, conclusion in my first 10 years of teaching.
I then changed the sequence by letting my students solve a representative work problem of the whole chapter first. By so doing, they understand why they need to learn that chapter.
Since 5 years ago when I first learnt the 3-Act tasks, I have formed the habit of beginning a lesson with a video/diagram/problem to spark their curiosity. That makes learning more meaningful. Students usually don’t care about definitions, theorems and mathematical vocabulary. However, if we pose a problem/video to them, the series of responses will lead to the need to introduce the mathematical vocabulary, the definition of new concepts, …
I like this change of teaching sequence.
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Beginning
with problem solving creates curiosity as well as builds resilience,
determination, and confidence in students. I also agree that practice should
have purpose in order for it to be more meaningful for students. I tend to be
pretty flexible already, but now I feel more comfortable with not needing to
put a time limit on each part of a lesson. -
I definitely think it is going to be a process to shift our thinking and teaching to a spiraling model, but I definitely think it’s doable. I liked seeing your clock visual and I like the idea of having that flexibility to adjust lessons as I see fit depending on how they are going. I like the idea of being ok spending an entire period on one problem if that is what the students needs and they are getting to the deeper level thinking and the problem solving. I am somewhat of a planner (as I think most teacher are), but I also consider myself pretty flexible and I don’t see myself having much trouble with the idea of deviating from the plan whenever I feel necessary to meet the student needs.
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When I realize I don’t have to frontload a well defined math concept before I allow my students to dig into their math, a lot of pressure is lifted. I like the idea of starting with problem solving, hooking them in so that the instruction and discussion that follows is more meaningful and connected.
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I think when discussing this framework, the largest question from teachers was about the frequency of 3-Act Tasks. Most teachers want to incorporate these tasks into their practice, but have struggled envisioning how to balance these tasks along with the practice and fluency pieces. I think sharing that flexibility is the key will be so liberating to teachers. It is a reminder that they have the professional knowledge to think about good teaching and modify instruction based on the needs of their students.
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Thanks these did help reinforce some of the conclusions i already had made.
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I was feeling rushed trying to get through teaching procedures within a time frame that supports low attention spans.
This approach sounds very promising, and I had a lot of fun with my students working through 3-act tasks as a warm-up. I wonder how I can extend these problems to take up the majority of a lesson block.
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The key for me is ensuring the goal of the task is to allow students to construct convincing arguments and also for me to bring student thinking out in the consolidation. This is where connections are made and we try to emerge new ideas through student generated solution strategies and mathematical models.
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Any recommendations for at 42 minute class? I teach 6th grade.
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Knowing that everyday your lesson could go completely wrong and being flexible is very important. My first year teaching I found out that you never know what could happen during the day that would change everything you had planned. Being flexible is key to being successful when it comes to teaching. Just going into the day knowing you might not finish everything, or you might complete too much, is the best way to start each day.
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The clock visual was very helpful.
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Thank you for taking time to give a visual of how things might be scheduled in a class. I appreciate the circle clock of how you break down your classroom day.
Misconceptions help us see that we can’t do perfect lessons everyday, there are other things that go on that may involved changes but we try to use this 3 part framework as often as possible to promote better learning.
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I especially appreciated the clock. Consolidating student thinking and me helping less are important for retention!
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As someone who only has 50 minutes with students, I am often thinking about how to make everything “fit” in a day. But I think that it’s okay to have a “lesson” that spans over the course of two class days. Then you can still have all of the parts that you’re referencing (application/problem solving, conceptual learning, and practice) in a lesson. It just may not fit within the span of one physical day.
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This makes perfect sense. When you explore our multi day problem based units (https://makemathmoments.com/tasks) you’ll notice that we stretch the context for many days so stretching a lesson over two days isn’t a bad idea!
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It’s going to feel so strange in the beginning not to show them exactly how to do the practice problems, but to remind and help them understand how the knowledge they gained during the problem solving phase of working through the task applies to the practice problems. I’m really hoping that the transition from conceptual to procedural is a smooth one, or at least becomes smoother after some time.
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Definitely a scary thought, I’m sure! When you are so accustomed to something it is hard to make a change. We promise it’ll be worth it!
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I’m sure this is too individualized to even answer, but how often should I attempt to make my math class follow a 3 part framework? Also, this might be coming up in one of the final lessons, but do either of you give “homework” (or did you? I think at least one of you is no longer a classroom teacher) and if so, what’s it like? @jon @kyle
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Hi @ashley-Bryant
This is a common wonder and I’d argue that we want to always be planning with the framework in mind… however the way it is delivered might look different.I’d check out an example of one of our units to see what I mean by this. For example, Donut Delight:
Have a look at each of the days of that unit and you’ll see elements of the 3 part frame work each day, but not necessarily a full 3 act math task each day… lots of productive struggle…
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Will do. Thank you.
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I must have gotten lost somewhere in between listening and notetaking. I have the first misconceiving as 1. do you do you need to use the three part frame work every day?, but then I don’t have misconceptions two through five. I’m not sure what they were.
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This reply was modified 2 years, 8 months ago by Stephanie Moore.
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This reply was modified 2 years, 8 months ago by
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I’m a visual learning which having the graphics as well as the different colours to show the multiple ways that a lesson and or a unit can look like was very helpful – thank you. I strongly believe that repeating the same ‘classroom clock’ format is harmful for the students learning and engagement within the lesson. I feel that changing things around, add a little bit of spice to the lesson will keep the students engaged and on their toes.
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I think my school is leaning towards all teachers giving the same homework. If we do a 3 act math task and the homework is out of the book will this work?
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It’s useful reading the comments here and see that others also are dealing with shorter class periods (I have 50 minutes). Thinking of 2 days for a full lesson is useful. I do wonder if I’ll be able to give some meaningful homework after the first day, although maybe that could be spiraling back to other content that needs practice.
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Thank you for taking the time to provide information such as the visual of the clock to help me understand how things may be scheduled throughout a typical day in the classroom. As teachers we have so much to cover and we also tend to put undue pressure (personally speaking!) on ourselves to plan, develop and implement the perfect lessons for our students. It is nice to know that we must keep at the forefront of our teaching that not only should one have to be flexible and open to change but also to become familiarized with the 3 part framework that you mentioned to guide and hopefully keep one on track.
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I like the idea of starting with the problem solving. If my class time is considerably shorter, do we just continue the sequence of things the next day?
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The graphics you used helped me put things into perspective a little better. This is definitely going to be a change in thinking, but I think if I’m flexible this will be very beneficial to students.
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I am very guilty of saving problem solving at the end of the lesson. I did try and begin with a “minds on” activity, it sometimes was related to what we’d done the day before or a consolidation/review of what we’d learn about the day before. The colourful graphic outlining where mastery/fluency show up in the lesson was also very helpful to me as I often feel like within my 60 minute math block, I have to sacrafice one thing or another from day to day. I need to work on this. I feel that spacing will be the key and it may make more sense to pay close attention to how I chunk my lessons so that I don’t feel that anything needs to be sacraficed.
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The visualization with the circle map helped.
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I really like the visuals of the clock and the three color coding of how lessons are started and how you progressed through them. But as far as the clock I don’t think you can have a specific one that you use every single day you do one of these tasks because sometimes these tasks will take longer than others. I don’t assume that they will be taking shorter periods of time, but I am sure times will be longer. But I guess it gives us a good visual to go by. You understand that this is not a cookie-cutter clock that would work for everyone but something for us to go by.
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It will be an adjustment to switch to problem solving as the first step in teaching a new concept, but I’m looking forward to trying it.
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Seeing the sample “daily schedule” was helpful for me to wrap my mind around a possible scenario. I have about 75 minutes of math class in 5th grade. However, about half of that, or at least 25-30 minutes of it has to be set aside for guided math, which throws a wrench in things for me. That leaves about 45-50 minutes for a lesson and the Curiosity Path approach. I would definitely need to break down the stages of the Curiosity Path lesson into at least two days. Is that something that could work?
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Very helpful
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While my own planning will have to rely on where my own students are it is helpful to see a possible scenario of how to lay out lessons and units. I also appreciate the graphics and color coding to help wrap my brain around the idea. I am sold on the idea of spiralling and the why behind it but am concerned about the response I will get from colleagues and parents who like being able to follow the textbook at least for an order. I have always felt like the no matter which textbook we use the ordering doesn’t feel right because so many topics can and are connected! I think this will require a lot of thought and planning but I am excited to embark on that journey.
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This reply was modified 2 years, 8 months ago by Josephine Bruno.
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This reply was modified 2 years, 8 months ago by
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When do you do exit slips?
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Very helpful visual of the clock. It is very important to be flexible with our plans. Many times it happens that things do not really turn out the way we have planned.
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This reply was modified 2 years, 7 months ago by Bhanuradha Bucktowar.
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This reply was modified 2 years, 7 months ago by
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You mentioned some activities in Misconception #2 and said you would provide links to learn more about them, but I can’t find any links.
The activities were the “random winner game with sticky notes”, Risk, row games, and speed dating.
Could you please supply the links? Thanks!
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Hey there @bryan-henning we just updated the lesson to include them.
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I found the it helpful to think about each lesson in the math clock format and also found the graphic at the end about the unit plan helpful.
I am starting a new job in a different school this year. Unfortunately, each period is only 45 minutes long. I will be teaching 6th grade math. In general, I am concerned that each lesson will feel rushed everyday. This is regardless of how I structure my lessons (using the 3 Part framework or another structure).
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I am wondering how I will do this while teaching virtually. Last spring it was so hard to get the kids to pay attention and participate. I am hoping that I can create a lesson that peeks their curiosity and helps with engagement, but conversations are choppy and not organic on Zoom. I am worried that technology will hinder the flow and lesson. Do you have any tips or ideas for making this work online?
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Such a good question and concern @danee-kennedy . While it’s outside the scope of this workshop we built a course in our Academy.
Just click the Upgrade To Academy link in your menu bar.
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I really liked the idea of looking at parts of our lesson on a clock. While we are often tasked with including times in our lesson plans for each component, I don’t think it’s often that we consider what percentage of the class period some things are really taking up. This can be really valuable when considering the things we “always do” – like collecting & reviewing HW, “stand at the door time”, etc. Looking at all of this in the clock format can help us pinpoint where we can shift time and make the most effective use of instructional and practice time with our students.
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I really liked the visuals in this lesson. The clock visual is something that really clicked with me. I know about the stand at the door time, and want to change that! Also, it was a nice reminder to be flexible!
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I love the idea of no set structure like we did in the past. Doing practice and problem solving especially are really important and need to be done throughout the lesson. Also, going from really tense about the time and worrying about things like assemblies to more relaxed helps.
Focusing on what needs to be done day to day can look different and I need to remember that it is what is important to make each day count.
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The color coding of lesson plans is an extremely helpful tool to help get your point across. This also is a great idea for us to use when doing our own planning.
I do believe if we break up the standards in to cycles, like you mentioned in the earlier module, that is will be easier for use to plan for week/month, etc. As I have stated before, I think what will help me out the most is once I am able to practice these lessons, using the plans, and implementing such practices that I will get better at figuring out how to best prep my lessons/classes.
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Another great visual with the clock. Just wondering …do you assign homework? If you do where do you fit it in the clock? Do you collect it? Go over it? Thanks.
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Yes we assign purposeful practice and sometimes that fits “in the clock” or a portion of it or sometimes for students on their own at home.
We tend to try and avoid doing the full “take up” but rather have students share their work the next day and do a mini consolidation.
Homework in general is tough because often times only a portion of the class is doing it – so committing too much class time to it can feel like time wasted. So it’s a tricky one with no “right” way to approach it.
In younger grades, being cognizant of how much you’re giving is really important as well.
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What an amazing way to approach math instruction. I really wish my teachers taught math this way when I was younger. Between spiraling the course content and using the curiosity path model–I´m sure your students enter your classroom knowing to expect a challenge but feeling up to the task. This is what all math classrooms should be like.
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Couldn’t agree more! However it isn’t always roses and butterflies when you first start. Some students are content just mimicking the teacher by copying examples because it is easier and they might be “done” faster. So just keep at it if the beginnings feel rocky.
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Am I right in thinking that you said you see the students for 75 mins each day? As a year 7 teacher I have 45 mins per day for Maths, and at least 5 of that is procedural (getting ready for the lesson or getting ready for the next lesson). It explains why I always had trouble getting through one of your suggested lessons in the time allocated!
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Yes there are so many variations of class lengths out there. 45 minutes isn’t much time for a math period – so efficiency will be key for you! But yes, splitting them up will be necessary as well.
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Thank you for addressing the need to be flexible. Sometimes that is so hard but we have to understand that things happen in schools! I like the visual of how you break up your class period. I don’t know what our schedule is going to look like next year so that is making this a little difficult but I am currently teaching in an 85 minute block so I am excited to try this!
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Great illustration of how to use time. I often feel guilty about not doing the right thing all the time. Sometimes, I resort to direct instruction; I don’t like to teach that way, and I know I can do better, but sometimes that’s all I’ve got. I have found that more practice on my part designing and implementing problem solving lessons, the easier it is to plan them. I’m also building up a repertoire of lessons and techniques I feel good about, which also makes it easier.
I think the color-coding at the end of this video was a great illustration of time use; also the classroom clock is something I think about a great deal.
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Glad to hear this was helpful. Again, don’t beat yourself up as every day can’t be perfect. However, thinking of ways to constantly improve is key. You’ve got this!
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I am looking forward to implementing more of the spiralling strategy into the new gr 9 curriculum in Ontario. You are spot on that it is difficult to spiral when you don’t know the curriculum, hopefully after 2 semesters of teaching it and the new examples and teacher instructions we will have better insight on what we are to teach. It is reassuring to hear that if I don’t manage a curiosity path every day it will still come out alright in the end.
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I want to see if I am understanding: A method of spiraling can be a Weekly Checkin and then working on mastering a previous concept?
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Curious if you still get some students standing up by the door at the end using the breakdown in the bar charts in this lessons video? It just seems like with many of the students in my school, that they have had so much trauma, that they struggle to get excited about learning. I hope learning these methods can spark more excitement into kids who struggle emotionally and have major trauma.
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Dawn, your idea of spiralling is just the beginning. It’s a bigger re-design of your units/course. Have you dove deeper yet and learned a bit more since this?
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I like the clock visual to ensure everything fits in the allotted time. The Unit Plan helps me understand that not all lessons will run the same way or take the same time. This will be very helpful when developing lessons. I wonder how the curriculum that we’re expected to teach from fits in all this.
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I have two questions:
1. When it is that practice time, are they still in groups or do you do individual practice?
2. I have been using guided notes for the times when I want to do some concept understanding, such as teach students about the Trig functions. These notes are problems and pictures and then they add the ideas and solving steps. I went to them when I had large number of students with IEP’s that had “notes to follow with teacher” in their plans and now give them to all students so that they can focus on the new concept vs writing/drawing. Do you recommend using those or do they create too much structure that would interrupt the flow of learning? If you don’t recommend them, how do you do direct teaching?
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I was shocked when I had an administrator observe my classroom for the whole period and show me a pie chart of where the time was spent in my classroom.
I worked really hard to transform my class.
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What did you see on the pie chart? How did that experience help you moving forward?
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The pie chart revealed how long it took me to get started every day. It also showed how bad my transitions were, the students and I took forever to get from one thing to the next.
It made me realize that I needed to pay attention to building habits and processes that kept students working.
Reading Peter L’s book really made the beginning of every period sing.
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Since we were presented with misconception #1, I think I still have a worry here. I understand that we cannot make every day a MMM day, but I do think creating these moments for the entire year is going to be a lot of work. Did you guys see any pushback from other team members when implementing and trying out your framework for the first time? When did other educators start coming on board with your team?
This year I will be working alone. I feel like I will be in my own bubble and I am scared to not have others to collaborate with. I like that I will have freedom to implement all of these moments into my classes, but I am afraid of getting away from content teams and trying to find a way back in the future when I do teach other courses.
Do you feel that your students end up doing well in your classes, and then move into a “traditional” setting and struggle? Or do they carry their math moments with them and still find a way to make math class their own in the future? I am afraid of seeing success in my class that doesn’t carry my students forward to the following school year if they are back in a traditional class.
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We would definitely start with a manageable amount of change. Creating or finding a problem based lesson for every new topic can be time consuming. Do what you can. We did this transformation over years….so don’t think you can recreate your whole course in the first year.
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I agree with others that seeing the clock was very helpful with envisioning what this may look like on a given day. We are a math workshop district and often have a warm up, mini lesson, then lots of stations/independent work time while the teacher does small groups. We do have flexibility to break from this with teacher discretion. It will be interesting trying to balance the ideas here with math workshop structure and mandated unit teaching…
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In my school, we have a template for “I do”, “We do”, “You do” and I’m just going to flip it, but it really will be a fluid thing. Your visual helped. I will not teach another year of students who ask why they need this and feel it is not related to their lives, except for those few who will always say that. It is much more natural to learn to satisfy your own curiosity than from a chore that may be a competition.
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I’m glad to hear I don’t necessarily have to follow the 3-part framework every single day, just as often as I can. I have a solid start, since I sat down with my 7th grade team and we made a ton of curious warm-ups (many of which are based on the “how to start a math fight” ideas). That means we’ll start every day with problem-solving.
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As much as I am sure that we all would love to do these 3-part framework lessons EVERY day, it is just not practical for many reasons, but especially so for the reasons stated in the video. My present issue that I have to wrangle with is how to work with my blocks that are two very different lengths. I have two 80 minute classes and two 40 minute classes which will rotate daily. On top of that I have three different “leveled” classes, so only 2 are the “same”. Of course I teach students and not content so that often leads me to be in sometimes 4 different places at once. I am trying to figure out how I could possibly juggle the varied length of class time and the variety of levels while maintaining sanity and giving my students the best possible education. Part of my insecurity lies in finding and selecting the appropriate prompts to spark curiosity. I am not too sure that I could develop such prompts on my own just yet. Maybe with time it will come but presently I am feeling a tad overwhelmed. Excited but a tad overwhelmed too.
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Re-thinking how I am going to spend my time on a big scale has been a big thinking question for me. Before this lesson I used the Lesson Procedures as Big Numeracy Tasks (aka Rich Tasks), Smaller Numeracy Tasks (Ex WODBs) Sequence Flows (Math Strings), Check Your Understandings, Numeracy Questions, Math Games & Math Fights. However, I like how you have sectioned each topic into different time dedication to conceptual understanding, procedural fluency and problem solving/application. This is something I definitely will be reflecting on.
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I have been trying to begin my lessons with problems for the kids to solve together for a couple of years now. Most times those problems have been word problems to give the math some context. I also appreciate and sometimes find that Peter L’s method of thin slicing is appropriate. Give the students problems they know what to do with and add complexity with each step. The visual at the end validates both starting points.
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When I look at your strand from this video of linear equations from Solving Linear Equations to Elimination (Systems), it looks like you get this all done in 5 days. In my class this is many months of building foundations and applying them. I am assuming you are doing the same.
What I am taking from this course though is that I don’t start with notes and a few problems and then practice and problem solving. I instead start with problem solving to spark interest. Once I have laid this foundation I have used the vocabulary and the students have found their own process to solve that gets internalized. I find when I do it backwards, I can do notes maybe at the end of class that bring together all the important pieces in a summary rather than vocab and processes that really had no meaning when I do it at the beginning. The practice gets woven in in chunks throughout the week.
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Thanks for clarifying this. I recently went through your 5 day Planting Flower Revisited Unit and appreciated that each day was a bit of a different balance. While there was always some sort of curiosity building step, sometimes is was more of a math talk rather than a full 3 act task and other days were balanced with more purposeful practice for students to build their fluency. Much appreciated.
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I appreciate knowing you split it up as I was thinking of having each act be a different day and the forth day for check-in. Day 1 math curiosity, Day 2 solutions (gives me time to sort them out to the progression I want to review them in), Day 3 consolidation. I’m also trying to put in station rotation, so that would give me part of my 50 minute class to do the math fight at the beginning and some targeted instruction / review with groups.
