Find answers, ask questions, and connect with our
community around the world.

  • Lesson 5-5: Question

    Posted by Jon on May 1, 2019 at 12:01 pm

    Take this time to reflect on your learning from this lesson. How might you use the information presented here in your lessons this week? Post any comments, questions, and reflections here.

    Noel McMillin replied 1 month, 2 weeks ago 26 Members · 30 Replies
  • 30 Replies
  • Rachael Young

    January 4, 2022 at 8:56 pm

    I’m currently on summer break so I won’t be back in the classroom for 3 more weeks so I am thinking about this question more theoretically. This area is one of the most challenging for me so far because my own Maths skills are not high. I’m a language and Humanities specialist who just scraped through high school Maths (Business Maths, baby!) and did 1 semester on teaching Maths at Uni. And although I’ve been teaching Year 6 and 7 Maths for over 20 years I still don’t feel confident with it and I get easily flustered if I make a mistake or I don’t understand what a student is asking or has done. I am learning to utilise student expertise in my classroom and to be more comfortable with saying I don’t know the answer and luckily my partner is a Physics PhD so I can usually go home and ask him to explain it to me but it makes things hard and it’s hard for me to not fall back on the textbook as being more in my comfort zone! But in another way I guess it’s an advantage – because I think like a Year 7 mathematically, I can usually anticipate what strategies they will try and what questions they will have! But I lack the mathematical language that you guys often use so it’s hard to categorise the strategies. Not sure what the solution is except more preparation! Hence the work over the summer!

    • Kyle Pearce

      January 5, 2022 at 7:16 am

      Good on you for taking on this learning despite your discomfort with mathematics. You’re right that coming at it from this angle gives you an advantage and the ability to appreciate the challenges many students are also facing. Once you’ve completed this work, The Concept Holding Your Students Back course will be a great next step as it goes through the roadmap to proportional relationships which is huge in middle grades and beyond! You got this!

  • Patricia Scheler

    March 3, 2022 at 5:28 pm

    I really appreciate all 5 practices. Even though ANTICIPATING wasn’t part of this lesson, I still value its part in the process.

    MONITORING is key in knowing which students are understanding and “getting it” and which ones are not.

    I have begun to notice students that are SELECTING to use different strategies than the one I present to the class. They are so proud of their different way to get to the same answer.

    SEQUENCING is still imperative. You don’t want to get too far ahead and miss steps.

    After being a 3rd grade teacher for a year, I understand the value of CONNECTING 2nd grade objectives and learning to what students will be doing the next year.

  • Kyle Pearce

    March 5, 2022 at 7:16 am

    Great reflections here!

    Also worth noting is that a lesson that truly incorporates the 5 practices is typically one where we don’t preteach or “show” strategies ahead of time. Maybe consider having them use their intuition and prior knowledge in the future and see which strategies emerge and then connect it to what you wanted them to learn from the doing of the lesson.

    Awesome work and reflections here!

  • Stephanie Pritchett

    March 21, 2022 at 10:31 pm

    I have read the 5 Practices book and am familiar with the strategies. I’m most uncomfortable with knowing moves to anticipate, knowing how to recognize them in students work and knowing the order to present them on the fly. I think if I spend more time on the anticipation face I won’t be so worried about how to sequence and connect strategies. I feel that my students usually come up with the same simple strategies and very few new strategies are brought up. As we do this more and more, I can introduce one new strategy that relates to their thinking. I hope my students will get better at different models and ways of thinking.

    • Kyle Pearce

      March 22, 2022 at 6:47 am

      Good on you to dig deeper here.

      Quick question: do you have any specific models / strategies in mind prior to facilitating the lesson? Often times we have to be intentional about which strategies and models we are after and craft the math experience around them so they can emerge.

  • Kerri Brodie

    March 22, 2022 at 9:54 pm

    I am really excited to try a lesson like this with my students. I like the idea of using the anticipation template as a tool during the class (although I did find it very tricky to figure out different ways). I typically just circulate around and try to remember which groups’ work I want to bring up. I think it will help me really solidify and keeps things moving at a productive pace if I use the guide while monitoring to help me with the selecting and sequencing steps. I like the idea too because it will let me choose student work to showcase for groups that may not typically have the “mathiest” way of doing it but still have a way that works. This lesson really resonates with me and helps me see how I will get to the learning goal at the end of the lesson by helping students make the connections.

  • Tarini Arte

    March 27, 2022 at 9:24 pm

    I really like the anticipating and sequencing recording sheet as a concrete tool to use during class. When student groups work through problems or 3 Act Tasks, I generally tend to circulate and mentally take note of who to ask to present anyway, but I feel like this sheet will help me consolidate and get better at sequencing. Anticipating can also be challenging since we often may not consider how a student approaches a problem, but is a great practice to really get in their minds. I agree in the idea of presenting concrete –> abstract strategies. It allows for a low floor and for students who are not as confident in math per se to have the opportunity to share, but also gives a high ceiling for abstract representations. The sequencing can help foster those “a-ha” moments.

  • Jonathan Lind

    April 3, 2022 at 10:38 pm

    Noticing some parallels between our classroom setups, Jon- cards on the boards, students standing, etc. Fun to see that in another classroom.

    I find the use of anticipation, when I can find the time, to be pretty powerful, particularly in cases like you mentioned where not all of the strategies you thought of are used, so it’s a good time to step in and share different ways of doing things.

    I feel like the during moves get easier with practice. They’re a little daunting at first, but they become just what you do every day.

  • David McKnight

    April 4, 2022 at 5:46 am

    I like the idea of the anticipating and sequencing recording sheet. I think that it would be valuable to include these notes from each class in their notes. Our students work on e-portfolios and this would be a great addition to that. It opens up an opportunity for reflection and to reinforce and build on their former understanding.

  • Dawn Oliver

    April 15, 2022 at 2:35 pm

    I am on a couple week break before classes start again for credit recovery. This lesson of the course is helping me plan for the first lesson of the unit I will teach during credit recovery. I liked the Anticipatory Template. I think it really made me think about how to anticipate what types of answers students would find and possible mistakes they could make solving these types of problems. I don’t always know the students I am teaching, so it can be hard to anticipate what they already known or if it will be necessary to do some reteaching or scaffolding before the lesson. I can use this approach for the students I do know from past classes.

  • Terry Hill

    May 26, 2022 at 9:35 am

    I understood exactly what was said about students saying their answer is the same as another student’s answer because I often get the same thing, so I like the idea of being selective. I believe that will be very beneficial moving forward.

  • Renee Holmquist

    June 21, 2022 at 12:34 pm

    The math discussion during group work is my favorite part of my class period. I have had a lot of years to practice this and I feel like I do a pretty good job of it. I found these 5 practice to be helpful though to refresh what I am doing and how to guide my students along during class time. I have got better at facilitating discussions as I have had more time in the classroom and a better idea of the sequencing of the learning they have over their years of math in our school.

    Two questions – when the class is going over the student answers and work, do you have the other groups sit down so that everyone can see while one group presents? Also how much do you recommend the teacher voice is heard in going over the solutions?

  • Jared Sliger

    July 6, 2022 at 8:51 am

    To me the one practice that really resonates is sequencing. While I am in the monitoring and the selecting phase I am constantly looking for approaches that will help move student understanding forward. Not just correct approaches, but some of the places where groups have gone wrong. I am looking for those and putting boxes around them. Students know they aren’t allowed to erase things in boxes. If I am really on my game I will start numbering those boxes as the lesson progresses…so my sequencing is ready when we start talking as a class.

  • Marion Mulgrew

    July 20, 2022 at 3:21 pm

    In thinking about the logistics of running class like this on a regular basis, how do you document student work? Do you take pics of everything? Do they? Is it someone’s job? Do they journal about it with a little sketch and explanation?

    I have done this when there are notebooks and a doc cam, but sometimes the whiteboards are more freeing to thought than “permanent” marks on paper.

    I like your ideas of most used to least used strategy as another way to approach sequencing other than building the conceptual thinking from more simple to more complex (or more grade level). It also helps groups not feel like if theirs is picked to go first, that it is the least powerful.

  • Stefania Lambusta

    July 22, 2022 at 10:40 am

    I am taking this course while on summer break and thinking about how to implement some of these strategies. I found the sequencing to be the most helpful. When I first began teaching I would want all groups to share, hear all voices. Now I am better at selecting a few to show some progression of my learning goal. The one comment in the video that really stuck was sharing some strategies that students may not have come up with that would lead to next moves. (The ones I might anticipate or want to share as a learning goal). This makes sense and of course will help with the progression. How do you plan for the length of time for activities to include all 5 practices? Any advice?

  • Julie Gonzales

    July 24, 2022 at 3:51 pm

    As a math coach I watched teachers struggle with knowing the sequencing of student work that would work best. This class has taught me to look at a broader approach in terms of pre-planning. I believe my teachers know where students are coming from and know where they need their students to go. However, I think the part they are missing is anticipating what student solutions may look like. I loved the templates this class has provided because I believe they could help teachers think about those student solutions and then mark which groups are using the strategies they have thought about. As far as the sequencing goes, I think it will be the learning goal that will dictate the order the teacher should choose. I have wondered may times if maybe teachers should worry more about CONNECTING student solutions than the actual sequencing of student solutions. It is those connections that I believe will help students grow their thinking – not so much the order the teacher chose to have students present!

  • Jorgelina Corral

    July 25, 2022 at 12:30 am

    I am reflecting on both this lesson and the previous one as I did them back to back. I am really concerned with the anticipation step. I 100% get the importance of anticipating and doing a lot of that leg work before a lesson. However, as a new teacher, that is a really hard task. I can see this getting easier with time, or having presented the material before–if you’re teaching it for the first time though, do you suggest asking colleagues? Or trying to figure out different ways of solving the same problem?

    From these 4 “during moves,” I think selecting and connecting are going to be the simplest to execute as they really have to do with the content. The monitoring and asking questions to push thinking forward is going to be a bit more challenging for me as I don’t want to just “give it away.” I think this is going to take practice.

    I’m glad I’m on my summer break, so that I can practice with my kids. Maybe attempt some of the kinder ones with my daughter.

  • Christine Pomatto

    July 25, 2022 at 7:55 pm

    I look forward to trying this strategy in class. I have many students who either give up quickly or ask for lots of hints, and focus only on the answer (not the process). During this lesson, I was thinking a lot about our proportional relationships unit, where students have to learn how to make tables, graphs, equations, etc. from a story and also decide if those are proportional or not. We consistently do a lot of lecturing in this unit, to teach students about k (constant of proportionality) and how it shows up in various forms (y = kx, k = y/x, unit rate, etc.). However, students rarely make these connections themselves and just try to memorize everything (partially our fault!). I’m excited to try a lesson similar to this one (with easier numbers) where students might figure out many ways to represent their solutions before we have even learned about the constant of proportionality.

  • Anna Clark

    July 29, 2022 at 12:03 pm

    I’m currently feeling like I will be much better at this after I’ve been teaching for a few years! I honestly feel overwhelmed with the idea of anticipating strategies but I know it will be easier the more strategies I see each year! I think I just need to take really good notes on the strategies I see pop up this year because there will undoubtedly be more than I come up with, so debriefing will be just as useful for me to learn about the mathematics as my students! I wonder how much I should plan also for common misconceptions here and if/how I should address them?

    • Kyle Pearce

      July 30, 2022 at 7:14 am

      Definitely don’t let the learning stress you or overwhelm you. Most teach with ignorance in this area which is a very low stress way to go – but not great re: maximizing student learning. Now that you have this awareness, do your best to anticipate what you might see from students, but don’t be expecting perfection from you (or them). Over time this will feel more natural and you’ll be so happy you took this journey 🙂

  • Nicolle Ristow

    August 1, 2022 at 3:53 pm

    I like the 4 step for during the lesson. I feel right now I am very good at monitoring the students with good feedback. In the past, I have tried to select and sequence, sometimes it works awesome and others it falls short. I need to keep working on these parts to continue to improve. I feel like my greatest weakness is the connecting. I rush to fast to the solution I feel is the best or shows the math algorithm the best. My advice to myself is to keep working at it.

    • Kyle Pearce

      August 2, 2022 at 7:52 am

      Definitely always a work in progress. Thinking about what you want them to learn / understand / do is so important to help you focus in on what matters for that lesson.

  • Heather Alden

    August 2, 2022 at 9:45 am

    I enjoyed learning about the 5 steps. I really like the sheet that you provided the lesson before for the anticipation step as it will also help with monitoring which groups do what and selecting and sequencing what to share at the end of the lesson. I also love that we can value and celebrate concrete, visual, and abstract each lesson, giving students a way to access the abstract when they see the connections across the strategies. I love that student work is the focus of the teaching at the end of the lesson.

  • Kristie D’Arcangelo

    August 19, 2022 at 10:24 am

    I truly enjoyed seeing the 5 practices in action and now have moved that book to the top of my next to read! I bought it this spring and have not had a chance to open it, but now that I have had a preview into its content I am hoping to get to it soon. Presently I am working through Productive Math Struggle which has been a struggle given all that I have on my plate right now. I wish that the summer were longer… I am excited to take this knowledge and share it with my planning partner who is new to math education. I will have to be careful to not overwhelm him though. 🙂

  • Victoria Murphy

    November 13, 2022 at 6:34 pm

    In the last few lessons, I have tried many of these pieces. I am not very good about ANTICIPATING and even though it was not part of THIS lesson, I mention it because it would help me with the other pieces while I am MONITORING and SELECTING which group’s work to show and in what order, SEQUENCING. Having a little forethought about a lesson about where and how it might go prevents thinking on the fly and maybe even confusing the students. I enjoy the vertical white boards and the kids do as well, but I have some work to do in polishing the actual lesson and bringing forward the ideas and strategies that we are looking for.

  • Alison Peternell

    November 27, 2022 at 9:30 am

    After doing a lesson like this, writing equations given two points of data, and seeing students talking to each other and figuring out how to not only answer the questions but answer them more efficiently as they go (by using the equation y=mx+b), I found that when it went to the note taking part to make sure we were all on the same page, this part went very quickly. It seemed as though students learned this material deeper than if I just told it to them. I would like to try all of my lessons like this in the future. It does take more time but I like that students are up at the white boards talking to each other. I am a facilitator to move them along. My hope is that they learn the material better because they figured it out themselves, which of course is what this course is all about.

  • Joseph Barnas

    December 12, 2022 at 9:09 am

    It is important to take into account selecting. I think I often try and talk to all groups so that everyone feels their thoughts, work, answers, and opinions are validated. However, this does get tedious at times. Being better at selecting to drive the class ace forward is an important aspect that I need to work further on.

  • Noel McMillin

    December 13, 2022 at 4:52 pm

    I also read the 5 Best Practices book a few years ago and it was a wonderful reminder to watch the lesson.

    One of the greatest joys I find is sharing a student’s strategy with the whole class, especially a student that does not typically exemplify the “good” math student. I can see the student’s face light up when I mention his or her name to the class. It is so powerful. It just cannot happen if I am doing 90% of the talking in a lesson.

    The practice that takes the most work for me is monitoring. I really need to get my steps in as a go from group to group. I find it challenging to keep all students in all groups on task. It helps immensely when I have good problems to start with, ones with a productive struggle.

    I also find that the questions from students are just better when they are given the chance to work on their own or in small groups. It took 2 1/2 weeks of work, but today was the first day of graphing a line in slope-intercept form without creating a table. The questions and comments made by the students were really good and it just would not happen if I was the holder of all knowledge.