Make Math Moments Academy › Forums › Full Workshop Reflections › Module 3: Teaching Through Problem Solving to Build Grit and Perseverance › Lesson 3-6: Tool #4 – Student Generated Solutions › Lesson 3-6: Discussion Prompt
Lesson 3-6: Discussion PromptPosted by Kyle Pearce on May 1, 2019 at 11:52 am
Which tool(s) from this module (concrete manipulatives, multiple representations, visuals, and student generated solutions) do you found to be most useful to make the math more accessible for your students?
Which will you try next week and how will you go about using it?
MemberJuly 12, 2019 at 9:05 pm
Fun, you showed 3 different ways of seeing the problem. My first one was different than all of them. I saw it as a nxn square on the right Plus a 1xn on the left and a 1x(n-1) on the bottom. So: n^2+n+n-1
This was fun!
- This reply was modified 2 years, 7 months ago by Kyle Pearce.
MemberFebruary 3, 2022 at 7:47 pm
For 2nd graders, I find that using concrete manipulatives really helps to solidify their understanding. I’ve used 1s, 10s, 100s, and 1,000s blocks to help not only with place value but with addition and subtraction with regrouping. Students who had the steps memorized made the connection. Students who had no clue had aha moments.
I also try to use multiple representations to help solidify understanding. For instance, most of my students can write the number 367 in expanded form, 300 + 60+7. However, when they are presented with a different format, they often fall apart. Providing multiple ways to ask questions and multiple ways for them to respond helps them to have a stronger grasp on numbers.
MemberFebruary 22, 2022 at 4:08 pm
I used concrete manipulatives with students to help them sort things by color or shape. These are students who are special ed, and are probably at a kindergarten level. I used manipulatives that have Velcro on each piece to match colors and shapes with appropriate piece. I have also used other objects, such as colored shapes (like erasers) that can be sorted by color or type of shape.
MemberMarch 10, 2022 at 12:15 am
I really like multiple representations mixed with student-generated responses (they go quite hand-in-hand with each other), since they allow for students to dive into their own reasoning (low entry point and high ceiling). The 3 Act Tasks facilitate this kind of learning well. I’m trying one this week with cup stacking that can allow students to show their own solutions (as an intro to systems).
MemberMarch 13, 2022 at 12:23 am
I find that the student generated are the most interesting for me as a teacher. For the sake of the students, I feel like using multiple respresentations is essential to make connections with the most students. Ideally, we should be using all 4 of these tools as much as possible.
MemberMarch 14, 2022 at 11:25 am
I like the idea of using visuals. I teach secondary math, so many of the ideas are extremely abstract for students, and traditionally are taught that way. The task asking how many small squares are needed to go around the circle is awesome and makes pi more accessible.
As I think about it more, I guess these are tied together; manipulatives such as algebra tiles provide visual representations of abstract concepts, and the student-generated responses develop student understanding.
MemberMarch 15, 2022 at 9:24 am
I am using concrete manipulatives this week to celebrate Pi Day. My students are “discovering” Pi using string and objects (like Jon did in the video), modelling the area of a circle using paper plates and forming into a “rectangle” and exploring surface area using mandarin orange peels. There have been lots of A-ha moments. Next week I hope to use pattern blocks to help my students understand the unit circle because they always have trouble with half the circle being one pi so I hope to use an activity similar to the one shown with pattern blocks.
MemberMarch 17, 2022 at 2:38 am
I reached out to some of my 6th grade teachers this week so we can collaborate and co-teach a lesson. I’ve come out with amazing ideas from this module. Thank you! I’ll come back to this and share how it went.
PS. your 3.7 summary module is out of place, it showed up right after the 3.3 lesson, fyi.
MemberMarch 19, 2022 at 4:06 am
Here’s a problem from a recent assessment where I used some student work to start a discussion about problem solving. The students both had similar strategies involving using subtraction to find irregular area on the coordinate plane. We can discuss efficiency (left student did a lot of extra work), connecting different representations (both students used labels pretty well), and areas where they could add strength to their solutions (confirming the answer in a different way).
I put together student work like this after assessments rather than going through the problems myself or providing answers myself, so that students have models for effective strategies. It’s a pretty effective way to show students expectations, while also showing them that they can do this, and don’t necessarily need a teacher to tell them how all the time.
- This reply was modified 3 months, 2 weeks ago by Jonathan Lind.
MemberMarch 19, 2022 at 6:49 pm
This week I used your sunflower model on how to solve two step equations. For the last few years I have been trying to teach my students with abstract reasoning. For this lesson I had manipulatives available to my students to come up with an expression. Most students gravitated to them almost immediately and started to use them to reason about the problem ( even though afterwards they enjoyed building other things). A physical model was so easy for them to build. From there we shared what visual models would match and then connected it to the abstract (maybe a little too soon?). It was a great start. I was a little nervous, because new things don’t always go as well as things you have done over and over. I knew by starting that this would get me to a better place as a teacher for my students, so I went for it.
MemberMarch 29, 2022 at 8:40 am
Love the sunflower model!
MemberApril 2, 2022 at 2:51 pm
I am going to use the visual of the paper and two stacks of paper and see what student generated responses I receive. I think it will provide some interesting results.
I just tried this, and only one student out of 17 did this correctly. What was interesting was that he did not think he did it correctly, and was unsure how to explain his answer. I had another student get the correct answer, but she did it by starting off estimating instead of actually doing math. She divided the 142.75 cm by 2, and then rounded that up to 72, then figured out that each pack of paper was 6 cm. While she got the right answer, and could explain her work quite well, she could have just as easily gotten a wrong answer. I encouraged her use of estimation, but also explained why it could have been wrong.
- This reply was modified 2 months, 3 weeks ago by Terry Hill.
MemberApril 11, 2022 at 11:53 pm
I don’t necessarily think that any tool is most useful for my MS students, it’s more about which suits the topic. For my G7 when first learning equations did an activity called bags and blocks (using physical blocks and bags) where the blocks represent a number/ constant and the bag a variable b/c we can’t see how many blocks are inside. Students represented equations with the manipulative and tried to find how many blocks were in each bag. The cool thing is I no longer have to teach equations with variables on both sides as a separate topic!
For my G8, last week we did speed eating hotdog Kaplinsky task to get student generated answers. We used those answers to discuss multiple representations of linear functions.
AdministratorApril 12, 2022 at 6:46 am
Totally agree. Being ready to use the tools as they are useful is the key!
Glad to hear you’re making some noise with problem based learning!
MemberApril 26, 2022 at 4:23 pm
I have 2 questions from this module:
1. Sometimes when we use student generated solutions in a whole class discussion (our alt classes are really small), there isn’t yet enough stamina/resilience in students to carry them through seeing another person’s approach. What are your thoughts on this? We will keep encouraging students to see the benefits of multiple perspectives…
2. Would you say that “consolidation” is really about deepening students’ own thinking by connecting that thinking to a mathematical model? (double bar/line model, table of values, equation, graph, etc?) Is that a direct part of the consolidation phase?
AdministratorApril 27, 2022 at 8:33 am
These are great questions.
When consolidating, it can be helpful to facilitate in a way that asks students to share very specific pieces or parts of their work to avoid each group running too long. Also, every group sharing might not be necessary – especially if some approaches are very similar. You can let one share then also ask the groups “whose approaches were similar?” Then move onto another.
Also, you can consider – if you feel the thinking / focus is spent for the day, consolidating can take place at the beginning of the next day.
For what to highlight – that depends specifically on your intentionality of the lesson. The consolidation is an opportunity to drive some of those ideas home be it a big idea, strategy and/or model. From what you see during the lesson, you can decide what the next day will look like. Do we dive deeper? Did they “get it”? Did they need more practice with a model explicitly? These are all things to consider.
MemberApril 27, 2022 at 1:20 pm
Thanks. Both responses are very helpful. I like the idea of sharing very specific parts. Also, thanks for the clarification re: consolidation… to drive home the point – whether model, big idea etc. Thanks!
MemberJune 9, 2022 at 3:16 pm
I teach G5 so visuals and manipulatives are staple, to a lesser extent different representations and less so student generated responses. I am going to try incorporate more representations. My next topic is fraction of an amount. The context will be from Kaplinskys “”what fraction of children are in the right car seat”. I could ask them for a visual representation and see what they come up and show them others’. I can give them linking cubes to show it too, they’ll all choose those for sure!
MemberJune 16, 2022 at 11:28 pm
Because I teach primarily students with IEPs, concrete manipulatives are often my go-to when building basic understanding (for example, understanding that four 1/4 tiles equal one whole). I loved seeing how these manipulatives can be used to build understanding of much more complex concepts as well, and I’m excited to try that in my class this upcoming school year.
I also love the idea of using student-generated solutions to guide students toward understanding abstract formulas, and then “mapping” future context-less problems onto the problems with context.
Thanks for a great module!
MemberJune 20, 2022 at 11:23 am
I love these tools. I think I am going to try and make the height of the table problem into a system of equations problem.
I think I will make a video of students, or me, walking into a room and stacking the paper. I think I would use different height reams of paper. I am not sure if this would create a system, but I am going to work on it right now.
MemberJune 20, 2022 at 4:09 pm
It is summer break so I don’t have a class to try this on but I would have chosen Student Generated Solutions. I would achieve this by having 9 groups of 3 work on vertical white boards on a thinking problem and then have each group share out what they did. I did a version of this in Precalculus last month and had them write a trig function for a sinusoidal graph that I gave them containing minimal information. First they did it alone, then with small group, and then with half the class. 2 people then shared out the groups solutions and how there were multiple ways to write the equations using different transformations. It was powerful to hear from their peers and work together to get a solution.
MemberJune 23, 2022 at 12:11 pm
I like the manipulatives and multiple representations. These seem doable to me as I start off teaching 4 new classes. In time I hope to use visuals, but I recognize a need for me to gain more comfort with concepts in order to get students to grow into the conceptualization with me. This is true for student generated ideas as well.