Hello and welcome to #octmchat! I am Jonelle Bell. I teach Kindergarten and am the Math Instructional Leader at Madeira Elementary. There is so much that is different in my classroom from how I was taught math, but the biggest change is more student talk and less teacher talk.
Sue from Maryland, math author/consultant. I teach math through context. Use stories, word problems, and models to show students that the numbers and symbols actually mean something! #octmchat
Hello! I'm Nicole Prater and I teach 2nd gr at Madeira Elementary.I allow my Ss choice when using strategies to solve computation problems. They use the strategy that the understand best.
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Matt Felton-Koestler, math ed faculty at Ohio University - I was taught with CGI principles as a young child, but as I got older it was more traditional, so I teach how I learned as a young child--and I also integrate more social and political issues #octmchat
Hi Everyone! I’m Karen Kresser from Cincinnati and I teach Kdg focusing on the process. I was taught to memorize facts and formulas and focus on the correct answer.
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Rachael Gorsuch, Columbus Academy in Gahanna
Algebra 2, Geometry, Precalc teacher
I teach math using as many connections to real life as possible, and encourage discussion instead of Ss always listening. #octmchat
Hi, everyone! Jodie Bailey - math coach @HilliardSchools & President Elect of @ohioctm I love that we focus on the WHY now. Why do things work? Where is the structure? What patterns do we notice? #octmchat
Hello! I'm Nicole Prater and I teach 2nd gr at Madeira Elementary.I allow my Ss choice when using strategies to solve computation problems. They use the strategy that the understand best.
#octmchat
I was taught algorithms from start to finish. Now I intentionally plan for discovery times so Ss can construct their knowledge of the concepts. #octmchat
#octmchat Melissa Unger from Madeira, OH (Third Grade Math Teacher) There are so many ways that my math classroom is different from my childhood: introducing a topic with a problem, more student talk, games for learning, and lots of manipulatives
Hi everyone! I'm Brenda Boring and I'm a math coach in Hilliard City Schools. One positive way that we teach math now is to allow Ss to explore and make discoveries about math!#octmchat
Kryssie Pratt here 3rd grade teacher from New Albany. Most of my mathematical "understanding" was very procedural. I avoid teaching procedures so my students learn to trust their own reasoning #octmchat
Hello! I'm Debbie Gabelman. I'm an Otterbein student working on the 4/5 generalist endorsement. I'm in Columbus. I was taught standard algorithms only in school. I like how a variety of strategies are taught in classrooms today.#octmchat
Brooke Lovely, kindergarten teacher at @WilsonElem. I was taught very procedural skills, not conceptual ideas. Also, worksheets! I want students to play and understand, not become worksheet zombies. #octmchat
A1: We tend to start with discussions where they talk about their lives, then we introduce the math. Class ends with cycling back to the real life scenario. #octmchat
Hi! I’m Christina one of the math consultant/coaches @HamiltonCoESC... and current Pres @ohioctm
I’m a lot more focused on building the conceptual understanding rather than just charging through the formulas 😬
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Hi! I’m Alexa Fulmer I teach intermediate math for Cincinnati Public but I just got the job as an elementary math coach for our district next year. So much is different-manipulatives, modeling, great problems, exploring, wondering, questioning... #octmchat
A1 In kindergarten we scaffold and allow students to explore the concrete before we ween to representational and then abstract. I want students to understand the concept before I take away the supports. #octmchat
A1: Bridging the concrete to representational to abstract helps students have a thorough understanding of math concepts. It is through this understanding that learners are able to use their math knowledge to be mathematical thinkers. #octmchat
A1 Often put varied models together and ask “What do you notice?” as they observe them. Let them tell me how they connect. Love when it is their insight! #octmchat
A1: It can be hard to find the right concrete context to work with to lead towards certain math concepts... Sometimes a semi-real context works better for teaching a particular concept, but may feel less real to kids. So I think there needs to be a mix of both #octmchat
A1: Asking Ss to solve problems multiple ways often requires them to use all of these modes. This often helps students visualize problems and understand them at a deeper level. #octmchat
A1: allow my Ss plenty of time and opportunities to take risks. Want to support them and help them feel secure. Also to build on their success by connecting new material with things they have already learned.
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Barb Weidus, math coach in SW Ohio; I’m glad students get to share strategies, not sit in rows, and in most cases don’t do worksheet, after worksheet, after worksheet with 50 problems!! #octmchat
A1: my "high achieving" math Ss often have difficulty representing a problem in a concrete way. My struggling Ss have trouble w/ abstract representations such as equations. Groupin Ss so their strengths complement one another has helped bridge gaps in Ss understanding #octmchat
Chris Bolognese from @ColumbusAcademy where I teach math and comp sci. Currently participating in #octmchat while waiting for a delayed plane to Montana.
A1: Asking Ss to solve problems multiple ways often requires them to use all of these modes. This often helps students visualize problems and understand them at a deeper level. #octmchat
A1: Asking Ss what they #notice and #wonder about the representations - as well as what is the #samediff. Sometimes Ss are surprised by the connections they find! #octmchat
A1: I also like to go slow as we go through the concrete to abstract to make sure students are ready. I also notice that many students tend to move abstractly when they are ready and slide into abstract #octmchat
Hi my name is Ann Howard and I am currently Student Teaching Pre-Algebra at Perrysburg Junior HS.
Inside my classroom, students are proposed problems that do not have a right or wrong answer in order to support critical thinking. #octmchat
#octmchat A1 Yes, my new favorite question (and that of my students) is 'What do you notice?" I started my data and graphs today by exploring bar graph samples with WDYN.
It is so important to allow students to move at their own pace through this process! Allowing multiple opportunities for discussion to make these connections is essential. #octmchat
A1: I also like to go slow as we go through the concrete to abstract to make sure students are ready. I also notice that many students tend to move abstractly when they are ready and slide into abstract #octmchat
A1 cont: Having Ss create concrete representations & explain them allows you to see where they are in stages of modeling- for example: are they using a tool to model a situation or are they using a tool to solve the problem?... #octmchat
A1: Watched several 1st grade lessons today where students were presented with a problem and then used their number racks to help make sense of the problem. Information was eventually moved to a white board #octmchat
A1: I think one of the most important roles of Ts is to help Ss make the connections among various representations... I find @numbertalks help us make those connections #octmchat
A1: I think having Ss draw representations for their concrete and abstract examples helps tremendously. Solving for Why by John Tapper is a great book on this topic. #octmchat
A2: one way models and manipulatives is to allow you to "see" the math and understand what is happening rather than this "foreign language" people speak #octmchat
A2: Models allow a common talking point and unified way to organize our thoughts. We act out songs for simple addition and subtraction.
Manips allow S’s to show thinking in a concrete way and they provide us with understanding for math discussions. #octmchat
A2 #octmchat Models and manipulatives allow students a mode to explore strategies for problem-solving. They open up discussion with peers and opportunities for trying to strategies. Manipulatives build the road to picture representations and then eventually abstract equations.
A2 Models help students visualize the problem – a big step toward comprehending the problem and then being able to figure out what to do to solve it. Manipulatives allow them to see, touch, and move as they model and explore the problem. #octmchat
A2- I've found that when students are able to be hands on with math tools/manipulative, they really get engaged in the math thinking. I catch students saying "how many counters should I start with" often when they first start to solve a problem #octmchat
A2: Models & manipulatives allow Ss access to nearly all SMPs. Manipulatives build a concrete understanding for Ss. Many of my Ss also use tools to justify their thinking. #octmchat
A3: Manipulatives can be tricky - sometimes they aid and other times they distract. I love having manipulatives around my room for kids to do when they feel it will help, or I can suggest the manipulative if I think it will help. It's all about us Ts knowing our Ss #octmchat
A2. Modeling with mathematics requires "mathematizing" a problem by imposing some form of mathematical structure (variables, representation, etc.) #octmchat
A2 models/manipulatives are an essential part of building conceptual understanding, Ss able to visually represent real-world problems before they try to memorize procedures and formulas #octmchat
I rarely use the word manipulatives. I like the word tools because it's their to help us and make sense of what we need. There are better tools than others, but you have to use them to realize what's the best #octmchat
A2: Again, critical to the development of number sense. I had the opportunity to work with some individual students this week who were being pushed to quickly into abstract thinking. I pulled out the counters to allow for a more concrete thinking. #octmchat
A1: One other thing I’d say about CRA is that if a child goes to the abstract with no understanding, back up to see if the representation is correct. If that is incorrect or suspect, go all the way back to the concrete to get those visual models rebuilt!. #octmchat
A2- I also have seen the importance of giving students choice in math tools and models. Allowing Ss to explore many strategies. Focusing more on the process rather than the answers!! #octmchat
A2 - I'm taking models to mean "math models (of the world)" - Lesh and others have argued for all problem solving to be seen as modeling--kids should always be asking how does my approach connect to the context? #octmchat
A2: I think models and manipulatives provide students with a great visual to assist them with solving a problem. These items can help students represent their thinking with actual objects. #octmchat
So important to offer Ss choice in tools. I'm often intrigued by how students use them - they notice ways to represent a problem that I'd never thought of before! #octmchat
Lesh and others describe this as mathematical modeling; modeling with mathematics is far broader and does not require a context to decontextualize as part of the modeling cycle. #octmchat
A2: I see manipulatives as physical items to do stuff with and models are representations of the manipulatives in a similar form usually on paper. #octmchat
A3. There are only two types of questions that help facilitate student thinking: probing questions (what has a student done to this point?) and pushing questions (what can the student do next?) #octmchat
A2: Models and manipulatives make the concept come to life... I have loved watching what the 3rd and 4th graders have discovered just by exploring with fraction bars
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A2: Modeling real world problems helps Ss make sense of the problem. Yes, it combines math practices which helps Ss understand conceptually what is going on. #octmchat
A3 I've really had to rethink how I ask Ss questions. What is the goal of the question? Do I want the right answer or do I want them to dive deeper in understanding?
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A1: The students are given the opportunity to explore different representations within the classroom in order to bridge concrete and representational models. @geogebra does a great job showing the proof of the Pythagorean Theorem. #octmchat
A3: questions have to be open enough to allow students to expand their thoughts and I have children talk to each other and look at each other rather than looking and telling me #octmchat
A3 open ended Q’s, which focus on process not answer. “turn and talks” with partners ensuring that several students respond is also helpful, especially when they realize there can be more than one correct answer or way to solve the problem. #octmchat
A2 Open ended questions allow a variety of responses, and it always amazes me how students respond. Yes, I am referring back to "What do you notice?" "What do you wonder?" and one I tried today---"What question can be answered by this bar graph?" #octmchat
A3 How about “Why?”, “How?”, “What if…”, “How is this like…?”, “What do you notice?”, “What is the rule?” or “What did you learn?” These start conversations, while “What is the answer?” does not. #octmchat
A3: Teachers need to use questions to help students construct their own learning. Math in Practice is a great resource for using questions as an instructional tool. #octmchat
A3- Earlier in the school year we did a whole math lesson on math conversations. It was so powerful to give the students language to talk about their math thinking! (I agree because, I disagree, Can you prove it?) #octmchat
A3: Questions are so important! They can open the door or slam it shut. I try to ask students to explain. “Can you tell me more?” is a favorite #octmchat
A3: wait time always allows for children to continue their thoughts after they are finished speaking. I also like to lean in and use the phrase "tell us more" #octmchat
A3 I’ll nudge them with questions, or feign cluelessness to get them to talk a little more. I want them to teach me how they’re thinking. The students need to be doing the questioning and the thinking. I’m just there to shift them into overdrive and reverse when needed. #octmchat
A3. I try to get my teacher candidates to ask questions designed to uncover children's thinking "why did you do that?" "can you show me with a picture?" instead of questions that direct kids towards the candidate's way of thinking #octmchat
A3: Teachers need to use questions to help students construct their own learning. Math in Practice is a great resource for using questions as an instructional tool. #octmchat
A3 Questioning is essential to guiding meaningful mathematical discussions. A lot of times, I restate what someone said and ask who thought of it like this or differently. Ss are eager to make connections to others thinking. We celebrate these! #octmchat
A3: My Ss love debates! My 5th graders last year would have at least 2-3 debates each week. Anytime there was a need for clarification, they would argue with one another. The questions they asked one another were amazing! #octmchat
A3: set up a classroom env't where mathematical discourse is valued. My Ss disagree (respectfully) OFTEN & this is when our best convos happen. Gallery walks also help engage Ss in convos & contribute to the learning of others- they really value helping others grow #octmchat
I absolutely love asking "What do you notice? What do you wonder? Why?" These questions promote so much thinking and talking. Before Ss were anxious about getting in wrong, with these open ended questions Ss are more confident and willing to share their thinking. #octmchat
A3- Also, asking students about what they are thinking or wondering is so important. I've fallen in love with 3 act tasks this year. Kids are so engaged and are able to really notice and wonder! #octmchat
A3 T questions should help Ss see patterns and relationships. ?s that lead Ss to discover and help them the reason, justify, and defend thinking are essential #mathpracticestandards#octmchat
A3: Strangely, I’m working hard to ask less questions in class because I’m really working to establish that I’m part of the community, not always the leader. Trying to encourage and reward student probing questions instead. (So tough!) #octmchat
I love these visuals to build vocabulary! Asking questions provides students with an opportunity to use precision in their vocabulary to clarify and explain their thinking. #octmchat
A3: as I visit classrooms, open vs. closed questions catch my attention... I love the idea of asking questions you don’t already know the answer to #octmchat
A3: We've also been working on critiquing the reasoning of others with questions like "What do you like about the reasoning of. . .?" "What can be improved. . . .?" "How could you solve this another way?" #octmchat
A2: Models and Manipulatives allows the students to explore math in a creative way. They are able to critically think with the support of these tools, which might be different to what they think math is about. #octmchat
Yes! I also often ask ?s that I don't plan on coming back to, just to get them thinking.... sometimes they try to explore it on their own- so cool! #octmchat
This is a great point! In my class last year, I intentionally planted myself further and further toward the back corner as Ss became more comfortable driving the conversation! #octmchat
A3: I try to be careful with how many times I say, “Why?” I watched a little one panic today cuz she thought she’d done something wrong. This came from Jennifer Bay-Williams work. #octmchat
A3: Asking open-ended questions is essential. Setting up a risk taking environment in your classroom and teaching Ss HOW to engage in mathematical discussions takes time but is definitely worth it in the end! I am a big fan of math chats in the classroom!#octmchat
A4: I am starting fractions next week in 1st using MIP. I am going to be more intentional about coming up with questions and allowing turn and talks. #octmchat
I think it is important that they get asked "why" whether they are right or wrong. After a while they get more comfortable with the question.
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A3: I try to be careful with how many times I say, “Why?” I watched a little one panic today cuz she thought she’d done something wrong. This came from Jennifer Bay-Williams work. #octmchat
A3 Aside from always asking “what do you notice about this”, I always find myself asking, “well, how do you know”. Kids are so eager to always give just an answer. They don’t think the process of HOW they got there is just as important. #octmchat
A4: I want to continue to infuse instruction with open-ended questions. I will use "What do you notice?" with line plots, pictographs & also add"What is another way to represent this data?" Multiple representations between graphs will strengthen student understanding. #octmchat
A4 After this chat I’m going to do the broken egg 3 act task. I was thinking about it the other day because we have done a lot of learning about eggs between an experiment, Easter, and farm field trip. Unintentional egg theme! 🥚 #octmchat
A3: I am still practicing with the use of engaging questions, and I have found @WODBMath helpful. Ss really like to express their thinking, and question each other. From this, Ss engage with questions that allows them to give a unique answer. #octmchat
Our chat is winding down, but that doesn’t mean you have to stop the conversation! Join #octmchat next week to talk about "Bridging the Gap Between Elementary and Middle School Math" with @brendaboring1 & @SammyAlthouse.
