Meaningful Mathematical Discourse

When we take the time to have rich and meaningful conversations (productive dialogue) about our math experiences, and encourage students to participate, we're nurturing a supportive culture of questioning, reflection, and understanding. 

One of the key factors in math achievement involves supporting math language development. This includes asking critical questions, encouraging students to seek clarity, and accepting our failures as opportunities for real growth. In doing this, we're motivating and encouraging students to work together to facilitate productive mathematical conversations. Engaging in meaningful mathematical discourse offers students an opportunity to reflect on their math knowledge and understanding, make connections with prior knowledge, identify patterns, hone in on their reasoning skills, and develop their higher order thinking skills. As teachers, it allows  us to observe and evaluate their mathematical understanding and development so that we can better support their math growth as we address gaps in student understanding and refine and redirect their approaches to reasoning and problem-solving.

Students are enjoying the opportunities to present their ideas and mathematical strategies with one another. As they seek out, listen to, and value the ideas and perspectives of others, they are able to maximize their own learning while supporting the growth and achievements of others. This is one example of what taking ownership of mathematical knowledge looks and feels like in The Hive. 

This week's guest bloggers reflect on these experiences. Enjoy.

Math conversations help me improve in math because we get new ideas about math when we talk it out. It also helps me think differently and in new ways. It's really helpful to share math strategies.    - Blocky

I think the conversations we have about math are a good way to understand different strategies. It allows us to see what's going on inside each other's brains when we think about math.    - EarthySmurf

Having conversations about math helps me learn about math in different ways and it makes math more interesting. I like math talks.   - G-Money

I think our conversations about math help us improve our understanding of math A LOT. For example, I was having a really hard time with bar models and forgetting how to set them up. When someone came up to the board and showed the class their work and how they set up their bar model, I think that helped all of us.   - Cheeto111

Talking about math is one of the ways that we we help each other in The Hive.  - Elizabeth_Schuyler

Our conversations about math help us improve our understanding of math. For example, yesterday we had a "ripple effect". I shared something about how I worked out a problem and then a classmate piggybacked on that and in the end, we all learned something new from sharing and talking about our math strategies.   - Pineapple

Our conversations about math are helpful. For example, I thought I knew my math facts pretty well, but then a classmate showed us a simpler way to learn our facts and it's so much easier for me now.   - Pickle03

I think conversations about math help us share our strategies with each other. Sometimes some strategies are quicker and better than others, but people can make their own choices about the strategy that works best for them.   - Recycle14

When we were sharing our bar models, I liked how lots of people got to share. One day, we were at the beginning of a math conversation about bar models and I thought I knew EVERYTHING. By the time the last person finished sharing, I knew a lot more than I did before we started. I learned that you can never know everything. There is always something new to learn. That's what I love about The Hive.   - WowWriter

Our math conversations help me a lot. One time, a classmate had a strategy that taught us how to check our work. This has helped me a lot with my own math work. Another time, a classmate came up to the board to show how to make sense of word problems and it really helped me.   - Dream

Conversations about math can help you see how other people think about math and so it helps you understand math better. When you hear someone explain how they were thinking about a math problem and how they solved it, it can help you understand how to solve it yourself.    - GoatLover

Sources:

Curtis, Jeannie. “More Talking in Math Class, Please.” Edutopia, George Lucas Educational Foundation, 31 Oct. 2017, https://www.edutopia.org/article/more-talking-math-class-please.

Audrey Jones, et al. “Let's Talk Math! Implementing Math Talk in the Classroom.” Mrs. Winter's Bliss, 23 Sept. 2020, https://mrswintersbliss.com/math-talk-in-the-classroom/.

“Talking Math: How to Engage Students in Mathematical Discourse.” Getting Smart, 29 Sept. 2015, https://www.gettingsmart.com/2015/09/29/talking-math-how-to-engage-students-in-mathematical-discourse/.

It's Getting a Little Sketchy In Here

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Let's first talk briefly about the power of visible thinking. 

Learning is the consequence of thinking. Expecting students to think deeply can be a challenge. How exactly should we expect our students to do this? What does it mean to think? How do we know what or how they're thinking about something if we can't see their thoughts? When we give our students specific tools to help them better structure and deploy their own thinking, learning outcomes improve. When we help them build, connect, and refine their thinking in more overt (visible) ways, we are essentially helping them to develop their metacognitive skills, which leads to better thinking. Visible thinking routines provide a window into what students understand and how they are understanding it. As teachers, this offers us an opportunity to be intentional about how we plan and adjust our learning experiences to help our learners dig deeper into content, and hear and see each other's questions, insights, and perspectives so that we can support the development their thinking habits and refine their thinking as needed.

There are a plethora of ways to make thinking visible and we will explore many of them in The Hive this year. One of the ways we recently asked students to process information visually, was through a sketchnoting exercise related to the pollination process. Sketchnoting is a form of visual note-taking where students (or really anyone) listen to, synthesize, and visualize ideas about what they are learning about through a combination of picture drawings, diagrams, and text. Creating these visual notes during our exploration of the pollination process and then having students participate in a gallery walk of their classmates' sketchnotes, was an engaging way for students to share and build upon one another's knowledge, ultimately gaining a deeper understanding of this information.

This week's guest bloggers reflect on this experience. Enjoy.

Sketchnoting helps me understand what I am learning because drawing pictures about what I've learned makes sense to me.   - Lonnie

Sketchnoting helps me see how other people are thinking about what we are learning about.  - McLovin

Sketchnoting helps me learn because it's easier to learn with art. When I created my sketchnote about pollination, I felt like I was learning more.  - WowWriter

Sketchnoting helps me better understand what I am learning about and it allows other people to see how I visualize my learning and maybe it will help them.   - EarthySmurf

I think sketchnoting is helpful because drawing what you learned is sometimes easier than writing about it. For example, describing the crown of a hummingbird would be better to see in a drawing with arrows and labels.   - Horse321

Sketchnoting is a great to to explain what I learned because I enjoy drawing and showing my learning with pictures.   - Elizabeth_Schuyler

Sketchnoting helps me to blend (synthesize) my ideas and make sense of what I am learning. Doing this with pictures is helpful for me.   - Dream

Sketchnoting helps me understand my learning more because when I sketchnote, I am drawing pictures and writing words, not sentences. Sketchnoting makes learning really fun and makes a lot of sense to me.  - Koala333

Sometimes I forget what I learned, but when I create a sketchnote, it helps me remember it better. Also, I can easily look back at my sketchnotes to help me instead of reading pages of notes.  - Lightning24

Sometimes it's hard to understand words, but pictures can help with that. Drawing pictures with short text helps me visualize my learning.  - GoatLover

When I am learning about the process of things, Sketchnoting is really helpful. It helps me understand what I am learning because it's easier to understand a process through drawings and text.  - TheBeeGuy101

Sketchnoting helps me to remember what I am learning about. The drawings are really helpful. - Zombie

Sketchnoting helps me organize my crazy mind.  - Strawberry

Sketchnoting forces me to think more deeply about what I am learning.  - Giraffe

Sketchnoting helps me see what I am thinking in a different way. It's like talking pictures.  - Wolverine12

Sources:

“Project Zero's Thinking Routine Toolbox.” PZ's Thinking Routines Toolbox | Project Zero, http://www.pz.harvard.edu/thinking-routines.

H, Sean. “What Is Visible Thinking Really?” Ideas Out There, 12 Apr. 2020, https://seanhamptoncole.wordpress.com/2017/09/02/what-is-visible-thinking-really/.

Making Thinking Visible - Harvard University. http://www.pz.harvard.edu/sites/default/files/makingthinkingvisibleEL.pdf.

Schwartz, Katrina. “Why Teachers Are so Excited about the Power of Sketchnoting - Mindshift.” KQED, 3 Nov. 2019, https://www.kqed.org/mindshift/54655/why-teachers-are-so-excited-about-the-power-of-sketchnoting.

 

Arguments Welcome!

 

“Curiosity—the desire to explain how the world works—drives the questions we ask and the investigations we conduct.”  - Kerry Emmanuel, MIT

Explorations in science and engineering should have purpose and lead to conclusions and claims. Scientists make claims all the time, but for their claims to be believable, they must be supported by evidence and reasoning. An effective tool for working through this type of scientific explanation is the C-E-R framework (Claim, Evidence, Reasoning) and it offers the perfect opportunity for fourth-graders to begin thinking and communicating like scientists. 

The C-E-R framework is a valuable inquiry method that promotes the development of critical thinking skills where students not only evaluate their own arguments, but the claims and arguments of others. Students learn to answer scientific questions by stating what they believe to be true and then providing evidentiary data and rationale to support their belief. Utilizing this practice in science instruction, as well as across all disciplines, increases rigor by incorporating a greater cognitive complexity of thinking. For elementary students who are first learning to engage in scientific argumentation, C-E-R provides a developmentally appropriate approach toward how students connect their experiences with previously learned content, boosting their scientific literacy. If it sounds like a tall task to you, it’s because it is. 

Unknowingly, students began engaging in this process a couple of weeks ago when they first started exploring the various structures and functions of plants and animals. Their explorations inspired curiosity about the subject and a desire to analyze factual information, make connections, and evaluate the meaning and implication of it. A great deal of time and thought was spent crafting logical and concise claims, identifying relevant and reliable evidence, and understanding the importance of explaining how the evidence supports their claims. This exercise provoked an intense and meaningful reflection on what they had learned. It provided students with the practice necessary to draw and support appropriate conclusions and the foundation to participate in effective and high-quality argumentation. 

Students ultimately crafted their own C-E-R argument about an investigation related to moss and were asked to argue whether or not they believed it was a plant. It was fascinating to observe students effectively evaluate the information they were given and synthesize it with their schema to make a claim and defend it. We spent some time as a whole class afterward discussing the merits of their arguments, identifying any potential holes, sharing the various methods as to how they analyzed and evaluated the data and information they were given, and how they arrived at their conclusions. It was an incredibly meaningful discussion that helped shaped their ideas not only about the topic, but the perspectives and methodology behind organizing their thinking and assembling it into the C-E-R framework. 

This week’s guest bloggers reflect on this experience. Enjoy. 

I think that reasoning is the most important part of a C-E-R because it explains how the evidence supports your claim and makes it more clear to understand what you are trying to prove. - Flash4

During our group discussion I learned that your claim has to be clear and simple. You don't want to say "I think this or I think that". You want to be sure. - PickleKitty

You can use the C-E-R framework for anything, including math, social studies, and books you are reading. You can also use C-E-R to make an argument for getting a pet. Hmmm... that gives me an idea...  - Cheesy

In my opinion, I think the most important part of an argument is the claim. The claim is the foundation of your argument. The evidence and reasoning are useless without it. Your claim tells your audience what you are trying to prove.  - Choney

I think that reasoning is the most important part of an argument because reasoning is explaining why you think what you think. It breaks down the argument so that you can see the evidence more clearly.  - Wolverine12

I think the most important part of an argument is the reasoning because your audience might not know how your evidence supports your claim if you don't explain it clearly.  - CHEETO111

I think that evidence is the most important part of an argument because without factual evidence, you can't support your claim and it's not believable and your argument is not believable.   - Pickle03

I think the claim is the most important part of an argument because you are making a statement about what you know and want to prove.  - Strawberry

Another example of when you can use the C-E-R framework is if you are a lawyer. For example, if you are a lawyer, you need to defend your client with a claim, evidence, and reasoning. If I were a lawyer and my client was accused of stealing a pencil from the classroom, I would say something like this: "My client is not guilty. The classroom got new pencils and Mrs. Valzania said that they could take a pencil if they needed one. This proves that my client was allowed to take a pencil and therefore my client is not guilty."  - Pineapple

When we were learning about moss and had to investigate whether or not it was a plant, it was very hard to do because there were a lot of reasons some people thought it was and a lot of reasons people thought it wasn't. Kids had to think, and think, and think. We had to have a discussion about the evidence and how we could analyze it to make a decision. It was really hard but also really fun.  - Galaxy 

If you use the C-E-R framework to write a strong argument, it can be a very powerful thing.  - Lightning24

Sources:

Brunsell, Eric. “Designing Science Inquiry: Claim + Evidence + Reasoning = Explanation.” Edutopia, George Lucas Educational Foundation, 25 Sept. 2012 

Cusamano, Jennifer, and David Janosz. “Using a Claim, Evidence, and Reasoning Platform With Next Generation Science Standards.” McGraw Hill Education.