Meaningful Mathematical Discourse

When we take the time to engage in 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 to 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.

When we have conversations about math, I think it helps us improve in many ways. One way is that we share strategies. Let's say somebody didn't understand multiplication the way we were taught, but then the teacher shows the class another student's work. Maybe that student did it another way that makes more sense to you and now you understand multiplication better. Another way is just the conversation itself. If you don't understand something, you need to raise your hand and speak up. If you do, maybe the teacher will answer your question and give you a better understanding of math.     - @Shrek_Dog

Our conversations about math help us improve our understanding. One way is when someone gets an answer that is different from yours, you can check your work together. Another way is when you have a multi-step word problem or a very challenging question, your classmate is there to help.      - @ShreksBigMac123

Our conversations about math help us improve our understanding of math because when somebody doesn't know how to do something in math and they are too shy to speak up, the conversations we have help us to understand.    - @LouiePony

Our math conversations improve our understanding of math. For example, when someone has absolutely NO idea how to do a problem, and someone else has a really good strategy to help solve that problem, it can be helpful. In a group discussion, we can share our strategies and improve our understanding of math.    - @Preppy_Shrek3572

One way we can understand math better is by working together. We can help the people that need help and do equations together. We can also ask questions during our group conversations or with classmates to deepen our understanding of math.    - @JustinJefferson18

Our math conversations are helpful. One reason they're helpful is that we can share strategies with each other. Another reason is that we can explain each other's mistakes.     - @Bassy

Our conversations about math help us improve our understanding of math. If you have a question because you don't understand something, then you can get an answer to your question and you will understand something better and improve. If someone shares a strategy, that strategy might work for you. Conversations make a difference.     - @MustardMan1

Our conversations in math helped me improve a lot. Math can be really hard sometimes if you don't get it, but you only need a group or partner to talk it out with and ask questions. For example, one time I was at a table and we were having a discussion and solving problems together. I didn't understand one of the division problems, so I asked a person in my group and they explained how to do it. After talking it out, I finally understood. If you don't know something, don't be afraid to ask. Someone will hear your question and answer it.     -  @ILoveCheer123

Our conversations about math help improve our understanding of math because talking or sharing always helps. What if someone doesn't understand what the teacher is saying? Sharing ideas would probably help. Trust me, it's happened to me before.    - @BabyDiggs

Our math conversations help us improve our understanding of math because it is two or more people putting their heads together to achieve success. For example, you can check answers with your partner to make sure you answered the question correctly.     - @Pookie2.0

Our math conversations help us improve our understanding in many different ways. One way is that we can ask questions. For example, some of us have good questions that help deepen our understanding.      - @Ritz159

This week, we had some great conversations about math. We shared our strategies and tried to make sense of the numbers that we were working with. It was hard, but fun with trying to get the numbers right.     - @FortniteGuy#1

Our conversations about math help us improve our understanding because by talking about the things we don't know or changing the way you're saying it or teaching it, will help make sense of it.      - @Dip-n-Dots

Throughout the year, our class has had a lot of conversations about math in the honeycomb. I have learned a lot from my classmates and how we share strategies with each other. It's important because everyone's ideas have helped me improve in math. I now use some of my classmates' strategies.      - @NuggetDiddy

Our conversations about math help us improve our understanding of math because when talking about math as a group, it sometimes answers your questions and then you will know what to do. Also, having a partner to work with during math can help you check each other's work and make sure you have it right.     - @ILoveGymnastics27 

Young Voters In Training

Students in The Hive have spent the last couple of weeks learning about the U.S. election process, with a particular focus on the presidential election process. It was an exciting and memorable month leading up to Election Day. We hope it sparked some interesting and meaningful conversations around your dinner tables. We can tell you that the spark was surely alive in our classroom!

Learning about the U.S. election process is crucial for fostering civic responsibility, understanding government structure, and developing critical thinking. It equips our youngest generation with the knowledge of their rights and duties within a democratic society, encouraging them to become active participants in their communities. Students learned about the importance of voting and how elections impact their lives, promoting an early appreciation for their role in democracy - for their role in our Constitutional Republic. Discussions around elections and governance introduced students to diverse perspectives, nurturing respect for differing opinions and the value of dialogue. This foundational learning experience not only prepares them to be informed voters but also instills a sense of duty toward participation in democratic processes. By connecting classroom learning with real-world events, it also enhances their interest and awareness of national affairs, laying the groundwork for a lifetime of engaged and responsible citizenship.

Students not only actively participated in our deep classroom discussions, posing some thoughtful questions and ideas of their own, but they also enjoyed a tour of the election polls at the Boxford town hall just before Election Day AND participated in a mock election experience. We asked students to reflect on our discussions and their experiences for this week's blog. We think you'll agree that their reflections demonstrate a healthy curiosity and the beginnings of active civic engagement. For some students, learning about the election process has even inspired a potential future in public service!

One question I still have about the presidential election progress is why does the electoral vote matter more than the popular vote? I ask this because what if the president won the electoral vote, but not the popular vote? Wouldn't the people want the president that was elected by the majority of the people? - @Preppy_Shrek3572

I learned that the first presidential candidate to get to 270 electoral votes will be the president, but they have to wait a few months to actually become president. - @NuggetDiddy

If you don't vote, the person you want to win might not get enough votes to win. - @Boo0134

It is important to vote because if a president is to make things right for the people, you should support them by voting for them. Otherwise, a president that won't do the right thing might get elected instead. - @bassy

One interesting thing that I learned about presidential elections is how a candidate wins. I used to think that whoever earned more votes wins, but it turns out that you actually have to earn 270 electoral votes. - @BabyGronk

I still have a couple of questions/thoughts about presidential elections. First, it doesn't make sense that one candidate could win the popular vote and another could win the electoral vote. Why does it usually come down to Democrats vs. Republicans? - @Guy-Alpha-Chad

I learned that the winner of a presidential election is not found by the majority. For example, if Maine was mostly voting red, then all of the electoral votes for Maine would go to the Republican candidate. The candidate who earns at least 270 electoral votes wins. - @DipLover100

I learned that you have to be at least 18 years-old to vote and that you have to have at least 270 electoral votes to win a presidential election. You don't need to win the popular vote - you only need to win the electoral vote. - @solo1235

Even though you don't have to vote, you should. Your candidate has a better chance of winning if you vote. - @GordonRamsey

It is important for U.S. citizens over the age of 18 to vote in all elections because if you are responsible enough to get a driver's license and a job, you are responsible enough to do your research on the candidates and vote for the best one. - @DeadPool

It is important to vote when you turn 18 because the person that wins an election will decide if your taxes will go up or down. - @Football

One of the more interesting things I learned about the presidential election process is that a candidate who wins the popular vote doesn't necessarily win the election because you actually have to win the electoral vote. Electoral votes are given to a state based on how many representatives they have in the House of Representatives. - @PeanutGuy125

It is important for U.S. citizens over the age of 18 to vote in all town, state and federal elections because if you don't vote, it means you don't have a say in anything. If you want a certain candidate to win, you have to vote. - @LouiePony

Something new and interesting I learned about the presidential election process is there are popular votes and electoral votes. I used to think that whoever won the popular vote won the election, but you actually have to win the electoral vote to win the presidential election. - @queenbee10

I learned that people running for President fly to many different places around the country to campaign for votes. The more places they visit, the more likely they are going to win. - @BombasticSigma

I learned that you don't need to win the popular vote. You only need to win the electoral vote. You need at least 270 electoral votes to be President. You also have to be at least 18 to vote. - @TacoBell

Learning about the U.S. election is the funnest thing I have learned in a while. I learned how the electoral college works and how presidential candidates get elected. I loved playing the game ELECTION NIGHT! and I also like voting in class for our "candy-dates" (candidates). - @Pookie2.0

It's important for U.S. citizens over the age of 18 to vote in all elections. One reason is that it's important to help the person that you want to get elected. Another reason to vote is that you will have a better four years of your life if your candidate wins. - @FortniteGuy#1

I learned that you aren't forced to vote for a Republican or Democrat candidate. You can also vote for an Independent party. If you do your research, you will learn a lot about the candidates. - @Angel232

It is important for U.S. citizens over the age of 18 to vote in all elections because it is important to have a candidate that will represent what you want. - @Lucky2BLefty

I used to think that whichever presidential candidate gets more votes wins, like a normal voting process, but that isn't how it works. First, a candidate has to get enough electoral votes. The number of electoral votes for each state is based on the population of each state. Popular votes don't really matter, only the electoral votes do. I also learned ballots sometimes have questions on them. When our school had our mock election at Town Hall, we had a ballot question (Should recess be scheduled before lunch). I thought it was cool that they had a ballot question for us! - @ILoveCheer123

With Gratitude

This weekend, we honor our nation's veterans by remembering their service to our country and thanking them for their tremendous self-sacrifice. We spent time learning about the importance of this holiday and what it truly represents.  

Here's the thing: Most of us won't ever have to pick between our lives and what we love the most, like family and friends, but we all have a choice to care deeply about something - something greater than ourselves. Veterans are heroes. They show us that living a great life means being ready to take chances - believing in things, staying committed, and loving others, even if it means taking some risks. Today and every day, let's choose to honor our veterans by choosing to live for the things that they would die for: for our families, for one another, and for our country; for freedom, for justice, and for peace.

Students in The Hive wrote some very heartfelt letters to veterans expressing their gratitude and respect for their selflessness and sacrifice. These letters will be delivered to the American Legion Post 227 in Middleton this weekend. For those of you who are interested attending Boxford's Veterans Day ceremony, you can find details below.