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.

Conversations help me improve my math because once someone would share their ideas with me, I would get a better understanding of what I needed to do.   - @booksrule

Our conversations in math help me a lot. For example, when I ask for help from a classmate, sometimes it helps me understand it better. Especially, @writingmachine. She is really kind and helpful and cares that you are struggling and she wants to help. Half the reason I understand multiplication is because of her (that, and practice).    - @softballpiggy

Our conversations about math help us improve our understanding of math in so many ways. For example, our big conversations that we have help me understand things WAY more. The conversations also help me see other students sharing their math tricks and different strategies for solving problems. All of this is helping me be a better mathematician.   - @Gamerhead41

My conversations about math help me a lot. I like talking about how to break math down so that I can understand it enough to use it. This also helps me feel confident enough to move on. I want to give a shout-out to @sunflower and @Burt for helping me understand something that was really hard, but was easy for others. They were really helpful and kind.    - @TheLightningDragon

The math conversations help me a lot. For example, when we are working with partners, we can help each other using different strategies . I would like to give a shout-out to @puppyonline because she recently helped me understand something I was having a lot of trouble with.   - @softballgirl123

The great thing about being able to have conversations about math is that you always learn something new. We never have to be afraid to ask someone for help because everyone always says "yes".    - @cheerqueen

Personally, I think our conversations about math help us be better listeners/learners and help us understand other people's concepts of math. It helps us be better listeners because we are listening to classmates' ideas and strategies that they use. The conversations also help me go above and beyond what I already know.    - @Potato 

Fasten Your Seat Belts!

The fourth-grade team embarked on a cross-classroom 'road trip' across the U.S. this week and oh, what an adventure it was!

The 'road trip' served a dual purpose: it provided an opportunity for students to apply their knowledge and understanding of map skills, and also allowed students to comingle with students from other classes while engaging with one another in an interactive community-building experience. In a time when we have access to sophisticated digital tools to navigate the world around us, learning basic map skills is an essential component of developing spatial reasoning skills. Spatial thinking helps us comprehend the phenomena related to spaces and places around us; it supports our ability to visualize and interpret data.

Students were provided a passport to explore and engage in a variety of interactive, self-directed, map-related learning experiences in each of the fourth-grade classrooms, including: 

• using a map grid (the entire floor was transformed into a giant map grid) where students followed directions on a map in order to arrive at specific landmarks on the map grid.

• using QR codes with links to Google Maps to experience some of the most unusual tourist attractions in the United States, while identifying the state on a map, and its cardinal direction within the U.S. 

• an integrated map experience (rounding numbers) where students used a map scale to measure the distance between two points on a map. 

• a fact-finding game related to interesting features about each of the states

This week's guest bloggers reflect on their adventures. Enjoy!

I learned how to calculate distances on a map as if a drone were flying across the United States (stopping to recharge, of course). I really liked working with my partner during the map grid challenge. It was fun trying to figure out how to find each place.   - @TheScienceGeek

I learned that Wisconsin is called 'The Badger State'. It's a state known for cheese, too. Another thing I learned is that South Carolina has the largest fire hydrant in the United States. Another fun fact is that something is hurricane and tornado-proof if it is built with 637,300 pounds of steel. I loved going into other fourth-grade classrooms and seeing my friends.     - @dragonfire56

I learned that you really need to pay attention to maps and map keys. During one of the experiences, you were supposed to use a map to measure the distance between two state capitals using a ruler or meter stick and convert those units into miles. One inch represented one hundred seventy miles, so you really had to pay attention to the map scale or you would completely miss the fact that you needed to convert the inches to miles. I love the fact that we got to use math with maps. I had a great experience with my partner. We really got to just let go and have fun.     - @writingmachine

Something new that I learned was that every map has its own map scale. I used to think that all maps used the same scale. It was also very nice to meet all of the other fourth-grade teachers because I got to find out what their personalities were like. I have to admit, they were all very, very, very nice.   - @RV17

I learned how to use Google Maps and discovered a place in Seattle, Washington called The Chewing Gum Wall. It's an actual alley with already chewed gum stuck all over it. Gross.    - @Daisy

I learned how to find places on a map and it's actually fun once you get the hang of it. Maps will come in handy once you get older. I also learned that map keys are really important.    - @CheerQueen

I learned that you can use a ruler to measure how far Boston is from Green Bay or Austin is from San Diego by using the map scale in the legend.   - @HockeyKitty

I really liked the map grid challenge. We had to follow directions and it made me challenge myself.   - @PotatoMonitor

I learned that Texas is the biggest state in the U.S.A. and that New Mexico and Oklahoma are two states that border Texas.   - @SoccerQueen6

I learned that Florida is known for its oranges and orange juice. I also learned that one of the weirdest tourist attractions in the United States is the Giant Prairie Dog Statue. It's located in South Dakota, which is in the northern region of the United States.    - @ChickenNugget

I learned that the Green Bay Packers play in Wisconsin because we had to find thirteen hidden clues in order to solve the name of the state. I also really liked working with my partner because my partner was someone  I never thought I'd be friends with and as it turns out, that person is an amazing friend. He is a kind-hearted and hard-working person.   - @soccerpro

I learned that maps don't always have a scale that means 1 inch = 100 miles. Some have 1 inch = 170 miles. I also learned that all map grids have coordinates like A7 and J2. I learned how well I can work with kids from other classes. When my partner and I needed help, we asked some kids from another class and they helped us figure out what we needed. This was a great experience.   - @Seafoam-da-Seawing

Thinking Inside the Box

This week, students were able to participate in the ultimate live Breakout EDU experience, using teamwork and critical thinking to complete a "mission", solving a series of challenging puzzles related to a recent novel study in order to open a locked box of treasure. For those not familiar with Breakout EDU, they are similar to "escape room" experiences. 

Breakout EDU games can be used in a variety of ways, including introducing a new topic or concept, strengthening learning, delving deeper into topics, or thinking critically about literature. The games provide a student-centered learning experience where students use critical thinking, collaboration, creativity, and communication to problem-solve and own their learning, apply their understanding of new content, or even discover it. One of the best aspects of these games is that they provide students with many opportunities to fail forward.  Every unsuccessful attempt to solve a puzzle and open a lock forces the player to try again. These map-reading fans were determined to complete their mission within the allotted 45-minute timeframe. The only team to successfully break the codes did it with only about 2 minutes to spare. Regardless of whether or not each of the teams had a successful breakout, they worked hard and had fun. It was just as thrilling for us to observe as it was for students to participate - they supported one another as learners and persevered through the more difficult aspects of the challenge. Student feedback:  "Please, can we do another one soon?"  You can bet we will and next time, we'll level up! 

Special thanks to Mrs. Kosakowski, our digital literacy specialist, for putting together this special mission for our students. There will definitely be more to come!

This week's guest bloggers reflect on their first live Breakout EDU experience. Enjoy.

I'd like to give a shout-out to @writingmachine because she helped out a lot with finding out what the clues meant and she also helped us set up the map. Another shout-out goes to @Jerry'sApples who helped out with finding out a secret code that all of us had no idea how to do. In the end, we were a good team and when the clock timed out, we were only two digits away from winning! Even though we didn't break out, we did great and gave it our all.    - @FireDragon5

First, I would like to give a shout-out to @Burt for helping us put together the map and a shout-out to @TheScienceGeek for motivating us. We definitely could have done a better job collaborating. We worked kind of independently and didn't really work as a group.    - @PotatoMonitor

If I were to give advice to another class about this challenge to set them up for success, I would tell them to talk everything out with your teammates first and make sure you include everyone. Teamwork and collaboration will help you out A LOT.    - @RockHam

I would like to give a shout-out to @SoftballPiggy because she really understood me when I was asking my team something or telling them something. She would listen to me and wait until I was done talking.     - @softballgirl123

If I were to give advice to another class about this challenge, I would tell them to only send a few people to find all of the clues. Meanwhile, have others stay at the table to try and figure out the clues to the locks with what they have.   - @Jerry'sApples

Our team was pretty good at this challenge. I have a BIG shout-out to @ClintHillsGhost. He was a fantastic team member because he was pretty serious about it and he was able to find a bunch of map pieces. He was VERY helpful. Next, although he wasn't perfect, I think he tried his hardest and I appreciate that A LOT. Last, he was good at the Breakout! Not only did he find a lot of the pieces, but he was able to put them together.     - @Gamerhead41

One way my team could improve our collaboration skills is to listen more carefully to the directions and to each other. We were kind of shouting over each other and we couldn't hear what each other was saying.    - @PuppyOnline

I would like to give a shout-out to @FireDragon5, @writingmaching, and @Jerry'sApples. @FireDragon5 went as fast as he could to unlock the locks and he was super helpful finding the clues. @writingmachine helped by figuring out where the map clues went. @Jerry'sApples helped by solving the code on the paper. All in all, our team worked really well together.    - @Lebamboom

I want to give a shout-out to @BobMcPickleson for assembling the map when no one would help him because they were busy figuring out other clues. Great work, @BobMcPickleson.     - @Magician-of-ice-cream

If I were to give advice to another class about this challenge and set them up for success, I would say, "Put your thinking caps on and pack an extra thinking cap!"    - @BuffBoiz

@Daisy, a member of my team, was an amazing teammate. @Daisy cooperated with everyone no matter what and she helped us win! I learned a lot from @Daisy about how to be a good teammate.    - @booksrule

If I were to play the Breakout again, I would personally make sure that everybody's ideas are valued. I would also be tidier so that we can find the clues and put them together. Finally, I would encourage everyone to stay on the same clue together.    - @HarryPotter

I would like to give a shout-out to @sunflower because she was an awesome key master and if someone didn't understand, she was there to help. @sunflower also helped people in other groups when they didn't understand. She is an awesome leader.     - @cheerqueen

I want to give a shout-out to @DragonFire5, our kind, responsible, risk-taking key master. He was very good about getting down to business quickly (not in a bad way, but in a very good taking-charge-responsible way). He was even saying things like, "Okay guys, I think we should split up, maybe two of us look for more clues and the other two try to put together what we have so far."  Even though he was the key master, there were four people in our group and four locks to unlock so he let each of us turn a key so that we could all get the thrill of unlocking something. Great job, @DragonFire5!    - @writingmachine

My team could have been better at collaborating. Everyone was talking over each other and some people were feeling left out. Next time, we need to pay attention to what each of us is saying and to make sure that everyone feels included. Otherwise, it was fun and once we got the hang of it, we did pretty well.    - @sunflower

I have a couple of shout-outs. First, @Burt contributed to our group in a positive way. She was very good at putting the map together. Also, @ArcticFox was very good at finding clues. She figured out three clues.    - @MaisyPaisy

If I were to give advice to another class about this Breakout to set them up for success, I would tell them to think outside the box and never give up. You have to try really hard.     - @soccerpro1

We're Banking On It!

By now, you've probably heard the buzz about our classroom economy. It's certainly been one of the most highlighted learning experiences since the start of the new school year. 

In a nutshell, our classroom economy provides an opportunity for students to learn the principles of economics and valuable financial life skills in an experiential way while promoting positive behavior. It not only teaches financial literacy and discipline but also the rewards that go with it. Students were very excited to learn that we'll be using it in The Hive for the entire school year. Students are:

• Taking part in a simulation of real-world economic activity
• Learning the responsibility that comes with completing a job and the value of earning a paycheck 
• Learning how to budget their spending and make scheduled payments (i.e. weekly rent and utilities) as well as unexpected expenses (i.e. fines)
• Understanding the importance of saving money to reach their goals
• Discovering that every decision has an opportunity cost
• Learning that the cost of goods and services fluctuates based on supply and demand and the rate of inflation
• Preparing to be responsible citizens in our nation’s economic system

This week's guest bloggers reflect on the first two weeks of engagement in our classroom economy. Enjoy.

One of the benefits of a classroom economy is that our teachers follow the real world costs of rent and salaries. Another reason is that it keeps our class organized because the teachers don't have to do all the work of keeping our classroom neat and clean. One final reason is that the real-world costs of things are going up and down all the time and our classroom economy is preparing us for that.    - @TheScienceGeek

Our classroom economy will help us be better mathematicians because we have an actual bank in our system. The bankers use their knowledge of addition and subtraction with dollars, and they pay salaries and collect rent each week. Even if you're not the banker one week, you still have to use addition and subtraction skills to keep track of your money and manage it so that you can use your money to buy rewards.   - @Daisy

There are many benefits of having a classroom economy. One is that you can get awesome rewards for going above and beyond expected behaviors (even though the rewards are very pricey). I love how we pay rent and collect salaries each week and when we have to pay a fine, we don't get called out. I absolutely love this - it is such a creative activity.   - @magician-of-icecream 

I am learning that an economy is basically a system of money. Once the government prints the money, it goes to the banks and then gets borrowed by people to pay for things from other businesses. The businesses can then use that money to buy things and pay their workers. The workers use the money to buy stuff from other businesses and it keeps repeating.   - @RockHam

One of the benefits of having a classroom economy is that you get to experience how real life works. For example, we have to pay rent and get a job that pays us a salary each week. Some jobs are easy and some are trickier than others and each job pays a salary depending on the type of job.   - @softballgirl123

I am learning that an economy is like a chain of money. It all depends on what you spend and save. An economy is also kind of like an environment mainly because many people are part of an economy and use it together.    -@booksrule

One of the benefits of having a classroom economy is that you learn how to figure out how to manage your money to spend on things you want (classroom rewards) and things you need (rent).   - @soccerqueen6

Having a classroom economy is helpful because you will need to know how to spend your money and save it later in life. Let's say you work at Chipotlé and you're saving up for a new car. You have to learn how to save up and not get tempted by certain other offers. Once you get enough money, you should get a little more so that you can pay monthly for the car. You also have to do the same thing for a house and any other expensive items. To sum it up, our classroom economy is good because it gives us practice in managing money.   - @RV17

One of the benefits of our classroom economy is that if you do your job each week, you get paid a salary. Also, you have to manage your money so that you don't get fined or can pay your weekly rent. You also learn how to save up money for rewards like Pajama Day, reserving the couch for a day, etc. These are just some of the benefits.   - @Burt

One of the benefits of having a classroom economy is that you will have skills for when you get a job. It helps us learn how to manage money and to get used to doing different kinds of jobs. It's also good for teachers because we help them get the classroom organized and ready for the next day.    - @ArcticFox

There are lots of benefits of having a classroom economy. First of all, we learn responsibility because we have to keep track of our money and take care of it. We also earn the trust of our classmates by paying our rent on time, paying fines if we owe them, and collecting our salaries for doing our jobs.   - @writingmachine

I think our classroom economy will help us be better mathematicians for a couple of reasons. My first reason is that in the real world, you always need to know how much money you have and you have to count it. Another reason is if you're a banker, landlord, or store manager, you'll have to count money to make sure you are either paying people the right amount of money or collecting the right amount of money.  - @Gamerhead41

One benefit of a classroom economy is that it teaches us to problem-solve and to spend our money wisely. Also, it helps us understand math better because we have to count how much money we have in our wallets and how to add or subtract money for fines or bonus cash rewards. This is helping us learn how a real economy works.    - @Puppyonline

The classroom economy is teaching us how to manage our own money. It's also teaching us to become more independent and to work as a team to ensure we have a clean and organized learning environment.    - @HarryPotter

One benefit of a classroom economy is that you learn how to spend your money. For example, you must know how to manage your money because you have to have enough left over to pay rent at the end of every week. Another reason is that it helps us grow in our independence. For example, you have to remember to do your job yourself otherwise you won't get paid.    - @softballpiggy

I think our classroom economy is going to be a helpful experience because our classroom works like the real world and because it encourages everyone to be more controlled and well-behaved. We get paid a salary each week, we have to pay rent, sometimes we have to pay fines, and sometimes we can earn bonus cash by going above and beyond the expectations. Our rent and the cost of rewards can go up or down depending on the rate of inflation, just like the real economy.   - @Potato