The image above was shared with me on Instagram (wait, you didn't know I started an Instagram account?! Check it out now!) by Ben Cogswell and the caption he included was one I just had to share (with his permission, of course):
Waiting for lunch discussing what makes this number special? 9 year old: use fractions to make this number. 7 year old: make this number with 3 addends. 4 year old: Make 7 on your fingers then make 10! I love it. With such an open prompt and one that was literally placed onto his table, Ben and his kids engaged in an appropriately-leveled task with each one of his kids. All are at different stages of their numeracy journey, yet they all were able to access the prompt he put forth. And yes, for those asking, Ben was sent a fresh signed copy of Table Talk Math :) When doing this with my students, I would put the "day" value of the date onto the whiteboard and have students come up with as many interesting expressions that equal that number in 60 seconds. For example, if today were August 10th, the number on the board would be 10 and I might get: (11+9) * 5 - 90 10 + 0 ...and a bunch of others The point here is that I am giving you the solution and you are being tasked with giving me the problem. No matter how old your child is, this is an idea you can use and it's also a great way to pass the time as you're waiting for that meal out as a family. Try it out! Ben isn't the only one getting a signed copy of the book; take a picture of the number, along with the problem and your child's work to prove that it's correct, and I'll pick one reply to get a signed copy of Table Talk Math. It's that easy! Things to encourage:
If--WHEN--there are incorrect answers, leave them until all expressions have been shared. Then, when everyone has had a turn, come back to the incorrect one and ask to go through it together. "Now that we have done this and realize that it isn't quite 17, what can we do to the existing problem to make it true?" By going in and correcting your child's work, you are making it less inviting to try again. On the contrary, building on top of the work that you notice together provides an opportunity to fix an incorrect response and make it more complex than original. This naturally empowers the child to try again and gives you a good basis of conversation. Try it out! What number did you show to your child (or your child show to you) and what expressions did you come up with? Reply to this email, Tweet it out to me, or share it on Facebook and tag Table Talk Math. Thanks for joining the Table! If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates. Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.
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If you have read Table Talk Math, you know how much I loved playing games as a kid and how much I love them now. That is why this week's newsletter, written by Daniel Finkel, resonated to much. Check out what he has to share about Tiny Polka Dot and get your set today: To help kids ____, we ____ with our kids. There’s a question floating around in the background when people talk about how to help young kids get off to a good start with math. We know what to do with reading, after all! To help our kids read, we read to our kids. What’s the math version? To help our kids math, we math to our kids? It just doesn’t have the right ring. It’s precisely because we are not clear what math means as a verb that this is so hard. There are a range of suggestions on what nurturing this mathematical instinct in young children looks like, including some, like Bedtime Math, that take the analogy with bedtime stories very literally. And I’m thrilled these ideas are out there! The good news is that children naturally are drawn to counting, and they won’t learn to dislike math unless someone teachers them to. But how do we help them have the opportunity to love math? For me, the answer was games. I played countless hours of Sorry, Rummy, Casino, Yahtzee, Hearts, Backgammon, and so on when I was younger. Cribbage, especially, was a popular game in my house. My brothers and I played endlessly, and I learned, as all cribbage players must, all the ways to make fifteen. To this day, I can casually glance at a hand of 6 cards and instantly tell you how many fifteens are in there. It’s a skill developed through hours of play, and one that made school math in Kindergarten through 2nd grade nearly effortless. So that’s my answer to fill in the blanks: To help kids love math, we play math with our kids. As I’ve understood more about how counting, logic, and reasoning develop, I’ve come to see virtually all card and board games as contributing to mathematical growth. Abstract logic games like chess, checkers, hex, go, Connect 4, and so on help build the critical “what if” creative/logical muscle in the mind. “If I go here, what will my opponent do?” I love these games, and there are plenty of great ones. But what about games to help with numbers, counting and arithmetic specifically? The games that exist in this capacity tend to have an academic feel, and play can be subordinate to “learning.” Young kids come to understand numbers through a surprisingly complex process that takes years. Fortunately, playing and counting and exploring their way through this process can be a pleasure, as long as they are unhurried. Kinesthetic work with blocks and other objects is critical, but games can be harder to find. We wanted to provide a rich structure to explore how numbers work and relate. Essentially, we wanted to make a deck of cards that would allow all the play I’d had as a child, but that made the mathematical and counting connections even richer and more fun. That’s why we built Tiny Polka Dot. It’s a mathematically enriched card deck with 16 games you can play with very young (3 year old) to older (8 and up) kids. There’s a ton of research that went into this game, but I think the most compelling case for its value is the fun kids have playing it, and how they engage with math and counting as they go. Setting up Hungry Numbers (more videos at tinypolkadot.com/learn-to-play) One fascinating thing about the deck is that it has all the versatility of an actual deck of cards, albeit one with 6 suits from 0 to 10. I haven’t played Tiny Polka Dot cribbage yet, but I want to. Meanwhile, I keep hearing about innovations and child-created games. For example, this older student invented her own take on the Polka Loop Puzzle that blew me away. And this, to me, is where play leads: to perseverance and ownership and curiosity and creativity; to pushing beyond the bounds of the puzzle into something new, for no other reason than it’s fun to explore. When we talk about learning to love math, this is what we’re talking about: not mere “mastery,” but ownership - the understanding that it belongs to you, and you can break it and put it back together again because it’s yours. That’s where play leads.
To help kids learn math, know math, and love math, we play math with our kids. Thanks for joining the Table! If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates. Thank you for taking the time to improve math fluency for children, one table talk conversation at a time. Rather than telling you about it myself, I've brought in Nanette Johnson, the co-creator of a phenomenal resource called Open Middle. Here is what she has to say: Having kids of my own, I have a 10, 8 and 7 year old, I like when they explain their reasoning, especially in math. One of the challenges that parents may have is helping their child explain their reasoning. I have found some success by asking questions. One of my favorite questions to ask my own kids is, “Can you think of a different way to get the same answer?” This helps them know that math, along with other things, has more than one way to get to the solution. Another reason I love this question is that it helps them validate their answer using a different method. If they get the same answer using 2 seemingly unrelated methods, this gives them confidence in their answer. First, let’s define what an Open Middle problem is. Imagine that a problem has a beginning (the problem or question), a middle (solution path) and an end (the answer or solution). Most problems from a textbook have closed beginning, closed middle and closed end - meaning, they all start, continue and end the same exact way. Instead, Open Middle problems are different in that, they have an open middle, meaning that there are multiple ways to get to the solution. These multiple ways allow students to approach the problem in different ways to validate their answer. Knowing various ways to arrive at the same solution and knowing how these methods are connected strengthens your child’s math skills. So here is an analogy to help better explain this. Imagine that you are at home, but need to go to somewhere (maybe the store or a friend’s house). Are there multiple ways to get there? If you said yes, that’s an example of something having an open middle. You have the same beginning and end, but the middle has different options. Consider these two problems: The traditional problem doesn’t offer much variation, especially in the middle, unless you prompt your student.
The Open Middle problem asks the student to find the LARGEST product. Once they get an answer, ask questions such as:
Another difference between these two problems is the level of complexity in thinking that each is asking of the student. The first problem is likely something their teacher may have shown them how to do. The second is asking something that they most likely have never been asked, but they have the ability to do (given that he/she has learned multiplication). You can help your child become a stronger mathematician not by asking them to do something (or variations of the something) they have seen and done before, but by giving them tasks that are different than what they’ve done before, yet have the ability to complete. So, how can you turn Open Middle Problems into Table Talks? Choose a problem from OpenMiddle.com. The site is organized by grade level, but I strongly suggest a problem that is two or three grade levels below (just to get them used to this kind of thinking). Also, begin with a lower DOK (depth of knowledge, which indicates the level of complexity of thinking required to complete the problem). Do the problem before you give it to them and read any hints or answers that your kid may need. Ask your kids to do the problem (or show them the problem). If your child gets stuck, start asking questions to help guide their thinking to get to the answer. Here are a some of questions that you can use:
Thanks for joining the Table! If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates. Thank you for taking the time to improve math fluency for children, one table talk conversation at a time. When is 100 + 100 NOT equal to 200?
I'm about to challenge everything you have ever thought about addition. After all, it's one of the absolutes in the world: 2 + 2 = 4 10 + 11 = 21 and... 100 + 100 = 50? Every week, I would give my students a challenge on the side board; a brain teaser, a puzzle, or an interesting math problem. The ones that got the most traction were the number puzzles like the ones I'm sharing in this week's newsletter. The only hint I will give you is that this whole activity is a conversation starters for why the proper units matter. With that said, I'll open the challenge up to you:
Here they are!!! When does 100 + 100 = 50? When does 100 + 100 = 3 1/3? When does 100 + 100 = 60.96? When does 100 + 100 = 1.5625? As a bonus, come up with one of your own and send it my way to see if my boys and I can figure it out! Thanks for joining the Table! If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates. Thank you for taking the time to improve math fluency for children, one table talk conversation at a time. |
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AuthorJohn Stevens is working to give parents ideas on how to have mathematics-based discussion at home. Archives
May 2018
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