February 2025
Welcome to EFM's February Newsletter!
It is essential that every caregiver in the world reads books and does math with their young children!
EFM believes in every child’s mathematical right to equity, opportunity, and personal fulfillment.
News
Counted Out – This significant 2024 movie about the failings of math education in the US and its effects on social equity, is seeking to have 314 special screenings on Pi Day. Although it spends relatively little time on very young children and the math that should be going on in their home, I would still urge you to watch this movie. Who knows, perhaps they will make a prequel “Counted Out from the Start” that looks at the early years.
Celebrating EFM Volunteers
Everyone at Early Family Math is an unpaid volunteer. Everyone. For the last few months I have been recognizing some of our wonderful volunteers, and I would like to continue that tradition.
Sylvie, Gill, Miriam, Rachel, Mounia, Echenne, Thomas – French
This wonderful group of translators has finished the translation of our EFM storybooks, translated our playing cards, and is busy translating our five Stages and Playdates. They all share a love of doing translations to their native language and feel the value of making EFM available to French speakers around the world. Sylvie is in Micronesia, one of the more exotic locales for one of our volunteers.
Relaxed Exploration
An interesting thing happened when families learned about studies that showed the importance of doing early mathematics in the home. Some of the families who took this to heart responded by doing math with their children in a very serious manner using workbooks, flashcards, and strongly directed instruction where any incorrect answers are not explored but merely corrected without any role for the child.
The problem is that other studies have shown that this serious approach is problematic. Not only is it likely to cause a child to dislike mathematics and feel that it is pointless drudgery, but this approach also is less educationally effective than a more relaxed approach that emphasizes playfulness and has a child experiencing and discovering what works and finding out what is interesting to them.
So, be enthusiastic about math in the home, and please do that using frequent discussions of all the math that is around you and using lots of playful and relaxed explorations of math games and ideas. Here are a few thoughts and examples for achieving this goal through gentle guiding and listening.
Guiding and Following
The simplest and most effective early guiding you can do is to talk a lot with your child, and that talk should include Math Talk. Initially that Math Talk will be pointing out all the math around you and verbalizing the math ideas going on in your thoughts already. As your child develops to be an equal partner in these discussions, listen to what interests them and follow up on their ideas and questions.
The EFM games, puzzles, and activities contain a bounty of possibilities for math to do with your child. When you introduce these activities, follow your child’s interests and feel free to ignore many of the activities. It is generally far better to do math your child enjoys than force them to do something “good for them” they don’t like.
Here are a few examples of some math activities and what it might look like to be a gentle guide with them. Some wonderful examples are the videos on the Love Maths website that Michael Minas made of playing games with his children. He is a master of playfully interacting with his children while guiding them to learn the math involved in the game.
Go Fish – Make 10
This is the classic game of Go Fish with the added wrinkle that cards match when they add up to 10 (other sums can also be used). Michael Minas has an example of playing this in his video in the Operations F-2 folder.
Michael lists some possible guiding questions for this game, such as: “What goes with __ to make 10?” and “If I ask for a __, what card does that mean I must be holding?” He has these sorts of discussion ideas for all his games.
Another good thing Michael does is have his son create his own variations of the games. Not only does this kind of agency create deeper engagement in these new games, it also adds interest to playing the old games because his son is thinking about possible ways to change them.
Nim 1-2
Nim has a great many variations; this is the most basic one. It’s a two-player game. You start at some agreed upon number, say 10, and work your way down to 0. The two players agree on who will have the first turn (a surprisingly important decision). On each turn, a player subtracts 1 or 2. The player who lands at 0 wins (you can also play that they lose). For players who aren’t good with numbers or subtraction yet, you can use a pile of 10 things that you take turns removing 1 or 2 from. You can also use a number line that you move a marker on.
This game can be played for a very long time without any discussion of strategies, and that can be fun and playful. At some point, you can start asking questions, such as: “When did you know for sure that you were going to win (or lose)? - What was different about that moment in the game?” or “What attracted you to that move rather than the other move?” or “Instead of guessing, is there a way you can figure out a good move?”
Starting at 10 is high enough that it’s hard to see how to win. You can ask your child if there are other smaller numbers for which it might be easier to see a winning strategy. If they are interested in pursuing this, and it’s okay if they are not, they will quickly find a winning strategy for all numbers.
As I mentioned at the beginning, there are a lot of variations for this game, so this is a rich playground for your child’s inventive side. They can choose *adding* 1 or 2, starting at 0 and going to 10. They can use {1, 2, 3} instead of {1, 2}, or they can even use other stranger sets such as {1, 2, 4} or {½, 1, 3/2}. Another option is to subtract any of the proper divisors of the current number. Yet another option is to have more than one pile of objects that you remove things from. If they are interested, they can take this in quite a few fun directions.
Turning the Tables
This puzzle, and its variations, is great for practicing multiplication. However, it goes a lot deeper than just that practice. These puzzles have a child thinking about factorizations, common factors, and even things like primes.
The idea is simple enough. Instead of filling out a traditional times table, which is a truly uninspiring activity, take that times table and mix it all up and leave in odd bits of information. Consider the following mixed up table for multiplying the numbers 2 through 9 times the numbers 2 through 9.
Doing one of these puzzles may take time, so please encourage your child to not be in a hurry. Also, the first few times you do these you may want to fill in a lot more of the squares or start with much smaller tables, such as the following. Note that the large puzzle we started with could be made harder by leaving out the 5 and 6 in the top row.
If your child is stumped in any of these activities, ask leading questions to remind them of a general approach they can consider for solving it. Do your best to avoid simply supplying answers.
Looking at any of these tables, rather than simply giving some answers, you can act as a helpful guide. What are some places to start? Why did you choose those places? What is it about the numbers 25, 49 and 81 that make them good places to go first? For rows or columns with two numbers, such as the row with 28 and 42, what can you say about that row?
If your child is having fun with these, suggest that they might have fun creating some of these of their own for you or others to solve. If they happen to make a puzzle that doesn’t have enough information, discuss it and see what should be added in so their puzzle can be solved.
Instead of pointing out mistakes, ask your child to explain their thinking. See if you can learn from their explanations how they are modeling the situation, and use that to form ideas for how to help them. Having them verbalize their thoughts may also make them confront their ideas and see them more clearly.
Guide Gently giving Agency to Explore
It is unrealistic to have your child wander freely in the world and expect them to discover on their own all the wonderful things the world has to offer. At the other extreme is being a very pushy tour guide insisting on going from place to place without regard to your child’s interests or choices. As caregivers and teachers, an important part of our role is to act as gentle guides for these young explorers. The hard question is: How much do we guide and how much do we follow their lead? There is of course no simple answer to this question, and the answer will be different for each child and situation.
Giving a child agency to explore and follow their interests will surely deepen engagement and encourage them to be lifelong learners. However, without creating rich learning environments and explicit nudges in the right directions, it is unlikely that a child will discover beautiful ideas such as prime numbers and prime factorization, negative numbers, or irrational numbers.
The trick is to guide gently and listen strongly. Guide your child gently enough that they still have control and agency, but guide wisely enough that they stay in sight of interesting math to do. Listen to what they are thinking and what they would like to explore. Let them take missteps and have a chance to learn from them, but be close enough to support them if they start to feel bewildered or frustrated.
Create rich learning environments for them to explore filled with appropriate levels of challenges. Children will grow through effort and facing challenges, but that does not mean that these efforts and challenges can’t be fun and playful. For example, learning to play a math game well can require persistence and effort, but it can also be playful and social.
You also have the power to guide through modeling attitudes that your child will adopt from you. You don’t have to have the answers, you just have to show that it is exciting and fun to play around and go in search of the answers, and increadibly satisfying to find them when you do.
It is vastly more important for your child to learn the full range of what math has to offer them, that math can be fun and fulfilling, than it is for them to get to more advanced math material a little earlier in their life. Play, explore, cherish the joyful moments together, and don’t be in a rush.
Wrapping Up
I hope you enjoy all the wonderful mathematical journeys you and your child go on while you follow your child’s interests and ideas. You are making a lifetime of difference for your child. Enjoy learning from them as you play with them and help guide them.
If you have any questions or comments, please send them our way! We would enjoy the opportunity to chat with you. Also, if you are interested in collaborating with us or supporting us in any fashion, we would love to talk with you about ways we can work together!
February 18, 2025
Chris Wright
Chris@EarlyFamilyMath.org
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Early Family Math is a California 501(c)(3) nonprofit corporation, #87-4441486.