August 2023
Welcome to EFM's August Newsletter!
EFM: Supporting families to play, explore, and love math
News
Activities for Educators – The activities are in a new unified format, so they are all in one place. Each activity has icons at the top that indicate the type of activity (game, puzzle), the grade range, and special uses for the activity (1-1 tutoring, classroom breaks, send home). Check these out on the Activities for Educators page.
Grade Levels: These activities are available as one big bundle, and are also now in packages for individual grades to make it easy for a teacher to just download the grade they want.
Playing Cards on Website – Development is progressing on the four EFM playing card decks. Learn more about these decks, including seeing all the card face images, by going to the Playing Cards Page on the EFM website.
The Educators K-3 deck now has a Google Slide deck that goes with it. These slides have links to the full page Puzzle of the Week and also an animated series of hints on each slide for how to get started on the puzzle.
Welcome Into The Math Tent
It is essential that every family and caregiver in the world read books and do math with their young children!
This simple statement should be foundational throughout all societies and governments. And yet, the best that most societies have done, and they have not done even this nearly well enough, is to say that families should read with their children.
Furthermore, even if this statement were broadcast universally, families would not know what it means to do math with their children. Most are so uncomfortable with math that they would not want to do it. Contrast this with reading books, where adults know that reading with a child means sitting together with their children and enjoying a story together.
Many families feel they have no time to do extra math activities. Even when told that the simplest and most powerful thing for them to do, that requires no extra time and no effort beyond changing a habit, is to do Math Talk with their young children – verbalizing the math going on in their heads anyway – even then, their dislike for math is great enough that they avoid it, to the lifelong detriment of their children.
Easy Access That Invites Deeper Engagement
How can we help adults change their feelings about math? How can we invite children and adults into the math tent?
Recently, a friend of mine who teaches math told me about sitting down with three former students who had gone into interesting art careers. When my friend described his ambitions for teaching math in his classroom, these former students said it sounded like the challenge presented by creating good art. They said:
Good art provides easy and welcoming access to the casual visitor. Once brought in, the visitor has inviting routes for expending effort that pay off in deeper understandings and engagement with the art.
This is a clear challenge for math. What are the welcoming access points to math that invite further engagement? Sadly, one reason access points to math are so rare is that most people only get brief glimpses of what real math is about. The “math” they do in school is artless, often meaningless, procedures and formulas that barely deserve to be called math – why would anyone want to go more deeply into that?
Access In Other Areas
Let’s look at other areas for comparison and possible inspiration.
Sports have lots of access points through schools, local parks, media, amateur groups, and watching professionals. People have many opportunities to see the beauty in the sports, and they have avenues for taking that budding interest, doing some practice or possibly some training, and seeing where that leads.
Music is all around us to enjoy, and that inspires people to sing or play an instrument. Seeing an orchestra playing when I was ten led me to a lifetime of playing the violin. Along with music, there is a great deal of exposure to dance, causing people to take up various forms of it. Beautiful pictures and designs are all around us in so many ways, and that inspires many to take up drawing, painting, or graphic design. Sculpture and theater are two arts that are not as accessible, and not as easy to pursue for the average person.
Reading and writing have many available access points for the young child. Many families read with their children and create lots of cozy memories with it. If they have a local library, children can go to it and enjoy many interesting resources there with librarians who love to talk about stories. There are YouTube and other resources for children to have stories read to them. And of course elementary schools spend a lot of energy in this area and most teachers enjoy teaching it.
Chess is an interesting example that is closer to math. There are essentially no access points here. A novice can’t watch a chess tournament, or even an individual chess match, and get much out of the experience. What it seems to require is a mentor. An enthusiastic and passionate person who introduces the game. Initially, it may simply be a way for the child to enjoy spending time with someone they like, and over time it may lead to deeper enjoyment of the game for its own sake.
Math is in a position similar to chess. An untrained person watching a math competition or watching someone tackle a math problem is not going to find it interesting. Most amazing mathematics is beyond casual, easy access. Many family members, friends, elementary school teachers, and librarians do not want to play around with math, so it is hard to find a good mentor. Unfortunately, unlike chess, engagement with math (and not its caricature) should not be optional – too much of life will be missed, from success in schools, comfort in real-life mathematical situations, seeing the beauty in math, and missing one of the best sources of problem solving training.
Access Points That Lead Away
One approach that is often taken to give access to math is the pill-in-the-peanut-butter approach. When we had a medicine pill we needed to give our dog, we would put it in the center of a big chunk of peanut butter and watch it be wolfed down.
The most obvious way this is done is to gamify arithmetic fact drills. “If you do these three exercises you can” ... “get through this castle door” or “reach the next level.”
Another example is using math formulas to do mundane calculations in service to some fun application such as building something. Yes, it’s fun to make a simple boat and figure out some things about it, but you are giving access to engineering, not to math. Similar to that is putting small children in story situations where they help some story characters solve a problem. This uses the excitement the children have being associated with the characters in the story to mask that the math problems they are doing are not very interesting.
Using any of these approaches defeats the chance to see math as a beautiful and worthy activity of its own. And because nothing is required of these versions of math (the reason for doing this math is elsewhere in the activity), the math is often poorly developed. You are sending the message that the only reason to do this horrible thing (math) is so you can do this other fun stuff. Ugh!
In Search of Access Points to Math
There are ways to find and enjoy beautiful mathematics. However, there is rarely any simple, casual access to it.
There are plenty of organizations producing mathematical products and environments beyond math games. Here are a few examples. There are many interesting math objects and activities produced by MathHappens.org. There are new pattern blocks to experiment with from MathForLove.com. Mathigon.org has a delightful, virtual mathematical playground. Unfortunately, all of these either require purchases or a mentor to lead you to the right places.
There are websites such as 3brown1blue.com that have beautiful and engaging mathematics, but they can only be appreciated by the mathematically savvy. There are tools such as Desmos or GeoGebra that can demonstrate beautiful mathematics, but only for those who have already learned a fair bit of math. One of my favorite classroom demonstrations was to draw an arbitrary quadrilateral in GeoGebra, connect up the midpoints of the sides in order, and show how that new figure was always a parallelogram no matter how I changed the original quadrilateral. An absolutely beautiful demonstration of an amazing geometric result, but one unlikely to invite in the casual, untrained visitor.
Mandelbrot sets are inspiring to view, and they can draw in a casual visitor, but they leave nowhere to go after that unless you know a lot of advanced mathematics.
Enough, What are Some Good Math Access Points?
By now you see that this is a hard problem, and there are very few easy answers.
The traditional solution to this problem is to have good mentors who provide access points and motivation, similar to chess. Unfortunately, such mentors are in short supply (and math tutors often do more damage than help). This situation has led to a world filled with relatively few people who think math is wonderful and a lot of people (those without good mentors) who think math is awful.
Using programming as an access point for mathematics is a mixed success. It is not for the casual visitor – even with simplified block programming environments or simple languages, such as Logo, it requires special tools and some training to enter that world. Also, a lot of the programming offered is for creating games and play environments, so once again those access points are into non-mathematical worlds. However, there is some good math done with programming. Logo (Turtle Geometry) offers a wonderful opportunity to play with creating beautiful geometric shapes, and gaining insights into geometry through active experimentation. The site Project Euler is a fun example of using programming to investigate math challenges. When used to further mathematics, programming is great at giving insights into a person's logic and understanding of underlying algorithms, as well as giving a dynamic environment for creation and experimentation.
Playing with math puzzles is another access point, but it does not tend to work for the casual passerby. Doing math puzzles is an acquired taste that needs an initial helping hand by an enthusiastic mentor. Once acquired, many visitors will see the pleasure in this activity and go more deeply into puzzles and mathematics, but that initial hurdle can be difficult to overcome.
The one almost universal access point to math for people everywhere is playing games. Playing games, defined by situations where choices produce better or worse outcomes, is the simplest casual access point to math. It is a context where problem solving occurs naturally, and effort and training lead to deeper understandings and better game outcomes. The playing of games, especially math games, should be encouraged in the home and at school, and that is certainly what Early Family Math promotes and supports through all its free materials.
Playing games does not appeal to everyone. We must find more access points that work for math, and ideally we need to find more mentors who are enthusiastic and passionate about mathematics. We do not need everyone to become mathematicians, but we do need everyone to experience what it really is and that it can be a very enjoyable and rewarding activity. Learning to play with mathematical problem solving pays a great many dividends beyond the significant value of being good at problem solving – it also teaches important life skills such as persistence, team work, critical thinking, logical reasoning, and communication of logical ideas.
There are a lot of wonderful things to experience in the math tent that will change lives. Let’s work together to find ways to invite more people to go inside and stay there a while to discover what it has to offer!
If you have any questions or comments, please send them my way. I would enjoy the opportunity to chat with you. Also, if you are interested in collaborating with us or supporting us in any fashion, I would love to talk with you about ways we can work together!
Chris Wright
August 18, 2023
Chris@EarlyFamilyMath.org
Twitter | Facebook | Instagram
Early Family Math is a California 501(c)(3) nonprofit corporation, #87-4441486.