Today your mission is...
Find an activity where you feel comfortable changing patterns and trying new things. Maybe you add new ingredients to recipes, tinker with your bicycle, improvise dances, write stories, or create exercise routines that are uniquely yours? Anchor that feeling in your mind. Some people call that feeling play, others freedom, others mastery. We’ll call this your activity.
Ready, Set, Go
Do you like doing your activity? Most people do. This is not accidental. Making your own patterns means a good level of mastery and comfort, and both feel pleasant. It also means the sense of belonging: the activity is yours, and you trust yourself with it.
What makes activities yours? What builds this trust? We will talk about children and adapting mathematics for them, but think back to your activity as you read.
1. Trust can come from familiar, beloved stories, backgrounds, interests. Think of how children can make math their own by making bridges to what they already love. Here are a few examples of such bridges. Connect math to:
2. Trust can come from being in a group that accepts your peculiarities, and designs for them. For example, math for:
3. Over time, trust builds through common experiences that are deep, meaningful, and significant. And through experiences from many different angles, in different contexts, different situations. So that you can say, about each area of math: “We’ve been through a lot together.”
Explain how your activity:
1 - is about something familiar
2 - validates who you are
3 - represents your experiences over time
Now think of multiplication. How can you make it familiar and validating for your kids, students, or yourself?
Why do it?
The goal is for every single person to make mathematics their own. We want to see everybody playing freely, noticing and remixing patterns, and achieving mastery in personally meaningful ways.
Frequently Asked Question
Making my own math sounds wonderful. But how would I know the difference between modifications and mistakes?
First of all, you can and should make lots of mistakes in your private play with math. They don’t have to be glorious (Neil Gaiman): silly, big, or numerous work too. Some mistakes pass by without anyone noticing, and it’s usually okay. But if a mistake grows too big or too silly, or maybe sits in the wrong place, it visibly wrecks an area of your mathematics, like Alice eventually broke the Wonderland and woke up.
Mathematics is a consistent endeavor. Its pieces must fit. Either you change the piece that does not fit, or you build another area of math to accommodate it. Want 2+2 to be 1? Sure! Imagine a clock on the planet where the day has 3 hours instead of our 12. If you make pieces fit, call it a modification. Call what does not fit a mistake. But there is always hope you can later make or find mathematics that fits that piece. This creation or discovery can make your mistake glorious.
For sustained support, do what every math explorer does: peer review! Think, pair, share. First, think and play by yourself or within a small group. If you notice a pattern, discuss it with a peer. Then share the improved pattern with a larger group: a circle of friends and colleagues, or an online forum. It takes a village to raise a baby mistake into a glorious discovery.
Answer by Sblair · Apr 09, 2014 at 09:22 PM
Right now. We are preparing to move from overseas back to the states. I have 3 different shipments. One for our car, one huge household goods, one smaller household goods. As I stroll through the house I am looking for those items that are needed for everyday, clothes that we can wear for the next 6 weeks and our favorite pastime activities. Every other day, I have been organizing those drawers that have collected 3 years of odds and ends. I divide the items into trash, thrift, sell and "that's where that was". Next will be to pack, I have to estimate the time I will need to read to my children plus field trips this week, cook what's in the pantry ( I want as little as possible once we leave) and detail my car (so it can sit in a crate for 2 months). I also have to be careful to leave under a quarter tank of gas. I must fill sparingly in 5 L increments over the next few days, my estimate is to put in 10L to last through Monday. My household goods with leave the middle of next week minus the 600 pounds for the smaller shipment in 6 weeks.
I am a military spouse. This scenario has reoccurred over the past 17 years. The beginning with my first move half way across the country, me and my clothes, although the load has increased, the dependents have increased, the process stays the same. The process of each move has a dependable chain of events that helps me let go to some of our stuff but always leaves a full brain of memories and an endless address book always written in pencil.
Answer by Tia Knuth · Apr 09, 2014 at 09:26 PM
I love to be in my garden and try new things with nobody watching, telling me what to do or not to do. I can learn from my mistakes without feeling criticized. I used grapevines to weave a trellis today and it's very neat and I can envision how to do it better next time.
Kids need space to explore math on their own with nobody telling them how or what to do. It can become as familiar as your own backyard if you are mulling over your ideas or letting them simmer all the time. To make a mistake and overcome it is as validating as making something amazing and we need both. Let kids take the lead and don't step in and guide quite so much. Be a partner in their exploration.... I tell myself because this is hard to do!
Answer by lisa.koops · Apr 16, 2014 at 02:28 PM
I love those quotes, especially the Gaiman!
The activity for me that came to mind is teaching early childhood music classes. I've been doing it for 10 years and I enjoy it; I use some music I've written myself and some I've learned from various sources. One of my vocations is to equip and empower individuals to make music a more meaningful part of life, so teaching early childhood music fulfills this both through the young children and their parents/adults who come to class. I've used the setting as the context for my research through my university job, so I've gradually shifted the way I teach based on what I've learned in my research. Lots of areas of life come together (music lessons as a child, teacher education in undergrad, research in grad school and in current position) in the 45 minute classes. I respond to the children's energy, mood, interest, vocalizations, and the class unfolds in similar and different ways each week.
Regarding multiplication, I can make it familiar and validating for my 7-year-old through connecting it to people. Since she was a toddler we've noticed her affinity for people (spending time with them and keeping track of them - who is in a class, which relative belongs with whom). Also to our home - we have lived here since she was an infant and the squares in the windows, tablecloth pattern, toys - are familiar and known.
Answer by perbui · Apr 09, 2014 at 01:25 PM
My activity is teaching. I have worked as a classroom teacher, librarian, homeschooler, trainer, and mentor for years. Designing and implementing learning activities and assessing student learning is a familiar process for me, so much so that sometimes I fall into the rut of routine. However, when I see light-bulbs going off in students minds, it is definitely gratifying and validates my love for the educational process.
The idea of building trust in myself with this activity is very interesting. I now trust myself to be able to take care of those entrusted to me (my students), but it has not always been this way. It took years of learning from mentor teachers, years of experience with different subjects and students of various cultures, and years of practice and lifelong learning. Along the way, I experimented often and made many mistakes.
Applying this to multiplication, somehow I need to create the right environment for learning: a place where experimentation and mistakes are encouraged, a place where learners are exposed to a variety of concepts and skills, a place where less experienced learners learn from those more experienced, and a place where all learning is validated. This is all theoretical, so I need to spend more time reflecting on what this means practically.
Answer by WendyGee · Apr 09, 2014 at 03:50 PM
I would go biking, something I do on a regular basis. It's not only getting around on the bike, but fixing, adjusting and caring for it that could fit into this activity. Of course I'm also primed to the idea of cooking and changing ingredients, something that seems to be coming with change of season and access to spring vegetables.
I love cycling because it validates me as someone who cares about our planet, it gives me a sense of community with other cyclists and pedestrians. I get to practise navigation and orientation skills, ETA, distance etc.
How can I make multiplication more familiar and validating for my children and students? I think by starting off with their interests. Getting to know them. At the same time leaving room for those interests to change and grow.
Asking questions, being curious, be willing to make a mistake, not to be the adult with all the answers. I think that's what holds me back, trying to get to the answer, rather than fumbling and playing with the process to get there.
Answer by jaaane · Apr 09, 2014 at 04:00 PM
My activity is cooking. I first learned to cook as a teenager when I became a vegetarian in a meat-eating household. The vegetarianism didn't last but the love of cooking did. At first I was very careful about following recipes and instructions to the letter, but over the years I've built up a foundation of skills and so can do a lot more experimenting and off-the-cuff cooking. I also have some foods that are heavy in the rotation that I could cook in my sleep. Last night my son was doing his homework (a skip-counting worksheet) and was having a tough time. He got so discouraged and frustrated that he cried. I would love for him to develop the same sense of mastery and playfulness with math as I have with food. After we both stood on a chair and yelled "I LOVE MATH, MATH IS AWESOME" we sat down with some scrap paper and tried to come up with some ways that he could figure out the skip counting on his own. The silliness with the chairs and yelling seemed to cut the tension he was feeling about the worksheet.
Answer by Ms_Matthews · Apr 09, 2014 at 04:11 PM
I chose to rewrite the song "Yankee Doodle Dandy" with lyrics that explore a sweet-and-sour experience I had yesterday as a substitute teacher. Writing a (comical) version of the interaction into verse grounded the experience in my creativity, and helped me have a sense of control over the experience, laugh at the absurdity of it and play with it. I validated my own experience of that interaction and took ownership of it. Also, I noticed that in the process of rewriting the lyrics, I became aware of the patterns of the song that I had never noticed before---its rhyme scheme and its chorus/verse pattern.
Many kids feel disconnected from or, even worse, afraid of math/multiplication. I do too sometimes. Here are some ways to make it more familiar and connected: use familiar manipulatives, multiplication rap cds, make food (we want each person to have 2 cookies, so how many cookies should we bake?), create real world word problems based on shared experiences---for example, one day we came home from a field trip learning about turtles on a local beach (true story). There were 4 turtle nests on the beach with up to 7 eggs in each nest. We figured out the highest number of baby turtles that could hatch. We had to multiply the highest number of eggs by the number of nests to get the answer. But more than just "getting the answer," our math was giving us information we wanted.
Answer by oxanavashina · Apr 09, 2014 at 04:54 PM
Cooking comes to my mind as 'my activity'. I am not a chef, but I do cook almost every day for many years. I enjoy the touch of fresh vegetables, the smell of spices and the look of a cooked meal on a plate. Besides immediate practical effect it gives a perfect topic of conversation in a multi-national environment I work in. I have a small set of familiar tools, the list of ingredients is fairly long, but I have been building its 'alphabet' slowly in time, adding not too many things at a time. So now I have an idea which things I can combine with each other, even if I have not been using this particular combination before. Once in a while there is a desaster (not a glorious one), but it adds to confidence strangely enough - the world is not going down, there's going to be next time.
Applying the metaphor of learning/getting familiar to cooking to multiplication: rather than cook straigtaway from an Escoffier book, kids should go to the market and learn what an avocado is, touch it and explore its qualities. Get familiar with what they have to deal with. Then use it in a salad. Probably use a simple recipe at first, but maybe even without. I would use tactile, bodily experience (jumping, going to the neigboring forest, building with Legos) to connect with multiplication (math concepts in general - well probably any kind of concepts?) in the first place. Having fun/sharing experiences is core. A couple of days ago we somehow started to talk about sets - and had big time making up noncensical sets. Making mistakes is a hard part - the idea of rules is omnipresent, time and again I have to insist on breaking the rules, and the first reaction of kids is horror. Now I rather suggest we/they make up own rules (kind of breaking rules as well, but doesn't sounds as dramatic).
Answer by juggling_ginny · Apr 09, 2014 at 10:37 PM
Recently I made a pair of trousers and a skirt for my daughter. She wanted a pair of 'juggling trousers' she could wear to the juggling convention we are going to next week. Whilst we were choosing the fabric for the trousers, she also fell in love with a fabric I felt would make a lovely skirt. I didn't have patterns for either, but chose to base the trousers on a pair I have (complete with applique flowers on the front) and the skirt was a cross between one I was wearing and one my daughter liked but had grown out of. Clothes often make a statement about how we feel and who we are, or want to be seen as. By choosing the fabrics and making the patterns, we were able to build on the familiar, things we already had, and create something new, something unique, something that affirmed identity. The clothes were a present for my daughter's ninth birthday, but will also become the trousers she wore to the British Juggling Convention 2014, the skirt she danced at the barn dance in and a whole load of memories yet to be thought of.
I did a maths circle session on multiplication a few weeks ago, where amongst other things we built multiplication towers. This activity didn't require any prior knowledge of multiplication, but I can see that since then my daughter's understanding of multiplication has increased. She's autonomously educated at home, so she's never followed a maths curriculum, but I can see that she has reached an age where suddenly she's ready to learn arithmetic and can mentally do calculations that a year ago would have defeated her. We were playing 'The Really Nasty Horse Racing Game' earlier in the week, and she was calculating the odds for a horse by skip counting (she needed to do 6*4 to get to 24:1) and I could see that she was beginning to see the need for memorising her times tables. For multiplication, or any maths, to make sense it needs to begin from something familiar (for example counting, or skip counting) and be useful for something that you want to do. This might be to play a game, to solve a problem (and not just an abstract worksheet kind) or to create something beautiful.
Answer by Elizabeth02 · Apr 09, 2014 at 09:33 PM
My activity could be cross stitching. I started by following simple patterns and directions and now I make my own patterns and designs and have my own technique. My mom used to cross stitch and taught me how to do it, so despite all the changes in life, it has been a sort of constant. I can't really say it validates who I am. It is something I sort of enjoy and I am happy to share with others, and is a small part of who I am, but it certainly isn't something that takes up a big enough part of my life to consider it a validation for being. It is great to be able to look back at some of my first attempts and see the improvement over the years though. I think the best way to make multiplication familiar is to take it outside of a 'lesson' and help them see how it applies to real life. Sometimes I do this by thinking out loud, so my sons can hear me using math, or by helping them see that something they did without realizing it, was, in fact, Math!
Maybe "validation" is not quite the right term here. We need a version that talks about small parts. Like the spice of our lives? There are walls and floors that provide shelter, but rugs and pictures can make a shelter into a home... Thanks for this food for thought!
Answer by sherylmorris · Apr 09, 2014 at 10:23 PM
My activity is familiar to me, or should I say that my materials are familiar to me. It is the "1,000 chain" of golden beads that you find in most Montessori classrooms beginning in those for 3-6 year-olds together. The chain is prominently hung in the math area alongside the "100" chain. Children generally work with the "1,000" chain along a hall wall where there is room to lay the chain and place corresponding arrow tabs marked for 1-9, 10-90, 100-900, and 1,000. Where there is less space, you might see the "1,000" chain laid out in a spiral for the same exercise.
You ask how my chosen activity validates who I am. I'm a former Montessori teacher who loves Montessori and would love to see the movement into the public sector continue to grow. I appreciate the structures and orderliness of the method; that said I have to admit that I want to stand things on their head sometimes, just to see what happens. There are differing opinions about using Montessori materials in manners in which they were not intended, so some will not like what I've done with the "1,000" chain. (Sending photo.)
You ask how my chosen activity represents my experiences over time. I fell in love with Montessori materials from the beginning. They just make sense to me. I understand there is a danger in "messing" with Montessori willy-nilly. However, over time I've come to believe Maria Montessori would be open to the exploration, engagement, and integration invited here.
Answer by AGray · Apr 10, 2014 at 01:17 AM
My activity is knitting. I recently re-discovered this hobby. I've definitely made all kinds of mistakes, it's been a good way to get comfortable with that. It's also very mathematical with the patterns, I need to use math when I am trying to adjust the instructions, or create my own. It is fun to have an area where I can just relax and experiment.
Answer by scpnorman · Apr 10, 2014 at 01:50 AM
Baking is an activity like that for me. You can't improvise as freely with it as you can with other cooking, but it's something I've enjoyed since I was a child, and I know the basic recipes well enough to feel very comfortable experimenting with them. Sometimes I tinker with proportions, substitute some whole wheat flour, or try creative substitutions for ingredients I don't have on hand. I haven't had any disasters in many years, but things definitely come out better sometimes than others. I think it's important to me partly because the orderly process with a tangible finished product is a form of stress relief for me, partly because I get a lot of joy out of feeding my family and friends, and partly because it helps me feel connected to my mother and late grandmother, who also love(d) to feed people.
Multiplication feels very familiar to mme now because I use it for small daily tasks all the time. I think I'm actually better at mental math now that I've been out of school for a while because in my advanced math and science classes, we used calculators so much that simple arithmetic became less familiar. My son enjoys animals and vehicles, so I'm sure either of those would help him connect with math and multiplication. Maybe we would need to calculate the number of new tires he needs for his fleet of Matchbox cars. He also adores the show Team Umizoomi, and I think his attachment to those characters is already partly responsible for his love of numbers. As long as he continues to be so enthralled with them, I'll keep using their catchphrases and songs to talk about math.
Answer by MerrilySpinning · Apr 10, 2014 at 01:53 AM
We do this all the time with favorite lines from movies, books, poems, songs -- either quote the line because it fits the situation, or quote it because it's so funnily the opposite of whatever's going on, or quote it changing the words to make it fit. My mom does this all the time with songs -- she knows a song for every situation and never has to change the words to make it fit the occasion.
I guess it's validating because it's so much a part of my family life -- it's the most fun when I'm with people who really know me, and love the same things I love.
How to do this with math? That's challenging. My daddy was a math genius. He could look at equations and see shapes or motions... "Oh, it's beautiful!" he'd say while trying to tutor me. "Can't you see it?" No. I couldn't. I just wanted to do my homework so I wouldn't fail the class. Boy, do I ever regret my hard-headedness! I need to spend some time thinking about how Daddy saw the world, the things he said, the stories he told. Maybe I can begin feeling connected to it that way. And of course, my children love hearing stories about their granddaddy.
Answer by katying · Apr 10, 2014 at 02:01 AM
I guess my activity would be either baking, cooking or maybe knitting. These are activities that I have a mastery of, such that I can tinker and change quantities seemingly instinctively.
I have worked with these formulas and recipes and patterns a lot. I have made the mistakes I needed to make to anticipate what would happen if I changed something too much, or what needs to be added to compensate. Like I have baked with too much baking soda and I know what will happen.
These activities are necessity and constant in my life.
Answer by CynthiaDadmun · Apr 10, 2014 at 02:51 AM
My "play" would be gardening. My mistakes are still heartbreaking though! (ie dead plants) Interestingly, it IS quite familiar / validating / reflective of me since I am a biologist, and doing edible gardening for my family or ornamental landscaping in our yard is highly meaningful. It is also much more interesting to me than to most people since I know a lot of background information about the plants that makes them fascinating. (eg, I have both a "mother fern" and "mother of thousands" succulent, both of which can form plantlets vegetatively off of their leaves... normal plants need to develop from an embryo in a seed -- fascinating! how did these manage to bypass that? ... Most people would just see a fern or a "cactus".)
I had mixed feelings reading this task, as follows: Isn't this a little touchy-feely? Where's the math? Oooh, I get it... But hey, traditionally math IS for a specific group of people, called "boys". How do we get away from that? Do we need to make Girl Math like there are now Girl Legos? (which I also have mixed feelings about)
Answer by PruSmith · Apr 10, 2014 at 04:26 AM
My activity is painting. It is a complex process, full of careful ratios and chemistry, most of which I don’t think about consciously at this point as I have been painting for so long. This makes me think that all of those occupation “identities” (like teacher, fireman, baker, race car driver, etc.) that preschool kids take on in play might be good opportunities to introduce the idea of multiplication as it applies in each case. Or connecting a math activity to some skill set they take pride in like building with Legos or riding a bike or throwing a basketball: mastery in one area providing them the confidence to master another. (Hopefully I've understood the point of the exercise.)
Answer by mirandamiranda · Apr 10, 2014 at 05:17 AM
I love to read aloud. Mostly I do this for my 6 year old twins (my oldest mostly reads independently and my baby is more interested in discussing the pictures than listening to the story) but we also read poetry all together. I have always loved to read, to see the story happening in my head and to immerse myself into beautiful words and phrases, reading them over to myself and relishing the language. I have also written stories since I was a child, and find writing is not so different from reading in some ways; it is all about your inner ear (metaphorical rather than anatomical!).
I have also always loved reading aloud to my (and other) children. I really enjoy putting expression into the voices and characters, using pace and volume to increase tension or funny voices to make my listeners laugh. Poetry is also lots of fun to read aloud, from the music and rhythm to the linguistic elements like alliteration and imagery that really bring the poems alive.
It is a great activity for experimenting and making mistakes. If you do a voice wrong, or slip on a word, no worries - just try it again or continue blithely on. Especially when you are reading to your own pre-readers there is no judgment or criticism. So you are free to try out how it would work if you did one character like this, or tried slowing down here, or added some sound effects there...
In terms of self-validation, stories, words and ideas are the most important things in the world to me. So enjoying and sharing them is about as good as it gets!
I found thinking about this in terms of teaching my children mathematics a revelation. It really helped me get an insight into their perspectives and how I might align my agenda with theirs! For example, my oldest daughter loves to draw and has been thinking about perspective recently. I can really imagine bringing ideas of scale and proportion in as we talk about art and experiment on paper. She is not fond of arithmetic AT ALL so I think this will be a great way to engage her interest. The only problem is that I myself am not very artistic so I will need to stretch a little there. But then again this could help to balance our positions which is only a good thing.
Answer by Shannon · Apr 10, 2014 at 05:53 AM
My activity is running our homeschool. This is familiar in the sense that we've been doing it for several years, we do it in a familiar environment, I am more or less familiar with the concepts we are studying, and I know my students well. It is validating in the sense that I can adapt instruction for both my comfort/learning style as well as theirs. While doing my activity I am amongst those people who love me most, and look upon me with generous, if not innocent, approval. I can definitely say "we've been through a lot together" not only to my kids, but to myself, my spouse, and the environment/materials/books/etc. around our homeschool.
I guess to make multiplication familiar and validating I can start with things they know and enjoy - Legos, for example (oodles of math concepts there). I can also be receptive to tangential (divergent) thinking in the process.
Answer by SarahKrieger · Apr 10, 2014 at 09:24 AM
Explain how your activity:
1 - is about something familiar
My activity is sewing. It is mine because it requires little input from others (after the basics of choosing fabric & taking measurements). I enjoy the mechanical rhythm of my sewing machine and the repetitive movement of sewing each seam. I also enjoy tinkering with patterns and re-mixing them to create something new from something familiar.
2 - validates who you are
Making garments for my family gives me a physical reminder of my household contribution (cf: recurring housework tasks or the long-term open-endedness of home schooling). I regard sewing as play and my enjoyment of each article extends beyond its construction. I feel validated when something I've made becomes a favourite garment and I find it less burdensome to care for and maintain the things I've made than the items that are handed down to us or purchased.
3 - represents your experiences over time
I started learning to sew when my children were small and the quality of my work wasn't so important. As I've become proficient, I am better able to anticipate the difficulties and adventures (mistakes and modifications) of the piece I'm constructing. Being aware of the limits of my skills gives me freedom to experiment and drive to fill the gaps in my abilities.
Now think of multiplication. How can you make it familiar and validating for your kids, students, or yourself?
This would be about taking the activities they already love and over-laying the maths information they need (language and concepts). It would be using their go-to activities as manipulatives (eg Lego) and creating the maths stories about those items.