Week 1 Task 3: Patterns and adaptations

One of the things my husband and I loved to do when we entertained (prior to having a child) was to "make things pretty." With food, an easy way to do this was to line the plate first with some greens or add some cherry tomatoes for a splash of color. Or to make the food table interesting, create some different heights to set the food. This was not an easy thing to learn how to do and in the beginning, as much as I wanted to make things pretty, I had a very difficult time with it as I would over-think everything and make things too structured, too forced. With time, I was finally able to feel comfortable enough in my ability to "make things pretty" to try new ways of presentation and experiment and just feel it out. And what was, initially, an activity that I would spend lots of time, energy and planning (and anxiety and stress), I have come to a point where I feel like I can "throw" together a pretty plate or spread with much less energy, planning and worry. Because I have come to a place now, where the activity is not so much about the end result but about having fun getting there.

To apply this experience to making multiplication familiar and validating, I think it means looking at and doing multiplication repeatedly. Sometimes, in the same way over and over again. Sometimes in slightly different ways. Sometimes in completely different ways. And to try to remember that the most important thing is not necessarily the end result but rather the process of getting there.

My activity is cooking. Many years ago I felt very inadequate as a cook. Then I lived with an excellent cook and began to learn by watching. Then I lived in a house with 25 other people and learned by doing (and learned to adjust recipes by multiplying and dividing as needed to feed the numbers involved). Today I tinker with recipes often and sometimes cook without any recipe at all. It's a great adventure to try new foods and new ways to cook or season foods.

Multiplication feels pretty comfortable to me. My son just finished some work on multiplication at his Montessori preschool which he found very challenging. I did not feel I knew how to support him through his process with it. Maybe for now the next time I need to double or triple a recipe I will make sure I show him what I am doing and why I am doing it, so that he will see multiplication at work in his home world. It might also be like my experience of watching a more practiced cook in action when I was just learning how.

My activity is hiking. I’d love to go hiking around two specific lakes close to my town. Going through the familiar route gives me a sense of security and calms me down. Once in a while, however, I’d like to try a new path around the same area or in a totally different area. I started with short walks while timing myself and returning the same path. Gradually, I became more confident to go for a loop. To connect this experience with multiplication for kids, I can say breaking down the steps and let them take their time and test the water before they jump in can be similar to what I did for myself. I also tried different shoes and outfits to find a more practical one for me. They should be allowed to try different strategies to find the ones that they feel they can connect to.

About the validating part, I should say I always disliked hiking until a friend insisted me to try a couple of mild hiking trips with my young family and my friends. Because of having younger children with us, the group went easy on choosing the path and goals to accomplish. We focused on the path more than on the final destination. That changed my idea about hiking and it became my favourite activity. I felt that I too could do it and enjoy it.

This is a very clever way of getting us to think how learning math is similar to any other activity in our daily life.

My activity is music. My wife and I are both musicians, and our love of music permeates the household - our daughter couldn't get away from it if she wanted. Fortunately, she likes it too! Music is a way to express inner feelings, and is just plain fun (not to mention a way to make a living...).

Multiplication comes into play in several ways with music, mostly dealing with rhythm. Like take a motif, repeat 4 times on a C chord, then 8 times on a G chord, 2 times on a D chord, 2 times on a G7 chord, then once on a C chord. Now you've got the foundation for adding melodic line. A bit of a stretch? maybe.

My activity would be gardening. It is something I have started doing myself in the past 3 years since we purchased our home. It is a familiar activity as I have a long history with gardening which I used to do with my Grandmother and Mother as a child. I really enjoy doing it and it validates me because it brings me joy and I love the practical need for it to grow my own fresh produce. As a child I would watch my Grandmother work in the garden but for the most part would just eat all the delicious things she grew. And now that I can participate in that activity with my own children, it is nice that it comes full circle.

Gardening is also something that I don't worry about making mistakes doing because I feel comfortable doing it in my own home and asking questions about it to learn new things. I think engaging my children in math activities at home and communicating that it is a game-and questions and mistakes are allowed and encouraged-would help them have a similar experience.

Having a baby under a year, running a household and homeschooling two other kids has kept me pretty busy this year with little time for my own pursuits. I did however, start a garden this spring, which has been a wonderful project. I live in a city in California and I haven't gardened since I was a teenager in semi rural Massachusetts. So its a good example something that is both a big learning curve (year round gardening!) and familiar (I love growing things and have always done so over time, just not always veggies). My daughter likes to play with math and is familiar with adding, hopefully I can tap into that familiarity and add on multiplication sort of the way I am tapping into my old gardening knowledge to build my new one. Other parallels between gardening and math-- you definitely make mistakes in both!

I am comfortable with playing the piano in the way you describe. I have played since I was a young child. All on my own, I explored and made mistakes. I played constantly, (I did not see it as "practice") and got good enough at it that I can sight read almost anything I want to, but also play by ear and make tunes up.

My eldest son has the same kind of "math sense" that I had "musical sense." I'm not sure if there is any way I can make it more familiar to him in this way...he already sees the world through math coloured glasses. I have a lot of math conversations with him, and I encourage his explorations. I bounce his questions back at him so he figures them out himself. I have manipulatives on hand and use them to demonstrate new concepts. He rarely makes mistakes, though, and that troubles me a little bit. I may have to find a way to encourage him to challenge himself more, maybe find a larger math project with a number of challenges for him.

I have been practicing yoga for the past 2 1/2 years and have recently been training to become an instructor. I am just beginning to feel comfortable "playing" with it, rather than following someone else's lead. It can be intimidating and scary, but also incredibly liberating. It's easy to make mistakes, get stuck, feel frustrated, imagine that I will never be as competent as I'd like to be, shrink back in fear... It's a good reminder to me that as my children are gaining skills and experience in all areas of their life, they are feeling these same things. It may seem simple and obvious to me that 7+2=9, but to my 5 year old, it is a wonderful discovery. One that she makes every time she sees those numbers, rather than being a "given" reality.

I think empathy is a big part of supporting someone else, and my taking on something completely new for me, has helped me greatly with that. It's just a little reminder of what the world was like for me when everything was new.

When learning something new, connecting it with familiar experiences can give it the glue that it needs to stick in the brain. My children always seem to be able to answer a division question if I say, "now, if I had 21 M & Ms, and 3 children, how many would each person get?" It's important to get it right because nobody wants to get the short end of that deal!

My activity is making music with synthesizers. It is very familiar to me as I've been interested since I was a child, and had purchased several synthesizers before I'd left school. It validates who I am since it I can express myself through music. In particular, I have a strong interest in comedy, and I enjoy making humourous music. It also represents my experiences over time, since I have devoted a lot of time to gaining knowledge in this area. To make multiplication familiar and validating for children, I would relate it to their favourite activities and stories, and try to find examples that link strongly with these. For my interest I would use examples such as that doubling the frequency of a waveform increases its pitch by an octave.

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.

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.

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.

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.)

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)

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.

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.

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.

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.

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.

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!