Week 1 Task 3: Patterns and adaptations

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!

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.

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).

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.

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.

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.

My activity would be photography. I am a visual learner and I enjoy nature. I like to capture images to share with others. Over time, I have taken more than 20,000 photos and now have them archived and organized chronologically.

For my kids and multiplication I think connecting it to food will be good. There are many other things like Legos and sports that they are familiar and comfortable with, but they love to eat. We always have something going on in the kitchen. Someone is always preparing or cleaning up and one or more of the kids is present. We often cook together, so there are many opportunities to explore multiplication in recipes. We will also look for patterns in the food it self - shapes, portions, etc.

1. Our activities we discussed were legos and piano. My son explained to me all the ways he thought math is involved or used when he is building his creations (counting, estimating, visualizing, multiplying, compare & contrast, and trial & error). He explained that what he does is different when he is following step-by-step directions or when he is trying to recreate something by just a picture with no directions. And both ways use math. When he discussed piano he explained that multiplication was used to determine time signatures. He also explained all the ways he thought math is involved or used when playing/reading music (counting, time signature, tempo, beats, metronome, patterns, and increments).

2. In our family everyone has their own strengths. Some overlap and some don't. Learning how to blend them is important. And learning to accept the differences is important.

3. We need to work on helping our son accepting mistakes and that not everything is perfect. When learning PEDMAS he can visually see how easy a mistake can change the answer. But need to work on not personalizing the mistake but rather learn from it.

My activity would be hiking. Hiking is one way I connect with nature, quiet my mind, and slow down the pace of life. I have found that when I set out to hike in one of my familiar parks, I take the same paths, the same direction....often hesitating to try something new. So today, I set out to explore new paths...to let go of that fear of breaking out of my norm.

I think I could encourage my boys to be okay trying a different way in math, even if it is uncomfortable at first and they get a little lost. Part of the journey is making mistakes and being curious about where to go from there.

My activity would have to be cooking. I come from a long line of very good Italian cooks. I grew up helping to make sauce for sunday dinners and big holidays. Since college, I've really branched out in what I enjoy eating (Thai, Japanese, BBQ, Southern Comfort Food, etc.) I also developed a dairy allergy which made me want to cook more for myself so I would know all of the ingredients. I am known for looking at 15 different recipes for the same type of dish and seeing the typical proportions of this spice to that spice. After reviewing a bunch of recipes I create what I think is a good combination of all that I've read. I know what spices are stronger and weaker and how to make it on a larger or smaller scale based on who I'm cooking for. I love getting compliments for something I've made, especially when it isn't coming from a true "recipe" it's coming from my thoughts and ideas. As time has passed I've had to use less and less recipes and tend to just throw things together that I think will taste interesting.

I think math (and multiplication) is very similar. In this analogy, the kids working through problems with me in my groups are like those days I would sit with my Grandma or my Mom and watch what they'd put in to their sauce. My students see my different processes in working problems out and become genuinely enthusiastic about solving a problem in a new way. I think my enthusiasm rubs off on them and allows them to feel safe and comfortable to take a chance and make a mistake in my room. This process will eventually lead to them making their own "recipes" to search their way to mastery of the topics we work on together.

My activity is playing guitar. I've played for many years now, so it's easy to get into patterns. I decided to play freely rather than concentrate on playing things just right. While writing songs, I tried new vocal patterns that were unusual for me. The result was I played in a completely different way. I stopped worrying if a song was ripping off someone else or too boring/unoriginal. And I came up with some pretty cool stuff! Also, it was fun and completely cathartic.

My takeaway from this for multiplication is to break some rules every once in a while. Try a new way even if it feels uncomfortable at first and make mistakes. I'm not sure how to try this with my daughter, but I'll be brainstorming on it for sure.

1. I have always loved working with paper and creating art: quilling, folding, overlaying, etc. The possibilities are endless, but I am often tentative about trying something new as opposed to mimicking a pattern or idea that I've seen somewhere else. Is that tentativeness a part of playing it safe or perhaps self-consciousness?

2. Some of my family members have exceptional art abilities: drawing, designing, painting, and textiles, so I have never felt adequate to "compete" with them. Paper craft is my arena and there is comfort in that!

3. Mistakes have certainly influenced my own paper craft. I have learned that much thought and reflection go into the process. I have also learned that sometimes leaving something on the table and walking away for a while can be more beneficial to succeeding later than being frustrated with a series of failed attempts.

The activity that comes to mind today is golf. This is a game with set rules but which can vary in so many ways. It is interesting to experiment with the game, from changing tee boxes to vary length to trying different types of clubs in similar situations to again change the nature of the game. I enjoy golf not only for the pleasant walking and camaraderie of friends but because for me it is tranquil. It also involves a great deal of mathematics - calculating distances, angles, scores, risk and probability, number comparisons and statistics. I have always considered the game of golf to be a microcosm of life and I would like to instill its skills, joys and its mathematical nature into my grandchildrens' lives as it is also a wonderful way to spend time with family.

There are many simple concepts to explore through play to introduce and teach multiplication to young toddlers and preschool children. I am hoping to learn and to adapt ideas that arise from this program.

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.