Week 1 Task 1: Your mathematical dreams and worries

1. I would like for my daughters to be so comfortable with numbers, mathematical thinking, and mathematical exploration that unfamiliarity or anxiety can never interfere with their ability to see the beauty and excitement of the math in the world around them.

2. Multiplication in particular? I don't think I have any specific dreams. But I would be delighted if this course's *approach* to multiplication - looking at a concept from all kinds of angles, with a view to uncovering beautiful truths, rather than spouting out particular numbers - became their standard approach to math in general.

I want my children to be good problem solvers (of problems involving math or not). I want my children to be creative and not afraid of taking risks. Multiplication should make sense. Answers to multiplication problems should be justifiable. If it makes sense to my kids, they should be able to explain it.

I want my daughter to be excited about math, to see it everywhere, andto feel confident that she can figure things out on a practical level.

I would like to see my children using math in real ways and seeing it as a helpful part of life, not an isolated subject. I need to think about what that would mean for my children to learn and use multiplication.

I want my son to love math as much as I did as a kid. I want him to approach math with less frustration and more of a sense of fun and adventure.

I want my kids to see the joy in math and discover the world through mathematical ideas. I want there to be curiosity and engagement, and yet challenging as well. I want there to be a freedom from finding the answer or the one way or filled with endless worksheets and drills. It is really about discovering the world and how these numbers all fit together.

If this came true they would learn math through doing and building and discovering the answers to real questions. Multplication would be discovered as part of pattern and the interconnection of patterns and design. It would be used to construct and create solutions and connections.

I son loves math. He taught himself multiplication early on when he figured out that it was just repetitive addition and skip counting.... His goal is to design and invent. So my goal is for him to keep his love of math and inquiry. I also want him to see other connections of math that are deeper than just math facts.

1. I would love for my children and any children I come into contact with around mathematics to be actively sharing with me their own insights and joy around the patterns in numbers!

That would be bound to defuse any of my residual fears about being able to be an effective support to them in learning more about mathematics :)

To me, it is really all about recognising that mathematics is just another language and portal into interacting with our world. That by understanding and interfacing with it in this way we can engage with its symbols and feel free to be creative about it and invent/re-invent fun ways of interacting with it.

2. How I see my children learn and use multiplication in my dream world? As part of the natural order of things...that patterns are made by numbers in the natural and man-made worlds and that these patterns are artistic, are fun, have spiritual connotations, are used by geographers, biologists, social scientists and artists. I desire my children to see this naturally and to share what they see and learn with me and to use it in the course of their other subjects, naturally!

I have amazing young problem-solving children and i want to love this part of themselves and see it as a talent. I want them to find math beautiful and I also hope, on a very practical level, that they can use it to take care of themselves - with good employment or just problem-solving things in their own life.

I see my children learning the different ways to multiply things, to have them memorized but to see symmetry, patterns, arrays, and let them lead them through their curiousity to other concepts. They'll use it in their games and their day to day lives.

1. I want my children to be curious about math, to be able to understand and solve the problems of any level not only using their knowledge, but trying to find creative way to get a solution. I want them to be able to apply all the mathematical concepts to the real life problems. Math is around us and I hope they will be seeing it.

2. Learn through the play, use - you need this knowledge all the time in so many fields of daily life, so, hopefully, they will be comfortable with such necessities of using their skills.

The notion of applying maths dreams to my children's maths development is somewhat foreign to me. After years of being a mainstream teacher, the demands of the curriculum have dampened my "child magic". I dream for them to have fun, to experience the joy of discovering the hiiden patterns of maths and to find practical and useful application of the maths concept. Once I verbalise these dreams, I realise that the maths experience that I offer to the children should be colourful, creative, real life and enjoyable. Maths games are useful, as are stimulating resources. Always looking for more guidance though, as I often sink back into the grind of the curriculum expectations

I'd love my kids to use maths as a natural resource for solving life problem and use multiplication on a natural way. My fears are they learn maths in the wrong way so they find them boring or unconnected to real life.

I see them using multiplication as if nothing was happening, I mean just using it as a resource an not as a goal itself.

During my national security graduate studies, I was exposed to a whole series of great thinkers whose collective works included seminal writings, research, theories, new schools of thought and Nobel Prizes. I was struck by how many of these men and women (including my Romanian professor) were Eastern Europeans with backgrounds in mathematics. Its my hope that my children's embrace of math will help develop a higher level of thinking that will serve as a pathway to brilliance.

1. I want my children to both find joy in the puzzling and play of mathematical thought, and to find strength in its logic and problem solving power. I hope the means are the ends, that is the process of learning math results in thinking joyfully, playfully, logically, and powerfully.

2. I see my children learn multiplication concepts by "seeing" (or being shown) multiplication around them (arrays, areas, scaling, etc). I see them learning multiplication facts by practice in using them in the context of meaningful problems, as opposed to drill or isolated numbers on a page. This too is how they will use multiplication - by recognizing inherent multiplication in the world and in solving problems.

1. I want them to recognize and apply mathematics to their everyday lives. Hopefully creating some incentive and inspiration to spend their lives continuing to see opportunities to find answers with a strong understanding of math in their tool box.

2. They have learned multiplication so far by using memory cues for quick recall of the times tables. We have used manipulables to make physical representations. I have pointed out daily activities when I use multiplication: cooking, calculating tips, shopping, measuring. I am interested in learning any other way I can incorporate math into their daily lives and inspire them to challenge themselves.

I would really like my son to *enjoy* doing math while being sufficiently challenged. I wish for his number sense and sense of wonder to lead the way. I would like math to be part of the regular conversations we have about everything else!

1. My dreams, what it is really all about for me in regards to my children, are to help my children see the world through the beauty of patterns. By making this a habitual observation, I believe problem solving in general becomes more interesting, with more options becoming noticeable.

2. If my dreams for my children came true, I see them learning multiplication spontaneously through their own observations and natural informal experiments. I see them using multiplication as a means to save time and energy when curious about finding answers to their questions regarding quantities.

For my children, I hope they come out of their years at home with:

- A sense of awe and wonder in mathematics as the language God built into the universe.

- The joy of discovery in mathematics that they had as preschoolers still burning bright.

- The foundational tools they needs to build on to figure out any math problem they want to figure out.

- An attitude that is conducive to problem solving, especially persistence and determination.

- A big picture, an understanding of the historical context of the study of math.

As with any other math concept in these early years, I see them learning multiplication through everyday conversation, through games and activities, and through step-by-step demonstration with manipulatives. I see them completely understanding the concept before any drill is introduced (I think drill is fun when children are motivated to gain fluency, but should not be used to gain mastery.).

1. I want to have conversations about mathematics with my children. I want problem solving to be a routine in our lives. I was struck by Sarah Flannery's book "In Code" and the beautiful routines and experiences she had with her family in regard to mathematics and problem solving. For them math was a part of their family and community - I think that is what I want. For my son to enjoy math and enjoy it with me and our family.

2. I'm not sure, but I hope this course gives me some direction!