When I think back on my childhood, it is difficult for me to pick one item or one experience that influenced the way I think or the direction I headed. I was constantly trying new things and had new interests all the time. So, I went to the only person who knows my childhood even more than I do: My mother. She actually replied similarly. She told me that I had new projects all the time. However, she also told me that was constantly creating new challenges or myself; how fast can I race my big wheel down the driveway? How many baskets can I make in a row, etc. Then, she reminded me that while most of the kids were playing house and dolls in preschool, I was often in the corner devouring jigsaw puzzle after jigsaw puzzle. I think playing with puzzles developed my love of challenges and problem solving, allowing me to pursue lots of different interests and informs the way that I attack problems and challenges now in my adult life.
The thing I liked most about puzzles, is that you had a vision of the solution: the box top. If you only saw the pieces, you have no idea how exactly the final solution is supposed to look. However, the box top allowed a constant reference to scaffold to the solution. Puzzles taught me how to break apart a large problem into many smaller pieces. The first thing I would do when given a puzzle was to separate the edges from the pieces in the middle. In other words, attacking the simplest part of the problem first. This is similar to beginning a problem with what you know to be true or figuring out the easy things first. Next, I would look back at the box and decide what the easiest section to complete would be. These were usually the places in the picture that had the most distinct features. I would see which colors were prevalent in these sections and begin to search through the piles of pieces for the ones that could be used in these sections. I would repeat this process over and over, ending with the most complex piece of the puzzle. However, the more difficult parts were much easier to complete once the amount of pieces were limited.
I now try to approach problems in a similar formula. I often find it helpful when learning mathematical concepts to begin by looking at the solution to sample problems and figure out what it takes to get to the solution. I enjoy taking complex problems and breaking them apart into smaller and more manageable mini-problems. I have also found it helpful to focus more on what I do know, rather than what I am missing. If you continue to look at the large pile of pieces left in a puzzle, it is easy to get overwhelmed. I like to keep focused on the small part of the problem I am working on and reassess the over all problem in between each section. It is always exciting when a puzzle begins to look like the picture you are trying to create. In the same way, I always gain a lot of satisfaction when I have chipped away at a difficult problem enough to have the solution in sight.
In elementary school and middle school Math was always my favorite subject, because the problems themselves felt like puzzles. I loved attacking problems from different angles and breaking them apart to put them back together again. In 5th grade, my teacher actually let one of my classmates and I form our own Math group and we taught ourselves in the hallway every math class. However, in 8th grade, I moved schools and began having a very different experience in Math class. I was no longer allowed to progress at my own pace, but was forced to follow along in the book with the rest of my class. Math no longer felt like a puzzle, but a set of rules to be followed. To extend the analogy of the puzzle, it was like having someone stand over your shoulder and telling you where to put each of the pieces and in what order, rather than helping you to develop strategies on your own. So, while you may have completed that single puzzle you felt little sense of accomplishment or desire to take on a more challenging puzzle. Little, by little, I lost my love for mathematics.
However, I never lost my love for challenges and puzzles and eventually found my way back to mathematics. I became a Math Teacher in hopes of inspiring this love of problem solving in my students. I tried to help them view math, not as arbitrary rules about numbers, but as a way of approaching challenges. By building stronger conceptual understanding, I hoped they would develop not just math skills, but strategies as well.
I came to Stanford for two main purposes: to learn more about how children process mathematical ideas and to design tools to help them learn these ideas better. In doing so, I am attacking the giant problem of math education in the same way I would any puzzle. One small section at a time.
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