I do get to work with children that comprehend and are able to reason above standard expectations. I don’t like the word gifted, but I will use it to maintain context. (It is a label that is often misunderstood as being pre-wired with knowledge, or the ability to grasp concepts quickly.) Gifted brains are not that simple. It is researched and proven that the brain of gifted individuals work differently than normal brains. The child may exhibit more emotion, another a complete disconnect from social awareness. One may show high levels of excitement, while another appears almost stoic. They may exhibit great command over one, two, or many subjects, but still need to hone skills such as spelling, or eye-hand coordination. Information fires across neurons faster and memory whether short or long term is more efficient.
The experience I think that will surprise people most about doing math with gifted children is that there is not often an epiphany or ah ha moment. Their thought process, conjectures, and actions are often very deliberate, or very abstract and vague. They rarely come to the same answer from the same direction, which is less telling of their ability, and more evident of the flexibility of mathematics.
I know the problem well that Dan Finkel and I explored deeper. We found some interesting patterns. I think we left off wondering does this sequence work all the time, and what if the pattern changed for example to 1,7,13,19, is it still true. It’s a beautiful sequence but the questions about patterns, and variation is where the real investigation starts. So the set problem in that pattern will always work. Dan moved it to conjecture using other sequences, and patterns. Those are questions for others to explore. We had a lot of fun with that. I do believe we posted some of our findings on Twitter (the problem is pinned @lilmathgirl).
Doing problems that are not typically taught in school or those problems not at grade level is where the fun begins. It’s where we get to play with math. And I mean play with math. I’m not one for dressing a wolf in sheep’s clothing. No masking of the subject. Math is a wolf. It is fierce. But if you get up close you’ll see just how beautiful it really is, and it becomes less scary.
The best environment is relaxed and familiar. The math usually surrounds social interactions: cooking which requires accuracy, building which is spatial development, drawing which uses imagination, reasoning, coordination and memory, I also love twisting a standard game or methodology. A few examples: Scrabble only spelling math terms or using words that relate to math. Telling time in fraction, decimal, or ratio form, dividing fractions without using the multiplicative inverse. Games that require finding and making patterns, such as Set, DaVinci’s Challenge, Othello, Checkers, Chess, all of these require reasoning and thinking ahead. Creating a path and strategy to get to the solution. There’s also a need for conjecture, if I do this the outcome will be ____.
Much of what gifted children know comes from letting them lead their curiosity. Let them puzzle it out. I answer their questions with a question, sending them Into deeper learning. Often times we don’t speak about math at all, because the more we understand one another as a person, the easier it becomes to communicate mathematically. I want everyone to think about that for a moment. Think how you talk with others. How you adjust you speech or train of thought based on to whom you’re speaking.
🤣 Everyone always asks how I come up with my ideas. So first a bit of a backstory. I was born 3 months and 2 weeks early. All of 2 pounds, 3 ounces, with pneumonia. I wasn’t suppose to survive the week. If I did survive, I most certainly wasn’t suppose to have full brain function. Well I did, and I do. I was clearly talking at eight months, and reading at two years old. At five years old I was working at a fifth grade level. I spent most of these years in the hospital. The doctors, the same ones that thought I would not live, were my teachers. They folloeed my mother’s wishes, and taught me everything. Never limiting me by any factors. Now the question stands, am I gifted or was I in the right environment, surrounded by those intent on nurturing my curiosity? I don’t know.
I know my brain doesn’t function normally, I know I thrive in the muck of what if, and curiosity is my driving force. Amongst everything that I am, I’m a master flutist, I speak or understand 6 languages fluently, and I truly don’t understand if one can see and draw a triangle, why can one not draw a face?
A mind like this is often a hindrance in traditional school settings because institutions are set up for balance and leveling education. Students not meeting requirements, and students excessively above requirements cause displacement of structure. Education systems fail to embrace this real life dynamic, and instead they push and pull on students, trying to fit them into one box.
Now back to the original question. How do I come up with creative ideas. I approach math from every direction. Not just a problem on paper. Math has to come out of the textbook, and become relatable to the world we live in. It’s when we take this abstract thing called math, and correlate it to reality, we give it tangibility and substance. Math becomes real and not just symbols. I explore all of math. The pedagogical approach, and the avante garde. ( That includes not shying away from “tricks”). For instance multiplying by 9 and knowing : 0 and 9, 1 and 8, 2 and 7, 3 and 6,.. the digit sums add to 9 and all the other patterns of 9. However it does not ensure comprehension of repeated addition. And that’s where we have to be mindful with clarity of information. I often take a problem or topic and explore it from several different angles. Word play, reverse the equation, change the sign, think through history, how does it relate to science or current events, can it be modeled and how? Some of the simplest ideas turn out to be the most complicated.
Don’t underestimate children. Don’t put a limit on their comprehension. Don’t expect the same reasoning. Math is limitless, and so are the minds of children.
This puzzle is not easy ( the blocks are from the game Visual Eyes). The switch up asks you to pick 1 or more blocks that represent a math word, phrase, problem, Etc. For example 2B and 4A = even plane. Children were very creative with this. When I did this on Twitter the responses were very good. When I did this with a group of educators they struggled. 🤔