I recently had the pleasure of writing an article for the New Jersey Association for Gifted Children. I wrote about creative thinking in mathematics. I spoke as a Kindergarten teacher, but advocated for creative mathematic thinking for all. One reader thought it might be better if I had emphasized the Kindergarten piece of my thinking. At first I misunderstood and stood my ground that creativity in mathematics is good for all. She explained her thinking, telling me that so many people think that one can never be creative in Kindergarten math in particular because there are so many facts they must learn, or because they are only Kindergartners.
Oh my gosh! Only Kindergartners???!!! She is right. Many people underestimate the amazing potential, big beautiful brains, and remarkable thinking abilities of Kindergartners. So, I revised my article, and share it here.
I’m always looking for ways to bring creativity into my Kindergarten classroom. Why? There are a plethora of reasons, but here are my top three:
- It makes the day more enjoyable for my students (and for me).
- It increases my students’ motivation, engagement, understanding, and learning.
- It helps my students develop mindsets and understandings about themselves, the subject matter, rules, and the world, which will allow them to make extraordinary contributions to our world as they continue to grow and learn.
- It allows me to have a deeper understanding of who my students are as mathematicians.
One of the subject matters I work to infuse with creativity is math. Before you faint, let me reassure you. Math is a domain that is filled with facts, rules, and precise procedures. I love math facts. I respect and appreciate mathematical procedures. I enjoy the challenge and struggle of solving a well-conceived and difficult problem. Additionally, I understand that Kindergarten is a time to grow in mathematical understanding and skills.
At the same time, I am intrigued by all the ways creativity is an inherent and essential part of mathematics – including Kindergarten mathematics. Creativity has the power to enhance my Kindergartner’s mathematical learning, understanding, and joy. It also gives me a powerful vantage point from which to observe and come to know them as mathematicians. Providing my Kindergartners with the opportunity to be creative allows them to show all they know rather than just what I happen to ask them. It works the same for all learners – regardless of their age.
Let’s consider something basic that my Kindergartners are working on these days – how to break apart and build numbers to ten. If we break any number into two parts, or build with two parts, there are that number +1 ways to make it. For instance the number four can be made five different ways. I’m sure the answers come quickly to mind: 1+3. 2+2. 3+1, 4+0, and 0+4.
But, are there really only +1 ways? Or are there only +1 ways because we are living within the constraints of addition, positive, whole numbers? What if we allowed any mathematical operation, fractions, and negative numbers. The possibilities for how we make four explode exponentially! Increase the number of parts, and the possibilities become endless.
As I wrote the article I wondered about mentioning negative numbers and Kindergarten in the same breath. Could they really understand them?
Then, one day, this happened.
This is one of my Kindergarten mighty mathematicians. She was hanging out with me after school waiting for after care. Let me tell you how this moment of learning came to be.
She enjoys writing on the D10 whiteboard and this day said to me “Look, Miss James!” I turned and saw her work. She had written: 100-200=0 Her face beamed with a look of discovery. I took a breath and scanned my brain for how to explain. Our conversation went something like this:
Me: “Hmmm. Are you sure? What is 100 take away 100?”
Her: “Oh. Zero.”
Me: “Yes! So do you think 100 take away 200 would be zero, too?”
She thought and wasn’t able to come up with an answer that satisfied her.
Me: “Let’s work with smaller numbers, okay?”
I handed her 4 counters.
Me: “You have 4 counters. I ask you for 5. What would you do?”
Her: “I’d give you the 4 I have.”
Me: ” Awesome. But, would I have what I need?”
Her: “No. But it’s all I have.”
Me: “Yes, I know. But I need 5. If I were buying them from you, and paid for 5, how many would you still owe me?”
She thought for a bit.
We moved to the board to begin writing the number sentence. I explained to her that when the number we are taking away is more than the number available we add a minus sign in front of the number. That means we don’t have all that were taken away, or we owe that many.
The smile of discovery had returned to her face. She began trying other numbers as I stood by her ready to accept the counters and support her as she thought, questioned, wrote, and grew as a mathematician. Finally we returned to her original number sentence 100 take away 200.
Me: So. What is 100 take away 200?
Her: Minus 100!
Me: You got it!
This photo was the second day. She did the work on her own. I don’t mean to suggest that she totally gets negative numbers. What I do mean to suggest is it’s possible, and it’s good, to be willing to step into those areas that seem unreachable, and think creatively how to make the reachable.
We are mighty. Our learners are mighty. Creative thinking is good. Mathematical thinking is good. Creative mathematical thinking is quite fantabulous — even, and perhaps especially, in Kindergarten