As a constructivist, I believe that young students bring a vast amount of knowledge with them when they first begin school. Whether that time is pre-school, transitional kindergarten, or kindergarten, all students come with experiences that have influenced how they think, what they believe, and what they know. They have constructed knowledge in the area of mathematics all on their own.
As an example, I have never met a five year old with siblings that didn’t have an excellent understanding of fair shares. One sibling means they know halves, but two, three or four siblings means they know thirds, fourths, or fifths! No one had to formally teach them those ideas. They were inherent in their every-day lives whenever something needed to be shared equally.
This week I had the privilege of working for three days with a large group of K-12 in-service teachers who, in six more months, will have their own classrooms. They were fresh faced and excited about teaching and learning. It made me feel excited to be working with them. They were open to new ideas, worked hard, and soaked up everything that was said like sponges. (They were not unlike many kindergarten students that I have met.) As the days progressed, we introduced many new math problems to this group. At one point a more challenging problem came up I found myself saying something like, “this problem is more of a sixth through eighth grade problem, so our kindergarten through second grade teachers may find it challenging.” Immediately, a young lady’s hand shot up and as I called on her I could already tell that I was about to be “called on the carpet.” She politely reminded me, “Hey, just because we teach primary grades doesn’t mean we can’t do math or problem solve. That was a fixed mindset message you just sent!” Ouch! She was correct, and I apologized then and there. We had talked about fixed and growth mindsets that day and she had applied the ideas perfectly in this situation. I was humbled.
It was a great reminder that we can all learn to high levels in mathematics and that, as teachers (of any level of learners) we have to maintain an open mindset and look for opportunities to foster the same in our learners!