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!
This highly nuanced topic is a core idea that we study here at the AIMS Center, and Ms. Beverly Ford has been a member of the Research Associates team longer than anyone around here. She gives us clear and coherent exposition what this idea means and how understanding it can be of benefit to teachers. This research focuses upon the idea of the “Epistemic Student,” a topic we have engaged with in earlier podcasts. We discuss some of the methodology of the Center in how we sort through deep ideas in the Mathematics of Students.
To see more from Beverly and her desire to understand the Mathematics of Students, head over to her most recent blog post at http://www.aimsedu.org/2017/01/18/mathematics-of-grace-using-finger-patterns/
“Culture eats strategy for breakfast.” I recently heard this line and it is one that may too often be true when viewing it through an educator’s lens. I’m thinking you may have made one or more New Year’s resolutions. Have you made any that apply to your professional life? We often get bogged down and… Continue Reading
The mathematics of students is a powerful tool for a teacher. It allows a teacher to hypothesize what is happening in the mind of a child and plan a next step that will allow that child to construct more sophisticated understanding. Today I want to look at the mathematics of a student we call Grace… Continue Reading
Hopefully last week you read the blog by Tiffany Friesen in which she discussed perturbation. In it, she gave a couple of examples from her own experience. Both of the situations that she mentioned were familiar enough to her that she had the capacity to resolve her confusion. She had familiarity with making the cookies… Continue Reading
Narrator: “Last time on Meet the Children Where They Are: Mr. Unnamed nerdy-looking stereotypical math Research Associate (RA) is down in the mud getting ready to do some math with an unsuspecting 5-year-old child named Bob. Can he find Bob’s ZPC without damaging the child for life? Let’s head back to the construction site where… Continue Reading
Understanding the mind of a child is a difficult if not impossible task and yet an elementary school teacher has the unenviable responsibility of doing just that in a classroom full of children. Historically, as far back as Aristotle, the human mind was thought to be an empty vessel just waiting to be filled with… Continue Reading
I am joined in the studio by four Research Associates from the AIMS Center for Math & Science Education. Elizabeth Gamino, Everett Gaston, Brook Lewis, and Aileen Rizo discuss some of the goals of this mode of teacher behavior, and provide a few strategies for its inclusion in the teacher repertoire. If you want to understand and assess the understandings that your students possess, you have to learn to notice how they communicate them.
Teachers must spend time collaborating, sharing experiences, and reflecting about what they are learning to assure deep, rich professional growth. Those who participate in long-term professional learning projects participate in and establish ways to collaborate, share, and reflect when meeting face to face. Equally important, are effective ways to do the same when some of… Continue Reading
We know that children do not learn simply because we have given them information that we find to be important. And I hope that we know that just because we list the objectives on the board, cover each one with diligence, and check it off doesn’t mean that we have taught the objective. So what… Continue Reading