“To teach mathematics well, you need to be an expert who is able to recover what it’s like to think like a novice”
– Brent Davis, 2017
When students enter our classrooms, they come to us with a wide range of pre-existing knowledge, skills, beliefs, and attitudes, often referred to as prior knowledge. In the process of learning new concepts and ideas, students use this prior knowledge. This prior knowledge influences how students then attend, interpret and organize new information provided to them. So, it makes sense to link into their prior knowledge. In fact, this is considered an essential part of a lesson for good teaching.
I spent hours designing and preparing lessons for my students including ways to activate their prior knowledge. I would take the time to evaluate the concepts and skills to be taught. Then determine previous skills, I believed, students needed to help them better understand the current material. Finally, I would build into my lessons problems or activities linking into skills or concepts taught in previous lessons. All with the intent of activating their prior knowledge to help them understand new the concepts. I can say I worked very hard in my preparation.
I now question “who’s prior knowledge” was I using. Children, many times, will have their ways of thinking about mathematical concepts and ideas. These ideas in many cases are different from that of an adult. Even though a child’s ways of thinking may not be the teacher’s way of thinking, for the child, it is viable and makes sense. During my decision making for lessons, I built off the concepts to be taught by using my understanding of mathematics and my connections of previous ideas to these current concepts. I realize now that as much as I knew about my students and math, in the end, I made decisions based on my understanding of the concepts and how they made sense to me.
Using the child’s thinking to build from is not the same as using an adult’s way of thinking of the math. Neither is building off a child’s current conceptions in mathematics the same as tying into concepts in the curriculum based on previous lessons. Brent Davis states that “teaching mathematics well requires as expertise merged with an ability to know and understand a child’s thinking.” Through listening to the child and asking questions of their explanations, teachers of mathematics can gain the insight into the child’s knowledge and use this in authentic and relevant ways to promote new understanding.
Are you listening to your students? Do you have a model of their mathematical thinking? Is this the prior knowledge you are building on? I’d like to hear your stories, questions, and comments.
Davis, B. (2017). Brent Davis on teaching math. Retrieved from http://www.alistapart.com/articles/writeliving