Author Archives: David Pearce

Who’s Prior Knowledge?

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


Down the Rabbit Hole

“The rabbit-hole went straight on like a tunnel for some way, and then dipped suddenly down, so suddenly that Alice had not a moment to think about stopping herself before she found herself falling down a very deep well.” ― Lewis Carroll, Alice’s Adventures in Wonderland Alice had it easy. In a recent colleague’s blog,… Continue Reading

Pointing Towards Finger Usage

“Sixteen!” My grandson shouts, sitting on the floor smiling, fingers extended. We had been playing with his toy cars. He counted out nine, gave them to me, and I put them behind me out of his sight. He then counted out seven more, gave them to me also, and I hid them under a nearby… Continue Reading

Teaching Children Fractions

“Fractions. Ugh! I’ve never been good with fractions.” I can’t count how many times I’ve heard this statement. Every teacher knows that working with fractions is an area where many kids struggle. As a middle school teacher, I saw these struggles and how they can lead to further struggles in math. In fact, mastery of… Continue Reading

Takeaways from Subtraction (Part 3): The Struggle

Every elementary school teacher has seen children struggle with subtraction. From these struggles, attitudes of “I’m not good at math” emerge. Our team recently worked with students on the concept of subtraction. We presented situations in which students would count out 23 cubes, hide them, and then remove some of the cubes. The students were… Continue Reading

Takeaways from Subtraction part 2: To Take Away or Not to Take Away

In my last blog entry, I described three goals suggested by Dr. Les Steffe which support introducing subtraction as take away. Yet, there is a belief among some math teachers that thinking of subtraction as take away interferes with future mathematical development. They argue that using the words “take away” should be eliminated completely from… Continue Reading

Takeaways from Subtraction (Part 1)

Why is subtraction hard? This question can be heard from many young children, but often even from adults. Whenever adults do mental math, they tend to have an easier time with addition, multiplication, and simple division than with subtraction. For the past three months we have been engaging young children in subtraction situations while considering… Continue Reading